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+%\DeclareCaptionFont{uiblack}{\color{uiblack}} +%\DeclareCaptionFont{uipoppy}{\color{uipoppy}} +%\captionsetup{labelfont={uipoppy},textfont=uiblack} + +% see the macros.tex file for definitions +\include{macros } + +% title slide definition +\title{$\Lambda_c \to p \mu \mu$ , $\Lambda_c \to \mu \mu \mu$} +%\subtitle{a bias report} +\author{Johannes Albrecht$^{1}$, \underline{Marcin Chrz\k{a}szcz}$^{2,3}$, Tadeusz Lesiak$^{3}$, Oliver Grunberg$^{4}$} +\institute[UTH] +{ +$ ^1$ Technische Universitaet Dortmund \\ +$ ^2$ University of Zurich \\ +$ ^3$ Institute of Nuclear Physics, Krakow \\ +$ ^4$ University of Rostock \\ +} + + + + +\date{$8^{th}$ May 2013} + +%-------------------------------------------------------------------- +% Introduction +%-------------------------------------------------------------------- + +\begin{document} + + + + +\setbeamertemplate{background} +{\includegraphics[width=\paperwidth,height=\paperheight]{frontpage_bg_mine}} +\setbeamertemplate{footline}[default] + +\begin{frame} +\vspace{1.1cm} +\begin{columns} +\column{2.75in} + \titlepage + + \begin{center} + % \includegraphics[height=1.0cm ]{pic/uzh.jpg} + % \hspace{0.5cm} + % \includegraphics[height=1.5cm]{pic/babar.jpg} + \hspace{1cm} + \includegraphics[height=1.0cm]{pic/ifj.png} + \hspace{1cm} + %\includegraphics[height=1.0cm]{pic/SNS.jpg} + \end{center} + \vspace{10cm} +\column{2.0in} +\end{columns} +\end{frame} + +%-------------------------------------------------------------------- +% OUTLINE +%-------------------------------------------------------------------- + + + + +\section[Outline]{} +\begin{frame} +\tableofcontents +\end{frame} + + + + + + + +%------------------------------------------------------------------- +% Introduction +%------------------------------------------------------------------- +% +% Set the background for the rest of the slides. +% Insert infoline +\setbeamertemplate{background} + {\includegraphics[width=\paperwidth,height=\paperheight]{slide_bg}} +\setbeamertemplate{footline}[bunsentheme] + +\title{Report on $\tau \to p \Plepton \Plepton$} + + +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% + +\setbeamertemplate{background} + {\includegraphics[width=\paperwidth,height=\paperheight]{slide_bg}} +\setbeamertemplate{footline}[bunsentheme] +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%2>%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% + +\section{Motivation} +\begin{frame}\frametitle{Motivation} + +\begin{small} +Following the success of $\tau \to 3 \mu$ and $\tau \to p \mu \mu$ (published 2 weeks ago) we decided to go one step further and analyse analogous channels for $\Lambda_c$. +\begin{itemize} +\item Decays have different physics motivations: +\end{itemize} +\begin{center} + \begin{tabular}{ l | l } + $\tau \to 3 \mu$ LFV & $\Lambda_c \to 3 \mu$ $|B-L|= 0$ \\ + $\tau^{+} \to p \mu^{-} \mu^{+} $ $|B-L|= 0$ & $\Lambda_c^{+} \to p \mu^{-} \mu^{+} $ FCNC \\ + $\tau^{+} \to \bar{p} \mu^{+} \mu^{+} $ $|B-L|= 0$ & $\Lambda_c^{+} \to \bar{p} \mu^{+} \mu^{+} $ $|B-L|= 0$ \\ + + \end{tabular} +\end{center} + +\begin{itemize} +\item The current limits ($@$ 90\% CL): +\end{itemize} +$\mathcal{B}( \Lambda_c^{+} \to p \mu^{-} \mu^{+} ) < 4.4 \times 10^{-5}$, arXiv:1107.4465 +\newline +$\mathcal{B}( \Lambda_c^{+} \to \bar{p} \mu^{+} \mu^{+} ) < 9.4 \times 10^{-6}$ +\newline +$\mathcal{B}( \Lambda_c^{+} \to 3 \mu )$ No constraints! +\end{small} + + \textref {M.Chrz\k{a}szcz 2012} +\end{frame} + +\section{Strategy} +\begin{frame} + +\frametitle{Strategy} +{~} +Follow the strategy of $\tau$ analysis: +\begin{itemize} +\item Take prompt $\Lambda_c$, separate approach to SL. +\item Loose cut preselection. +\item Train MVA on MC prompt signal and recalibrate on data. +\item Mass resolution we expect similar to $\tau$. $15 MeV$ for $3 \mu$ and $9 Mev$ for $p \mu \mu$. Mean recalibrated from data on $\Lambda_c^{+} \to p K^{-} \pi^{+}$. +\item Normalize to $\Lambda_c^{+} \to p K^{-} \pi^{+}$. +\item Optimise the binning in MVA. +\item CLs method for limit. +\end{itemize} + +\end{frame} + +\section{Comparison $\Lambda_c$ vs $\tau$} +\begin{frame}\frametitle{Comparison $\Lambda_c$ vs $\tau$} +\colorbox{green}{Strong sides of $\Lambda_c$:} + + +\begin{itemize} +\item {No SM background in $3 \mu$ case ($\PDs \to \eta(\mu\mu\gamma) \mu \nu$)} +\item {Smaller combinatorial background than in $\tau$ decays. \Simley{1} } +%\item {Better prospers of observing something. Rare is better than forbidden \Simley{1} } +\end{itemize} + +\colorbox{red}{Weaker sides of $\Lambda_c$:} +\begin{itemize} +\item {Smaller no. of $\Lambda_c$ than $\tau$ to begin with.} +\item {Need to study very carefully $\Lambda_c$ production and backgrounds. } +\Simley{-1} + +\end{itemize} + + + + +\end{frame} + +\section{Work done so far} +\begin{frame}\frametitle{Work done so far} +\begin{itemize} +\item $\Lambda_c \to p \mu \mu$ is already stripped(line was with $\tau$ line all along). +\item $\Lambda_c \to 3\mu$ is being stripped in incremental stripping. +\item Requested 1M signal samples. Production will start next weak. +\item Background studies. (see backup slides). + +\end{itemize} + + + + +\end{frame} + +\begin{frame} +\begin{LARGE} +Backup Slides +\end{LARGE} + + + + + + +\end{frame} + + + +\subsection{} +\begin{frame}\frametitle{Work done so far} +\begin{itemize} +\item $\Lambda_c \to p \mu \mu$ is already stripped(line was with $\tau$ line all along). +\item $\Lambda_c \to 3\mu$ is being stripped in incremental stripping. +\item Requested 1M signal samples. Production will start next weak. +\item Background studies. (see backup slides). + +\end{itemize} + + + +\end{frame} + + + + + + + + + + + + +\end{document} diff --git a/HQL_2014/Lc2pll.toc b/HQL_2014/Lc2pll.toc new file mode 100644 index 0000000..92cd541 --- /dev/null +++ b/HQL_2014/Lc2pll.toc @@ -0,0 +1,6 @@ +\beamer@endinputifotherversion {3.10pt} +\select@language {english} +\beamer@sectionintoc {2}{Motivation}{3}{0}{1} +\beamer@sectionintoc {3}{Strategy}{4}{0}{2} +\beamer@sectionintoc {4}{Comparison $\Lambda _c$ vs $\tau $}{5}{0}{3} +\beamer@sectionintoc {5}{Work done so far}{6}{0}{4} diff --git a/HQL_2014/Lifetime-eff.pdf b/HQL_2014/Lifetime-eff.pdf new file mode 100644 index 0000000..ad0dc45 --- /dev/null +++ b/HQL_2014/Lifetime-eff.pdf Binary files differ diff --git a/HQL_2014/Lifetime-eff.svg b/HQL_2014/Lifetime-eff.svg new file mode 100644 index 0000000..6c1da0e --- /dev/null +++ b/HQL_2014/Lifetime-eff.svg @@ -0,0 +1,3181 @@ + + + + + + image/svg+xml + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + 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For more information, see [this blog post](http://www.drbunsen.org/custom-beamer-theme.html). + +#### Dependencies: + ++ [XeTeX](http://en.wikipedia.org/wiki/XeTeX) ++ [The Fontin Font](http://www.exljbris.com/fontin.html) diff --git a/HQL_2014/SS/geo0p4_0p7.png b/HQL_2014/SS/geo0p4_0p7.png new file mode 100644 index 0000000..7e1ef69 --- /dev/null +++ b/HQL_2014/SS/geo0p4_0p7.png Binary files differ diff --git a/HQL_2014/SS/geo0p7_1p1.png b/HQL_2014/SS/geo0p7_1p1.png new file mode 100644 index 0000000..0b833b8 --- /dev/null +++ b/HQL_2014/SS/geo0p7_1p1.png Binary files differ diff --git a/HQL_2014/SS_banan_un.png b/HQL_2014/SS_banan_un.png new file mode 100644 index 0000000..d606523 --- /dev/null +++ b/HQL_2014/SS_banan_un.png Binary files differ diff --git a/HQL_2014/TODO b/HQL_2014/TODO new file mode 100644 index 0000000..12edfbb --- /dev/null +++ b/HQL_2014/TODO @@ -0,0 +1,5 @@ +reference to liang sun +backup on lifetime +lumi prospects +model dependence +hyperlinks diff --git 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b/HQL_2014/beamerouterthemebunsen.sty new file mode 100644 index 0000000..5ee921c --- /dev/null +++ b/HQL_2014/beamerouterthemebunsen.sty @@ -0,0 +1,33 @@ +% This program can be redistributed and/or modified under the terms +% of the GNU Public License, version 3. + +\mode + +% color definitions +\definecolor{uipaleblue}{RGB}{96,123,139} + +% footer styling +\setbeamercolor{section in footer}{fg=white,bg=uipaleblue} +\setbeamercolor{subsection in footer}{fg=white,bg=uipaleblue} +\setbeamercolor{pagenumber in footer}{fg=white,bg=uipaleblue} + +\defbeamertemplate*{footline}{bunsentheme} +{ + \leavevmode% + \hbox{% + \begin{beamercolorbox}[wd=.33\paperwidth,ht=2.25ex,dp=1ex,center]{section in footer}% + \inserttitle + \end{beamercolorbox}% + \begin{beamercolorbox}[wd=.34\paperwidth,ht=2.25ex,dp=1ex,center]{subsection in footer}% + \insertsectionhead + \end{beamercolorbox}% + \begin{beamercolorbox}[wd=.34\paperwidth,ht=2.25ex,dp=1ex,center]{pagenumber in footer}% + \insertframenumber{} / \inserttotalframenumber\hspace*{2ex} + \end{beamercolorbox}}% + \vskip0pt% +} + +\setbeamersize{text margin left=1em,text margin right=1em} + +\mode + diff --git a/HQL_2014/beamerthemeSybila.sty b/HQL_2014/beamerthemeSybila.sty new file mode 100644 index 0000000..eddf87b --- /dev/null +++ b/HQL_2014/beamerthemeSybila.sty @@ -0,0 +1,123 @@ +\mode + +%------------------------------------------------------------------------------- +% Themes +%------------------------------------------------------------------------------- + +\useoutertheme{split} +\useinnertheme{rounded} +\usefonttheme{structurebold} +\useoutertheme{shadow} + +%------------------------------------------------------------------------------- +% Templates +%------------------------------------------------------------------------------- + +\beamertemplatenavigationsymbolsempty +\beamertemplateheadempty +\beamertemplateshadowblocks + +%------------------------------------------------------------------------------- +% Own templates +%------------------------------------------------------------------------------- + +% Normal title page. +\defbeamertemplate*{title page}{simple}[1][] +{ + \vfill + \begin{centering} + \begin{beamercolorbox}[center, rounded=true]{title} + \usebeamerfont{title}\inserttitle\par% + \ifx\insertsubtitle\@empty% + \else% + \vskip0.25em% + {\usebeamerfont{subtitle}\usebeamercolor[fg]{subtitle}\insertsubtitle\par}% + \fi% + \end{beamercolorbox}% + + \vskip1em + + \begin{beamercolorbox}[sep=8pt,center,#1]{author} + \usebeamerfont{author}\insertauthor + \end{beamercolorbox} + + \vskip1em + + {\usebeamercolor[fg]{titlegraphic}\inserttitlegraphic\par} + \begin{beamercolorbox}[sep=8pt,center,#1]{institute} + \usebeamerfont{date}\insertinstitute + \end{beamercolorbox} + + \vskip1em + + \begin{beamercolorbox}[sep=8pt,center,#1]{date} + \usebeamerfont{date}\insertdate + \end{beamercolorbox} + \end{centering} + \vfill +} +\defbeamertemplate*{footline}{shadow theme} +{% + \leavevmode% + \hbox{\begin{beamercolorbox}[wd=.5\paperwidth,ht=2.5ex,dp=1.125ex,leftskip=.3cm plus1fil,rightskip=0.3cm,center]{author in head/foot}% + \usebeamerfont{author in head/foot}\insertshortauthor \insertinstitute\par + \end{beamercolorbox}% + \begin{beamercolorbox}[wd=.5\paperwidth,ht=2.5ex,dp=1.125ex,leftskip=.3cm,rightskip=.3cm plus1fil]{title in head/foot}% + \usebeamerfont{title in head/foot}\insertshorttitle \hfill \insertframenumber\,/\,\inserttotalframenumber\hfill% + \end{beamercolorbox}}% + \vskip0pt% +} +%------------------------------------------------------------------------------- +% Logo +%------------------------------------------------------------------------------- + +%\logo{\hspace*{0.6\textwidth}\includegraphics[width=1.8cm]{images/uzh.jpg}\hspace*{0.3cm}} +\logo{% + \includegraphics[width=1.8cm,keepaspectratio]{images/uzh.jpg}\hspace*{0.3cm}% + \includegraphics[height=0.6cm,keepaspectratio]{images/ifj.png}% +} + + +%------------------------------------------------------------------------------- +% Colors +%------------------------------------------------------------------------------- + +\setbeamercovered{dynamic} + +\setbeamercolor{math text}{fg=white!0!black} +\setbeamercolor{title}{bg=white!30!black} +\setbeamercolor{frametitle}{bg=white!45!black} +\setbeamercolor{footline}{bg=black,fg=white} +\setbeamercolor{author in head/foot}{bg=black,fg=white} +\setbeamercolor{title in head/foot}{bg=white!45!black} +\setbeamercolor{block title}{bg=white!45!black} +\setbeamercolor{block title example}{bg=white!45!black} +\setbeamercolor{block title alerted}{bg=white!15!black} + +\colorlet{redshaded}{red!25!bg} +\colorlet{shaded}{black!25!bg} +\colorlet{shadedshaded}{black!10!bg} +\colorlet{blackshaded}{black!40!bg} + +\usecolortheme{whale} +\usecolortheme{orchid} + +%------------------------------------------------------------------------------- +% Fonts +%------------------------------------------------------------------------------- + +\setbeamerfont{block title}{size={}} +\setbeamerfont{date}{size=\small} + +%------------------------------------------------------------------------------- +% Other +%------------------------------------------------------------------------------- + +\titlegraphic{ +\includegraphics[width=3.0cm]{images/uzh.jpg}\hspace*{0.3cm} +\includegraphics[height=0.9cm,keepaspectratio]{images/ifj.png}% + +} + +\mode + diff --git a/HQL_2014/beamerthemebunsen.sty b/HQL_2014/beamerthemebunsen.sty new file mode 100644 index 0000000..64fcfbb --- /dev/null +++ b/HQL_2014/beamerthemebunsen.sty @@ -0,0 +1,44 @@ +% This program can be redistributed and/or modified under the terms +% of the GNU Public License, version 3. + +\mode + +\newif\ifbeamer@secheader +\beamer@secheaderfalse + +\DeclareOptionBeamer{secheader}{\beamer@secheadertrue} +\ProcessOptionsBeamer + +\useoutertheme{bunsen} + +% color definitions 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mode 100644 index 0000000..87f09f5 --- /dev/null +++ b/HQL_2014/ckm2012_3.snm @@ -0,0 +1,4 @@ +\beamer@slide {babarB}{9} +\beamer@slide {cleolnv}{9} +\beamer@slide {bellelnv}{9} +\beamer@slide {xxxxx}{9} diff --git a/HQL_2014/ckm2012_3.synctex.gz b/HQL_2014/ckm2012_3.synctex.gz new file mode 100644 index 0000000..6e528e5 --- /dev/null +++ b/HQL_2014/ckm2012_3.synctex.gz Binary files differ diff --git a/HQL_2014/ckm2012_3.tex b/HQL_2014/ckm2012_3.tex new file mode 100644 index 0000000..fa2d8a1 --- /dev/null +++ b/HQL_2014/ckm2012_3.tex @@ -0,0 +1,900 @@ +% This program can be redistributed and/or modified under the terms +% of the GNU Public License, version 3. +% +% Seth Brown, Ph.D. +% sethbrown@drbunsen.org +% +% Compiled with XeLaTeX +% Dependencies: +% Fontin Sans font (http://www.exljbris.com/fontinsans.html) +% +\documentclass{beamer} +\usepackage{pgf} +\usepackage{times} +\usepackage[T1]{fontenc} +%\usepackage[mathscr]{eucal} +%\usepackage{mathptmx} +%\usepackage{mathrsfs} +\usepackage{hyperref} +% \usepackage{pgfpagfes} +% \setbeameroption{show notes on second screen} +%\pgfpagesuselayout{4 on 1}[a4paper,border shrink=5mm,landscape] +\usepackage{xcolor} +%\usepackage[dvipsnames]{xcolor} +%\usepackage{amsfonts} +%\usepackage{amsmath} +% \usepackage[amssymb]{SIunits} +%\usepackage{natbib} +%\usepackage{amssymb} +\usepackage{hepparticles} +\usepackage{hepnicenames} +\usepackage{hepunits} +\usepackage{tikz} +\usepackage[polish]{babel} +%%\usepackage{lmodern} +%\usepackage{feynmp} +% suppress navigation bar +\beamertemplatenavigationsymbolsempty +\usepackage[mathscr]{eucal} +\usepackage{mathrsfs} +\mode +{ + \usetheme{bunsen} + \setbeamercovered{transparent} + \setbeamertemplate{items}[circle] +} + +% set fonts +\usepackage{amsfonts} +\usepackage{amsmath} +\usepackage{verbatim} + +\usetikzlibrary{arrows} +\usetikzlibrary{shapes} + +%\usepackage{gfsartemisia-euler} +%\usepackage[T1]{fontenc} +\setbeamerfont{frametitle}{size=\LARGE,series=\bfseries} +\tikzstyle{decision} = [diamond, draw, fill=gray!20, + text width=4.5em, text badly centered, node distance=3cm, inner sep=0pt] +\tikzstyle{block} = [rectangle, draw, fill=blue!10, + text width=5em, text centered, rounded corners, minimum height=2em] +\tikzstyle{line} = [draw, -latex'] +\tikzstyle{cloud} = [draw, ellipse,fill=red!10, node distance=3cm, + minimum height=2em] + +\tikzstyle{every picture}+=[remember picture] + + +\renewcommand{\PKs}{{\HepParticle{K}{S}{}\xspace}} +\newcommand{\at}{\makeatletter @\makeatother} + +% color definitions +\usepackage{color} +\definecolor{uipoppy}{RGB}{225, 64, 5} +\definecolor{uipaleblue}{RGB}{96,123,139} +\definecolor{uiblack}{RGB}{0, 0, 0} + +% caption styling +%\DeclareCaptionFont{uiblack}{\color{uiblack}} +%\DeclareCaptionFont{uipoppy}{\color{uipoppy}} +%\captionsetup{labelfont={uipoppy},textfont=uiblack} + +% see the macros.tex file for definitions +\include{macros} + +% title slide definition +\title{Searches for New Physics with LHCb} +\author{Marcin Chrz\k{a}szcz} +\institute[Institute of Nuclear Physics] +{ +University of Zurich, +\newline Institute of Nuclear Physics Krakow, +\newline on behalf of LHCb collaboration +\\{~}\\ +} + + +\date{$29^{th}$ May 2014} + +%-------------------------------------------------------------------- +% Introduction +%-------------------------------------------------------------------- + +\begin{document} + + + +\setbeamertemplate{background} +{\includegraphics[width=\paperwidth,height=\paperheight]{frontpage_bg_mine}} +\setbeamertemplate{footline}[default] + +\begin{frame} +\vspace{1.1cm} +\begin{columns} +\column{2.75in} + \titlepage + + \begin{center} + \includegraphics[height=1cm,keepaspectratio ]{uzh.jpg} + \hspace{0.5cm} + \includegraphics[height=1cm]{pic/LHCb_logo.jpg} + \hspace{0.5cm} + \includegraphics[height=1cm]{pic/ifj.png} + \end{center} + \vspace{10cm} +\column{2.0in} +\end{columns} +\end{frame} + +%-------------------------------------------------------------------- +% OUTLINE +%-------------------------------------------------------------------- + + + + +\section[Outline]{} +\begin{frame} +\tableofcontents +\end{frame} + + + + + + + +%------------------------------------------------------------------- +% Introduction +%------------------------------------------------------------------- +% +% Set the background for the rest of the slides. +% Insert infoline +\setbeamertemplate{background} + {\includegraphics[width=\paperwidth,height=\paperheight]{slide_bg}} +\setbeamertemplate{footline}[bunsentheme] + + + +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% + +\setbeamertemplate{background} + {\includegraphics[width=\paperwidth,height=\paperheight]{slide_bg}} +\setbeamertemplate{footline}[bunsentheme] +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +\section{LHCb detector} + +\begin{frame}\frametitle{LHCb detector} +\begin{columns} +\column{3.in} +\begin{center} +\includegraphics[width=0.98\textwidth]{det.jpg} +\end{center} + +\column{2.1in} +\begin{footnotesize} + +\begin{block}{} + \circled{1} LHCb is a forward spectrometer: + \begin{itemize} + \item Excellent vertex resolution. + \item Efficient trigger. + \item High acceptance for $\Ptau$ and $\PB$. + \item Great Particle ID. + \end{itemize} + + + \end{block} + +\end{footnotesize} +\end{columns} + + \textref{M.Chrz\k{a}szcz 2014} +\end{frame} + +\section{Lepton Flavour Violation} +\begin{frame}\frametitle{Lepton Flavour/Number Violation} +\begin{small} + Lepton Flavour Violation(LFV): +\end{small} + + +\begin{footnotesize} + +After $\Pmuon$ was discovered it was logical to think of it as an excited $\Pelectron$. +\begin{columns} +\column{3in} +\begin{itemize} +\item Expected: $B(\mu\to\Pe\gamma) \approx 10^{-4}$ +\item Unless another $\Pnu$, in intermediate vector boson loop cancels. +\end{itemize} +\column{2in} +{~}\includegraphics[width=0.98\textwidth]{rabi.png} + +\end{columns} +\begin{columns} +\column{1in} +{~} +\column{3in} +\begin{block}{I.I.Rabi:} +"Who ordered that?" +\end{block} +\column{2in} +{~}\includegraphics[scale=0.08]{II_Rabi.jpg} + +\end{columns} + + +\begin{itemize} +\item Up to this day charged LFV is being searched for in various decay modes. +\item LFV was already found in neutrino sector. +\end{itemize} +\end{footnotesize} + + +\begin{footnotesize} + +\begin{columns} +\column{3.5in} +\begin{small} + Lepton Number Violation (LNV) +\end{small} + +\begin{itemize} +\item Even with LFV, lepton number is a conserved quantity. +\item Many new thesis predict it violation(Majorana neutrinos) +\item Searched in so called Neutrinoless double $\beta$ decays. +\end{itemize} + +\column{1.5in} +\includegraphics[width=0.8\textwidth]{Double_beta_decay_feynman.png} + +\end{columns} + +\end{footnotesize} +%Double_beta_decay_feynman.png + + \textref{M.Chrz\k{a}szcz 2014} +\end{frame} + + +% \section{Lepton Number Violation} +\section{$\PB$ decays} +\subsection{$\PBminus\to h^{+}\Plepton^{-}\Plepton^{-}$} +\begin{frame}%[t] +\frametitle{LNV in bottom decays}%$\PBminus\to h^{+}\ell^{-}\ell^{-}$} + +\only<1>{ +\begin{columns}\begin{column}{.5\textwidth} +on-shell neutrino + +\includegraphics[width=\textwidth]{pic/B-Majorana2.pdf} +\end{column} +{\begin{column}{.45\textwidth} +virtual neutrino + +\includegraphics[width=\textwidth]{pic/B-Majorana1.pdf} +\end{column} +} +\end{columns} +\begin{columns} +\begin{column}{.5\textwidth} +\begin{itemize} +\item resonant production in accessible mass range +\item rates depend on Majorana neutrino--lepton coupling $|V_{\mu 4}|$ +\newline {\footnotesize{(e.g.\ \href{http://arxiv.org/abs/0901.3589}{arXiv:0901.3589)}}} +\item $m_4 = m_{\Plepton^{-},\Ppiplus}$ +\end{itemize} +\end{column} +{ +\begin{column}{.5\textwidth} +\begin{exampleblock}{Special for $\PB$ decays} +%\begin{itemize} +Diagram without mass restriction + Cabbibo favoured for $\PB\to\PD$ + Analogous to double $\beta$ decay. +%\end{itemize} +\end{exampleblock} +\end{column} +} +\end{columns} +} + \textref{M.Chrz\k{a}szcz 2014} +\end{frame} + +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +\setbeamertemplate{background} + {\includegraphics[width=\paperwidth,height=\paperheight]{slide_bg}} +\setbeamertemplate{footline}[bunsentheme] + + +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% + +\begin{frame}[t] +\frametitle{Virtual Majorana neutrinos} + + +\begin{columns} +\only<1>{ +\begin{column}{.78\textwidth} +\begin{block}{} +%\begin{itemize} + $\PBminus\to\PDplus\Pmuon\Pmuon\quad\quad\quad\quad\quad\quad\PBminus\to\PD^{*+}\Pmuon\Pmuon$ +%\end{itemize} +\includegraphics[width=\textwidth]{pic/MassFitDp_.pdf} +\end{block} +\end{column} +} + + +\end{columns} +\only<1>{{ +{~} + + +$\mathcal{B}(\PBminus\to\PDplus\Pmuon\Pmuon)<6.9\times 10^{-7} \quad \quad \mathcal{B}(\PBminus\to\PD^{*+}\Pmuon\Pmuon)<2.4\times 10^{-6}$ +}} + + + {@ 95\,\% CL}\hspace{.35\textwidth} + {@ 95\,\% CL} +\\ Based on $0.41fb^{-1}${~}$7TeV$ data. + +{~} + +\begin{columns} +\begin{column}{6.5cm} +\end{column} +\begin{column}{1.5cm} +%\includegraphics[width=\textwidth]{pic/LHCb_logo.jpg} +\end{column} +\begin{column}{4cm} +\hspace{.4cm} + + {\footnotesize{\href{http://prd.aps.org/abstract/PRD/v85/i11/e112004}{\texttt{Phys. Rev.D85 (2012) 112004 }}}} + +\end{column} +\end{columns} + +%LHCb, arXiv:1201.5600 +%\includegraphics[width=.5\textwidth]{UpperAll} + \textref{M.Chrz\k{a}szcz 2014} +\end{frame} + +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% + +\begin{frame}[t] +\frametitle{On-shell Majorana neutrinos} +\begin{itemize} +\item Based on full data set${~}3fb^{1}$. +\item Cut based analysis. +\item Normalization channel $\PBplus \to \PJpsi(\mu\mu)\PKplus$. +\item Searched performed for two scenarios: +\begin{itemize} +\item Short life-time neutrinos: $\tau_4 <1ps$ +\item Long life-time neutrinos: $\tau_4 \in (1,1000) ps$ +\end{itemize} +\end{itemize} +\begin{columns} + +\only<1>{ +\includegraphics[width=\textwidth]{Figure2.png} +} + +\end{columns} + + +\begin{columns} +\begin{column}{8.5cm} + +\includegraphics[width=\textwidth]{Figure3.png} + +\end{column} +\begin{column}{.5cm} +%\includegraphics[width=\textwidth]{pic/LHCb_logo.jpg} +\end{column} + +\begin{column}{4cm} +\hspace{.4cm} + + + {\footnotesize{\href{http://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.131802}{\texttt{Phys. Rev. Lett. 112, 131802 }}}} + +\end{column} +\end{columns} + + + \textref{M.Chrz\k{a}szcz 2014} +\end{frame} + + + +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% + +\begin{frame}[t] +\frametitle{On-shell Majorana neutrinos} +{~}\\ +\begin{columns} +\column{2.in} +\includegraphics[width=\textwidth]{Figure5.png}\\ +\includegraphics[width=\textwidth]{Figure6.png}\\ + + +\column{3.0in} +\begin{small} +\begin{itemize} +\item In absence of signal UL. were set. +\item $Br(\PBminus \to \Ppiplus \Pmuon \Pmuon)$ in range $10^{-9}$. +\item Limits also set for the coupling $| V_{\mu 4} |^2$ +\end{itemize} +{~}{~}$Br(\PBminus \to \Ppiplus \Pmuon \Pmuon) = \dfrac{G_f^4 f_B^2f_{\pi}^2}{128\pi\hbar } \tau_B m_B^5 |V_{ub}V_{ud}|^2|V_{\mu4}|^4(1- \dfrac{m_4^2}{m_B^2})\dfrac{m_4}{\Gamma_{N_4}}$ +\end{small} +\end{columns} + \textref{M.Chrz\k{a}szcz 2014} +\end{frame} + + +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% johan %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% + +\begin{frame} +\frametitle{Summary on LNV in $\PB$ decays} +\vspace{0.5cm} +\begin{columns} +\begin{column}{.65\textwidth} +\begin{footnotesize} +\begin{tabular}{lclr} +channel & limit & & \\\hline + $\mathcal{B}(\PBminus\to\Ppi^{+}\Pelectron\Pelectron) $ & $<2.3\times 10^{-8}$ & @$90\,\%$ CL &\includegraphics[height=.25cm]{babar}\footnote{BaBar,\href{http://link.aps.org/doi/10.1103/PhysRevD.85.071103}{Phys.\ Rev.\ D \textbf{85}, 071103} (2012)\label{babarB}}\\ + $\mathcal{B}(\PBminus\to\PK^{+}\Pelectron\Pelectron) $ & $<3.0\times 10^{-8}$ & @$90\,\%$ CL &\includegraphics[height=.25cm]{babar}\footnotesize{$^{\text{\ref{babarB}}}$}\\ + $\mathcal{B}(\PBminus\to\PK^{*+}\Pelectron\Pelectron) $ & $<2.8\times 10^{-6}$ & @$90\,\%$ CL & \includegraphics[height=.25cm]{cleo}\footnote{CLEO, \href{http://link.aps.org/doi/10.1103/PhysRevD.65.111102}{Phys.\ Rev.\ D \textbf{65}, 111102} (2002)\label{cleolnv}}\\ + $\mathcal{B}(\PBminus\to\Prho^{+}\Pelectron\Pelectron) $ & $<2.6\times 10^{-6}$ & @$90\,\%$ CL & \includegraphics[height=.25cm]{cleo}\footnotesize{$^{\text{\ref{cleolnv}}}$}\\ + $\mathcal{B}(\PBminus\to\PD^{+}\Pelectron\Pelectron) $ & $<2.6\times 10^{-6}$ & @$90\,\%$ CL & \includegraphics[height=.25cm]{belle2-logo}\footnote{Belle, \href{http://link.aps.org/doi/10.1103/PhysRevD.84.071106}{Phys.\ Rev.\ D \textbf{84}, 071106(R)}, (2011)\label{bellelnv}}\\ + $\mathcal{B}(\PBminus\to\PD^{+}\Pelectron\Pmuon) $ & $<1.8\times 10^{-6}$ & @$90\,\%$ CL & \includegraphics[height=.25cm]{belle2-logo}\footnotesize{$^{\text{\ref{bellelnv}}}$}\\ +$\mathcal{B}(\PBminus\to\Ppi^{+}\Pmuon\Pmuon)$ & $<1.3\times 10^{-8}$ & @$95\,\%$ CL & \includegraphics[height=.25cm]{pic/LHCb_logo.jpg}\footnote{LHCb, CERN-PH-EP-2012-006, \href{http://arxiv.org/abs/1201.5600}{\texttt{arXiv:1201.5600}} (2012)\label{xxxxx}} \\ + $\mathcal{B}(\PBminus\to\PK^{+}\Pmuon\Pmuon) $ & $<5.4\times 10^{-7}$ & @$95\,\%$ CL &\includegraphics[height=.25cm]{pic/LHCb_logo.jpg}\footnote{LHCb, \href{http://link.aps.org/doi/10.1103/PhysRevLett.108.101601}{Phys.\ Rev.\ Lett.\ 108 101601} (2012)} \\ + %$\mathcal{B}(\PBminus\to\PK^{*+}\Pmuon\Pmuon) $ & $<4.4\times 10^{-6}$ & @$90\,\%$ CL & \includegraphics[height=.25cm]{cleo}\footnotesize{$^{\text{\ref{cleolnv}}}$}\\ + %$\mathcal{B}(\PBminus\to\Prho^{+}\Pmuon\Pmuon) $ & $<5.0\times 10^{-6}$ & @$90\,\%$ CL & \footnotesize{$^{\text{\ref{cleolnv}}}$}\\ + $\mathcal{B}(\PBminus\to\PD^{+}\Pmuon\Pmuon) $ & $<6.9\times 10^{-7}$ & @$95\,\%$ CL & \includegraphics[height=.25cm]{pic/LHCb_logo.jpg}\footnotesize{$^{\text{\ref{xxxxx}}}$}\\ + $\mathcal{B}(\PBminus\to\PD^{*+}\Pmuon\Pmuon)$ & $<2.4\times 10^{-6}$ & @$95\,\%$ CL & \includegraphics[height=.25cm]{pic/LHCb_logo.jpg}\footnotesize{$^{\text{\ref{xxxxx}}}$}\\ + $\mathcal{B}(\PBminus\to\PDs^{+}\Pmuon\Pmuon)$ & $<5.8\times 10^{-7}$ & @$95\,\%$ CL & \includegraphics[height=.25cm]{pic/LHCb_logo.jpg}\footnotesize{$^{\text{\ref{xxxxx}}}$}\\ + $\mathcal{B}(\PBminus\to\PDzero\Ppiminus\Pmuon\Pmuon)$ & $<1.5\times 10^{-6}$ & @$95\,\%$ CL & \includegraphics[height=.25cm]{pic/LHCb_logo.jpg}\footnotesize{$^{\text{\ref{xxxxx}}}$}\\ +\hline +\end{tabular} %pic/LHCb_logo.jpg +\end{footnotesize} +\end{column} +\end{columns} +\textref{M.Chrz\k{a}szcz 2014} +\end{frame} + + +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% + +\subsection{$\PB\to \Plepton^{+}\Plepton^{-}$} +\begin{frame}%[t] +\frametitle{$\PB\to \Plepton^{+}\Plepton^{-}$ 1}%$\PBminus\to h^{+}\ell^{-}\ell^{-}$} +\begin{footnotesize} +\begin{columns} + +\column{3in} + +\begin{itemize} +\item A separate physics interest are LFV $\PB$ decays. +\item Predicted by various NP models: lepto-quarks, SUSY, GUT. +\item Analysis based on $1fb^{-1}$ 2011 data. +\item Analogues to our $\PBs \to \mu \mu$ analysis(Phys. Rev. Lett. 110, 021801 (2013)) +\end{itemize} + + + +\column{2in} +\includegraphics[width=\textwidth]{blind.png}\\ +\end{columns} + +\begin{enumerate} +\item Loose reselection based on topology and PID. +\item Classifier trained on MC signal and $b\bar{b} \to \Plepton \Plepton X$ +\item Calibration channel: $\PBzero_{(s)} \to h^+ h^{'-}$ +\item Normalization Channel: $\PBzero \to \PKplus \Ppiminus$ +\item CLs method for limit extraction. +\end{enumerate} +\end{footnotesize} + + + +\begin{columns} +\begin{column}{6.5cm} +\end{column} +\begin{column}{1.5cm} +%\includegraphics[width=\textwidth]{pic/LHCb_logo.jpg} +\end{column} +\begin{column}{4cm} +\hspace{.4cm} + {\footnotesize{\href{http://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.141801}{\texttt{Phys. Rev. Lett. 111, 141801 (2013) }}}} + +\end{column} +\end{columns} + \textref{M.Chrz\k{a}szcz 2014} +\end{frame} + +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% + + + +\begin{frame}%[t] +\frametitle{$\PB_{(s)} \to \Plepton^{+}\Plepton^{-}$ 2} +\begin{footnotesize} +\begin{columns} + +\column{3.1in} + +\begin{itemize} +\item Correction to MC and DATA discrepancies. +\item Excellent proxy: $\PBzero_{(s)} \to h h'$. +\item Fit each BDT bin for $\PBzero_{(s)} \to h h'$ and extract number of events. +\item Correct MC efficiency for each bin. +\item Electron Bremsstrahlung corrected on $\PJpsi \to \Pe \Pe$. +\end{itemize} + +\column{1.9in} +\includegraphics[width=\textwidth]{Fig4a-supp.pdf}\\ +\end{columns} +\begin{columns} + +\column{2.3in} +%\includegraphics[width=\textwidth]{ClsB.png}\\ +\includegraphics[width=\textwidth]{CLS2.png}\\ +\column{3.1in} +%\includegraphics[width=\textwidth]{Fig1a-supp.pdf}\\ +\begin{tabular}{ c | c | c } + {~} & $Br(\PB \to \Pe \Pmu)$ & $Br(\PB_s \to \Pe \Pmu)$ \\ + {~} & \at~$ 90(95)\% CL$ & at~$90(95)\% CL$ \\ \hline +\textcolor{blue}{Expected} & \textcolor{blue}{$4.0(5.0)\times 10^{-9}$}& \textcolor{blue}{$1.5(2.0)\times 10^{-8}$} \\ +\textcolor{red}{Observed} & \textcolor{red}{$2.8(3.7)\times 10^{-9}$}& \textcolor{red}{$1.1(1.4)\times 10^{-8}$} \\ + +\end{tabular} + + +\end{columns} + + +\end{footnotesize} + \textref{M.Chrz\k{a}szcz 2014} +\end{frame} + +%%%%%%%%%% +\begin{frame}%[t] +\frametitle{$\PB_{(s)} \to \Plepton^{+}\Plepton^{-}$ Implications} +\begin{footnotesize} +\begin{itemize} +\item LHCb limits exceeds previous CDF by $20$ times. +\item CDF implications to lepto-quarks mass\footnote{Theoretical formula Phys. Rev. D 50 (1994) 6843}. +\begin{itemize} +\item $m_{LQ}(\PBs \to \Pe \Pmu) >47.8(44.9) TeV$ \@ $90(95\%)$ \at CL. +\item $m_{LQ}(\PBzero \to \Pe \Pmu) >59.3(56.3) TeV$ \@ $90(95\%)$ \at CL. + +\end{itemize} +\end{itemize} + +\begin{center} +\begin{columns} +\column{0.4in} +{~} +\column{1.85in} +\includegraphics[width=\textwidth]{Fig2a-supp.pdf}\\ +\column{0.2in} +{~} +\column{1.85in} +\includegraphics[width=\textwidth]{Fig2b-supp.pdf}\\ +\column{0.4in} +{~} +\end{columns} + +\end{center} +LHCb limits: +\begin{itemize} +\item $m_{LQ}(\PBs \to \Pe \Pmu) >107(101) TeV$ \@ $90(95\%)$ \at CL. +\item $m_{LQ}(\PBzero \to \Pe \Pmu) >135(126) TeV$ \@ $90(95\%)$ \at CL. + +\end{itemize} + +\end{footnotesize} + \textref{M.Chrz\k{a}szcz 2014} +\end{frame} + + + + + + + + +%%%%%%%%%%%%%%%%%%%%%%%%% +%%%%%%%%%%%%%%%%%%%%%%%%%% +%%%%%%%%%%%%%%%%%%%%%%%% + + + + + + +%\section{Lepton Flavour Violation} +\section{$\tau$ decays} + + +\subsection{$\Ptauon\to\Pmuon\Pmuon\APmuon$} +\begin{frame}\frametitle{Curent status} + + + + +\frametitle{$\Ptau \to \mu \mu \mu$} + +\only<1>{ + + + +\begin{center} +\begin{columns} +\column{3in} +\begin{block}{} + \circled{1} In SM small $\mathcal{B}( \Ptauon\to\Pmuon\Pmuon\APmuon ) \sim 10^{-50} $ \\ + \circled{2} NP can enhance $\mathcal{B}$. \\ + \circled{3} Nature still hides $\Ptauon\to\Pmuon\Pmuon\APmuon$ from us.\\ + \circled{4} Current limits: +\end{block} +\column{2in} +\includegraphics[width=\textwidth]{tau23mu.png}\\ + + +\end{columns} + + + \begin{center} + \begin{tabular}{| l | l |} + \hline Experiment & $90\%$ CL limit \\ + \hline + \hline BaBar & $3.3 \times 10^{-8}$ \\ + \hline Belle & $2.1 \times 10^{-8}$ \\ + \hline +\end{tabular} +\end{center} +\begin{block}{} + \circled{5} Can a hadron collider change the picture? \\ +\end{block} + + + + + + +\end{center} +} +\textref{M.Chrz\k{a}szcz 2012} +\end{frame} + +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% + +\begin{frame}\frametitle{Analysis approach} +\begin{columns} +\column{2.5in} +$\mathcal{B}$ factories + + +\column{2.5in} +LHCb, ($7 TeV$, 2011 data) + + + +\end{columns} +\begin{columns} +\column{2.5in} + + +\begin{block}{} + \circled{1} Clean signal: $\APelectron\Pelectron\to\APtauon\Ptauon$ \\ + \circled{2} Calculate the thrust axis \\ + \circled{3} "Partial tag" the other $\tau$ \\ + \circled{4} Small cross section $0.919nb$ \\ +\end{block} +\column{2.5in} + +\begin{block}{} + \circled{1} Inclusive $\tau$ cross section: \newline $79.5\pm\unit{8.3}{\micro\barn}$. \\ + \circled{2} $8 \times 10^{10} \tau$ produced. \\ + \circled{3} Dominant contribution: \newline $\PDs\to\Ptau\Pnut$ ($78\%$) \\ + \circled{4} No tag possible. \\ +\end{block} + + + +\end{columns} + + +\textref{M.Chrz\k{a}szcz 2012} +\end{frame} + +\begin{frame} +\frametitle{Strategy} +\begin{columns} +\begin{column}{.5\textwidth} +\begin{itemize} +\item Loose cut based selection +\item Classification in 3D space: +\begin{itemize} +\item invariant mass +\item decay topology\newline (multivariate) +\item particle identification\newline (multivariate) +\end{itemize} +\item Classifier trained on simulation +\item Calibration with control channel +\item Normalization with $\PDs \to \phi(\mu \mu) \pi$ +\item CLs method to extract the result +\end{itemize} +\end{column} +\begin{column}{.5\textwidth} + +\begin{block}{Signal \& Calibration \& Background channel} +\includegraphics[width=.7\textwidth]{topos} +\newline +\includegraphics[width=.7\textwidth]{topob2.png} +\end{block} +\end{column} +\end{columns} +\textref{M.Chrz\k{a}szcz 2012} +\end{frame} + +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%5 + + +\begin{frame} +\frametitle{Signal likelihoods} +\begin{columns}\begin{column}{.48\textwidth} +\begin{block}{particle identification} +\begin{itemize} +\item hits in muon chambers +\item energy in calorimeters +\begin{itemize} +\item compatible with MIP +\end{itemize} +\item RICH response +\end{itemize} +\end{block} +\begin{exampleblock}{Calibration} +$\PJpsi\to\APmuon\Pmuon$ +\end{exampleblock} +\includegraphics[width=\textwidth]{Fig4b.png} +\end{column} + +\begin{column}{.48\textwidth} + +\begin{block}{3 body decay likelihood} +\begin{itemize} +\item vertex properties +\begin{itemize} +\item vertex fit, pointing +\end{itemize} +\item track quality +\item isolation +\end{itemize} +\end{block} +\begin{exampleblock}{Calibration} +$\PDs\to\Pphi\Ppi$ +\end{exampleblock} +\includegraphics[width=\textwidth]{Fig4a.png} +\end{column} + +\end{columns} + + + + + +\textref{M.Chrz\k{a}szcz 2014} +\end{frame} +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +% \underbrace{•} + + +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% + + +\begin{frame} +\frametitle{Signal likelihoods} +\begin{columns} +\begin{column}{.8\textwidth} +\begin{block}{combined signal distribution} +\begin{itemize} +\item events distributed over 25 likelihood bins +\item background estimate from mass side-bands + +\end{itemize} +\end{block} +Signal efficiency in 3-BODY BDT vs PID BDT plane. +\end{column} +\begin{column}{.2\textwidth} + + + +\end{column} + +\end{columns} +\begin{columns} +\begin{column}{.48\textwidth} +%\only<1>{\includegraphics[width=\textwidth]{./2d-data2.pdf}} +\only{\includegraphics[width=\textwidth]{FIG6.png}} +\end{column} +\begin{column}{.48\textwidth} +%\only<1>{\includegraphics[width=\textwidth]{./2d-data2.pdf}} +\only{\includegraphics[width=\textwidth]{Fig2a.png}} +\end{column} + +\end{columns} +\textref{M.Chrz\k{a}szcz 2014} + +\end{frame} + + + + +\begin{frame} +\frametitle{Extracted upper limit} +\begin{columns}\begin{column}{.8\textwidth} + +\vspace{1.0cm} + +\begin{tabular}{|l|l|l|l|} +\hline + & \text{observed} & \text{expected} & \text{CL} \\ +\hline +$\mathcal{B}(\Ptau\to\Pmu\Pmu\Pmu)$ & $8.0\times 10 ^{-8}$ & $8.3\times 10^{-8}$ & $90\%$\\ + & $ 9.8\times 10 ^{-8}$ & $10.2\times 10^{-8}$ & $95\%$ \\ +\hline +\end{tabular} + + + +\end{column} +\begin{column}{.2\textwidth} +\includegraphics[width=.46\textwidth]{pic/LHCb_logo.jpg} +\hspace{.5em}$\unit{1}{\reciprocal\femtobarn}$ + + {\footnotesize{\href{http://www.sciencedirect.com/science/article/pii/S0370269313004450}{\texttt{PLB 724 (2013) 36-45 }}}} +\end{column} +\end{columns} +\begin{columns} +\begin{column}{.65\textwidth} +\includegraphics[width=0.8\textwidth]{Fig3a.png} +\end{column} +\begin{column}{.04\textwidth} + +\end{column} +\begin{column}{.35\textwidth} + + +\end{column} +\end{columns} +\textref{M.Chrz\k{a}szcz 2014} +\end{frame} +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% + +\begin{frame} +\frametitle{Summary} +\begin{itemize} +\item LFV and LNV processes are doing very well in LHCb. +\item Lots of best limits already in our hands. +\item Keep tune, lots of new results are coming very soon. +\end{itemize} + + +\textref{M.Chrz\k{a}szcz 2014} + +\end{frame} + + + + + + +\end{document} diff --git a/HQL_2014/ckm2012_3.toc b/HQL_2014/ckm2012_3.toc new file mode 100644 index 0000000..26409e6 --- /dev/null +++ b/HQL_2014/ckm2012_3.toc @@ -0,0 +1,9 @@ +\beamer@endinputifotherversion {3.10pt} +\select@language {polish} +\beamer@sectionintoc {2}{LHCb detector}{3}{0}{1} +\beamer@sectionintoc {3}{Lepton Flavour Violation}{4}{0}{2} +\beamer@sectionintoc {4}{$\PB $ decays}{5}{0}{3} +\beamer@subsectionintoc {4}{1}{$\PBminus \to h^{+}\Plepton ^{-}\Plepton ^{-}$}{5}{0}{3} +\beamer@subsectionintoc {4}{2}{$\PB \to \Plepton ^{+}\Plepton ^{-}$}{10}{0}{3} +\beamer@sectionintoc {5}{$\tau $ decays}{13}{0}{4} +\beamer@subsectionintoc {5}{1}{$\Ptauon \to \Pmuon \Pmuon \APmuon $}{13}{0}{4} diff --git a/HQL_2014/ckm2012_4.pdf b/HQL_2014/ckm2012_4.pdf new file mode 100644 index 0000000..c44daf3 --- /dev/null +++ b/HQL_2014/ckm2012_4.pdf Binary files differ diff --git a/HQL_2014/cleanktaue-mtau-MCbkgnorm2data-RomanTimes-Final.pdf 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+%\definecolor{mygreen}{cmyk}{0.82,0.11,1,0.25} + + +% color definitions +\usepackage{color} +\definecolor{uipoppy}{RGB}{225, 64, 5} +\definecolor{uipaleblue}{RGB}{96,123,139} +\definecolor{uiblack}{RGB}{0, 0, 0} + +% caption styling +%\DeclareCaptionFont{uiblack}{\color{uiblack}} +%\DeclareCaptionFont{uipoppy}{\color{uipoppy}} +%\captionsetup{labelfont={uipoppy},textfont=uiblack} + +% see the macros.tex file for definitions + + + +\renewcommand{\PKs}{{\HepParticle{K}{S}{}\xspace}} +\newcommand{\at}{\makeatletter @\makeatother} + +%-------------------------------------------------------------------- +% Introduction +%-------------------------------------------------------------------- + +\usetheme{Sybila} + +\title[LFV \& LNV at LHCb]{Lepton flavour and number violation measurements at LHCb} +\author{Marcin Chrz\k{a}szcz$^{1,2}$} +\institute{$^1$~University of Zurich,\\ $^2$~Institute of Nuclear Physics, Krakow} +\date{\today} +\begin{document} +% --------------------------- SLIDE -------------------------------------------- +\frame[plain]{\titlepage} +\author{Marcin Chrz\k{a}szcz} +% ------------------------------------------------------------------------------ +% --------------------------- SLIDE -------------------------------------------- + +\institute{~(UZH, IFJ)} + +%-------------------------------------------------------------------- +% OUTLINE +%-------------------------------------------------------------------- + + + + +\section[Outline]{} +\begin{frame} +\tableofcontents +\end{frame} + + + + + + + +%------------------------------------------------------------------- +% Introduction +%------------------------------------------------------------------- +% +% Set the background for the rest of the slides. +% Insert infoline +%\setbeamertemplate{background} +% {\includegraphics[width=\paperwidth,height=\paperheight]{slide_bg}} +%\setbeamertemplate{footline}[bunsentheme] + + + +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% + +%\setbeamertemplate{background} +% {\includegraphics[width=\paperwidth,height=\paperheight]{slide_bg}} +%\setbeamertemplate{footline}[bunsentheme] +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +\section{LHCb detector} + +\begin{frame}\frametitle{LHCb detector} +\begin{columns} +\column{3.in} +\begin{center} +\includegraphics[width=0.98\textwidth]{det.jpg} +\end{center} + +\column{2.0in} +\begin{footnotesize} + + + LHCb is a forward spectrometer: + \begin{itemize} + \item Excellent vertex resolution. + \item Efficient trigger. + \item High acceptance for $\Ptau$ and $\PB$. + \item Great Particle ID + \end{itemize} + + + +\end{footnotesize} +\end{columns} + +\end{frame} + +\section{Lepton Flavour Violation} +\begin{frame}\frametitle{Lepton Flavour/Number Violation} +\begin{small} + Lepton Flavour Violation(LFV): +\end{small} + + +\begin{footnotesize} + +After $\Pmuon$ was discovered it was natural to think of it as an excited $\Pelectron$. +\begin{columns} +\column{3in} +\begin{itemize} +\item Expected: $B(\mu\to\Pe\gamma) \approx 10^{-4}$ +\item Unless another $\Pnu$, in intermediate vector boson loop, cancels. +\end{itemize} + +\column{2in} +{~}\includegraphics[width=0.98\textwidth]{rabi.png} + +\end{columns} +\begin{columns} +\column{0.5in} +{~} +\column{3in} +\begin{block}{I.I.Rabi:} +"Who ordered that?" +\end{block} +\column{0.3in}{~} +\column{2in} +{~}\includegraphics[scale=0.08]{II_Rabi.jpg} + +\end{columns} + + +\begin{itemize} +\item Up to this day charged LFV is being searched for in various decay modes. +\item LFV was already found in neutrino sector. +\end{itemize} +\end{footnotesize} + + +\begin{footnotesize} + +\begin{columns} +\column{3.5in} +\begin{small} + Lepton Number Violation (LNV) +\end{small} + +\begin{itemize} +\item Even with LFV, lepton number can be a conserved quantity. +\item Many NP models predict it violation(Majorana neutrinos) +\item Searched in so called Neutrinoless double $\beta$ decays. +\end{itemize} + +\column{1.5in} +\includegraphics[width=0.8\textwidth]{Double_beta_decay_feynman.png} + +\end{columns} + +\end{footnotesize} +%Double_beta_decay_feynman.png + + % \textref{M.Chrz\k{a}szcz 2014} +\end{frame} + + +% \section{Lepton Number Violation} +\section{$\PB$ decays} +\subsection{$\PBminus\to h^{+}\Plepton^{-}\Plepton^{-}$} +\begin{frame}%[t] +\frametitle{LNV in bottom decays}%$\PBminus\to h^{+}\ell^{-}\ell^{-}$} + +\only<1>{ +\begin{columns}\begin{column}{.5\textwidth} +on-shell neutrino + +\includegraphics[width=\textwidth]{pic/B-Majorana2.pdf} +\end{column} +{\begin{column}{.45\textwidth} +virtual neutrino + +\includegraphics[width=\textwidth]{pic/B-Majorana1.pdf} +\end{column} +} +\end{columns} +\begin{columns} +\begin{column}{.5\textwidth} +\begin{itemize} +\item resonant production in accessible mass range +\item rates depend on Majorana neutrino--lepton coupling $|V_{\mu 4}|$ +\newline {\footnotesize{(e.g.\ \href{http://arxiv.org/abs/0901.3589}{arXiv:0901.3589)}}} +\item $m_4 = m_{\Plepton^{-},\Ppiplus}$ +\end{itemize} +\end{column} +{ +\begin{column}{.5\textwidth} +\begin{exampleblock}{~} +%\begin{itemize} +Diagram without mass restriction + Cabbibo favoured for $\PB\to\PD$ + Analogous to double $\beta$ decay. +%\end{itemize} +\end{exampleblock} +\end{column} +} +\end{columns} +} + % \textref{M.Chrz\k{a}szcz 2014} +\end{frame} + +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% + + +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% + +\begin{frame}[t] +\frametitle{Virtual Majorana neutrinos} + + +\begin{columns} +\only<1>{ +\begin{column}{.78\textwidth} +\begin{block}{} +%\begin{itemize} + $\PBminus\to\PDplus\Pmuon\Pmuon\quad\quad\quad\quad\quad\quad\PBminus\to\PD^{*+}\Pmuon\Pmuon$ +%\end{itemize} +\includegraphics[width=\textwidth]{pic/MassFitDp_.pdf} +\end{block} +\end{column} +} + + +\end{columns} +\only<1>{{ +{~} + + +$\mathcal{B}(\PBminus\to\PDplus\Pmuon\Pmuon)<6.9\times 10^{-7} \quad \quad \mathcal{B}(\PBminus\to\PD^{*+}\Pmuon\Pmuon)<2.4\times 10^{-6}$ +}} + + + {@ 95\,\% CL}\hspace{.35\textwidth} + {@ 95\,\% CL} +\\ Based on $0.41fb^{-1}${~}$7TeV$ data. + +{~} + +\begin{columns} +\begin{column}{6.5cm} +\end{column} +\begin{column}{1.5cm} +%\includegraphics[width=\textwidth]{pic/LHCb_logo.jpg} +\end{column} +\begin{column}{4cm} +\hspace{.4cm} + + {\footnotesize{\href{http://prd.aps.org/abstract/PRD/v85/i11/e112004}{\texttt{Phys. Rev.D85 (2012) 112004 }}}} + +\end{column} +\end{columns} + +%LHCb, arXiv:1201.5600 +%\includegraphics[width=.5\textwidth]{UpperAll} + % \textref{M.Chrz\k{a}szcz 2014} +\end{frame} + +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% + +\begin{frame}[t] +\frametitle{On-shell Majorana neutrinos} +\begin{itemize} +\item $\PBminus \to \Ppiplus \Pmuon \Pmuon$ searched with full data set${~}3fb^{-1}$. +\item Cut based analysis. +\item Normalization channel $\PBplus \to \PJpsi(\mu\mu)\PKplus$. +\item Searches performed for two scenarios: +\begin{itemize} +\item Short life-time neutrinos: $\tau_4 <1ps$ +\item Long life-time neutrinos: $\tau_4 \in (1,1000) ps$ +\end{itemize} +\end{itemize} +\begin{columns} + +\only<1>{ +\includegraphics[width=\textwidth]{Figure2.png} +} + +\end{columns} + + +\begin{columns} +\begin{column}{8.5cm} + +\includegraphics[width=\textwidth]{Figure3.png} + +\end{column} +\begin{column}{.5cm} +%\includegraphics[width=\textwidth]{pic/LHCb_logo.jpg} +\end{column} + +\begin{column}{4cm} +\hspace{.4cm} + + + {\footnotesize{\href{http://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.131802}{\texttt{Phys. Rev. Lett. 112, 131802 }}}} + +\end{column} +\end{columns} + + +% \textref{M.Chrz\k{a}szcz 2014} +\end{frame} + + + +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% + +\begin{frame}[t] +\frametitle{On-shell Majorana neutrinos} +{~}\\ +\begin{columns} +\column{2.in} +\includegraphics[width=\textwidth]{Figure5.png}\\ +\includegraphics[width=\textwidth]{Figure6.png}\\ + + +\column{3.0in} +\begin{small} +\begin{itemize} +\item In absence of signal UL. were set. +\item $Br(\PBminus \to \Ppiplus \Pmuon \Pmuon)$ in range $10^{-9}$. +\item Limits also set for the coupling $| V_{\mu 4} |^2$ +\end{itemize} +{~}{~}$Br(\PBminus \to \Ppiplus \Pmuon \Pmuon) = \dfrac{G_f^4 f_B^2f_{\pi}^2}{128\pi\hbar } \tau_B m_B^5 |V_{ub}V_{ud}|^2|V_{\mu4}|^4(1- \dfrac{m_4^2}{m_B^2})\dfrac{m_4}{\Gamma_{N_4}}$ +\end{small} +\end{columns} +% \textref{M.Chrz\k{a}szcz 2014} +\end{frame} + + +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% johan %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% + +\begin{frame} +\frametitle{Summary on LNV in $\PB$ decays} +\vspace{0.5cm} +\begin{columns} +\begin{column}{.65\textwidth} +\begin{footnotesize} +\begin{tabular}{lclr} +channel & limit & & \\\hline + $\mathcal{B}(\PBminus\to\Ppi^{+}\Pelectron\Pelectron) $ & $<2.3\times 10^{-8}$ & @$90\,\%$ CL &\includegraphics[height=.25cm]{babar}\footnote{BaBar,\href{http://link.aps.org/doi/10.1103/PhysRevD.85.071103}{Phys.\ Rev.\ D \textbf{85}, 071103} (2012)\label{babarB}}\\ + $\mathcal{B}(\PBminus\to\PK^{+}\Pelectron\Pelectron) $ & $<3.0\times 10^{-8}$ & @$90\,\%$ CL &\includegraphics[height=.25cm]{babar}\footnotesize{$^{\text{\ref{babarB}}}$}\\ + $\mathcal{B}(\PBminus\to\PK^{*+}\Pelectron\Pelectron) $ & $<2.8\times 10^{-6}$ & @$90\,\%$ CL & \includegraphics[height=.25cm]{cleo}\footnote{CLEO, \href{http://link.aps.org/doi/10.1103/PhysRevD.65.111102}{Phys.\ Rev.\ D \textbf{65}, 111102} (2002)\label{cleolnv}}\\ + $\mathcal{B}(\PBminus\to\Prho^{+}\Pelectron\Pelectron) $ & $<2.6\times 10^{-6}$ & @$90\,\%$ CL & \includegraphics[height=.25cm]{cleo}\footnotesize{$^{\text{\ref{cleolnv}}}$}\\ + $\mathcal{B}(\PBminus\to\PD^{+}\Pelectron\Pelectron) $ & $<2.6\times 10^{-6}$ & @$90\,\%$ CL & \includegraphics[height=.25cm]{belle2-logo}\footnote{Belle, \href{http://link.aps.org/doi/10.1103/PhysRevD.84.071106}{Phys.\ Rev.\ D \textbf{84}, 071106(R)}, (2011)\label{bellelnv}}\\ + $\mathcal{B}(\PBminus\to\PD^{+}\Pelectron\Pmuon) $ & $<1.8\times 10^{-6}$ & @$90\,\%$ CL & \includegraphics[height=.25cm]{belle2-logo}\footnotesize{$^{\text{\ref{bellelnv}}}$}\\ +%$\mathcal{B}(\PBminus\to\Ppi^{+}\Pmuon\Pmuon)$ & $<1.3\times 10^{-8}$ & @$95\,\%$ CL & \includegraphics[height=.25cm]{pic/LHCb_logo.jpg}\footnote{LHCb, CERN-PH-EP-2012-006, \href{http://arxiv.org/abs/1201.5600}{\texttt{arXiv:1201.5600}} (2012)\label{xxxxx}} \\ + + $\mathcal{B}(\PBminus\to\PK^{+}\Pmuon\Pmuon) $ & $<5.4\times 10^{-7}$ & @$95\,\%$ CL &\includegraphics[height=.25cm]{pic/LHCb_logo.jpg}\footnote{LHCb, \href{http://link.aps.org/doi/10.1103/PhysRevLett.108.101601}{Phys.\ Rev.\ Lett.\ 108 101601} (2012)} \\ + %$\mathcal{B}(\PBminus\to\PK^{*+}\Pmuon\Pmuon) $ & $<4.4\times 10^{-6}$ & @$90\,\%$ CL & \includegraphics[height=.25cm]{cleo}\footnotesize{$^{\text{\ref{cleolnv}}}$}\\ + %$\mathcal{B}(\PBminus\to\Prho^{+}\Pmuon\Pmuon) $ & $<5.0\times 10^{-6}$ & @$90\,\%$ CL & \footnotesize{$^{\text{\ref{cleolnv}}}$}\\ + $\mathcal{B}(\PBminus\to\PD^{+}\Pmuon\Pmuon) $ & $<6.9\times 10^{-7}$ & @$95\,\%$ CL & \includegraphics[height=.25cm]{pic/LHCb_logo.jpg}\footnote{LHCb,Phys. Rev. Lett. (112) 131802 (2014)\label{xxxxx}} \\ + $\mathcal{B}(\PBminus\to\PD^{*+}\Pmuon\Pmuon)$ & $<2.4\times 10^{-6}$ & @$95\,\%$ CL & \includegraphics[height=.25cm]{pic/LHCb_logo.jpg}\footnotesize{$^{\text{\ref{xxxxx}}}$}\\ + $\mathcal{B}(\PBminus\to\PDs^{+}\Pmuon\Pmuon)$ & $<5.8\times 10^{-7}$ & @$95\,\%$ CL & \includegraphics[height=.25cm]{pic/LHCb_logo.jpg}\footnotesize{$^{\text{\ref{xxxxx}}}$}\\ + $\mathcal{B}(\PBminus\to\PDzero\Ppiminus\Pmuon\Pmuon)$ & $<1.5\times 10^{-6}$ & @$95\,\%$ CL & \includegraphics[height=.25cm]{pic/LHCb_logo.jpg}\footnotesize{$^{\text{\ref{xxxxx}}}$}\\ +\hline +\end{tabular} %pic/LHCb_logo.jpg +\end{footnotesize} +\end{column} +\end{columns} +%\textref{M.Chrz\k{a}szcz 2014} +\end{frame} + + +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% + +\subsection{$\PB_{(s)}\to \Plepton^{+}_1\Plepton_2^{-}$} +\begin{frame}%[t] +\frametitle{$\PB_{(s)}\to \Pelectron \Pmu^{+}$}%$\PBminus\to h^{+}\ell^{-}\ell^{-}$} +\begin{footnotesize} +\begin{columns} + +\column{3in} + +\begin{itemize} +\item A separate physics interest is LFV $\PB$ decays. +\item Predicted by various NP models: lepto-quarks, SUSY, GUT. +\item Analysis based on $1fb^{-1}$ 2011 data. +\item Analogous to our $\PBs \to \mu \mu$ analysis(PRL 111 (2013) 101804) +\end{itemize} + + + +\column{2in} +{~}\\{~}\\ + +\includegraphics[width=0.95\textwidth]{blind.png}\\ +\end{columns} + +\begin{enumerate} +\item Loose preselection based on topology and PID. +\item Classifier trained on MC signal and $b\bar{b} \to \Plepton \Plepton X$ +\item Calibration channel: $\PBzero_{(s)} \to h^+ h^{'-}$ +\item Normalization Channel: $\PBzero \to \PKplus \Ppiminus$ +\item \href{http://cds.cern.ch/record/451614/files/p81.ps.gz}{CLs}\footnote{A.L.Read, The CLs technique, \\ Journal of Physics G (2012) +} + method for limit extraction. +\end{enumerate} +\end{footnotesize} + + + +\begin{columns} +\begin{column}{6.5cm} +\end{column} +\begin{column}{1.5cm} +%\includegraphics[width=\textwidth]{pic/LHCb_logo.jpg} +\end{column} +\begin{column}{4cm} +\hspace{.4cm} + {\footnotesize{\href{http://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.141801}{\texttt{Phys. Rev. Lett. 111, 141801 (2013) }}}} + +\end{column} +\end{columns} +% \textref{M.Chrz\k{a}szcz 2014} +\end{frame} + +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% + + + +\begin{frame}%[t] +\frametitle{$\PB_{(s)} \to \Pelectron \Pmu^{+}$} +\begin{footnotesize} +\begin{columns} + +\column{3.1in} + +\begin{itemize} +\item Correction to MC and DATA discrepancies. +\item Excellent proxy: $\PBzero_{(s)} \to h h'$. +\item Fit each BDT bin for $\PBzero_{(s)} \to h h'$ and extract number of events. +\item Correct MC efficiency for each bin. +\item Electron Bremsstrahlung corrected on $\PJpsi \to \Pe \Pe$. +\end{itemize} + +\column{1.9in} +\includegraphics[width=\textwidth]{Fig4a-supp.pdf}\\ +\end{columns} +\begin{columns} + +\column{2.3in} +%\includegraphics[width=\textwidth]{ClsB.png}\\ +\includegraphics[width=\textwidth]{CLS2.png}\\ +\column{3.1in} +%\includegraphics[width=\textwidth]{Fig1a-supp.pdf}\\ + +\begin{tabular}{ c | c | c } + \multicolumn{3}{c}{Upper limits} \\ \hline + + {~} & $Br(\PB \to \Pe \Pmu)$ & $Br(\PB_s \to \Pe \Pmu)$ \\ + {~} & \at~$ 90(95)\% CL$ & at~$90(95)\% CL$ \\ \hline +\textcolor{blue}{Expected} & \textcolor{blue}{$3.8(4.8)\times 10^{-9}$}& \textcolor{blue}{$1.5(2.0)\times 10^{-8}$} \\ +\textcolor{red}{Observed} & \textcolor{red}{$1.5(1.8)\times 10^{-9}$}& \textcolor{red}{$1.1(1.4)\times 10^{-8}$} \\ + +\end{tabular} + + +\end{columns} + + +\end{footnotesize} +% \textref{M.Chrz\k{a}szcz 2014} +\end{frame} + +%%%%%%%%%% +\begin{frame}%[t] +\frametitle{$\PB_{(s)}\to \Plepton^{+}_1\Plepton_2^{-}$ Implications} +\begin{footnotesize} +\begin{itemize} +\item LHCb limits two times better than previous ones from CDF\footnote{Phys. Rev. Lett. 102 (2009) 201801}. +\item CDF implications to lepto-quarks mass\footnote{Theoretical formula Phys. Rev. D 50 (1994) 6843}. +\begin{itemize} +\item $m_{LQ}(\PBs \to \Pe \Pmu) >47.8(44.9) TeV$ \@ $90(95\%)$ \at CL. +\item $m_{LQ}(\PBzero \to \Pe \Pmu) >59.3(56.3) TeV$ \@ $90(95\%)$ \at CL. + +\end{itemize} +\end{itemize} + +\begin{center} +\begin{columns} +\column{0.4in} +{~} +\column{1.85in} +\includegraphics[width=0.8\textwidth]{Fig2a-supp.pdf}\\ +\column{0.2in} +{~} +\column{1.85in} +\includegraphics[width=0.8\textwidth]{Fig2b-supp.pdf}\\ +\column{0.4in} +{~} +\end{columns} + +\end{center} +LHCb limits: +\begin{itemize} +\item $m_{LQ}(\PBs \to \Pe \Pmu) >107(101) TeV$ \@ $90(95\%)$ \at CL. +\item $m_{LQ}(\PBzero \to \Pe \Pmu) >135(126) TeV$ \@ $90(95\%)$ \at CL. + +\end{itemize} + +\end{footnotesize} +% \textref{M.Chrz\k{a}szcz 2014} +\end{frame} + + + + + + + + +%%%%%%%%%%%%%%%%%%%%%%%%% +%%%%%%%%%%%%%%%%%%%%%%%%%% +%%%%%%%%%%%%%%%%%%%%%%%% + + + + + + +%\section{Lepton Flavour Violation} +\section{$\tau$ decays} + + +\subsection{$\Ptauon\to\Pmuon\Pmuon\APmuon$} +\begin{frame}\frametitle{Curent status} + + + + +\frametitle{$\Ptau \to \mu \mu \mu$} + +\only<1>{ + + + +\begin{center} +\begin{columns} +\column{3in} +\begin{enumerate} + \item In SM small $\mathcal{B}( \Ptauon\to\Pmuon\Pmuon\APmuon ) \sim 10^{-50} $ \\ + \item NP can enhance $\mathcal{B}$. \\ + \item Nature still hides $\Ptauon\to\Pmuon\Pmuon\APmuon$ from us.\\ + \item Current limits: +\end{enumerate} +\column{2in} +\includegraphics[width=\textwidth]{tau23mu.png}\\ + + +\end{columns} + + + \begin{center} + \begin{tabular}{| l | l |} + \hline Experiment & $90\%$ CL limit \\ + \hline + \hline BaBar{~}\footnote{Phys.Rev.D81:111101(R),2010} & $3.3 \times 10^{-8}$ \\ + \hline Belle{~}\footnote{Phys.Lett.B687:139-143,2010} & $2.1 \times 10^{-8}$\\ + \hline +\end{tabular} +\end{center} +\begin{itemize} +\item Can a hadron collider change the picture? \\ +\end{itemize} + + + + + + +\end{center} +} +% \textref{M.Chrz\k{a}szcz 2014} +\end{frame} + +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% + +\begin{frame}\frametitle{Analysis approach} +\begin{columns} +\column{0.2in} +{~}\\ +\column{2.5in} +$\mathcal{B}$ factories + + +\column{2.5in} +LHCb, ($7 TeV$, 2011 data) + + + +\end{columns} +\begin{columns} +\column{0.2in} +{~}\\ +\column{2.5in} + + +\begin{enumerate} + + + \item signal: $\APelectron\Pelectron\to\APtauon\Ptauon$ \\ + \item $1.2\times 10^9$ $\tau$ pairs \\ + \item Calculate the thrust axis \\ + \item Tag the other $\tau$ \\ + \item Small cross section $0.919nb$ \\ +\end{enumerate} +\column{2.5in} + +\begin{enumerate} + \item Inclusive $\tau$ cross section: \newline $79.5\pm\unit{8.3}{\micro\barn}$. \\ + \item $8 \times 10^{10} \tau$ produced. \\ + \item Dominant contribution: \newline $\PDs\to\Ptau\Pnut$ ($78\%$) \\ + \item No partial tag possible. \\ +\end{enumerate} + + + +\end{columns} + + +% \textref{M.Chrz\k{a}szcz 2014} +\end{frame} + +\begin{frame} +\frametitle{Strategy} +\setbeamercolor{block body}{use=structure,fg=black,bg=white!70!white} + +\begin{columns} +\begin{column}{.5\textwidth} +\begin{itemize} +\item Loose cut based selection +\item Classification in 3D space: +\begin{itemize} +\item invariant mass +\item decay topology\newline (multivariate) +\item particle identification\newline (multivariate) +\end{itemize} +\item Classifier trained on simulation +\item Calibration with control channel +\item Normalization with $\PDs \to \phi(\mu \mu) \pi$ +\item CLs method to extract the result +\end{itemize} +\end{column} +\begin{column}{.5\textwidth} + +%\begin{block}{Signal \& Calibration \& Background channel} +%\includegraphics[width=.7\textwidth]{topos} +%\newline +%\includegraphics[width=.7\textwidth]{topob2.png} +%\end{block} +Signal \& Calibration \& Background channel:\\ +\includegraphics[width=.7\textwidth]{topos} +\newline +\includegraphics[width=.7\textwidth]{topob2.png} + +\end{column} +\end{columns} +%\textref{M.Chrz\k{a}szcz 2014} +\end{frame} + +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%5 + + +\begin{frame} +\frametitle{Signal likelihoods} +\begin{columns}\begin{column}{.48\textwidth} +\begin{block}{particle identification} +\begin{itemize} +\item hits in muon chambers +\item energy in calorimeters +\begin{itemize} +\item compatible with MIP +\end{itemize} +\item RICH response +\end{itemize} +\end{block} +\begin{exampleblock}{Calibration} +$\PJpsi\to\APmuon\Pmuon$ +\end{exampleblock} +\includegraphics[width=\textwidth]{Fig4b.png} +\end{column} + +\begin{column}{.48\textwidth} + +\begin{block}{3 body decay likelihood} +\begin{itemize} +\item vertex properties +\begin{itemize} +\item vertex fit, pointing +\end{itemize} +\item track quality +\item isolation +\end{itemize} +\end{block} +\begin{exampleblock}{Calibration} +$\PDs\to\Pphi\Ppi$ +\end{exampleblock} +\includegraphics[width=\textwidth]{Fig4a.png} +\end{column} + +\end{columns} + + + + + +% \textref{M.Chrz\k{a}szcz 2014} +\end{frame} +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +% \underbrace{•} + + +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% + + +\begin{frame} +\frametitle{Signal likelihoods} +\begin{columns} +\begin{column}{.8\textwidth} +\begin{block}{combined signal distribution} +\begin{itemize} +\item events distributed over 25 likelihood bins +\item background estimate from mass side-bands + +\end{itemize} +\end{block} +Signal efficiency in 3-BODY BDT vs PID BDT plane. +\end{column} +\begin{column}{.2\textwidth} + + + +\end{column} + +\end{columns} +\begin{columns} +\begin{column}{.48\textwidth} +%\only<1>{\includegraphics[width=\textwidth]{./2d-data2.pdf}} +\only{\includegraphics[width=\textwidth]{FIG6.png}} +\end{column} +\begin{column}{.48\textwidth} +%\only<1>{\includegraphics[width=\textwidth]{./2d-data2.pdf}} +\only{\includegraphics[width=\textwidth]{Fig2a.png}} +\end{column} + +\end{columns} +%\textref{M.Chrz\k{a}szcz 2014} + +\end{frame} + + + + +\begin{frame} +\frametitle{Extracted upper limit} +\begin{columns}\begin{column}{.8\textwidth} + +\vspace{1.0cm} + +\begin{tabular}{|l|l|l|l|} +\hline + \multicolumn{4}{|c|}{Upper limits} \\ \hline + & \text{observed} & \text{expected} & \text{CL} \\ +\hline + +$\mathcal{B}(\Ptau\to\Pmu\Pmu\Pmu)$ & $8.0\times 10 ^{-8}$ & $8.3\times 10^{-8}$ & $90\%$\\ + & $ 9.8\times 10 ^{-8}$ & $10.2\times 10^{-8}$ & $95\%$ \\ +\hline +\end{tabular} + + + +\end{column} +\begin{column}{.2\textwidth} +\includegraphics[width=.46\textwidth]{pic/LHCb_logo.jpg} +\hspace{.5em}$\unit{1}{\reciprocal\femtobarn}$ + + {\footnotesize{\href{http://www.sciencedirect.com/science/article/pii/S0370269313004450}{\texttt{PLB 724 (2013) 36-45 }}}} +\end{column} +\end{columns} +\begin{columns} +\begin{column}{.65\textwidth} +\includegraphics[width=0.8\textwidth]{Fig3a.png} +\end{column} +\begin{column}{.04\textwidth} + +\end{column} +\begin{column}{.35\textwidth} + + +\end{column} +\end{columns} +%\textref{M.Chrz\k{a}szcz 2014} +\end{frame} +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% + +\begin{frame} +\frametitle{Summary} +\begin{itemize} + + +\item Analyses of LFV and LNV processes are going very well in LHCb +\item We already have a number of best limits in our hands. +\item Stay tuned, more new results coming up soon. +\end{itemize} + + + + +\end{frame} + + + + + + +\end{document} diff --git a/HQL_2014/hql2.toc b/HQL_2014/hql2.toc new file mode 100644 index 0000000..a8661f9 --- /dev/null +++ b/HQL_2014/hql2.toc @@ -0,0 +1,9 @@ +\beamer@endinputifotherversion {3.10pt} +\select@language {english} +\beamer@sectionintoc {2}{LHCb detector}{3}{0}{1} +\beamer@sectionintoc {3}{Lepton Flavour Violation}{4}{0}{2} +\beamer@sectionintoc {4}{$\PB $ decays}{5}{0}{3} +\beamer@subsectionintoc {4}{1}{$\PBminus \to h^{+}\Plepton ^{-}\Plepton ^{-}$}{5}{0}{3} +\beamer@subsectionintoc {4}{2}{$\PB _{(s)}\to \Plepton ^{+}_1\Plepton 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+\setcounter{subsection}{0} +\setcounter{subsubsection}{0} +\setcounter{subsectionslide}{0} +\setcounter{framenumber}{0} +\setcounter{figure}{0} +\setcounter{table}{0} +\setcounter{parentequation}{0} +\setcounter{theorem}{0} +} diff --git a/HQL_2014/macros.log b/HQL_2014/macros.log new file mode 100644 index 0000000..e69de29 --- /dev/null +++ b/HQL_2014/macros.log diff --git a/HQL_2014/macros.tex b/HQL_2014/macros.tex new file mode 100644 index 0000000..51f4820 --- /dev/null +++ b/HQL_2014/macros.tex @@ -0,0 +1,15 @@ +% This program can be redistributed and/or modified under the terms +% of the GNU Public License, version 3. + +% adds reference to bottom right of corner of a slide +\usepackage[absolute,overlay]{textpos} % text references in slide corners +\newcommand\textref[1]{% + \begin{textblock*}{\paperwidth}(0pt,0.99\textheight) + \raggedleft \tiny{\emph{#1}}\hspace{.5em} + \end{textblock*}} + +% for drawing circles around numbers +% ex. \circled{1} Add some text here. +\usepackage{tikz} +\newcommand*\circled[1]{\tikz[baseline=(char.base)]{ + \node[shape=circle,draw,inner sep=2pt] (char) {#1};}} diff --git a/HQL_2014/mass_bins.pdf b/HQL_2014/mass_bins.pdf new file mode 100644 index 0000000..8d87cb0 --- /dev/null +++ b/HQL_2014/mass_bins.pdf Binary files differ diff --git a/HQL_2014/masssim.pdf b/HQL_2014/masssim.pdf new file mode 100644 index 0000000..10e0a73 --- /dev/null +++ b/HQL_2014/masssim.pdf Binary files differ diff --git a/HQL_2014/multihiggs.1 b/HQL_2014/multihiggs.1 new file mode 100644 index 0000000..61d8a7b --- /dev/null +++ b/HQL_2014/multihiggs.1 @@ -0,0 +1,53 @@ +%!PS +%%BoundingBox: 0 0 170 80 +%%HiResBoundingBox: 0 0 169.36447 79.70093 +%%Creator: MetaPost 1.504 +%%CreationDate: 2012.05.16:1707 +%%Pages: 1 +%%BeginProlog +%%EndProlog +%%Page: 1 1 + 0 0 0 setrgbcolor 0 0.99626 dtransform truncate idtransform setlinewidth pop + [] 0 setdash 1 setlinecap 1 setlinejoin 10 setmiterlimit +newpath 0 26.56656 moveto +84.68224 26.56656 lineto stroke +newpath 38.94792 23.63191 moveto +49.90034 26.56656 lineto +38.94792 29.5012 lineto + closepath fill +newpath 169.36447 0 moveto +0 0 lineto stroke +newpath 88.07417 2.93431 moveto +77.12347 0 lineto +88.07417 -2.93431 lineto + closepath fill +newpath 169.36447 53.13315 moveto +84.68224 53.13315 lineto stroke +newpath 130.41655 56.0678 moveto +119.46413 53.13315 lineto +130.41655 50.1985 lineto + closepath fill +newpath 84.68224 53.13315 moveto +169.36447 79.69969 lineto stroke +newpath 124.66408 62.60048 moveto +134.23637 68.6793 lineto +122.90712 68.20088 lineto + closepath fill + 0.99626 0 dtransform exch truncate exch idtransform pop setlinewidth +newpath 84.68224 53.13315 moveto +84.68224 49.8123 lineto stroke +newpath 84.68224 46.4915 moveto +84.68224 43.17065 lineto stroke +newpath 84.68224 39.84985 moveto +84.68224 36.529 lineto stroke +newpath 84.68224 33.2082 moveto +84.68224 29.88736 lineto stroke + 0 0.99626 dtransform truncate idtransform setlinewidth pop +newpath 84.68224 26.56656 moveto +169.36447 26.56656 lineto stroke +newpath 123.63016 23.63191 moveto +134.58258 26.56656 lineto +123.63016 29.5012 lineto + closepath fill +showpage +%%EOF diff --git a/HQL_2014/multihiggs.log b/HQL_2014/multihiggs.log new file mode 100644 index 0000000..f01baeb --- /dev/null +++ b/HQL_2014/multihiggs.log @@ -0,0 +1,13 @@ +This is MetaPost, version 1.504 (kpathsea version 6.1.0dev) 16 MAY 2012 17:07 +**multihiggs +(mpost.mp (/usr/share/texlive/texmf-dist/metapost/base/plain.mp +Preloading the plain mem file, version 1.004)) (./multihiggs.mp +(/usr/share/texmf/metapost/feynmf/feynmp.mp) [1] ) + +Here is how much of MetaPost's memory you used: + 426 strings using 6821 characters + 728968 bytes of node memory + 914 symbolic tokens + 14i,71n,28p,108b,3f stack positions out of 16i,84n,32p,200b,4f +1 output file written: multihiggs.1 + diff --git a/HQL_2014/multihiggs.mp b/HQL_2014/multihiggs.mp new file mode 100644 index 0000000..a9783e7 --- /dev/null +++ b/HQL_2014/multihiggs.mp @@ -0,0 +1,30 @@ +% multihiggs.mp -- do not edit, generated automatically by pseyfert.tex +input feynmp +require_RCS_revision "1.30"; +beginchar(1, 170*1.0pt#, 80*1.0pt#, 0); +"feynmf: 1"; +LaTeX_unitlength:=1.0pt; +subgraph (0, 0, w, h); +vinit; +pickup pencircle scaled thin; +straight_galleries; +vleft (__i2, __i3, __i4, __i5); +vright (__o2, __o3, __o4, __o5); +vconnect ("phantom", __i4, __g1); +vconnect ("fermion,lab.side=left,label=$\APelectron $", __o4, __g1); +vconnect ("phantom,lab.side=right,label=$\PDplus $", __i2, __i3); +vconnect ("phantom,lab.side=right,label=$\Ppiplus $", __o2, __o3); +vconnect ("fermion,lab.side=right,label=$\Pcharm $", __i3, __g3); +vconnect ("fermion,lab.side=right,label=$\Pdown $", __g3, __o3); +vconnect ("fermion,lab.side=left,label=$\APdown $", __o2, __i2); +vfreeze; +vfreeze; +vconnect ("fermion,lab.side=left,label=$\Pmuon $", __g1, __o5); +vconnect ("dashes,lab.side=right,label=$\Phi _S$", __g1, __g3); +vfreeze; +vdraw; +endsubgraph; +endchar; +% the end. +end. +endinput; diff --git a/HQL_2014/multihiggs.t1 b/HQL_2014/multihiggs.t1 new file mode 100644 index 0000000..d1d4b41 --- /dev/null +++ b/HQL_2014/multihiggs.t1 @@ -0,0 +1,9 @@ +% multihiggs.t1 -- generated from multihiggs.mp +\fmfL(6,13.33315,l){$\PDplus $}% +\fmfL(42.50002,20.66624,t){$\Pcharm $}% +\fmfL(176,13.33315,l){$\Ppiplus $}% +\fmfL(84.99998,-6,t){$\APdown $}% +\fmfL(127.49998,47.33252,t){$\APelectron $}% +\fmfL(125.70401,72.39055,b){$\Pmuon $}% +\fmfL(79,39.99939,r){$\Phi _S$}% +\fmfL(127.50002,20.66624,t){$\Pdown $}% diff --git a/HQL_2014/multihiggs2.1 b/HQL_2014/multihiggs2.1 new file mode 100644 index 0000000..b9e1fd4 --- /dev/null +++ b/HQL_2014/multihiggs2.1 @@ -0,0 +1,53 @@ +%!PS +%%BoundingBox: 0 0 200 80 +%%HiResBoundingBox: 0 0 199.25232 79.70093 +%%Creator: MetaPost 1.208 +%%CreationDate: 2012.09.09:1952 +%%Pages: 1 +%%BeginProlog +%%EndProlog +%%Page: 1 1 + 0 0 0 setrgbcolor 0 0.99626 dtransform truncate idtransform setlinewidth pop + [] 0 setdash 1 setlinecap 1 setlinejoin 10 setmiterlimit +newpath 0 26.56656 moveto +99.62616 26.56656 lineto stroke +newpath 46.42024 23.6322 moveto +57.37128 26.56656 lineto +46.42024 29.50092 lineto + closepath fill +newpath 199.25232 0 moveto +0 0 lineto stroke +newpath 103.019 2.93436 moveto +92.0685 0 lineto +103.019 -2.93436 lineto + closepath fill +newpath 199.25232 53.13315 moveto +99.62616 53.13315 lineto stroke +newpath 152.83208 56.0675 moveto +141.88104 53.13315 lineto +152.83208 50.19879 lineto + closepath fill +newpath 99.62616 53.13315 moveto +199.25232 79.69969 lineto stroke +newpath 146.9172 62.70668 moveto +156.74402 68.36436 lineto +145.40494 68.37788 lineto + closepath fill + 0.99626 0 dtransform exch truncate exch idtransform pop setlinewidth +newpath 99.62616 53.13315 moveto +99.62616 49.8123 lineto stroke +newpath 99.62616 46.4915 moveto +99.62616 43.17065 lineto stroke +newpath 99.62616 39.84985 moveto +99.62616 36.529 lineto stroke +newpath 99.62616 33.2082 moveto +99.62616 29.88736 lineto stroke + 0 0.99626 dtransform truncate idtransform setlinewidth pop +newpath 99.62616 26.56656 moveto +199.25232 26.56656 lineto stroke +newpath 146.0464 23.6322 moveto +156.99744 26.56656 lineto +146.0464 29.50092 lineto + closepath fill +showpage +%%EOF diff --git a/HQL_2014/multihiggs2.log b/HQL_2014/multihiggs2.log new file mode 100644 index 0000000..8bc4c68 --- /dev/null +++ b/HQL_2014/multihiggs2.log @@ -0,0 +1,12 @@ +This is MetaPost, version 1.208 (kpathsea version 5.0.0) (mem=mpost 2012.09.09) 9 SEP 2012 19:52 +**multihiggs2.mp +(./multihiggs2.mp (/usr/share/texmf/metapost/feynmf/feynmp.mp) [1] ) + +Here is how much of MetaPost's memory you used: + 2575 strings out of 2977 + 7931 string characters out of 11932 + 23637 words of memory out of 3000000 + 893 symbolic tokens out of 16384 + 14i,71n,28p,107b,3f stack positions out of 300i,84n,10000p,200b,15f + 21 string compactions (moved 110397 characters, 24556 strings) +1 output file written: multihiggs2.1 diff --git a/HQL_2014/multihiggs2.mp b/HQL_2014/multihiggs2.mp new file mode 100644 index 0000000..a1c2097 --- /dev/null +++ b/HQL_2014/multihiggs2.mp @@ -0,0 +1,28 @@ +% multihiggs2.mp -- do not edit, generated automatically by ckm2012_1.tex +input feynmp +require_RCS_revision "1.30"; +beginchar(1, 200*1.0pt#, 80*1.0pt#, 0); +"feynmf: 1"; +LaTeX_unitlength:=1.0pt; +subgraph (0, 0, w, h); +vinit; +pickup pencircle scaled thin; +straight_galleries; +vleft (__i2, __i3, __i4, __i5); +vright (__o2, __o3, __o4, __o5); +vconnect ("phantom", __i4, __g1); +vconnect ("fermion,lab.side=left,label=$\APmuon $", __o4, __g1); +vconnect ("fermion,lab.side=right,label=$\Pbottom $", __i3, __g3); +vconnect ("fermion,lab.side=right,label=$\Pstrange $", __g3, __o3); +vconnect ("fermion,lab.side=left,label=$\APup $", __o2, __i2); +vfreeze; +vfreeze; +vconnect ("fermion,lab.side=left,label=$\Ptauon $", __g1, __o5); +vconnect ("dashes,lab.side=right,label=$\Phi _S$", __g1, __g3); +vfreeze; +vdraw; +endsubgraph; +endchar; +% the end. +end. +endinput; diff --git a/HQL_2014/multihiggs2.t1 b/HQL_2014/multihiggs2.t1 new file mode 100644 index 0000000..afc2334 --- /dev/null +++ b/HQL_2014/multihiggs2.t1 @@ -0,0 +1,7 @@ +% multihiggs2.t1 -- generated from multihiggs2.mp +\fmfL(50.00002,20.66624,t){$\Pbottom $}% +\fmfL(99.99998,-6,t){$\APup $}% +\fmfL(149.99998,47.33252,t){$\APmuon $}% +\fmfL(148.45406,72.46306,b){$\Ptauon $}% +\fmfL(94,39.99939,r){$\Phi _S$}% +\fmfL(150.00002,20.66624,t){$\Pstrange $}% diff --git a/HQL_2014/multihiggs2.t1.log b/HQL_2014/multihiggs2.t1.log new file mode 100644 index 0000000..e69de29 --- /dev/null +++ b/HQL_2014/multihiggs2.t1.log diff --git a/HQL_2014/pic/2d-data2.pdf b/HQL_2014/pic/2d-data2.pdf new file mode 100644 index 0000000..c1b70e3 --- /dev/null +++ b/HQL_2014/pic/2d-data2.pdf Binary files differ diff --git a/HQL_2014/pic/2d-data2.svg b/HQL_2014/pic/2d-data2.svg new file mode 100644 index 0000000..320bf29 --- /dev/null +++ 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\hspace{1.5cm}\strut\insertframetitle\strut}\par% + {% + \ifx\insertframesubtitle\@empty% + \else% + {\usebeamerfont{framesubtitle}\usebeamercolor[fg]{framesubtitle}\insertframesubtitle\strut\par}% + \fi + }}% + \end{beamercolorbox}% + }% +} + + +\usepackage[english]{babel} +\usepackage[utf8]{inputenc} +\usepackage{graphicx} +\DeclareGraphicsRule{*}{mps}{*}{} + +\usepackage{pgf} +\usepackage{times} +\usepackage[T1]{fontenc} +\usepackage[mathscr]{eucal} +\usepackage{mathrsfs} + +% \usepackage{pgfpages} +% \setbeameroption{show notes on second screen} +%\pgfpagesuselayout{4 on 1}[a4paper,border shrink=5mm,landscape] + +\usepackage{amsfonts} +\usepackage{amsmath} +\usepackage{verbatim} +% \usepackage[amssymb]{SIunits} +%\usepackage{natbib} +\usepackage{amssymb} +\usepackage{hepparticles} +\usepackage{hepnicenames} +\usepackage{hepunits} +\usepackage{tikz} +%\usetikzlibrary{trees} +%\usetikzlibrary{decorations.pathmorphing} +%\usetikzlibrary{decorations.markings} +\usetikzlibrary{arrows} +\usetikzlibrary{shapes} +%\usetikzlibrary{positioning} +%\usetikzlibrary{patterns} +%\usetikzlibrary{fit} +%\usepackage{verbatim} + +\tikzstyle{decision} = [diamond, draw, fill=gray!20, + text width=4.5em, text badly centered, node distance=3cm, inner sep=0pt] +\tikzstyle{block} = [rectangle, draw, fill=blue!10, + text width=5em, text centered, rounded corners, minimum height=2em] +\tikzstyle{line} = [draw, -latex'] +\tikzstyle{cloud} = [draw, ellipse,fill=red!10, node distance=3cm, + minimum height=2em] + +\tikzstyle{every picture}+=[remember picture] + + +\renewcommand{\PKs}{{\HepParticle{K}{S}{}\xspace}} + + +\title[LFV and LNV]{Searches for Lepton Flavour Violation\newline and Lepton Number Violation in Hadron Decays} +\titlegraphic{%\begin{center}{~~~~~~~~~~~}Flavour Physics and CP Violation 2012 +%\newline + +\includegraphics[width=2.5cm]{../bmbf_engl.jpg}\hspace{7cm}\includegraphics[width=2cm]{fpcp_logo} +%\end{center} +} +%\subtitle{T 60.1} + +% \subtitle{} +\author[Paul Seyfert]{Paul Seyfert\newline{\footnotesize{ on behalf of the LHCb collaboration\newline including results from the B factories}}} +\institute[Heidelberg University]{Heidelberg University} +\date[FPCP 2012]{Flavour Physics and CP Violation 2012} +\subject{} + +% \pgfdeclareimage[height=0.5cm]{university-logo}{3Ddoublewell} +% \pgfdeclareimage[width=1.2cm]{university-logo}{weak} +% \logo{\pgfuseimage{university-logo}} +% \pgfdeclareimage[width=\paperwidth,height=\paperheight]{hbild}{condensate} +% \usebackgroundtemplate{\pgfuseimage{hbild}} + +\newcommand{\myhref}[2]{\href{#1}{\textcolor{blue}{#2}}} +\begin{document} +\begin{frame} +\titlepage +\end{frame} + +\begin{frame} +\frametitle{Outline} +\tableofcontents +\end{frame} + +\begin{frame} +\begin{center} +{\Huge{Lepton Number Violation}} + +{~} + +\begin{itemize} +\item {$\PDminus\to\Ppiplus/\PKplus\ell^{-}\ell^{-}$} +\item {$\PBminus\to h^{+}\ell^{-}\ell^{-}$} +\item {$\PBminus\to\PDzero\Ppiplus\Pmuon\Pmuon$} +\end{itemize} + +\end{center} +\end{frame} +%\section{LNV in $\PBminus/\PDminus\to h^{+}\Plepton^{-}\Plepton^{-}$} %LHCb LHCb (Belle ell) (BaBar ell other) +\section{Lepton Number Violation} +\begin{frame}{Lepton Number Violation} +\begin{columns} +\begin{column}{.75\textwidth} +\begin{itemize} +\item Lepton number is conserved in the Standard Model +\item Lepton number violation introduced in many New Physics models, e.\,g.: +{\footnotesize{ +\begin{itemize} +\item 4$^{\rm{th}}$ quark generation\newline (\myhref{http://arxiv.org/abs/1106.0343}{\texttt{arXiv:hep-ph/1106.0343}}) +\item $SO(10)$ SUSY GUT\newline (\myhref{http://arxiv.org/abs/hep-ph/9501298}{\texttt{arXiv:hep-ph/9501298}}) +\item exotic Higgs\newline (A.\ Zee, \myhref{http://dx.doi.org/10.1016/0370-2693(80)90349-4}{Phys.\ Lett.\ B93, 389 (1980)}) +\end{itemize} +}} +\item Majorana neutrinos violate Lepton Number\newline +classic search: neutrinoless double beta-decay ($\rightarrow$\myhref{http://hep.ustc.edu.cn/indico/contributionDisplay.py?contribId=36&confId=7}{Dongming Mei's talk}) +\item Similar fundamental process with mesons +\end{itemize} +\end{column} +\begin{column}{.25\textwidth} +\includegraphics[width=\textwidth]{double} +\end{column} +\end{columns} +\end{frame} + +\begin{frame}[t] +\frametitle{LNV in meson decays} +\begin{columns}\begin{column}{.5\textwidth} +{\Large{$\PDplus\to\Ppiminus\APmuon\APmuon$}} + +\includegraphics[width=\textwidth]{./D-Majorana} +\begin{itemize} +\item resonant production in accessible mass range +\item rates depend on Majorana neutrino--lepton coupling $|V_{\mu 4}|$ +\newline {\footnotesize{(e.g.\ \myhref{http://arxiv.org/abs/0901.3589}{arXiv:0901.3589)}}} +\item $m_4 = m_{\Plepton^{-},\Ppiplus}$ +\end{itemize} +\end{column} +\begin{column}{.5\textwidth} +\invisible<1>{ +\includegraphics[width=.85\textwidth]{./exclusion} + +{\footnotesize{\myhref{http://arxiv.org/abs/0901.3589}{\texttt{arXiv:0901.3589}}}} +\begin{itemize} +\item strong constraints from $\PK$ decays at low $m_4$ +\item high mass region accessible in $\PD$ and $\PB$ decays +\end{itemize} +} +\end{column} +\end{columns} +\end{frame} + +\begin{frame}[t] +\frametitle{LNV in meson decays} +\begin{columns}\begin{column}{.4\textwidth} +{\Large{$\PDplus\to\Ppiminus\APmuon\APmuon$}} + +\includegraphics[width=\textwidth]{./D-Majorana} +{\footnotesize{\begin{itemize} +\item resonant production in accessible mass range +\item rates depend on Majorana neutrino--lepton coupling $|V_{\mu 4}|$ +\newline {\footnotesize{(e.g.\ \myhref{http://arxiv.org/abs/0901.3589}{arXiv:0901.3589)}}} +\item $m_4 = m_{\Plepton^{-},\Ppiplus}$ +\end{itemize}}} +\end{column} +\begin{column}{.6\textwidth} +{\includegraphics[width=.85\textwidth]{./exclusion} + +Status of 2009 + +{\footnotesize{\myhref{http://arxiv.org/abs/0901.3589}{\texttt{arXiv:0901.3589}}}} +%\begin{itemize} +%\item strong constraints from $\PK$ decays at low $m_4$ +%\item high mass region accessible in $\PD$ and $\PB$ decays +%\end{itemize} +} +\end{column} +\end{columns} +\end{frame} + + + +\subsection{$\PDminus\to\Ppiplus/\PKplus\ell^{-}\ell^{-}$} +\begin{frame} +\frametitle{limits on LNV in charm decays} +\begin{columns} +{\begin{column}{.46\textwidth} +%{\Large{$\PDplus\to h^{-}\ell^{+}\ell^{+}$}} +{\Large{charm decays}} +\begin{itemize} +\item latest limits from BaBar% using $\unit{384}{\reciprocal\femtobarn}$ +%\item normalisation relative to $\PDs^{+}\to\Pphi(\PK\PK)\Ppi^{+}$ +%\item $\APelectron\Pelectron\to\PD\APD$ +\item includes Lepton Number and Flavour Violation +\item comprehensive list of $\PDplus, \PDs^{+}, $ and $\Lambda_c^{+}$ decays +\item<2> best limit for most channels +\end{itemize} +\only<1>{\includegraphics[width=.4\textwidth]{./babar}} +%\only<2>{ +%{~} +% +%\includegraphics[width=\textwidth]{./DLNVpeaks}} + + +%\only<2>{\begin{alertblock}{background sources} +%\begin{itemize} +%\item combinatorics +%\item QED events +%\item semileptonic decays +%\item $\Ppizero, \Pphi$ resonance +%\end{itemize} +%\end{alertblock}} +\end{column} +\begin{column}{.5\textwidth} +%\only<2>{ +%\begin{block}{Strategy} +%\begin{itemize} +%\item exclude semileptonic charm production +%\item[$\Rightarrow$] reject most combinatorics +%\item require 5 tracks and electron veto on hadron +%\item[$\Rightarrow$] rejects QED background +%\item vertex requirements reject semileptonic background +%\end{itemize} +%\end{block} +%\begin{exampleblock}{Normalisation} +%\begin{itemize} +%\item Measure yield wrt.\ $\PD\to\Pphi(\PKplus\PKminus)\Ppi$ +%\item[$\Rightarrow$] most systematics cancel +%\item PID as remaining systematics +%\end{itemize} +%\end{exampleblock} +%} +\only<1>{\includegraphics[width=\textwidth]{./babarcharmtableLNV} + +{\footnotesize{\myhref{http://link.aps.org/doi/10.1103/PhysRevD.84.072006}{Phys.\ Rev.\ D \textbf{84}, 072006 (2011)}}}} +\only<2>{\includegraphics[width=\textwidth]{./lnvhfag.pdf}} +\end{column}} +\end{columns} +%\only<2>{ +%{~} +% +%{~} +% +%{\footnotesize{ +%$\mathcal{B}(\PDplus\to\Ppiminus\APelectron\APelectron)<1.1\times 10^{-6}$ by CLEO (Phys.\ Rev.\ D \textbf{82}, 092007 (2010))}}} +\end{frame} + + + +\subsection{$\PBminus\to h^{+}\ell^{-}\ell^{-}$} + +\begin{frame}%[t] +\frametitle{LNV in bottom decays}%$\PBminus\to h^{+}\ell^{-}\ell^{-}$} +\only<1>{ +\Large{$\PBminus\to h^{+}\Plepton^{-}\Plepton^{-}$} +} +\only<2>{ +\begin{columns}\begin{column}{.5\textwidth} +on-shell neutrino + +\includegraphics[width=\textwidth]{./B-Majorana2} +\end{column} +{\begin{column}{.45\textwidth} +virtual neutrino + +\includegraphics[width=\textwidth]{./B-Majorana1} +\end{column} +} +\end{columns} +\begin{columns} +\begin{column}{.5\textwidth} +\begin{itemize} +\item resonant production in accessible mass range +\item rates depend on Majorana neutrino--lepton coupling $|V_{\mu 4}|$ +\newline {\footnotesize{(e.g.\ \myhref{http://arxiv.org/abs/0901.3589}{arXiv:0901.3589)}}} +\item $m_4 = m_{\Plepton^{-},\Ppiplus}$ +\end{itemize} +\end{column} +{ +\begin{column}{.5\textwidth} +\begin{exampleblock}{special for $\PB$ decays} +%\begin{itemize} +diagram without mass restriction + Cabbibo favoured for $\PB\to\PD$ +%\end{itemize} +\end{exampleblock} +\end{column} +} +\end{columns} +} + +\end{frame} + + +\begin{frame}{search for Majorana neutrinos at LHCb} +\begin{columns} +\begin{column}{.8\textwidth} +\begin{itemize} +\item searches at B factories in \myhref{http://hep.ustc.edu.cn/indico/contributionDisplay.py?contribId=4&confId=7}{Liang Sun's talk} +\item LHCb: search for \begin{itemize}\item $\PBminus\to\Ppiplus\Pmuon\Pmuon$\item $\PBminus\to\PDplus\Pmuon\Pmuon$\item $\PBminus\to\PDs^{+}\Pmuon\Pmuon$\item $\PBminus\to\PD^{*+}\Pmuon\Pmuon$\end{itemize} +%\item $\unit{0.41}{\reciprocal\femtobarn}$ analysed +\item consider topology in reconstruction +\begin{itemize} +\item allow for flight distance for on-shell neutrinos +\item common vertex for virtual neutrinos +\end{itemize} +\end{itemize} +\end{column} +\begin{column}{.2\textwidth} +\includegraphics[width=2cm]{../lhcb-logo} +\end{column} +\end{columns} +\begin{columns} +\begin{column}{.42\textwidth} +\includegraphics[width=.7\textwidth]{reco} +\end{column} +\begin{column}{.52\textwidth} +\includegraphics[width=.7\textwidth]{reco2} +\end{column} +\end{columns} +\end{frame} + + + + +\begin{frame}[t] +\frametitle{virtual Majorana neutrinos} + +%\begin{itemize} +%\item best limits for $h = \PDplus, \PD^{*+}, \Ppiplus, \PDs$ from LHCb using $\unit{0.41}{\reciprocal\femtobarn}$ %, \PKplus +%\item normalisation relative to $\PBplus\to\PKplus\PJpsi$ and $\PBplus\to\PKplus\Ppsi(2S)$ +%\end{itemize} +\begin{columns} +\only<1>{ +\begin{column}{.78\textwidth} +\begin{block}{} +%\begin{itemize} + $\PBminus\to\PDplus\Pmuon\Pmuon\quad\quad\quad\quad\quad\quad\PBminus\to\PD^{*+}\Pmuon\Pmuon$ +%\end{itemize} +\includegraphics[width=\textwidth]{./MassFitDp_.pdf} +\end{block} +\end{column} +} + + +\end{columns} +\only<1>{{ +{~} + + +$\mathcal{B}(\PBminus\to\PDplus\Pmuon\Pmuon)<6.9\times 10^{-7} \quad \quad \mathcal{B}(\PBminus\to\PD^{*+}\Pmuon\Pmuon)<2.4\times 10^{-6}$ +}} + + + {@ 95\,\% CL}\hspace{.35\textwidth} + {@ 95\,\% CL} + +{~} + +\begin{columns} +\begin{column}{6.5cm} +\end{column} +\begin{column}{1.5cm} +\includegraphics[width=\textwidth]{../lhcb-logo} +\end{column} +\begin{column}{4cm} +\hspace{.4cm} + +$\unit{0.41}{\reciprocal\femtobarn}$ + + {\footnotesize{\myhref{http://arxiv.org/abs/1201.5600}{\texttt{arXiv:1201.5600}}}} + +\end{column} +\end{columns} + +%LHCb, arXiv:1201.5600 +%\includegraphics[width=.5\textwidth]{UpperAll} +\end{frame} + + +\begin{frame}[t] +\frametitle{on-shell Majorana neutrinos} + +\begin{itemize} +%\item best limits for $h = \PDplus, \PD^{*+}, \Ppiplus, \PDs$ from LHCb using $\unit{0.41}{\reciprocal\femtobarn}$ %, \PKplus +%\item normalisation relative to $\PBplus\to\PKplus\PJpsi$ and $\PBplus\to\PKplus\Ppsi(2S)$ +\item mis-identification rates from data with mass shape from simulation +\end{itemize} +\begin{columns} + +\only<1>{ +\begin{column}{.72\textwidth} +\begin{block}{} +$\PBminus\to\Ppiplus\Pmuon\Pmuon\quad\quad\quad\quad\PBminus\to\PDs^{+}\Pmuon\Pmuon$ +\only<1>{\includegraphics[width=.44\textwidth]{./MassFitPi2}\hspace{.04\textwidth}\includegraphics[width=.46\textwidth]{./MassFitDs_}} +\end{block} +\end{column} +} + +\end{columns} + + +\only<1>{{ +{~} + +assuming $\PBminus$ phase space decay: + +$\mathcal{B}(\PBminus\to\Ppiplus\Pmuon\Pmuon)<1.3\times 10^{-8} \quad \quad \mathcal{B}(\PBminus\to\PDs\Pmuon\Pmuon)<5.8\times 10^{-7}$ +}} + + {@ 95\,\% CL}\hspace{.35\textwidth} + {@ 95\,\% CL} +\begin{columns} +\begin{column}{6.5cm} +\end{column} +\begin{column}{1.5cm} +\includegraphics[width=\textwidth]{../lhcb-logo} +\end{column} +\begin{column}{4cm} +\hspace{.4cm} + +$\unit{0.41}{\reciprocal\femtobarn}$ + + {\footnotesize{\myhref{http://arxiv.org/abs/1201.5600}{\texttt{arXiv:1201.5600}}}} + +\end{column} +\end{columns} + + +%LHCb, arXiv:1201.5600 +%\includegraphics[width=.5\textwidth]{UpperAll} +\end{frame} + + +\begin{frame} +\frametitle{implications on Majorana mass} +\begin{exampleblock}{mass extraction} +Determine limit as function of $h^{+}\Pmuon$ mass +\end{exampleblock} +{\begin{center} +$\PBminus\to\Ppiplus\Pmuon\Pmuon\quad\quad\quad\PBminus\to\PDs^{+}\Pmuon\Pmuon$ + +{~} + +\includegraphics[width=.82\textwidth]{./UpperTwoBody}\end{center}} + +\begin{columns} +\begin{column}{6.5cm} +\end{column} +\begin{column}{1.2cm} +\includegraphics[width=\textwidth]{../lhcb-logo} +\end{column} +\begin{column}{4cm} +\hspace{.4cm} + +$\unit{0.41}{\reciprocal\femtobarn}$ + + {\footnotesize{\myhref{http://arxiv.org/abs/1201.5600}{\texttt{arXiv:1201.5600}}}} + +\end{column} +\end{columns} + + +\end{frame} + +\begin{frame} +\frametitle{new bounds for on shell Majorana neutrinos} +%LHCb starts to explore the region of $m_4>\unit{2}{\GeV}$ + +%{~} + +%\only<2>{\includegraphics[width=.48\textwidth]{./constrain.pdf}\includegraphics[width=.48\textwidth]{./boundsUmu.pdf}} +\begin{columns} +\begin{column}{.4\textwidth} +LHCb limit on $|V_{\mu 4}|$ + +\includegraphics[width=.98\textwidth]{./constrain.pdf} + +{\includegraphics[width=1.2cm]{../lhcb-logo}~~{\footnotesize{\myhref{http://arxiv.org/abs/1201.5600}{\texttt{arXiv:1201.5600}}}}} +\end{column} +\begin{column}{.55\textwidth} +Status of 2009 + +\includegraphics[width=.98\textwidth]{./vmu4mod} + +{\footnotesize{\myhref{http://arxiv.org/abs/0901.3589}{\texttt{arXiv:0901.3589}}}} +\end{column} +\end{columns} +\end{frame} + + + + + +\subsection{$\PBminus\to\PDzero\Ppiplus\Pmuon\Pmuon$} +%\section{LNV in $\PBminus\to h^{0} h^{\prime+}\Plepton^{-}\Plepton^{-}$} %LHCb +\begin{frame}{$\PBminus\to\PDzero \Ppiplus\Pmuon\Pmuon$} +\begin{columns}\begin{column}{.5\textwidth} +\includegraphics[width=\textwidth]{./B-Majorana3} +\end{column} +\end{columns} +\begin{itemize} +\item Four body $\PB$ decay complementary to three body decay\newline{\footnotesize{ (\myhref{http://arxiv.org/abs/1108.6009}{\texttt{arXiv:1108.6009}})}} +%\item Constraints predict $\mathcal{B}(\PB\to\PD\ell\ell)<10^{-6}$ +\item $m_4=m(\Ppiplus\Pmuon)$ +\item[+] enhanced by $\PW$ couplings +\item[-] smaller mass range accessible ($\unit{260}{\MeV}enhancement predicted in many New Physics models, e.g. +\end{itemize} +\end{column} + +\begin{column}{.55\textwidth} +\only<1>{ +Standard Model + neutrino oscillation + +\begin{center} +${\PDplus\to\Ppiplus\Pmuon\APelectron}$ +\end{center} + + \begin{fmffile}{smlfv} + %\begin{figure} + %\begin{fmffile}{peng} +\begin{fmfgraph*}(170,100) + %bottom and top verticies + \fmfstraight + \fmfleft{i2,i3,i4,i5} + \fmfright{o2,o3,o4,o5} + + %\fmf{fermion,lab.side=left,label=$d$}{i0,o0} + + \fmf{phantom}{i4,g1} + \fmfipath{p[]} + + \fmf{plain,label=$\Pnum\to\Pnue$,tag=1}{g1,g2} + + \fmf{fermion,lab.side=left,label=$\APelectron$}{o4,g2} + \fmf{phantom,lab.side=right,label=$\PDplus$}{i2,i3} + \fmf{phantom,lab.side=right,label=$\Ppiplus$}{o2,o3} + \fmf{fermion,lab.side=right,label=$\Pcharm$}{i3,g3} + \fmf{fermion,lab.side=right,label=$\Pstrange/\Pdown$}{g3,g4} + \fmf{fermion,lab.side=right,label=$\Pup$}{g4,o3} + \fmf{fermion,lab.side=left,label=$\APdown$}{o2,i2} + + + \fmffreeze + \fmfiset{p1}{vpath1(__g1,__g2)} + \fmfiv{d.sh=cross,d.ang=0,d.size=5thick}{point length(p1)/2 of p1} + + %\fmf{fermion}{g2,o4} + %\fmf{fermion}{i3,g3,g4,o3} + %\fmf{fermion}{o2,i2} + + \fmffreeze + + \fmf{fermion,lab.side=left,label=$\Pmuon$}{g1,o5} + %\fmf{fermion}{g2,o4} + \fmf{dashes,lab.side=right,label=$\PW$}{g1,g3} + \fmf{dashes,lab.side=left,label=$\PW$}{g2,g4} + +% \fmfipath{p[]} +% \fmf{plain,tension=0,right,label={$\Pgngt\to\Pgngm$},tag=1}{w1,w2} +% \fmffreeze +% \fmfiset{p1}{vpath1(__w1,__w2)} +% \fmfiv{d.sh=cross,d.ang=0,d.size=5thick}{point length(p1)/2 of p1} + + + + \end{fmfgraph*} + + \end{fmffile} +} +\only<2>{ +extended Higgs + +\begin{center} +${\PDplus\to\Ppiplus\Pmuon\APelectron}$ +\end{center} + + + + \begin{fmffile}{multihiggs} + %\begin{figure} + %\begin{fmffile}{peng} +\begin{fmfgraph*}(170,80) + %bottom and top verticies + \fmfstraight + \fmfleft{i2,i3,i4,i5} + \fmfright{o2,o3,o4,o5} + + %\fmf{fermion,lab.side=left,label=$d$}{i0,o0} + + \fmf{phantom}{i4,g1} + + + \fmf{fermion,lab.side=left,label=$\APelectron$}{o4,g1} + \fmf{phantom,lab.side=right,label=$\PDplus$}{i2,i3} + \fmf{phantom,lab.side=right,label=$\Ppiplus$}{o2,o3} + \fmf{fermion,lab.side=right,label=$\Pcharm$}{i3,g3} + \fmf{fermion,lab.side=right,label=$\Pdown$}{g3,o3} + \fmf{fermion,lab.side=left,label=$\APdown$}{o2,i2} + + + \fmffreeze + + %\fmf{fermion}{g2,o4} + %\fmf{fermion}{i3,g3,g4,o3} + %\fmf{fermion}{o2,i2} + + \fmffreeze + + \fmf{fermion,lab.side=left,label=$\Pmuon$}{g1,o5} + %\fmf{fermion}{g2,o4} + \fmf{dashes,lab.side=right,label=$\Phi_S$}{g1,g3} + +% \fmfipath{p[]} +% \fmf{plain,tension=0,right,label={$\Pgngt\to\Pgngm$},tag=1}{w1,w2} +% \fmffreeze +% \fmfiset{p1}{vpath1(__w1,__w2)} +% \fmfiv{d.sh=cross,d.ang=0,d.size=5thick}{point length(p1)/2 of p1} + + + + \end{fmfgraph*} + + \end{fmffile} +} +\end{column} +\end{columns} +\only<2>{ +\begin{itemize} +\item multi-Higgs extensions\footnote{ \invisible<1>{\myhref{http://link.aps.org/doi/10.1103/PhysRevD.44.1461}{Phys.\ Rev.\ D \textbf{44}, 1461}}} +\item leptoquarks\footnote{ \invisible<1>{\myhref{http://arxiv.org/abs/hep-ph/9309310}{Z.\ Phys.\ C \textbf{61}, 613}}} +\item low scale seesaw models\footnote{\invisible<1>{\myhref{http://link.aps.org/doi/10.1103/PhysRevD.73.074011}{Phys.\ Rev.\ D \textbf{73}, 074011}}} +\end{itemize} +} +\end{frame} + +\begin{frame} +\frametitle{LFV in charm decays} +\begin{columns} +%\begin{column}{.5\textwidth} +%\begin{itemize} +%\item same analysis as LNV search +%\end{itemize} +%\includegraphics[width=\textwidth]{./babarLFV} +%\end{column} +%\begin{column}{.5\textwidth} +%\includegraphics[width=\textwidth]{./babarcharmtableLFV} +% +%{\footnotesize{Phys.\ Rev.\ D \textbf{84}, 072006 (2011)}} +%\end{column} +\begin{column}{.93\textwidth} +\includegraphics[width=\textwidth]{./lfvhfag2} +\end{column} +\end{columns} +{~} + +\myhref{http://gersabec.web.cern.ch/gersabec/hfag/rare/rare_charm.html}{[HFAG]} +\end{frame} + +%\section{LFV in $\PBminus\to h^{-}\ell^{+}\ell^{\prime -}$} %BaBar tau, other +\subsection{$\PBminus\to\Ppiminus/\PKminus\Ptau^{\pm}\ell^{\mp}$} +\begin{frame} +\frametitle{LFV in bottom decays} +\begin{center} + + \begin{fmffile}{multihiggs2} + %\begin{figure} + %\begin{fmffile}{peng} +\begin{fmfgraph*}(200,80) + %bottom and top verticies + \fmfstraight + \fmfleft{i2,i3,i4,i5} + \fmfright{o2,o3,o4,o5} + + %\fmf{fermion,lab.side=left,label=$d$}{i0,o0} + + \fmf{phantom}{i4,g1} + + + \fmf{fermion,lab.side=left,label=$\APmuon$}{o4,g1} + \fmf{fermion,lab.side=right,label=$\Pbottom$}{i3,g3} + \fmf{fermion,lab.side=right,label=$\Pstrange$}{g3,o3} + \fmf{fermion,lab.side=left,label=$\APup$}{o2,i2} + + + \fmffreeze + + %\fmf{fermion}{g2,o4} + %\fmf{fermion}{i3,g3,g4,o3} + %\fmf{fermion}{o2,i2} + + \fmffreeze + + \fmf{fermion,lab.side=left,label=$\Ptauon$}{g1,o5} + %\fmf{fermion}{g2,o4} + \fmf{dashes,lab.side=right,label=$\Phi_S$}{g1,g3} + +% \fmfipath{p[]} +% \fmf{plain,tension=0,right,label={$\Pgngt\to\Pgngm$},tag=1}{w1,w2} +% \fmffreeze +% \fmfiset{p1}{vpath1(__w1,__w2)} +% \fmfiv{d.sh=cross,d.ang=0,d.size=5thick}{point length(p1)/2 of p1} + + + + \end{fmfgraph*} + + \end{fmffile} +\end{center} + +{~} + +\begin{itemize} +\item LFV $\Ptau$ sector not probed by $\PD$ decays +\item enough energy available in $\PB$ decays +\item multi Higgs models enhance $\PB\to h\Ptau\Pmu$ over other channels\footnote{\myhref{http://link.aps.org/doi/10.1103/PhysRevD.44.1461}{Phys.\ Rev.\ D \textbf{44} 1461}} +\item challenging: neutrino in $\Ptau$ decay similar to $\PB\to X\ell\nu$ +\end{itemize} +\end{frame} + + +\begin{frame} +\frametitle{LFV in bottom decays} +%\includegraphics[height=2cm]{babar}\hspace{.2cm}{\texttt{arXiv:1204.2852v2}} +\begin{columns} +\begin{column}{.6\textwidth} +{\footnotesize{ +\begin{tabular}{lclr} +channel & limit & & \\\hline +$\mathcal{B}(\PBplus\to\PKplus\Ptauon\APmuon)$ & $<4.5\times 10 ^{-5}$ & \includegraphics[height=.25cm]{babarlong}{\footnotesize{a}}\\%\\ +$\mathcal{B}(\PBplus\to\PKplus\APtauon\Pmuon)$ & $<2.8\times 10 ^{-5}$ & \includegraphics[height=.25cm]{babarlong}{\footnotesize{a}}\\%\\ +$\mathcal{B}(\PBplus\to\PKplus\Ptauon\APelectron)$ & $<4.3\times 10 ^{-5}$ & \includegraphics[height=.25cm]{babarlong}{\footnotesize{a}}\\%\\ +$\mathcal{B}(\PBplus\to\PKplus\APtauon\Pelectron)$ & $<1.5\times 10 ^{-5}$ & \includegraphics[height=.25cm]{babarlong}{\footnotesize{a}}\\%\\ +$\mathcal{B}(\PBplus\to\Ppiplus\Ptauon\APmuon)$ & $<6.2\times 10 ^{-5}$ & \includegraphics[height=.25cm]{babarlong}{\footnotesize{a}}\\%\\ +$\mathcal{B}(\PBplus\to\Ppiplus\APtauon\Pmuon)$ & $<4.5\times 10 ^{-5}$ & \includegraphics[height=.25cm]{babarlong}{\footnotesize{a}}\\%\\ +$\mathcal{B}(\PBplus\to\Ppiplus\Ptauon\APelectron)$ & $<7.4\times 10 ^{-5}$ & \includegraphics[height=.25cm]{babarlong}{\footnotesize{a}}\\%\\ +$\mathcal{B}(\PBplus\to\Ppiplus\APtauon\Pelectron)$ & $<2.0\times 10 ^{-5}$ & \includegraphics[height=.25cm]{babarlong}{\footnotesize{a}}\\% +$\mathcal{B}(\PBplus\to\Ppiplus\Pmu^{\pm}\Pe^{\mp})$ & $<1.7\times 10 ^{-7}$ & \includegraphics[height=.25cm]{babarlong}{\footnotesize{b}}\\%\footnote{BaBar, Phys.\ Rev.\ Let.\ \textbf{99}, 051801 (2007)\label{babar..}}\\ +$\mathcal{B}(\PBplus\to\PKplus\APmuon\Pelectron)$ & $<9.1\times 10 ^{-8}$ & \includegraphics[height=.25cm]{babarlong}{\footnotesize{b}}%\footnotesize{$^{\text{\ref{babar..}}}$} +\end{tabular} + +}} +\end{column} +\begin{column}{.4\textwidth} +details in \myhref{http://hep.ustc.edu.cn/indico/contributionDisplay.py?contribId=28&confId=7}{talk of Giovanni Marchiori} + +{~} + +\begin{block}{LFV energy scale} +\vspace{-.5cm} +\begin{align*} +\Lambda_{\APbottom\Pdown}:&\\ +\unit{2.2}{\TeV}&\rightarrow \unit{11}{\TeV}\\ +\Lambda_{\APbottom\Pstrange}:&\\ +\unit{2.6}{\TeV}&\rightarrow \unit{15}{\TeV} +\end{align*} +\end{block} +%{\footnotesize{Phys.\ Rev.\ D \textbf{66}, 053002}} +% +% +\end{column} +\end{columns} +{~} + +{~} + +{\footnotesize{a: BaBar, \myhref{http://arxiv.org/abs/1204.2852}{arXiv:1204.2852}, $\unit{429}{\reciprocal\femtobarn}$}} + +{\footnotesize{b: BaBar, \myhref{http://link.aps.org/doi/10.1103/PhysRevLett.99.051801}{Phys.\ Rev.\ Let.\ \textbf{99}, 051801} (2007), $\unit{209}{\reciprocal\femtobarn}$}} +\end{frame} + + + +%\section{other LFV probes from charm} % \tau\to\mu\mu\mu +%\begin{frame} +%\frametitle{$\Ptau\to\Pmu\Pmu\Pmu$} +%\begin{exampleblock}{LFV in $\Ptau$ decays} +%\begin{itemize} +%\item dominated by B factories in $\APtauon\Ptauon$ production \newline +%see next talk by Francesco Renga +%\item also possible to probe with semileptonic $\Ptau$ production +%\item $\PDs^{+}\to\APmuon\APmuon\Pmuon\Pnut$ +%\item normalisation with $\PDs\to\Pphi(\Pmuon\APmuon)\Ppi$ +%\item[$\Rightarrow$] chance to probe $\Ptau$ decays at hadron colliders +%\end{itemize} +%\end{exampleblock} +% +%\end{frame} + +\section{$\Ptauon\to\Pmuon\Pmuon\APmuon$ at hadron colliders -- {first time shown!}} +\begin{frame} +\frametitle{$\Ptauon\to\Pmuon\Pmuon\APmuon$ at hadron colliders} +\begin{columns} +\begin{column}{.5\textwidth} +\begin{itemize} +\item in Standard Model + neutrino oscillation introduced in penguin diagrams +\item highly suppressed ($\mathcal{B}\ll 10^{-50}$) +\item enhanced by e.g. charged Higgs +\item best measurements conducted at B factories (\myhref{http://hep.ustc.edu.cn/indico/contributionDisplay.py?contribId=43&confId=7}{Francesco Renga's talk}) +\item[!] also possible at hadron colliders +\end{itemize} +\end{column} +\begin{column}{.5\textwidth} +%\only<1>{ + \begin{fmffile}{smtau} + %\begin{figure} + %\begin{fmffile}{peng} +\begin{fmfgraph*}(170,80) + %bottom and top verticies + \fmfstraight + \fmfleft{is3,is2,is1,i1,i2,i3,i4,i5,i6} + \fmfright{os3,os2,os1,o1,o2,o3,o4,o5,o6} + + %\fmf{fermion,lab.side=left,label=$d$}{i0,o0} + + \fmf{phantom}{o1,g1} + \fmf{phantom,tension=1.5}{g1,i1} + + \fmffreeze + + \fmf{photon, tension=2.,lab.side=left, lab=$\Pphoton/\PZ$}{g1,g2} + \fmf{fermion,lab.side=left,label=$\APmuon$}{o3,g2} + \fmf{fermion,lab.side=left,label=$\Pmuon$}{g2,o5} + \fmf{phantom,tension=1.5}{i6,g2} + + \fmffreeze + + + \fmf{fermion,lab.side=left,label=$\Pgtm$}{i1,w1} + \fmf{dashes,lab.side=right,label=$\PWminus$}{w1,w2} + \fmf{fermion,lab.side=right,label=$\Pmuon$}{w2,o1} + + % \fmf{fermion}{i1,w1} + % \fmf{fermion}{w1,g1} + % \fmf{fermion,tension=2}{g1,w2} + % \fmf{fermion}{w2,o1} + + \fmfipath{p[]} + \fmf{plain,tension=0,right,label={$\Pgngt\to\Pgngm$},tag=1}{w1,w2} + \fmffreeze + \fmfiset{p1}{vpath1(__w1,__w2)} + \fmfiv{d.sh=cross,d.ang=0,d.size=5thick}{point length(p1)/2 of p1} + + % \fmfv{lab=g1}{g1} + % \fmfv{lab=g2}{g2} + % \fmfv{lab=w1}{w1} + % \fmfv{lab=w2}{w2} + + \end{fmfgraph*} + + %\caption{Test 4. is $\propto e^{0}$} + %\end{figure} + \end{fmffile} +%} + +{~} + + +{~} + +%\only<2>{ +\begin{fmffile}{chargedhiggs} +\begin{fmfgraph*}(170,80) + +\fmfstraight + +\fmfleft{i} +\fmfright{o1,o2,o3} +\fmf{phantom}{i,g,o2} +\fmffreeze +\fmf{fermion,lab.side=right,label=$\Ptauon$}{i,g} +\fmf{dashes,tension=2,lab.side=left,label=$H^{--}$}{g,h} +\fmf{fermion,lab.side=left,label=$\APmuon$}{o1,g} +\fmf{fermion,lab.side=right,label=$\Pmuon$}{h,o2} +\fmf{fermion,lab.side=left,label=$\Pmuon$}{h,o3} + +\end{fmfgraph*} +\end{fmffile} +%} + + +\end{column} +\end{columns} + +\end{frame} + +\begin{frame}[t] +\frametitle{$\Ptau\to\Pmu\Pmu\Pmu$ in hadron collisions} +\begin{columns} +\begin{column}{.45\textwidth} +\begin{exampleblock}{$\Ptau$ sources at B factories} +\begin{itemize} +\item $\APelectron\Pelectron\to\APtauon\Ptauon$ +\item allows $\tau$ tag +\end{itemize} +\end{exampleblock} +%\visible<2>{ +%\begin{block}{$\dagger$ cross section} +%\begin{itemize} +%\item $\Pbottom\APbottom$ production\newline \myhref{http://arxiv.org/abs/arXiv:1103.0423}{Eur.\ Phys.\ J.\ C \textbf{71} 1645 (2011)} +%\item $\Pcharm\APcharm$ production\newline \myhref{http://cdsweb.cern.ch/record/1311236}{LHCb-CONF-2010-013} +%\item branching fractions from PDG\newline (LEP \& B factories) +%\end{itemize} +%\end{block} +%} +\end{column} +\begin{column}{.45\textwidth} +\begin{alertblock}{$\Ptau$ sources at the LHC} +\begin{itemize} +\item inclusive $\Ptau$ cross section $79.5\pm\unit{8.3}{\micro\barn}$ at $\sqrt{s}=\unit{7}{\TeV}$ in the LHCb acceptance% $^{\dagger}$ +\item[$\rightarrow$] $7.9\times 10^{10}\, \Ptau$ produced% in 2011 +\item dominant: $\PDs\to\Ptau\Pnut$ ($78\%$) +\item[!] no $\tau$ tag possible +\item standard $\tau$ signatures very similar to $\PD$ decays +\newline($\PDplus\to\Ppiplus\Ppiminus\Ppiplus\Ppizero$\newline vs.\ $\APtauon\to\Ppiplus\Ppiminus\Ppiplus\APnut$) +\end{itemize} +\end{alertblock} +\end{column} +\end{columns} +%\begin{exampleblock}{Normalisation channel} +%\begin{itemize} +%\item use $\mathcal{B}(\PDs\to\Pphi\Ppi)$ and $\mathcal{B}(\PDs\to\Ptau\Pnut)$ +%\item[$\Rightarrow$] normalise relative to $\PDs\to\Pphi(\APmuon\Pmuon)\Ppi$ +%\end{itemize} +%\end{exampleblock} +\end{frame} + +\begin{frame} +\frametitle{Strategy} +\begin{columns} +\begin{column}{.5\textwidth} +\begin{itemize} +\item Loose cut based selection +\item Classification in 3D space: +\begin{itemize} +\item invariant mass +\item decay topology\newline (multivariate) +\item particle identification\newline (multivariate) +\end{itemize} +\item Classifier trained on simulation +\item Calibration with control channel +\item Normalisation with $\PDs$ +\item CLs method to extract the result +\end{itemize} +\end{column} +\begin{column}{.5\textwidth} +\hspace{4.5cm}\includegraphics[width=.2\textwidth]{../lhcb-logo}\hspace{.5em} +%\texttt{LHCb-CONF-2012-015} + +\only<1>{\begin{block}{Signal \& Calibration channel} +\includegraphics[width=.9\textwidth]{topos} +\end{block}} +\only<2>{\begin{alertblock}{Signal \& peaking background} +\includegraphics[width=.9\textwidth]{topob} +\end{alertblock}} +\end{column} +\end{columns} + +\end{frame} + + +\begin{frame} +\frametitle{Normalisation channel $\PDs^{+}\to\Pphi(\APmuon\Pmuon)\Ppiplus$} +\begin{block}{produced $\tau$ leptons} +\vspace{-.3cm} +\begin{align*} +%N_\tau = \frac{\sigma(pp\to\Ptau)}{\sigma(pp\to\PDs\to\Ptau)}\times \frac{\mathcal{B}(\PDs\to\Ptau\Pnut)}{\mathcal{B}(\PDs\to\Pphi\Ppi)\times\mathcal{B}(\Pphi\to\Pmu\Pmu)} \times N_{\PDs\to\Pphi(\Pmu\Pmu)\Ppi} +\mathcal{B}(\tau\to\mu\mu\mu)=\frac{\sigma(pp\to\PDs\to\Ptau)}{\sigma(pp\to\Ptau)} \frac{\mathcal{B}(\PDs\to\Pphi(\Pmu\Pmu)\Ppi)}{\mathcal{B}(\PDs\to\Ptau\Pnut)} \frac{\varepsilon_{norm}}{\varepsilon_{sig}}\frac{N_{\tau\to\mu\mu\mu}}{N_{\PDs\to\Pphi(\Pmu\Pmu)\Ppi}} +\end{align*} +\end{block} +\begin{columns} +\begin{column}{.48\textwidth} +\begin{exampleblock}{ingredients} +\begin{itemize} +\item $\Pbottom\APbottom$ and $\Pcharm\APcharm$ production measurements from LHCb +\item $\PB\to\Ptau$ and $\PD\to\Ptau$ branching ratios from LEP / B factories +\item $\Pmu\Pmu\Ppi$ final state +\item[$\rightarrow$] systematics cancel +\only<1>{ +\begin{itemize} +\item trigger +\item reconstruction +%\item kinematics +\item selection +\end{itemize} +} +\only<2>{\item non resonant contribution $<2\,\%$} +\end{itemize} +\end{exampleblock} +\end{column} +\begin{column}{.48\textwidth} +\includegraphics[width=.2\textwidth]{../lhcb-logo}\hspace{.5em} +\texttt{LHCb-CONF-2012-015} + +\only<1>{\includegraphics[width=\textwidth]{./Fig3a_mDs} + +$45\,515\, \PDs\to\Pphi(\APmuon\Pmuon)\Ppi$ decays +} +\only<2>{\includegraphics[width=\textwidth]{./Fig3b_mPhi} + +{\footnotesize{background substracted $\APmuon\Pmuon$ mass}} +} +\end{column} +\end{columns} +\end{frame} + +\begin{frame} +\frametitle{signal likelihoods} +\begin{columns} +\begin{column}{.48\textwidth} + +\begin{block}{3 body decay likelihood} +\begin{itemize} +\item vertex properties +\begin{itemize} +\item vertex fit, pointing +\end{itemize} +\item track quality +\item isolation +\end{itemize} +\end{block} +\begin{exampleblock}{Calibration} +$\PDs\to\Pphi\Ppi$ +\end{exampleblock} +\includegraphics[width=.88\textwidth]{./Fig1a_geobinning3} +\end{column} +\begin{column}{.48\textwidth} +\begin{block}{particle identification} +\begin{itemize} +\item hits in muon chambers +\item energy in calorimeters +\begin{itemize} +\item compatible with MIP +\end{itemize} +\item RICH information +\end{itemize} +\end{block} +\begin{exampleblock}{Calibration} +$\PJpsi\to\APmuon\Pmuon$ +\end{exampleblock} +\includegraphics[width=.88\textwidth]{./Fig1b_pidbinning3} +\end{column} +\end{columns} +\end{frame} + +\begin{frame} +\frametitle{invariant mass} +\begin{columns} +\begin{column}{.8\textwidth} +\begin{block}{two fold role} +\begin{itemize} +\item background estimation in sidebands +\item different signal likelihood inside signal region +\end{itemize} +\end{block} +\end{column} +\begin{column}{.2\textwidth} +\includegraphics[width=.46\textwidth]{../lhcb-logo} +\hspace{.5em}$\unit{1}{\reciprocal\femtobarn}$ + +\texttt{LHCb-CONF-} \texttt{2012-015} +\end{column} + +\end{columns} +\begin{columns} +\begin{column}{.65\textwidth} +\includegraphics[width=\textwidth]{./masssim} +\end{column} +\begin{column}{.35\textwidth} +\begin{itemize} +\item mass resolution and mass scale calibrated on data +\end{itemize} +\end{column} +\end{columns} + +\end{frame} + +\begin{frame} +\frametitle{signal likelihoods} +\begin{columns} +\begin{column}{.8\textwidth} +\begin{block}{combined signal distribution} +\begin{itemize} +\item events distributed over 25 likelihood bins +\item background estimate from mass sidebands +\end{itemize} +\end{block} +\end{column} +\begin{column}{.2\textwidth} +\includegraphics[width=.46\textwidth]{../lhcb-logo} +\hspace{.5em}$\unit{1}{\reciprocal\femtobarn}$ + +\texttt{LHCb-CONF-} \texttt{2012-015} +\end{column} + +\end{columns} +\begin{columns} +\begin{column}{.65\textwidth} +%\only<1>{\includegraphics[width=\textwidth]{./2d-data2.pdf}} +\only{\includegraphics[width=\textwidth]{./2d-data2_both.pdf}} +\end{column} +\begin{column}{.35\textwidth} +\begin{itemize} +\item \textcolor{red}{11\,\% signal efficiency} +\item \textcolor{blue}{21\,\% signal efficiency} +\item for illustration:\newline high likelihood range shown +\end{itemize} +\end{column} +\end{columns} + +\end{frame} + + +\begin{frame} +\frametitle{observed events} +\begin{columns} +\begin{column}{.5\textwidth} +%four best bins + +\includegraphics[width=.98\textwidth]{./Fig4a_1stbin3.pdf} +\end{column} +\begin{column}{.5\textwidth} +%four best bins + +\includegraphics[width=.98\textwidth]{./Fig4b_2ndbin3.pdf} +\end{column} + +\end{columns} +\begin{columns} +\begin{column}{.37\textwidth} +11\,\% of the signal + +0.03\,\% of the background +\end{column} +\begin{column}{.13\textwidth} +\includegraphics[width=\textwidth]{./2d-data2_1st} +\end{column} +\begin{column}{.37\textwidth} +21\,\% of the signal + +0.14\,\% of the background +\end{column} +\begin{column}{.13\textwidth} +\includegraphics[width=\textwidth]{./2d-data2_2nd} +\end{column} +\end{columns} +%\end{column} +%\begin{column}{.5\textwidth} +%%next four best bins +%\includegraphics[width=.98\textwidth]{./Fig4b_2ndbin.pdf} +%\begin{columns} +%\begin{column}{.9\textwidth} +%21\,\% of the signal +% +%0.14\,\% of the background +%\end{column} +%\begin{column}{.1\textwidth} +%\includegraphics[width=\textwidth]{./2d-data2_2nd} +%\end{column} +%\end{columns} +%\end{column} +%\end{columns} + +{~} + + +\begin{columns} +\begin{column}{.65\textwidth} +\begin{description} +\item[\textcolor{red}{red dashed}] combinatorial background +\item[\textcolor{green}{green}] $\PDs^{+}\to\Peta(\Pmuon\APmuon\Pphoton)\APmuon\Pnum$ +\item[\textcolor{blue}{blue}] combined background +\end{description} +\end{column} + +\begin{column}{.35\textwidth} +\includegraphics[width=.26\textwidth]{../lhcb-logo} +\hspace{.5em}$\unit{1}{\reciprocal\femtobarn}$ + +\texttt{LHCb-CONF-}\texttt{2012-015} + +\end{column} +\end{columns} +%no excess observed + +\end{frame} + +\begin{frame} +\frametitle{extracted limit} +\begin{columns}\begin{column}{.8\textwidth} +\begin{block}{result (preliminary)} +\vspace{-.5cm} +\begin{align*} + & \text{observed} & \text{expected}\\ +\mathcal{B}(\Ptau\to\Pmu\Pmu\Pmu) <\ & 6.3\times 10 ^{-8} & 8.2\times 10^{-8} &\ @\, 90\,\% CL \\ + <\ & 7.8\times 10 ^{-8} & 9.9\times 10^{-8} &\ @\, 95\,\% CL +\end{align*} +\end{block} +\end{column} +\begin{column}{.2\textwidth} +\includegraphics[width=.46\textwidth]{../lhcb-logo} +\hspace{.5em}$\unit{1}{\reciprocal\femtobarn}$ + +\texttt{LHCb-CONF-} \texttt{2012-015} +\end{column} +\end{columns} +\begin{columns} +\begin{column}{.65\textwidth} +\includegraphics[width=\textwidth]{./Fig5_withbkg3.pdf} +\end{column} +\begin{column}{.04\textwidth} + +\end{column} +\begin{column}{.35\textwidth} + +\begin{itemize} +\item[Belle] $2.1 x 10^{-8}$ \ {\footnotesize{@ 90\,\% CL\newline \myhref{http://dx.doi.org/10.1016/j.physletb.2010.03.037}{Phys.\ Lett.\ B \textbf{687}, 139} (2010)}} +\item[BaBar] $3.3 x 10^{-8}$ \ {\footnotesize{@ 90\,\% CL\newline \myhref{http://link.aps.org/doi/10.1103/PhysRevD.81.111101}{Phys.\ Rev.\ D \textbf{81}, 111101(R)} (2010)}} +\end{itemize} +\end{column} +\end{columns} + +\end{frame} + +\section*{Summary} +\begin{frame} +\frametitle{Summary} +\begin{itemize} +\item neither lepton number violation nor lepton flavour violation observed (yet) +\item hadron decays provide good probes for Lepton Number \& Flavour Violation +\item excellent sensitivity achieved at B factories +\begin{itemize} +\item LNV and LFV excluded to $10^{-5}$ for $\PD$ decays +\end{itemize} +\item LHCb extends knowledge on forbidden $\PB$ decays +\begin{itemize} +\item LNV excluded to $10^{-6\dots -8}$ +\end{itemize} +\item LHCb approaching B factories for $\tau\to\mu\mu\mu$ +\item[$\Rightarrow$] first time done at hadron colliders +\end{itemize} +\end{frame} +\appendix +\begin{frame}[t] +\begin{columns} +\begin{column}{.3\textwidth} +{~} + +{~} + + +\huge{BACKUP} +\end{column} +\end{columns} +\end{frame} + +%\begin{frame} +%\frametitle{LFV in bottom decays} +%{\footnotesize{ +%\begin{tabular}{lclr} +%channel & limit & & \\\hline +%$\mathcal{B}(\PBplus\to\PKplus\Ptauon\APmuon)$ & $<4.5\times 10 ^{-5}$ & \includegraphics[height=.25cm]{babar}\footnote{BaBar, arXiv:1204.2852\label{babartau}}\\ +%$\mathcal{B}(\PBplus\to\PKplus\APtauon\Pmuon)$ & $<2.8\times 10 ^{-5}$ & \includegraphics[height=.25cm]{babar}\footnotesize{$^{\text{\ref{babartau}}}$}\\ +%$\mathcal{B}(\PBplus\to\PKplus\Ptauon\APelectron)$ & $<4.3\times 10 ^{-5}$ & \includegraphics[height=.25cm]{babar}\footnotesize{$^{\text{\ref{babartau}}}$}\\ +%$\mathcal{B}(\PBplus\to\PKplus\APtauon\Pelectron)$ & $<1.5\times 10 ^{-5}$ & \includegraphics[height=.25cm]{babar}\footnotesize{$^{\text{\ref{babartau}}}$}\\ +%$\mathcal{B}(\PBplus\to\Ppiplus\Ptauon\APmuon)$ & $<6.2\times 10 ^{-5}$ & \includegraphics[height=.25cm]{babar}\footnotesize{$^{\text{\ref{babartau}}}$}\\ +%$\mathcal{B}(\PBplus\to\Ppiplus\APtauon\Pmuon)$ & $<4.5\times 10 ^{-5}$ & \includegraphics[height=.25cm]{babar}\footnotesize{$^{\text{\ref{babartau}}}$}\\ +%$\mathcal{B}(\PBplus\to\Ppiplus\Ptauon\APelectron)$ & $<7.4\times 10 ^{-5}$ & \includegraphics[height=.25cm]{babar}\footnotesize{$^{\text{\ref{babartau}}}$}\\ +%$\mathcal{B}(\PBplus\to\Ppiplus\APtauon\Pelectron)$ & $<2.0\times 10 ^{-5}$ & \includegraphics[height=.25cm]{babar}\footnotesize{$^{\text{\ref{babartau}}}$}\\ +%$\mathcal{B}(\PBplus\to\Ppiplus\Pmu^{\pm}\Pe^{\mp})$ & $<1.7\times 10 ^{-7}$ & \includegraphics[height=.25cm]{babar}\footnote{BaBar, Phys.\ Rev.\ Let.\ \textbf{99}, 051801 (2007)\label{babar..}}\\ +%$\mathcal{B}(\PBplus\to\PKplus\APmuon\Pelectron)$ & $<9.1\times 10 ^{-8}$ & \includegraphics[height=.25cm]{babar}\footnotesize{$^{\text{\ref{babar..}}}$} +%\end{tabular} +%}} +%\end{frame} +% +\begin{frame} +\frametitle{Sensitivity to long lived Majorana neutrinos} +\begin{itemize} +\item analysis allows for neutrino flight distance +\item probes only Majorana neutrinos decaying inside the detector +\item sensitivity to lifetime provided +\end{itemize} + +{\footnotesize{ +\begin{tabular}{p{.31\textwidth}p{.32\textwidth}p{.34\textwidth}} +a) $\PBminus\to\Ppiplus\Pmuon\Pmuon$&b) $\PBminus\to\PDs^{+}\Pmuon\Pmuon$&c) $\PBminus\to\PDzero\Ppiplus\Pmuon\Pmuon$\\ +$\unit{250}{\MeV} +Babel and hyphenation patterns for english, dumylang, nohyphenation, bu +lgarian, ukrainian, russian, french, 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+\usepackage{mathrsfs} + +% \usepackage{pgfpages} +% \setbeameroption{show notes on second screen} +%\pgfpagesuselayout{4 on 1}[a4paper,border shrink=5mm,landscape] + +\usepackage{amsfonts} +\usepackage{amsmath} +\usepackage{verbatim} +% \usepackage[amssymb]{SIunits} +%\usepackage{natbib} +\usepackage{amssymb} +\usepackage{hepparticles} +\usepackage{hepnicenames} +\usepackage{hepunits} +\usepackage{tikz} +%\usetikzlibrary{trees} +%\usetikzlibrary{decorations.pathmorphing} +%\usetikzlibrary{decorations.markings} +\usetikzlibrary{arrows} +\usetikzlibrary{shapes} +%\usetikzlibrary{positioning} +%\usetikzlibrary{patterns} +%\usetikzlibrary{fit} +%\usepackage{verbatim} + +\tikzstyle{decision} = [diamond, draw, fill=gray!20, + text width=4.5em, text badly centered, node distance=3cm, inner sep=0pt] +\tikzstyle{block} = [rectangle, draw, fill=blue!10, + text width=5em, text centered, rounded corners, minimum height=2em] +\tikzstyle{line} = [draw, -latex'] +\tikzstyle{cloud} = [draw, ellipse,fill=red!10, node distance=3cm, + minimum height=2em] + +\tikzstyle{every picture}+=[remember picture] + + +\renewcommand{\PKs}{{\HepParticle{K}{S}{}\xspace}} + + +\title[LFV and LNV]{Searches for Lepton Flavour Violation\newline and Lepton Number Violation in Hadron Decays} +\titlegraphic{%\begin{center}{~~~~~~~~~~~}Flavour Physics and CP Violation 2012 +%\newline + +\includegraphics[width=2.5cm]{../bmbf_engl.jpg}\hspace{7cm}\includegraphics[width=2cm]{fpcp_logo} +%\end{center} +} +%\subtitle{T 60.1} + +% \subtitle{} +\author[Paul Seyfert]{Paul Seyfert\newline{\footnotesize{ on behalf of the LHCb collaboration\newline including results from the B factories}}} +\institute[Heidelberg University]{Heidelberg University} +\date[FPCP 2012]{Flavour Physics and CP Violation 2012} +\subject{} + +% \pgfdeclareimage[height=0.5cm]{university-logo}{3Ddoublewell} +% \pgfdeclareimage[width=1.2cm]{university-logo}{weak} +% \logo{\pgfuseimage{university-logo}} +% \pgfdeclareimage[width=\paperwidth,height=\paperheight]{hbild}{condensate} +% \usebackgroundtemplate{\pgfuseimage{hbild}} + +\newcommand{\myhref}[2]{\href{#1}{\textcolor{blue}{#2}}} +\begin{document} +\begin{frame} +\titlepage +\end{frame} + +\begin{frame} +\frametitle{Outline} +\tableofcontents +\end{frame} + +\begin{frame} +\begin{center} +{\Huge{Lepton Number Violation}} + +{~} + +\begin{itemize} +\item {$\PDminus\to\Ppiplus/\PKplus\ell^{-}\ell^{-}$} +\item {$\PBminus\to h^{+}\ell^{-}\ell^{-}$} +\item {$\PBminus\to\PDzero\Ppiplus\Pmuon\Pmuon$} +\end{itemize} + +\end{center} +\end{frame} +%\section{LNV in $\PBminus/\PDminus\to h^{+}\Plepton^{-}\Plepton^{-}$} %LHCb LHCb (Belle ell) (BaBar ell other) +\section{Lepton Number Violation} +\begin{frame}{Lepton Number Violation} +\begin{columns} +\begin{column}{.75\textwidth} +\begin{itemize} +\item Lepton number is conserved in the Standard Model +\item Lepton number violation introduced in many New Physics models, e.\,g.: +{\footnotesize{ +\begin{itemize} +\item 4$^{\rm{th}}$ quark generation\newline (\myhref{http://arxiv.org/abs/1106.0343}{\texttt{arXiv:hep-ph/1106.0343}}) +\item $SO(10)$ SUSY GUT\newline (\myhref{http://arxiv.org/abs/hep-ph/9501298}{\texttt{arXiv:hep-ph/9501298}}) +\item exotic Higgs\newline (A.\ Zee, \myhref{http://dx.doi.org/10.1016/0370-2693(80)90349-4}{Phys.\ Lett.\ B93, 389 (1980)}) +\end{itemize} +}} +\item Majorana neutrinos violate Lepton Number\newline +classic search: neutrinoless double beta-decay ($\rightarrow$\myhref{http://hep.ustc.edu.cn/indico/contributionDisplay.py?contribId=36&confId=7}{Dongming Mei's talk}) +\item Similar fundamental process with mesons +\end{itemize} +\end{column} +\begin{column}{.25\textwidth} +\includegraphics[width=\textwidth]{double} +\end{column} +\end{columns} +\end{frame} + +\begin{frame}[t] +\frametitle{LNV in meson decays} +\begin{columns}\begin{column}{.5\textwidth} +{\Large{$\PDplus\to\Ppiminus\APmuon\APmuon$}} + +\includegraphics[width=\textwidth]{./D-Majorana} +\begin{itemize} +\item resonant production in accessible mass range +\item rates depend on Majorana neutrino--lepton coupling $|V_{\mu 4}|$ +\newline {\footnotesize{(e.g.\ \myhref{http://arxiv.org/abs/0901.3589}{arXiv:0901.3589)}}} +\item $m_4 = m_{\Plepton^{-},\Ppiplus}$ +\end{itemize} +\end{column} +\begin{column}{.5\textwidth} +\invisible<1>{ +\includegraphics[width=.85\textwidth]{./exclusion} + +{\footnotesize{\myhref{http://arxiv.org/abs/0901.3589}{\texttt{arXiv:0901.3589}}}} +\begin{itemize} +\item strong constraints from $\PK$ decays at low $m_4$ +\item high mass region accessible in $\PD$ and $\PB$ decays +\end{itemize} +} +\end{column} +\end{columns} +\end{frame} + +\begin{frame}[t] +\frametitle{LNV in meson decays} +\begin{columns}\begin{column}{.4\textwidth} +{\Large{$\PDplus\to\Ppiminus\APmuon\APmuon$}} + +\includegraphics[width=\textwidth]{./D-Majorana} +{\footnotesize{\begin{itemize} +\item resonant production in accessible mass range +\item rates depend on Majorana neutrino--lepton coupling $|V_{\mu 4}|$ +\newline {\footnotesize{(e.g.\ \myhref{http://arxiv.org/abs/0901.3589}{arXiv:0901.3589)}}} +\item $m_4 = m_{\Plepton^{-},\Ppiplus}$ +\end{itemize}}} +\end{column} +\begin{column}{.6\textwidth} +{\includegraphics[width=.85\textwidth]{./exclusion} + +Status of 2009 + +{\footnotesize{\myhref{http://arxiv.org/abs/0901.3589}{\texttt{arXiv:0901.3589}}}} +%\begin{itemize} +%\item strong constraints from $\PK$ decays at low $m_4$ +%\item high mass region accessible in $\PD$ and $\PB$ decays +%\end{itemize} +} +\end{column} +\end{columns} +\end{frame} + + + +\subsection{$\PDminus\to\Ppiplus/\PKplus\ell^{-}\ell^{-}$} +\begin{frame} +\frametitle{limits on LNV in charm decays} +\begin{columns} +{\begin{column}{.46\textwidth} +%{\Large{$\PDplus\to h^{-}\ell^{+}\ell^{+}$}} +{\Large{charm decays}} +\begin{itemize} +\item latest limits from BaBar% using $\unit{384}{\reciprocal\femtobarn}$ +%\item normalisation relative to $\PDs^{+}\to\Pphi(\PK\PK)\Ppi^{+}$ +%\item $\APelectron\Pelectron\to\PD\APD$ +\item includes Lepton Number and Flavour Violation +\item comprehensive list of $\PDplus, \PDs^{+}, $ and $\Lambda_c^{+}$ decays +\item<2> best limit for most channels +\end{itemize} +\only<1>{\includegraphics[width=.4\textwidth]{./babar}} +%\only<2>{ +%{~} +% +%\includegraphics[width=\textwidth]{./DLNVpeaks}} + + +%\only<2>{\begin{alertblock}{background sources} +%\begin{itemize} +%\item combinatorics +%\item QED events +%\item semileptonic decays +%\item $\Ppizero, \Pphi$ resonance +%\end{itemize} +%\end{alertblock}} +\end{column} +\begin{column}{.5\textwidth} +%\only<2>{ +%\begin{block}{Strategy} +%\begin{itemize} +%\item exclude semileptonic charm production +%\item[$\Rightarrow$] reject most combinatorics +%\item require 5 tracks and electron veto on hadron +%\item[$\Rightarrow$] rejects QED background +%\item vertex requirements reject semileptonic background +%\end{itemize} +%\end{block} +%\begin{exampleblock}{Normalisation} +%\begin{itemize} +%\item Measure yield wrt.\ $\PD\to\Pphi(\PKplus\PKminus)\Ppi$ +%\item[$\Rightarrow$] most systematics cancel +%\item PID as remaining systematics +%\end{itemize} +%\end{exampleblock} +%} +\only<1>{\includegraphics[width=\textwidth]{./babarcharmtableLNV} + +{\footnotesize{\myhref{http://link.aps.org/doi/10.1103/PhysRevD.84.072006}{Phys.\ Rev.\ D \textbf{84}, 072006 (2011)}}}} +\only<2>{\includegraphics[width=\textwidth]{./lnvhfag.pdf}} +\end{column}} +\end{columns} +%\only<2>{ +%{~} +% +%{~} +% +%{\footnotesize{ +%$\mathcal{B}(\PDplus\to\Ppiminus\APelectron\APelectron)<1.1\times 10^{-6}$ by CLEO (Phys.\ Rev.\ D \textbf{82}, 092007 (2010))}}} +\end{frame} + + + +\subsection{qedewqdqewd} + +\begin{frame}%[t] +\frametitle{LNV in bottom decays}%$\PBminus\to h^{+}\ell^{-}\ell^{-}$} +\only<1>{ +\Large{$\PBminus\to h^{+}\Plepton^{-}\Plepton^{-}$} +} +\only<2>{ +\begin{columns}\begin{column}{.5\textwidth} +on-shell neutrino + +\includegraphics[width=\textwidth]{pic/B-Majorana2.pdf} +\end{column} +{\begin{column}{.45\textwidth} +virtual neutrino + +\includegraphics[width=\textwidth]{pic/B-Majorana1.pdf} +\end{column} +} +\end{columns} +\begin{columns} +\begin{column}{.5\textwidth} +\begin{itemize} +\item resonant production in accessible mass range +\item rates depend on Majorana neutrino--lepton coupling $|V_{\mu 4}|$ +\newline {\footnotesize{(e.g.\ \myhref{http://arxiv.org/abs/0901.3589}{arXiv:0901.3589)}}} +\item $m_4 = m_{\Plepton^{-},\Ppiplus}$ +\end{itemize} +\end{column} +{ +\begin{column}{.5\textwidth} +\begin{exampleblock}{special for $\PB$ decays} +%\begin{itemize} +diagram without mass restriction + Cabbibo favoured for $\PB\to\PD$ +%\end{itemize} +\end{exampleblock} +\end{column} +} +\end{columns} +} + +\end{frame} + + +\begin{frame}{search for Majorana neutrinos at LHCb} +\begin{columns} +\begin{column}{.8\textwidth} +\begin{itemize} +\item searches at B factories in \myhref{http://hep.ustc.edu.cn/indico/contributionDisplay.py?contribId=4&confId=7}{Liang Sun's talk} +\item LHCb: search for \begin{itemize}\item $\PBminus\to\Ppiplus\Pmuon\Pmuon$\item $\PBminus\to\PDplus\Pmuon\Pmuon$\item $\PBminus\to\PDs^{+}\Pmuon\Pmuon$\item $\PBminus\to\PD^{*+}\Pmuon\Pmuon$\end{itemize} +%\item $\unit{0.41}{\reciprocal\femtobarn}$ analysed +\item consider topology in reconstruction +\begin{itemize} +\item allow for flight distance for on-shell neutrinos +\item common vertex for virtual neutrinos +\end{itemize} +\end{itemize} +\end{column} +\begin{column}{.2\textwidth} +\includegraphics[width=2cm]{../lhcb-logo} +\end{column} +\end{columns} +\begin{columns} +\begin{column}{.42\textwidth} +\includegraphics[width=.7\textwidth]{reco} +\end{column} +\begin{column}{.52\textwidth} +\includegraphics[width=.7\textwidth]{reco2} +\end{column} +\end{columns} +\end{frame} + + + + +\begin{frame}[t] +\frametitle{virtual Majorana neutrinos} + +%\begin{itemize} +%\item best limits for $h = \PDplus, \PD^{*+}, \Ppiplus, \PDs$ from LHCb using $\unit{0.41}{\reciprocal\femtobarn}$ %, \PKplus +%\item normalisation relative to $\PBplus\to\PKplus\PJpsi$ and $\PBplus\to\PKplus\Ppsi(2S)$ +%\end{itemize} +\begin{columns} +\only<1>{ +\begin{column}{.78\textwidth} +\begin{block}{} +%\begin{itemize} + $\PBminus\to\PDplus\Pmuon\Pmuon\quad\quad\quad\quad\quad\quad\PBminus\to\PD^{*+}\Pmuon\Pmuon$ +%\end{itemize} +\includegraphics[width=\textwidth]{./MassFitDp_.pdf} +\end{block} +\end{column} +} + + +\end{columns} +\only<1>{{ +{~} + + +$\mathcal{B}(\PBminus\to\PDplus\Pmuon\Pmuon)<6.9\times 10^{-7} \quad \quad \mathcal{B}(\PBminus\to\PD^{*+}\Pmuon\Pmuon)<2.4\times 10^{-6}$ +}} + + + {@ 95\,\% CL}\hspace{.35\textwidth} + {@ 95\,\% CL} + +{~} + +\begin{columns} +\begin{column}{6.5cm} +\end{column} +\begin{column}{1.5cm} +\includegraphics[width=\textwidth]{../lhcb-logo} +\end{column} +\begin{column}{4cm} +\hspace{.4cm} + +$\unit{0.41}{\reciprocal\femtobarn}$ + + {\footnotesize{\myhref{http://arxiv.org/abs/1201.5600}{\texttt{arXiv:1201.5600}}}} + +\end{column} +\end{columns} + +%LHCb, arXiv:1201.5600 +%\includegraphics[width=.5\textwidth]{UpperAll} +\end{frame} + + +\begin{frame}[t] +\frametitle{on-shell Majorana neutrinos} + +\begin{itemize} +%\item best limits for $h = \PDplus, \PD^{*+}, \Ppiplus, \PDs$ from LHCb using $\unit{0.41}{\reciprocal\femtobarn}$ %, \PKplus +%\item normalisation relative to $\PBplus\to\PKplus\PJpsi$ and $\PBplus\to\PKplus\Ppsi(2S)$ +\item mis-identification rates from data with mass shape from simulation +\end{itemize} +\begin{columns} + +\only<1>{ +\begin{column}{.72\textwidth} +\begin{block}{} +$\PBminus\to\Ppiplus\Pmuon\Pmuon\quad\quad\quad\quad\PBminus\to\PDs^{+}\Pmuon\Pmuon$ +\only<1>{\includegraphics[width=.44\textwidth]{./MassFitPi2}\hspace{.04\textwidth}\includegraphics[width=.46\textwidth]{./MassFitDs_}} +\end{block} +\end{column} +} + +\end{columns} + + +\only<1>{{ +{~} + +assuming $\PBminus$ phase space decay: + +$\mathcal{B}(\PBminus\to\Ppiplus\Pmuon\Pmuon)<1.3\times 10^{-8} \quad \quad \mathcal{B}(\PBminus\to\PDs\Pmuon\Pmuon)<5.8\times 10^{-7}$ +}} + + {@ 95\,\% CL}\hspace{.35\textwidth} + {@ 95\,\% CL} +\begin{columns} +\begin{column}{6.5cm} +\end{column} +\begin{column}{1.5cm} +\includegraphics[width=\textwidth]{../lhcb-logo} +\end{column} +\begin{column}{4cm} +\hspace{.4cm} + +$\unit{0.41}{\reciprocal\femtobarn}$ + + {\footnotesize{\myhref{http://arxiv.org/abs/1201.5600}{\texttt{arXiv:1201.5600}}}} + +\end{column} +\end{columns} + + +%LHCb, arXiv:1201.5600 +%\includegraphics[width=.5\textwidth]{UpperAll} +\end{frame} + + +\begin{frame} +\frametitle{implications on Majorana mass} +\begin{exampleblock}{mass extraction} +Determine limit as function of $h^{+}\Pmuon$ mass +\end{exampleblock} +{\begin{center} +$\PBminus\to\Ppiplus\Pmuon\Pmuon\quad\quad\quad\PBminus\to\PDs^{+}\Pmuon\Pmuon$ + +{~} + +\includegraphics[width=.82\textwidth]{./UpperTwoBody}\end{center}} + +\begin{columns} +\begin{column}{6.5cm} +\end{column} +\begin{column}{1.2cm} +\includegraphics[width=\textwidth]{../lhcb-logo} +\end{column} +\begin{column}{4cm} +\hspace{.4cm} + +$\unit{0.41}{\reciprocal\femtobarn}$ + + {\footnotesize{\myhref{http://arxiv.org/abs/1201.5600}{\texttt{arXiv:1201.5600}}}} + +\end{column} +\end{columns} + + +\end{frame} + +\begin{frame} +\frametitle{new bounds for on shell Majorana neutrinos} +%LHCb starts to explore the region of $m_4>\unit{2}{\GeV}$ + +%{~} + +%\only<2>{\includegraphics[width=.48\textwidth]{./constrain.pdf}\includegraphics[width=.48\textwidth]{./boundsUmu.pdf}} +\begin{columns} +\begin{column}{.4\textwidth} +LHCb limit on $|V_{\mu 4}|$ + +\includegraphics[width=.98\textwidth]{./constrain.pdf} + +{\includegraphics[width=1.2cm]{../lhcb-logo}~~{\footnotesize{\myhref{http://arxiv.org/abs/1201.5600}{\texttt{arXiv:1201.5600}}}}} +\end{column} +\begin{column}{.55\textwidth} +Status of 2009 + +\includegraphics[width=.98\textwidth]{./vmu4mod} + +{\footnotesize{\myhref{http://arxiv.org/abs/0901.3589}{\texttt{arXiv:0901.3589}}}} +\end{column} +\end{columns} +\end{frame} + + + + + +\subsection{$\PBminus\to\PDzero\Ppiplus\Pmuon\Pmuon$} +%\section{LNV in $\PBminus\to h^{0} h^{\prime+}\Plepton^{-}\Plepton^{-}$} %LHCb +\begin{frame}{$\PBminus\to\PDzero \Ppiplus\Pmuon\Pmuon$} +\begin{columns}\begin{column}{.5\textwidth} +\includegraphics[width=\textwidth]{./B-Majorana3} +\end{column} +\end{columns} +\begin{itemize} +\item Four body $\PB$ decay complementary to three body decay\newline{\footnotesize{ (\myhref{http://arxiv.org/abs/1108.6009}{\texttt{arXiv:1108.6009}})}} +%\item Constraints predict $\mathcal{B}(\PB\to\PD\ell\ell)<10^{-6}$ +\item $m_4=m(\Ppiplus\Pmuon)$ +\item[+] enhanced by $\PW$ couplings +\item[-] smaller mass range accessible ($\unit{260}{\MeV}enhancement predicted in many New Physics models, e.g. +\end{itemize} +\end{column} + +\begin{column}{.55\textwidth} +\only<1>{ +Standard Model + neutrino oscillation + +\begin{center} +${\PDplus\to\Ppiplus\Pmuon\APelectron}$ +\end{center} + + \begin{fmffile}{smlfv} + %\begin{figure} + %\begin{fmffile}{peng} +\begin{fmfgraph*}(170,100) + %bottom and top verticies + \fmfstraight + \fmfleft{i2,i3,i4,i5} + \fmfright{o2,o3,o4,o5} + + %\fmf{fermion,lab.side=left,label=$d$}{i0,o0} + + \fmf{phantom}{i4,g1} + \fmfipath{p[]} + + \fmf{plain,label=$\Pnum\to\Pnue$,tag=1}{g1,g2} + + \fmf{fermion,lab.side=left,label=$\APelectron$}{o4,g2} + \fmf{phantom,lab.side=right,label=$\PDplus$}{i2,i3} + \fmf{phantom,lab.side=right,label=$\Ppiplus$}{o2,o3} + \fmf{fermion,lab.side=right,label=$\Pcharm$}{i3,g3} + \fmf{fermion,lab.side=right,label=$\Pstrange/\Pdown$}{g3,g4} + \fmf{fermion,lab.side=right,label=$\Pup$}{g4,o3} + \fmf{fermion,lab.side=left,label=$\APdown$}{o2,i2} + + + \fmffreeze + \fmfiset{p1}{vpath1(__g1,__g2)} + \fmfiv{d.sh=cross,d.ang=0,d.size=5thick}{point length(p1)/2 of p1} + + %\fmf{fermion}{g2,o4} + %\fmf{fermion}{i3,g3,g4,o3} + %\fmf{fermion}{o2,i2} + + \fmffreeze + + \fmf{fermion,lab.side=left,label=$\Pmuon$}{g1,o5} + %\fmf{fermion}{g2,o4} + \fmf{dashes,lab.side=right,label=$\PW$}{g1,g3} + \fmf{dashes,lab.side=left,label=$\PW$}{g2,g4} + +% \fmfipath{p[]} +% \fmf{plain,tension=0,right,label={$\Pgngt\to\Pgngm$},tag=1}{w1,w2} +% \fmffreeze +% \fmfiset{p1}{vpath1(__w1,__w2)} +% \fmfiv{d.sh=cross,d.ang=0,d.size=5thick}{point length(p1)/2 of p1} + + + + \end{fmfgraph*} + + \end{fmffile} +} +\only<2>{ +extended Higgs + +\begin{center} +${\PDplus\to\Ppiplus\Pmuon\APelectron}$ +\end{center} + + + + \begin{fmffile}{multihiggs} + %\begin{figure} + %\begin{fmffile}{peng} +\begin{fmfgraph*}(170,80) + %bottom and top verticies + \fmfstraight + \fmfleft{i2,i3,i4,i5} + \fmfright{o2,o3,o4,o5} + + %\fmf{fermion,lab.side=left,label=$d$}{i0,o0} + + \fmf{phantom}{i4,g1} + + + \fmf{fermion,lab.side=left,label=$\APelectron$}{o4,g1} + \fmf{phantom,lab.side=right,label=$\PDplus$}{i2,i3} + \fmf{phantom,lab.side=right,label=$\Ppiplus$}{o2,o3} + \fmf{fermion,lab.side=right,label=$\Pcharm$}{i3,g3} + \fmf{fermion,lab.side=right,label=$\Pdown$}{g3,o3} + \fmf{fermion,lab.side=left,label=$\APdown$}{o2,i2} + + + \fmffreeze + + %\fmf{fermion}{g2,o4} + %\fmf{fermion}{i3,g3,g4,o3} + %\fmf{fermion}{o2,i2} + + \fmffreeze + + \fmf{fermion,lab.side=left,label=$\Pmuon$}{g1,o5} + %\fmf{fermion}{g2,o4} + \fmf{dashes,lab.side=right,label=$\Phi_S$}{g1,g3} + +% \fmfipath{p[]} +% \fmf{plain,tension=0,right,label={$\Pgngt\to\Pgngm$},tag=1}{w1,w2} +% \fmffreeze +% \fmfiset{p1}{vpath1(__w1,__w2)} +% \fmfiv{d.sh=cross,d.ang=0,d.size=5thick}{point length(p1)/2 of p1} + + + + \end{fmfgraph*} + + \end{fmffile} +} +\end{column} +\end{columns} +\only<2>{ +\begin{itemize} +\item multi-Higgs extensions\footnote{ \invisible<1>{\myhref{http://link.aps.org/doi/10.1103/PhysRevD.44.1461}{Phys.\ Rev.\ D \textbf{44}, 1461}}} +\item leptoquarks\footnote{ \invisible<1>{\myhref{http://arxiv.org/abs/hep-ph/9309310}{Z.\ Phys.\ C \textbf{61}, 613}}} +\item low scale seesaw models\footnote{\invisible<1>{\myhref{http://link.aps.org/doi/10.1103/PhysRevD.73.074011}{Phys.\ Rev.\ D \textbf{73}, 074011}}} +\end{itemize} +} +\end{frame} + +\begin{frame} +\frametitle{LFV in charm decays} +\begin{columns} +%\begin{column}{.5\textwidth} +%\begin{itemize} +%\item same analysis as LNV search +%\end{itemize} +%\includegraphics[width=\textwidth]{./babarLFV} +%\end{column} +%\begin{column}{.5\textwidth} +%\includegraphics[width=\textwidth]{./babarcharmtableLFV} +% +%{\footnotesize{Phys.\ Rev.\ D \textbf{84}, 072006 (2011)}} +%\end{column} +\begin{column}{.93\textwidth} +\includegraphics[width=\textwidth]{./lfvhfag2} +\end{column} +\end{columns} +{~} + +\myhref{http://gersabec.web.cern.ch/gersabec/hfag/rare/rare_charm.html}{[HFAG]} +\end{frame} + +%\section{LFV in $\PBminus\to h^{-}\ell^{+}\ell^{\prime -}$} %BaBar tau, other +\subsection{$\PBminus\to\Ppiminus/\PKminus\Ptau^{\pm}\ell^{\mp}$} +\begin{frame} +\frametitle{LFV in bottom decays} +\begin{center} + + \begin{fmffile}{multihiggs2} + %\begin{figure} + %\begin{fmffile}{peng} +\begin{fmfgraph*}(200,80) + %bottom and top verticies + \fmfstraight + \fmfleft{i2,i3,i4,i5} + \fmfright{o2,o3,o4,o5} + + %\fmf{fermion,lab.side=left,label=$d$}{i0,o0} + + \fmf{phantom}{i4,g1} + + + \fmf{fermion,lab.side=left,label=$\APmuon$}{o4,g1} + \fmf{fermion,lab.side=right,label=$\Pbottom$}{i3,g3} + \fmf{fermion,lab.side=right,label=$\Pstrange$}{g3,o3} + \fmf{fermion,lab.side=left,label=$\APup$}{o2,i2} + + + \fmffreeze + + %\fmf{fermion}{g2,o4} + %\fmf{fermion}{i3,g3,g4,o3} + %\fmf{fermion}{o2,i2} + + \fmffreeze + + \fmf{fermion,lab.side=left,label=$\Ptauon$}{g1,o5} + %\fmf{fermion}{g2,o4} + \fmf{dashes,lab.side=right,label=$\Phi_S$}{g1,g3} + +% \fmfipath{p[]} +% \fmf{plain,tension=0,right,label={$\Pgngt\to\Pgngm$},tag=1}{w1,w2} +% \fmffreeze +% \fmfiset{p1}{vpath1(__w1,__w2)} +% \fmfiv{d.sh=cross,d.ang=0,d.size=5thick}{point length(p1)/2 of p1} + + + + \end{fmfgraph*} + + \end{fmffile} +\end{center} + +{~} + +\begin{itemize} +\item LFV $\Ptau$ sector not probed by $\PD$ decays +\item enough energy available in $\PB$ decays +\item multi Higgs models enhance $\PB\to h\Ptau\Pmu$ over other channels\footnote{\myhref{http://link.aps.org/doi/10.1103/PhysRevD.44.1461}{Phys.\ Rev.\ D \textbf{44} 1461}} +\item challenging: neutrino in $\Ptau$ decay similar to $\PB\to X\ell\nu$ +\end{itemize} +\end{frame} + + +\begin{frame} +\frametitle{LFV in bottom decays} +%\includegraphics[height=2cm]{babar}\hspace{.2cm}{\texttt{arXiv:1204.2852v2}} +\begin{columns} +\begin{column}{.6\textwidth} +{\footnotesize{ +\begin{tabular}{lclr} +channel & limit & & \\\hline +$\mathcal{B}(\PBplus\to\PKplus\Ptauon\APmuon)$ & $<4.5\times 10 ^{-5}$ & \includegraphics[height=.25cm]{babarlong}{\footnotesize{a}}\\%\\ +$\mathcal{B}(\PBplus\to\PKplus\APtauon\Pmuon)$ & $<2.8\times 10 ^{-5}$ & \includegraphics[height=.25cm]{babarlong}{\footnotesize{a}}\\%\\ +$\mathcal{B}(\PBplus\to\PKplus\Ptauon\APelectron)$ & $<4.3\times 10 ^{-5}$ & \includegraphics[height=.25cm]{babarlong}{\footnotesize{a}}\\%\\ +$\mathcal{B}(\PBplus\to\PKplus\APtauon\Pelectron)$ & $<1.5\times 10 ^{-5}$ & \includegraphics[height=.25cm]{babarlong}{\footnotesize{a}}\\%\\ +$\mathcal{B}(\PBplus\to\Ppiplus\Ptauon\APmuon)$ & $<6.2\times 10 ^{-5}$ & \includegraphics[height=.25cm]{babarlong}{\footnotesize{a}}\\%\\ +$\mathcal{B}(\PBplus\to\Ppiplus\APtauon\Pmuon)$ & $<4.5\times 10 ^{-5}$ & \includegraphics[height=.25cm]{babarlong}{\footnotesize{a}}\\%\\ +$\mathcal{B}(\PBplus\to\Ppiplus\Ptauon\APelectron)$ & $<7.4\times 10 ^{-5}$ & \includegraphics[height=.25cm]{babarlong}{\footnotesize{a}}\\%\\ +$\mathcal{B}(\PBplus\to\Ppiplus\APtauon\Pelectron)$ & $<2.0\times 10 ^{-5}$ & \includegraphics[height=.25cm]{babarlong}{\footnotesize{a}}\\% +$\mathcal{B}(\PBplus\to\Ppiplus\Pmu^{\pm}\Pe^{\mp})$ & $<1.7\times 10 ^{-7}$ & \includegraphics[height=.25cm]{babarlong}{\footnotesize{b}}\\%\footnote{BaBar, Phys.\ Rev.\ Let.\ \textbf{99}, 051801 (2007)\label{babar..}}\\ +$\mathcal{B}(\PBplus\to\PKplus\APmuon\Pelectron)$ & $<9.1\times 10 ^{-8}$ & \includegraphics[height=.25cm]{babarlong}{\footnotesize{b}}%\footnotesize{$^{\text{\ref{babar..}}}$} +\end{tabular} + +}} +\end{column} +\begin{column}{.4\textwidth} +details in \myhref{http://hep.ustc.edu.cn/indico/contributionDisplay.py?contribId=28&confId=7}{talk of Giovanni Marchiori} + +{~} + +\begin{block}{LFV energy scale} +\vspace{-.5cm} +\begin{align*} +\Lambda_{\APbottom\Pdown}:&\\ +\unit{2.2}{\TeV}&\rightarrow \unit{11}{\TeV}\\ +\Lambda_{\APbottom\Pstrange}:&\\ +\unit{2.6}{\TeV}&\rightarrow \unit{15}{\TeV} +\end{align*} +\end{block} +%{\footnotesize{Phys.\ Rev.\ D \textbf{66}, 053002}} +% +% +\end{column} +\end{columns} +{~} + +{~} + +{\footnotesize{a: BaBar, \myhref{http://arxiv.org/abs/1204.2852}{arXiv:1204.2852}, $\unit{429}{\reciprocal\femtobarn}$}} + +{\footnotesize{b: BaBar, \myhref{http://link.aps.org/doi/10.1103/PhysRevLett.99.051801}{Phys.\ Rev.\ Let.\ \textbf{99}, 051801} (2007), $\unit{209}{\reciprocal\femtobarn}$}} +\end{frame} + + + +%\section{other LFV probes from charm} % \tau\to\mu\mu\mu +%\begin{frame} +%\frametitle{$\Ptau\to\Pmu\Pmu\Pmu$} +%\begin{exampleblock}{LFV in $\Ptau$ decays} +%\begin{itemize} +%\item dominated by B factories in $\APtauon\Ptauon$ production \newline +%see next talk by Francesco Renga +%\item also possible to probe with semileptonic $\Ptau$ production +%\item $\PDs^{+}\to\APmuon\APmuon\Pmuon\Pnut$ +%\item normalisation with $\PDs\to\Pphi(\Pmuon\APmuon)\Ppi$ +%\item[$\Rightarrow$] chance to probe $\Ptau$ decays at hadron colliders +%\end{itemize} +%\end{exampleblock} +% +%\end{frame} + +\section{$\Ptauon\to\Pmuon\Pmuon\APmuon$ at hadron colliders -- {first time shown!}} +\begin{frame} +\frametitle{$\Ptauon\to\Pmuon\Pmuon\APmuon$ at hadron colliders} +\begin{columns} +\begin{column}{.5\textwidth} +\begin{itemize} +\item in Standard Model + neutrino oscillation introduced in penguin diagrams +\item highly suppressed ($\mathcal{B}\ll 10^{-50}$) +\item enhanced by e.g. charged Higgs +\item best measurements conducted at B factories (\myhref{http://hep.ustc.edu.cn/indico/contributionDisplay.py?contribId=43&confId=7}{Francesco Renga's talk}) +\item[!] also possible at hadron colliders +\end{itemize} +\end{column} +\begin{column}{.5\textwidth} +%\only<1>{ + \begin{fmffile}{smtau} + %\begin{figure} + %\begin{fmffile}{peng} +\begin{fmfgraph*}(170,80) + %bottom and top verticies + \fmfstraight + \fmfleft{is3,is2,is1,i1,i2,i3,i4,i5,i6} + \fmfright{os3,os2,os1,o1,o2,o3,o4,o5,o6} + + %\fmf{fermion,lab.side=left,label=$d$}{i0,o0} + + \fmf{phantom}{o1,g1} + \fmf{phantom,tension=1.5}{g1,i1} + + \fmffreeze + + \fmf{photon, tension=2.,lab.side=left, lab=$\Pphoton/\PZ$}{g1,g2} + \fmf{fermion,lab.side=left,label=$\APmuon$}{o3,g2} + \fmf{fermion,lab.side=left,label=$\Pmuon$}{g2,o5} + \fmf{phantom,tension=1.5}{i6,g2} + + \fmffreeze + + + \fmf{fermion,lab.side=left,label=$\Pgtm$}{i1,w1} + \fmf{dashes,lab.side=right,label=$\PWminus$}{w1,w2} + \fmf{fermion,lab.side=right,label=$\Pmuon$}{w2,o1} + + % \fmf{fermion}{i1,w1} + % \fmf{fermion}{w1,g1} + % \fmf{fermion,tension=2}{g1,w2} + % \fmf{fermion}{w2,o1} + + \fmfipath{p[]} + \fmf{plain,tension=0,right,label={$\Pgngt\to\Pgngm$},tag=1}{w1,w2} + \fmffreeze + \fmfiset{p1}{vpath1(__w1,__w2)} + \fmfiv{d.sh=cross,d.ang=0,d.size=5thick}{point length(p1)/2 of p1} + + % \fmfv{lab=g1}{g1} + % \fmfv{lab=g2}{g2} + % \fmfv{lab=w1}{w1} + % \fmfv{lab=w2}{w2} + + \end{fmfgraph*} + + %\caption{Test 4. is $\propto e^{0}$} + %\end{figure} + \end{fmffile} +%} + +{~} + + +{~} + +%\only<2>{ +\begin{fmffile}{chargedhiggs} +\begin{fmfgraph*}(170,80) + +\fmfstraight + +\fmfleft{i} +\fmfright{o1,o2,o3} +\fmf{phantom}{i,g,o2} +\fmffreeze +\fmf{fermion,lab.side=right,label=$\Ptauon$}{i,g} +\fmf{dashes,tension=2,lab.side=left,label=$H^{--}$}{g,h} +\fmf{fermion,lab.side=left,label=$\APmuon$}{o1,g} +\fmf{fermion,lab.side=right,label=$\Pmuon$}{h,o2} +\fmf{fermion,lab.side=left,label=$\Pmuon$}{h,o3} + +\end{fmfgraph*} +\end{fmffile} +%} + + +\end{column} +\end{columns} + +\end{frame} + +\begin{frame}[t] +\frametitle{$\Ptau\to\Pmu\Pmu\Pmu$ in hadron collisions} +\begin{columns} +\begin{column}{.45\textwidth} +\begin{exampleblock}{$\Ptau$ sources at B factories} +\begin{itemize} +\item $\APelectron\Pelectron\to\APtauon\Ptauon$ +\item allows $\tau$ tag +\end{itemize} +\end{exampleblock} +%\visible<2>{ +%\begin{block}{$\dagger$ cross section} +%\begin{itemize} +%\item $\Pbottom\APbottom$ production\newline \myhref{http://arxiv.org/abs/arXiv:1103.0423}{Eur.\ Phys.\ J.\ C \textbf{71} 1645 (2011)} +%\item $\Pcharm\APcharm$ production\newline \myhref{http://cdsweb.cern.ch/record/1311236}{LHCb-CONF-2010-013} +%\item branching fractions from PDG\newline (LEP \& B factories) +%\end{itemize} +%\end{block} +%} +\end{column} +\begin{column}{.45\textwidth} +\begin{alertblock}{$\Ptau$ sources at the LHC} +\begin{itemize} +\item inclusive $\Ptau$ cross section $79.5\pm\unit{8.3}{\micro\barn}$ at $\sqrt{s}=\unit{7}{\TeV}$ in the LHCb acceptance% $^{\dagger}$ +\item[$\rightarrow$] $7.9\times 10^{10}\, \Ptau$ produced% in 2011 +\item dominant: $\PDs\to\Ptau\Pnut$ ($78\%$) +\item[!] no $\tau$ tag possible +\item standard $\tau$ signatures very similar to $\PD$ decays +\newline($\PDplus\to\Ppiplus\Ppiminus\Ppiplus\Ppizero$\newline vs.\ $\APtauon\to\Ppiplus\Ppiminus\Ppiplus\APnut$) +\end{itemize} +\end{alertblock} +\end{column} +\end{columns} +%\begin{exampleblock}{Normalisation channel} +%\begin{itemize} +%\item use $\mathcal{B}(\PDs\to\Pphi\Ppi)$ and $\mathcal{B}(\PDs\to\Ptau\Pnut)$ +%\item[$\Rightarrow$] normalise relative to $\PDs\to\Pphi(\APmuon\Pmuon)\Ppi$ +%\end{itemize} +%\end{exampleblock} +\end{frame} + +\begin{frame} +\frametitle{Strategy} +\begin{columns} +\begin{column}{.5\textwidth} +\begin{itemize} +\item Loose cut based selection +\item Classification in 3D space: +\begin{itemize} +\item invariant mass +\item decay topology\newline (multivariate) +\item particle identification\newline (multivariate) +\end{itemize} +\item Classifier trained on simulation +\item Calibration with control channel +\item Normalisation with $\PDs$ +\item CLs method to extract the result +\end{itemize} +\end{column} +\begin{column}{.5\textwidth} +\hspace{4.5cm}\includegraphics[width=.2\textwidth]{../lhcb-logo}\hspace{.5em} +%\texttt{LHCb-CONF-2012-015} + +\only<1>{\begin{block}{Signal \& Calibration channel} +\includegraphics[width=.9\textwidth]{topos} +\end{block}} +\only<2>{\begin{alertblock}{Signal \& peaking background} +\includegraphics[width=.9\textwidth]{topob} +\end{alertblock}} +\end{column} +\end{columns} + +\end{frame} + + +\begin{frame} +\frametitle{Normalisation channel $\PDs^{+}\to\Pphi(\APmuon\Pmuon)\Ppiplus$} +\begin{block}{produced $\tau$ leptons} +\vspace{-.3cm} +\begin{align*} +%N_\tau = \frac{\sigma(pp\to\Ptau)}{\sigma(pp\to\PDs\to\Ptau)}\times \frac{\mathcal{B}(\PDs\to\Ptau\Pnut)}{\mathcal{B}(\PDs\to\Pphi\Ppi)\times\mathcal{B}(\Pphi\to\Pmu\Pmu)} \times N_{\PDs\to\Pphi(\Pmu\Pmu)\Ppi} +\mathcal{B}(\tau\to\mu\mu\mu)=\frac{\sigma(pp\to\PDs\to\Ptau)}{\sigma(pp\to\Ptau)} \frac{\mathcal{B}(\PDs\to\Pphi(\Pmu\Pmu)\Ppi)}{\mathcal{B}(\PDs\to\Ptau\Pnut)} \frac{\varepsilon_{norm}}{\varepsilon_{sig}}\frac{N_{\tau\to\mu\mu\mu}}{N_{\PDs\to\Pphi(\Pmu\Pmu)\Ppi}} +\end{align*} +\end{block} +\begin{columns} +\begin{column}{.48\textwidth} +\begin{exampleblock}{ingredients} +\begin{itemize} +\item $\Pbottom\APbottom$ and $\Pcharm\APcharm$ production measurements from LHCb +\item $\PB\to\Ptau$ and $\PD\to\Ptau$ branching ratios from LEP / B factories +\item $\Pmu\Pmu\Ppi$ final state +\item[$\rightarrow$] systematics cancel +\only<1>{ +\begin{itemize} +\item trigger +\item reconstruction +%\item kinematics +\item selection +\end{itemize} +} +\only<2>{\item non resonant contribution $<2\,\%$} +\end{itemize} +\end{exampleblock} +\end{column} +\begin{column}{.48\textwidth} +\includegraphics[width=.2\textwidth]{../lhcb-logo}\hspace{.5em} +\texttt{LHCb-CONF-2012-015} + +\only<1>{\includegraphics[width=\textwidth]{./Fig3a_mDs} + +$45\,515\, \PDs\to\Pphi(\APmuon\Pmuon)\Ppi$ decays +} +\only<2>{\includegraphics[width=\textwidth]{./Fig3b_mPhi} + +{\footnotesize{background substracted $\APmuon\Pmuon$ mass}} +} +\end{column} +\end{columns} +\end{frame} + +\begin{frame} +\frametitle{signal likelihoods} +\begin{columns} +\begin{column}{.48\textwidth} + +\begin{block}{3 body decay likelihood} +\begin{itemize} +\item vertex properties +\begin{itemize} +\item vertex fit, pointing +\end{itemize} +\item track quality +\item isolation +\end{itemize} +\end{block} +\begin{exampleblock}{Calibration} +$\PDs\to\Pphi\Ppi$ +\end{exampleblock} +\includegraphics[width=.88\textwidth]{./Fig1a_geobinning3} +\end{column} +\begin{column}{.48\textwidth} +\begin{block}{particle identification} +\begin{itemize} +\item hits in muon chambers +\item energy in calorimeters +\begin{itemize} +\item compatible with MIP +\end{itemize} +\item RICH information +\end{itemize} +\end{block} +\begin{exampleblock}{Calibration} +$\PJpsi\to\APmuon\Pmuon$ +\end{exampleblock} +\includegraphics[width=.88\textwidth]{./Fig1b_pidbinning3} +\end{column} +\end{columns} +\end{frame} + +\begin{frame} +\frametitle{invariant mass} +\begin{columns} +\begin{column}{.8\textwidth} +\begin{block}{two fold role} +\begin{itemize} +\item background estimation in sidebands +\item different signal likelihood inside signal region +\end{itemize} +\end{block} +\end{column} +\begin{column}{.2\textwidth} +\includegraphics[width=.46\textwidth]{../lhcb-logo} +\hspace{.5em}$\unit{1}{\reciprocal\femtobarn}$ + +\texttt{LHCb-CONF-} \texttt{2012-015} +\end{column} + +\end{columns} +\begin{columns} +\begin{column}{.65\textwidth} +\includegraphics[width=\textwidth]{./masssim} +\end{column} +\begin{column}{.35\textwidth} +\begin{itemize} +\item mass resolution and mass scale calibrated on data +\end{itemize} +\end{column} +\end{columns} + +\end{frame} + +\begin{frame} +\frametitle{signal likelihoods} +\begin{columns} +\begin{column}{.8\textwidth} +\begin{block}{combined signal distribution} +\begin{itemize} +\item events distributed over 25 likelihood bins +\item background estimate from mass sidebands +\end{itemize} +\end{block} +\end{column} +\begin{column}{.2\textwidth} +\includegraphics[width=.46\textwidth]{../lhcb-logo} +\hspace{.5em}$\unit{1}{\reciprocal\femtobarn}$ + +\texttt{LHCb-CONF-} \texttt{2012-015} +\end{column} + +\end{columns} +\begin{columns} +\begin{column}{.65\textwidth} +%\only<1>{\includegraphics[width=\textwidth]{./2d-data2.pdf}} +\only{\includegraphics[width=\textwidth]{./2d-data2_both.pdf}} +\end{column} +\begin{column}{.35\textwidth} +\begin{itemize} +\item \textcolor{red}{11\,\% signal efficiency} +\item \textcolor{blue}{21\,\% signal efficiency} +\item for illustration:\newline high likelihood range shown +\end{itemize} +\end{column} +\end{columns} + +\end{frame} + + +\begin{frame} +\frametitle{observed events} +\begin{columns} +\begin{column}{.5\textwidth} +%four best bins + +\includegraphics[width=.98\textwidth]{./Fig4a_1stbin3.pdf} +\end{column} +\begin{column}{.5\textwidth} +%four best bins + +\includegraphics[width=.98\textwidth]{./Fig4b_2ndbin3.pdf} +\end{column} + +\end{columns} +\begin{columns} +\begin{column}{.37\textwidth} +11\,\% of the signal + +0.03\,\% of the background +\end{column} +\begin{column}{.13\textwidth} +\includegraphics[width=\textwidth]{./2d-data2_1st} +\end{column} +\begin{column}{.37\textwidth} +21\,\% of the signal + +0.14\,\% of the background +\end{column} +\begin{column}{.13\textwidth} +\includegraphics[width=\textwidth]{./2d-data2_2nd} +\end{column} +\end{columns} +%\end{column} +%\begin{column}{.5\textwidth} +%%next four best bins +%\includegraphics[width=.98\textwidth]{./Fig4b_2ndbin.pdf} +%\begin{columns} +%\begin{column}{.9\textwidth} +%21\,\% of the signal +% +%0.14\,\% of the background +%\end{column} +%\begin{column}{.1\textwidth} +%\includegraphics[width=\textwidth]{./2d-data2_2nd} +%\end{column} +%\end{columns} +%\end{column} +%\end{columns} + +{~} + + +\begin{columns} +\begin{column}{.65\textwidth} +\begin{description} +\item[\textcolor{red}{red dashed}] combinatorial background +\item[\textcolor{green}{green}] $\PDs^{+}\to\Peta(\Pmuon\APmuon\Pphoton)\APmuon\Pnum$ +\item[\textcolor{blue}{blue}] combined background +\end{description} +\end{column} + +\begin{column}{.35\textwidth} +\includegraphics[width=.26\textwidth]{../lhcb-logo} +\hspace{.5em}$\unit{1}{\reciprocal\femtobarn}$ + +\texttt{LHCb-CONF-}\texttt{2012-015} + +\end{column} +\end{columns} +%no excess observed + +\end{frame} + +\begin{frame} +\frametitle{extracted limit} +\begin{columns}\begin{column}{.8\textwidth} +\begin{block}{result (preliminary)} +\vspace{-.5cm} +\begin{align*} + & \text{observed} & \text{expected}\\ +\mathcal{B}(\Ptau\to\Pmu\Pmu\Pmu) <\ & 6.3\times 10 ^{-8} & 8.2\times 10^{-8} &\ @\, 90\,\% CL \\ + <\ & 7.8\times 10 ^{-8} & 9.9\times 10^{-8} &\ @\, 95\,\% CL +\end{align*} +\end{block} +\end{column} +\begin{column}{.2\textwidth} +\includegraphics[width=.46\textwidth]{../lhcb-logo} +\hspace{.5em}$\unit{1}{\reciprocal\femtobarn}$ + +\texttt{LHCb-CONF-} \texttt{2012-015} +\end{column} +\end{columns} +\begin{columns} +\begin{column}{.65\textwidth} +\includegraphics[width=\textwidth]{./Fig5_withbkg3.pdf} +\end{column} +\begin{column}{.04\textwidth} + +\end{column} +\begin{column}{.35\textwidth} + +\begin{itemize} +\item[Belle] $2.1 x 10^{-8}$ \ {\footnotesize{@ 90\,\% CL\newline \myhref{http://dx.doi.org/10.1016/j.physletb.2010.03.037}{Phys.\ Lett.\ B \textbf{687}, 139} (2010)}} +\item[BaBar] $3.3 x 10^{-8}$ \ {\footnotesize{@ 90\,\% CL\newline \myhref{http://link.aps.org/doi/10.1103/PhysRevD.81.111101}{Phys.\ Rev.\ D \textbf{81}, 111101(R)} (2010)}} +\end{itemize} +\end{column} +\end{columns} + +\end{frame} + +\section*{Summary} +\begin{frame} +\frametitle{Summary} +\begin{itemize} +\item neither lepton number violation nor lepton flavour violation observed (yet) +\item hadron decays provide good probes for Lepton Number \& Flavour Violation +\item excellent sensitivity achieved at B factories +\begin{itemize} +\item LNV and LFV excluded to $10^{-5}$ for $\PD$ decays +\end{itemize} +\item LHCb extends knowledge on forbidden $\PB$ decays +\begin{itemize} +\item LNV excluded to $10^{-6\dots -8}$ +\end{itemize} +\item LHCb approaching B factories for $\tau\to\mu\mu\mu$ +\item[$\Rightarrow$] first time done at hadron colliders +\end{itemize} +\end{frame} +\appendix +\begin{frame}[t] +\begin{columns} +\begin{column}{.3\textwidth} +{~} + +{~} + + +\huge{BACKUP} +\end{column} +\end{columns} +\end{frame} + +%\begin{frame} +%\frametitle{LFV in bottom decays} +%{\footnotesize{ +%\begin{tabular}{lclr} +%channel & limit & & \\\hline +%$\mathcal{B}(\PBplus\to\PKplus\Ptauon\APmuon)$ & $<4.5\times 10 ^{-5}$ & \includegraphics[height=.25cm]{babar}\footnote{BaBar, arXiv:1204.2852\label{babartau}}\\ +%$\mathcal{B}(\PBplus\to\PKplus\APtauon\Pmuon)$ & $<2.8\times 10 ^{-5}$ & \includegraphics[height=.25cm]{babar}\footnotesize{$^{\text{\ref{babartau}}}$}\\ +%$\mathcal{B}(\PBplus\to\PKplus\Ptauon\APelectron)$ & $<4.3\times 10 ^{-5}$ & \includegraphics[height=.25cm]{babar}\footnotesize{$^{\text{\ref{babartau}}}$}\\ +%$\mathcal{B}(\PBplus\to\PKplus\APtauon\Pelectron)$ & $<1.5\times 10 ^{-5}$ & \includegraphics[height=.25cm]{babar}\footnotesize{$^{\text{\ref{babartau}}}$}\\ +%$\mathcal{B}(\PBplus\to\Ppiplus\Ptauon\APmuon)$ & $<6.2\times 10 ^{-5}$ & \includegraphics[height=.25cm]{babar}\footnotesize{$^{\text{\ref{babartau}}}$}\\ +%$\mathcal{B}(\PBplus\to\Ppiplus\APtauon\Pmuon)$ & $<4.5\times 10 ^{-5}$ & \includegraphics[height=.25cm]{babar}\footnotesize{$^{\text{\ref{babartau}}}$}\\ +%$\mathcal{B}(\PBplus\to\Ppiplus\Ptauon\APelectron)$ & $<7.4\times 10 ^{-5}$ & \includegraphics[height=.25cm]{babar}\footnotesize{$^{\text{\ref{babartau}}}$}\\ +%$\mathcal{B}(\PBplus\to\Ppiplus\APtauon\Pelectron)$ & $<2.0\times 10 ^{-5}$ & \includegraphics[height=.25cm]{babar}\footnotesize{$^{\text{\ref{babartau}}}$}\\ +%$\mathcal{B}(\PBplus\to\Ppiplus\Pmu^{\pm}\Pe^{\mp})$ & $<1.7\times 10 ^{-7}$ & \includegraphics[height=.25cm]{babar}\footnote{BaBar, Phys.\ Rev.\ Let.\ \textbf{99}, 051801 (2007)\label{babar..}}\\ +%$\mathcal{B}(\PBplus\to\PKplus\APmuon\Pelectron)$ & $<9.1\times 10 ^{-8}$ & \includegraphics[height=.25cm]{babar}\footnotesize{$^{\text{\ref{babar..}}}$} +%\end{tabular} +%}} +%\end{frame} +% +\begin{frame} +\frametitle{Sensitivity to long lived Majorana neutrinos} +\begin{itemize} +\item analysis allows for neutrino flight distance +\item probes only Majorana neutrinos decaying inside the detector +\item sensitivity to lifetime provided +\end{itemize} + +{\footnotesize{ +\begin{tabular}{p{.31\textwidth}p{.32\textwidth}p{.34\textwidth}} +a) $\PBminus\to\Ppiplus\Pmuon\Pmuon$&b) $\PBminus\to\PDs^{+}\Pmuon\Pmuon$&c) $\PBminus\to\PDzero\Ppiplus\Pmuon\Pmuon$\\ +$\unit{250}{\MeV} + + + + + + + + + + + + + + + + + + + image/svg+xml + + + + + + + + + + + + + + + B + µ + π + N + + + - + + + + + µ + PV + + diff --git a/HQL_2014/reco2.pdf b/HQL_2014/reco2.pdf new file mode 100644 index 0000000..9dd589e --- /dev/null +++ b/HQL_2014/reco2.pdf Binary files differ diff --git a/HQL_2014/reco2.svg b/HQL_2014/reco2.svg new file mode 100644 index 0000000..3802898 --- /dev/null +++ b/HQL_2014/reco2.svg @@ -0,0 +1,405 @@ + + + + + + + + + + + + + + + + + + + + + + + + + + image/svg+xml + + + + + + + + + + + + + + + B + µ + π + + + - + + + + + µ + PV + π + - + K + + + + D + + N + - + + diff --git a/HQL_2014/slide_bg.png b/HQL_2014/slide_bg.png new file mode 100644 index 0000000..6dee5a4 --- /dev/null +++ b/HQL_2014/slide_bg.png Binary files differ diff --git a/HQL_2014/smlfv.1 b/HQL_2014/smlfv.1 new file mode 100644 index 0000000..147c416 --- 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version 1.004)) (./smlfv2.mp +(/usr/share/texmf/metapost/feynmf/feynmp.mp) [1] ) + +Here is how much of MetaPost's memory you used: + 462 strings using 7356 characters + 754544 bytes of node memory + 914 symbolic tokens + 14i,71n,28p,104b,3f stack positions out of 16i,84n,32p,200b,4f +1 output file written: smlfv2.1 + diff --git a/HQL_2014/smlfv2.mp b/HQL_2014/smlfv2.mp new file mode 100644 index 0000000..73675c6 --- /dev/null +++ b/HQL_2014/smlfv2.mp @@ -0,0 +1,34 @@ +% smlfv2.mp -- do not edit, generated automatically by pseyfert.tex +input feynmp +require_RCS_revision "1.30"; +beginchar(1, 200*1.0pt#, 80*1.0pt#, 0); +"feynmf: 1"; +LaTeX_unitlength:=1.0pt; +subgraph (0, 0, w, h); +vinit; +pickup pencircle scaled thin; +straight_galleries; +vleft (__i2, __i3, __i4, __i5); +vright (__o2, __o3, __o4, __o5); +vconnect ("phantom", __i4, __g1); +path p[]; +vconnect ("plain,label=$\Pnum \to \Pnue $,tag=1", __g1, __g2); +vconnect ("fermion,lab.side=left,label=$\APmuon $", __o4, __g2); 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+Preloading the plain mem file, version 1.004)) (./smtau.mp +(/usr/share/texmf/metapost/feynmf/feynmp.mp) [1] ) + +Here is how much of MetaPost's memory you used: + 454 strings using 6813 characters + 824136 bytes of node memory + 917 symbolic tokens + 14i,71n,28p,103b,3f stack positions out of 16i,84n,32p,200b,4f +1 output file written: smtau.1 + diff --git a/HQL_2014/smtau.mp b/HQL_2014/smtau.mp new file mode 100644 index 0000000..fddcb5d --- /dev/null +++ b/HQL_2014/smtau.mp @@ -0,0 +1,35 @@ +% smtau.mp -- do not edit, generated automatically by pseyfert.tex +input feynmp +require_RCS_revision "1.30"; +beginchar(1, 170*1.0pt#, 80*1.0pt#, 0); +"feynmf: 1"; +LaTeX_unitlength:=1.0pt; +subgraph (0, 0, w, h); +vinit; +pickup pencircle scaled thin; +straight_galleries; +vleft (__is3, __is2, __is1, __i1, __i2, __i3, __i4, __i5, __i6); +vright (__os3, __os2, __os1, __o1, __o2, __o3, __o4, __o5, __o6); +vconnect ("phantom", __o1, __g1); +vconnect ("phantom,tension=1.5", __g1, __i1); 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b/Inflaton/Full_dst_numbers/MM.snm new file mode 100644 index 0000000..e69de29 --- /dev/null +++ b/Inflaton/Full_dst_numbers/MM.snm diff --git a/Inflaton/Full_dst_numbers/MM.synctex.gz b/Inflaton/Full_dst_numbers/MM.synctex.gz new file mode 100644 index 0000000..78b4daf --- /dev/null +++ b/Inflaton/Full_dst_numbers/MM.synctex.gz Binary files differ diff --git a/Inflaton/Full_dst_numbers/MM.tex b/Inflaton/Full_dst_numbers/MM.tex new file mode 100644 index 0000000..2e9ab92 --- /dev/null +++ b/Inflaton/Full_dst_numbers/MM.tex @@ -0,0 +1,1097 @@ +\documentclass[]{beamer} +\setbeamertemplate{navigation symbols}{} +\usepackage{beamerthemesplit} +\useoutertheme{infolines} +\usecolortheme{dolphin} +%\usetheme{Warsaw} +\usetheme{progressbar} +\usecolortheme{progressbar} + +\usefonttheme{progressbar} +\useoutertheme{progressbar} +\useinnertheme{progressbar} +\usepackage{graphicx} +%\usepackage{amssymb,amsmath} +\usepackage[latin1]{inputenc} +\usepackage{amsmath} +\newcommand\abs[1]{\left|#1\right|} +\usepackage{iwona} +\usepackage{hepparticles} +\usepackage{hepnicenames} +\usepackage{hepunits} +\progressbaroptions{imagename=images/lhcb} +%\usetheme{Boadilla}f + +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%5 +\definecolor{mygreen}{cmyk}{0.82,0.11,1,0.25} +\setbeamertemplate{blocks}[rounded][shadow=false] +\addtobeamertemplate{block begin}{\pgfsetfillopacity{0.8}}{\pgfsetfillopacity{1}} +\setbeamercolor{structure}{fg=mygreen} +\setbeamercolor*{block title example}{fg=mygreen!50, +bg= blue!10} +\setbeamercolor*{block body example}{fg= blue, +bg= blue!5} + + + + + +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%\beamersetuncovermixins{\opaqueness<1>{25}}{\opaqueness<2->{15}} +\title{Method of moments for $\PB \to \PKstar \mu \mu$} +\author{\underline{Marcin Chrzaszcz}$^{1,2}$} +\date{\today} + +\begin{document} + +{ +\institute{$^1$ University of Zurich, $^2$ Institute of Nuclear Physics} +\setbeamertemplate{footline}{} +\begin{frame} +\logo{ +\vspace{2 mm} +\includegraphics[height=1cm,keepaspectratio]{images/uzh.jpg}~ +\includegraphics[width=1cm,keepaspectratio]{images/ifj.png}} + + \titlepage +\end{frame} +} +\institute{UZH,IFJ} + +\section[Outline]{} +\begin{frame} +\tableofcontents +\end{frame} + +\section{Introduction} +\begin{frame}\frametitle{Plan} +Why method of moments: +\begin{enumerate} +\item Complementary approach in performing the fit. +\item Allows to extract info measuring quantities in event basis depending on the angular distribution. +\item Used in $\PB \to \rho \Plepton \nu$(SLAC-386 UC-414),\\ $\PJpsi \to \PK \PK \gamma$(PRD 71, 032005 (2005) ), etc. +\end{enumerate} + + +\end{frame} +\section{Method of Moments - Theory} +\begin{frame}\frametitle{Method of moments} +{~} +Let's assume we have our pdf with $k$ unknown parameters :$PDF(x_i, \alpha)$, $dim(\alpha)=k$. One can calculate $k$ moments, which are the functions of $\alpha_i$: +\begin{equation} +\mu_i=f(\alpha_1,..., \alpha_k) = E[W_i] +\end{equation} +If we have $n$ events in our $q^2$ bin, we can estimate: +\begin{equation} +\widehat{\mu}_i=\dfrac{1}{n}\sum_{j=0}^{j=n-1} w_j +\end{equation} +, where $w_j=g(x_i)$ + +\end{frame} + +\begin{frame}\frametitle{Trivial example} +{~} +Lets see how this works in practice: +\begin{equation} +f(x)=\dfrac{x^{a-1}e^{-x/b}} {b^a \Gamma(a)} +\end{equation} +we measure the moments:\\ +\begin{center} $m_1=\dfrac{X_1+X_2+...+X_n}{n}$,\\ $m_2=\dfrac{X_1^2+X_2^2+...+X_n^2}{n}$.\\\end{center} +and calculate them analytically: +\begin{center} $m_1=ab$, $m_2=b^2a(a+1)$\end{center} +So one just needs to solve this and get the answer: +\center $a=\dfrac{m_1^2}{m_2-m_1^2}$, $b=\dfrac{m_2-m_1^2}{m_1}$ +\end{frame} + +\section{Moments of Ss} + + +\begin{frame}\frametitle{Our PDF} +{~} +The angular terms: +\begin{multline} +\dfrac{d^4\Gamma}{dq^2 dcos\theta_k dcos\theta_l d\phi}=\dfrac{9}{32\pi}( \dfrac{3}{4}(1-F_l)\sin^2 \theta_k + F_l \cos^2 \theta_k + (\dfrac{1}{4}(1-F_l)\sin^2 \theta_k \\ -F_l\cos^2) \cos 2\theta_l + J_3 \sin^2 \theta_k \sin^2 \theta_l cos2\phi + J_4 \sin2 \theta_k \sin \theta_l \cos\phi +\\ J_5 \sin 2 \theta_k \sin \theta_l \cos \phi + (J_{6s} \sin^2 \theta_k + J_{6c} \cos^2 \theta_k) \cos \theta_l + \\ J_7 \sin 2\theta_k \sin \theta_l \sin \phi + J_8 \sin 2 \theta_k \sin 2 \theta_l \sin \phi + J_9 \sin^2 \theta_k \sin^2 \theta_l \sin 2 \phi) +\end{multline} +Since we are fitting a PDF we need to ensure it is normalized: +\begin{equation} +\int_{-\pi}^{\pi} d\phi \int_{-1}^{1} d cos\theta_l \int_{-1}^{1} d cos\theta_k \dfrac{d^4\Gamma}{dq^2 dcos\theta_k dcos\theta_l d\phi}=1 +\end{equation} + + +\end{frame} +\begin{frame}\frametitle{Measuring Js} +{~} +From equation 2 we have the following: + +\begin{equation} +\dfrac{1}{4}(3 J_{1c} + 6 J_{1s} - J_{2c} - 2 J_{2s}) =1 +\end{equation} +For now we will consider the following PDF: +\begin{equation} + \dfrac{d^3\Gamma}{\Gamma dcos\theta_k dcos\theta_l d\phi }(cos\theta_k , cos\theta_l, \phi) +\end{equation} + +Becouse our PDF is not normalized and we are measuring $\Gamma+\overline{\Gamma} +$ we are effectively fitting the $S_i$ (aka $J_i \to S_i$) +\end{frame} + + +\begin{frame}\frametitle{Moments for $\PB \to \PKstar \mu \mu$} +{~} +Let's calculate the moments for Ss: +\begin{equation} + \dfrac{d^3\Gamma}{\Gamma dcos\theta_k dcos\theta_l d\phi }sin^2 \theta_k sin^2 \theta_l cos 2 \phi= \dfrac{8 S_3 }{25} +\end{equation} +\begin{equation} + \dfrac{d^3\Gamma}{\Gamma dcos\theta_k dcos\theta_l d\phi } sin 2 \theta_k sin 2 \theta_k cos\phi= \dfrac{8 S_4 }{25} +\end{equation} +\begin{equation} + \dfrac{d^3\Gamma}{\Gamma dcos\theta_k dcos\theta_l d\phi }sin2\theta_k sin\theta_l cos\phi = \dfrac{2 S_5 }{5} +\end{equation} +\begin{equation} + \dfrac{d^3\Gamma}{\Gamma dcos\theta_k dcos\theta_l d\phi} sin 2 \theta_k sin \theta_l sin \phi = \dfrac{2 S_7 }{5} +\end{equation} +\begin{equation} + \dfrac{d^3\Gamma}{\Gamma dcos\theta_k dcos\theta_l d\phi} sin 2 \theta_k sin2 \theta_l sin \phi = \dfrac{8 S_8 }{25} +\end{equation} + + + +\end{frame} +\begin{frame}\frametitle{Moments for $\PB \to \PKstar \mu \mu$} +{~} +\begin{itemize} +\item The simplest solution one could imagine. +\item We are abusing the fact that the basis is orthogonal. +\item Each of the J doesn't know about other. +\item Only $S_{1s}$, $S_{2s}$, $S_{1c}$, $S_{2c}$ and $S_{6s}$, $S_{6c}$ are not orthogonal, but to get the answer you just need to solve a linear equation system so it's not a tragedy. +\end{itemize} +\begin{equation} + \dfrac{d^3\Gamma}{\Gamma dcos\theta_k dcos\theta_l d\phi} sin^2 \theta_k cos \theta_l = 0.1(S_6c+4S_6s) +\end{equation} +\begin{equation} + \dfrac{d^3\Gamma}{\Gamma dcos\theta_k dcos\theta_l d\phi} cos \theta_l = 0.25(S_{6}c+2S_{6s}) +\end{equation} + +solution: $S_{6c}=2 (4 M_{S_{6c}} - 5 M_{S_{6s}})$, $S_{6s}= -2 M_{S_{6c}} + 5 M_{S_{6s}}$ + + + +\end{frame} + + + +\section{Toy MC study} + +\begin{frame}\frametitle{Moments for $\PB \to \PKstar \mu \mu$} +{~} +Lets see if this method actually works. Let's take some random parameters for the PDF and make a toy. +\begin{columns} +\column{2.5in} +\includegraphics[scale=0.25]{images/J5.png} + + + +\column{2.5in} +\includegraphics[scale=0.25]{images/J7.png} + + +\end{columns} +\begin{itemize} +\item let's take 300 signal events as a working case. +\end{itemize} + +\end{frame} + + + + +\begin{frame}\frametitle{Moments for $\PB \to \PKstar \mu \mu$} +{~} +\small Lets see if this method actually works. Let's take some random parameters for the PDF and make a toy. +\begin{columns} +\column{2.5in} +\includegraphics[scale=0.25]{images/J3.png} + + + +\column{2.5in} +\includegraphics[scale=0.25]{images/J4.png} + + +\end{columns} + + +\begin{itemize} +\item let's take 300 signal events as a working case... we might still change the binning +\end{itemize} + +\end{frame} + + + +\begin{frame}\frametitle{Moments for $\PB \to \PKstar \mu \mu$} +{~} +Lets see if this method actually works. Let's take some random parameters for the PDF and make a toy. +\begin{columns} +\column{2.5in} +\includegraphics[scale=0.25]{images/J8.png} + + + +\column{2.5in} +\includegraphics[scale=0.25]{images/J9.png} + + +\end{columns} + +\begin{itemize} +\item let's take 300 signal events as a working case... we might still change the binning +\end{itemize} + +\end{frame} + +\begin{frame}\frametitle{Error Estimation} +{~} +\begin{itemize} +\item Since moment is the mean of a given distribution the error can be estimated as $mean/RMS$ +\item use TOY MC to check this assumption +\end{itemize} + +\includegraphics[scale=0.3]{plots/conw.png}\\ + + +\end{frame} +%%%%%%%%%%%%%%%%%%%%%%%%5 +\begin{frame}\frametitle{Correlation check} +{~} +\begin{itemize} +\item In theory $S_i$ shouldn't be correlated to $S_j$ in the moment calculation. +\item Lets put this to a test. +\end{itemize} + +\begin{columns} +\column{2.5in} +\includegraphics[scale=0.2]{plots/J9J4.png}\\ + + +\column{2.5in} +\includegraphics[scale=0.2]{plots/J8J5.png}\\ + + +\end{columns} + + +\end{frame} + + +%%%%%%%%%%%%%%%%%%%%%%%%5 +\begin{frame}\frametitle{Correlation check 2} +{~} +\begin{itemize} +\item Let's now FIX $J_x$ and simulate different $J_y$ +\item Again theory would suggest that one J shouldn't know about the other, so $J_x$ shouldn't change with scanning $J_y$ parameter +\end{itemize} + +\begin{columns} +\column{2.5in} +\includegraphics[scale=0.24]{plots/J5_vs_J9_300.png}\\ + + +\column{2.5in} +\includegraphics[scale=0.24]{plots/J3_vs_J9_300.png}\\ + + +\end{columns} + + +\end{frame} + + + +\section{2 am discovery} +\begin{frame}\frametitle{What will happen to our problem with an S-wave?} +{~} +Reminder: +\begin{multline} +\dfrac{d^4\Gamma}{dq^2 dcos\theta_k dcos\theta_l d\phi}=\dfrac{9}{32\pi}( J_{1s}sin^2 \theta_k + J_{1c}cos^2 \theta_k + (J_{2s}sin^2 \theta_k + \\ J_{2c}cos^2) cos 2\theta_l + J_3 sin^2 \theta_k sin^2 \theta_l cos2\phi + J_4 sin2 \theta_k sin \theta_l cos\phi +\\ J_5 sin2 \theta_k sin \theta_l cos \phi + (J_{6s} sin^2 \theta_k + J_{6c} cos^2 \theta_k) cos \theta_l + \\ J_7 sin 2\theta_k sin \theta_l sin \phi + J_8 sin 2 \theta_k sin 2 \theta_l sin phi + J_9 sin^2 \theta_k sin^2 \theta_l sin 2 \phi) +\end{multline} +Let's add a very discussing things that keeps us awake at night: +\begin{multline} +W_s =\dfrac{2}{3} F_s \sin^2 \theta_l + \frac{4}{3} A_s \sin^2 \theta_l \cos \theta_k + I_4 sin \theta_k sin 2 \theta_lcos \phi \\+ I_5 sin \theta_k sin \theta_l cos \phi + I_7 sin \theta_k sin \theta_l + sin \phi + I_8 sin \theta_k sin 2\theta_l sin\phi) +\end{multline} + + +\end{frame} + +\begin{frame}\frametitle{What will happen to our problem with an S-wave?} +{~} +So now our PDF is sum of eq. 15 and 16. Of coz we need to require normalization: +\begin{equation} +\dfrac{1}{12}(32 I_{1a} + 9 J_{1c} + 18 J_{1s} - 3 J_{2c} - 6 J_{2s}) =1 +\end{equation} +No surprises here. If we have a S-wave it has to enter in $\Gamma$. +To build up the preasure, what will happen to our Ss? + + + +\end{frame} + + +\begin{frame}\frametitle{NOTHING!!!!!!!!} +{~} +We are completely insensitive to S-wave: +\begin{equation} + \dfrac{d^3\Gamma}{\Gamma dcos\theta_k dcos\theta_l d\phi }sin^2 \theta_k sin^2 \theta_l cos 2 \phi= \dfrac{8 S_3 }{25} +\end{equation} +\begin{equation} + \dfrac{d^3\Gamma}{\Gamma dcos\theta_k dcos\theta_l d\phi } sin 2 \theta_k sin 2 \theta_k cos\phi= \dfrac{8 S_4 }{25} +\end{equation} +\begin{equation} + \dfrac{d^3\Gamma}{\Gamma dcos\theta_k dcos\theta_l d\phi }sin2\theta_k sin\theta_l cos\phi = \dfrac{2 S_5 }{5} +\end{equation} +\begin{equation} + \dfrac{d^3\Gamma}{\Gamma dcos\theta_k dcos\theta_l d\phi} sin 2 \theta_k sin \theta_l sin \phi = \dfrac{2 S_7 }{5} +\end{equation} +\begin{equation} + \dfrac{d^3\Gamma}{\Gamma dcos\theta_k dcos\theta_l d\phi} sin 2 \theta_k sin2 \theta_l sin \phi = \dfrac{8 S_8 }{25} +\end{equation} + + + +\end{frame} + +\begin{frame}\frametitle{Thins get better :)} +{~} +We can even measure directly the S-wave: +\begin{equation} + \dfrac{d^3\Gamma}{\Gamma dcos\theta_k dcos\theta_l d\phi }sin^2 \theta_l cos \theta_k = \dfrac{32 I_{1b} }{45} +\end{equation} +\begin{equation} + \dfrac{d^3\Gamma}{\Gamma dcos\theta_k dcos\theta_l d\phi } sin \theta_k sin 2 \theta_l cos \phi = \dfrac{16 I_4 }{45} +\end{equation} +\begin{equation} + \dfrac{d^3\Gamma}{\Gamma dcos\theta_k dcos\theta_l d\phi } sin\theta_k sin\theta_l cos\phi = \dfrac{4 I_5 }{9} +\end{equation} +\begin{equation} + \dfrac{d^3\Gamma}{\Gamma dcos\theta_k dcos\theta_l d\phi} sin \theta_k sin 2 \theta_l sin \phi = \dfrac{4 I_7 }{9} +\end{equation} +\begin{equation} + \dfrac{d^3\Gamma}{\Gamma dcos\theta_k dcos\theta_l d\phi} sin \theta_k sin2 \theta_l sin \phi = \dfrac{16 S_8 }{45} +\end{equation} + + + +\end{frame} + + +\begin{frame}\frametitle{Conclusions on S-wave} +{~} +\begin{itemize} +\item S-wave components are transparent to method of moments. +\item If they are orthogonal to others all they toy studies holds for them as well(will reapat for robustness but can bet my house that there is nothing going on there). +\item +\end{itemize} + +\end{frame} + + + +\begin{frame}\frametitle{Conclusions} +{~} +\begin{itemize} +\item Implemented moments method for the K*mm and start testing with toy MC +\item The method converge fast and works for the "simple case", i.e. signal only. +\item Method completely insensitive to S-wave component, thanks to orthogonality. +\item Complementary one can measure in-depended S-wave component. +\end{itemize} +TO DO: +\begin{itemize} +\item add realism: backgrounds +\item Do the unfolding +\item Study binning +\end{itemize} + +\end{frame} +%%%%%%%%%%%%%%%%%%%%%%%%%55 +\begin{frame}\frametitle{~} +{~} +\center \Huge BACKUPS + +\end{frame} + +\begin{frame} +{~} + +\begin{columns} +\column{2.5in} +\includegraphics[scale=0.17]{plots/pool_plots/J1c_50.png}\\ +\includegraphics[scale=0.17]{plots/pool_plots/J1c_75.png}\\ + + +\column{2.5in} +\includegraphics[scale=0.17]{plots/pool_plots/J1c_50E.png}\\ +\includegraphics[scale=0.17]{plots/pool_plots/J1c_75E.png} + + +\end{columns} +\end{frame} + +\begin{frame} +{~} + +\begin{columns} +\column{2.5in} +\includegraphics[scale=0.17]{plots/pool_plots/J1c_125.png}\\ +\includegraphics[scale=0.17]{plots/pool_plots/J1c_175.png}\\ + + +\column{2.5in} +\includegraphics[scale=0.17]{plots/pool_plots/J1c_125E.png}\\ +\includegraphics[scale=0.17]{plots/pool_plots/J1c_175E.png} + + +\end{columns} +\end{frame} + +\begin{frame} +{~} + +\begin{columns} +\column{2.5in} +\includegraphics[scale=0.17]{plots/pool_plots/J1c_225.png}\\ +\includegraphics[scale=0.17]{plots/pool_plots/J1c_300.png}\\ + + +\column{2.5in} +\includegraphics[scale=0.17]{plots/pool_plots/J1c_225E.png}\\ +\includegraphics[scale=0.17]{plots/pool_plots/J1c_300E.png} + + +\end{columns} +\end{frame} + + +\begin{frame} +{~} + +\begin{columns} +\column{2.5in} +\includegraphics[scale=0.17]{plots/pool_plots/J1c_400.png}\\ + + + +\column{2.5in} +\includegraphics[scale=0.17]{plots/pool_plots/J1c_400E.png}\\ + + + +\end{columns} +\end{frame} + +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%55 +\begin{frame} +{~} + +\begin{columns} +\column{2.5in} +\includegraphics[scale=0.17]{plots/pool_plots/J1s_50.png}\\ +\includegraphics[scale=0.17]{plots/pool_plots/J1s_75.png}\\ + + +\column{2.5in} +\includegraphics[scale=0.17]{plots/pool_plots/J1s_50E.png}\\ +\includegraphics[scale=0.17]{plots/pool_plots/J1s_75E.png} + + +\end{columns} +\end{frame} + +\begin{frame} +{~} + +\begin{columns} +\column{2.5in} +\includegraphics[scale=0.17]{plots/pool_plots/J1s_125.png}\\ +\includegraphics[scale=0.17]{plots/pool_plots/J1s_175.png}\\ + + +\column{2.5in} +\includegraphics[scale=0.17]{plots/pool_plots/J1s_125E.png}\\ +\includegraphics[scale=0.17]{plots/pool_plots/J1s_175E.png} + + +\end{columns} +\end{frame} + +\begin{frame} +{~} + +\begin{columns} +\column{2.5in} +\includegraphics[scale=0.17]{plots/pool_plots/J1s_225.png}\\ +\includegraphics[scale=0.17]{plots/pool_plots/J1s_300.png}\\ + + +\column{2.5in} +\includegraphics[scale=0.17]{plots/pool_plots/J1s_225E.png}\\ +\includegraphics[scale=0.17]{plots/pool_plots/J1s_300E.png} + + +\end{columns} +\end{frame} + + +\begin{frame} +{~} + +\begin{columns} +\column{2.5in} +\includegraphics[scale=0.17]{plots/pool_plots/J1s_400.png}\\ + + + +\column{2.5in} +\includegraphics[scale=0.17]{plots/pool_plots/J1s_400E.png}\\ + + + +\end{columns} +\end{frame} + +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +\begin{frame} +{~} + +\begin{columns} +\column{2.5in} +\includegraphics[scale=0.17]{plots/pool_plots/J2c_50.png}\\ +\includegraphics[scale=0.17]{plots/pool_plots/J2c_75.png}\\ + + +\column{2.5in} +\includegraphics[scale=0.17]{plots/pool_plots/J2c_50E.png}\\ +\includegraphics[scale=0.17]{plots/pool_plots/J2c_75E.png} + + +\end{columns} +\end{frame} + +\begin{frame} +{~} + +\begin{columns} +\column{2.5in} +\includegraphics[scale=0.17]{plots/pool_plots/J2c_125.png}\\ +\includegraphics[scale=0.17]{plots/pool_plots/J2c_175.png}\\ + + +\column{2.5in} +\includegraphics[scale=0.17]{plots/pool_plots/J2c_125E.png}\\ +\includegraphics[scale=0.17]{plots/pool_plots/J2c_175E.png} + + +\end{columns} +\end{frame} + +\begin{frame} +{~} + +\begin{columns} +\column{2.5in} +\includegraphics[scale=0.17]{plots/pool_plots/J2c_225.png}\\ +\includegraphics[scale=0.17]{plots/pool_plots/J2c_300.png}\\ + + +\column{2.5in} +\includegraphics[scale=0.17]{plots/pool_plots/J2c_225E.png}\\ +\includegraphics[scale=0.17]{plots/pool_plots/J2c_300E.png} + + +\end{columns} +\end{frame} + + +\begin{frame} +{~} + +\begin{columns} +\column{2.5in} +\includegraphics[scale=0.17]{plots/pool_plots/J2c_400.png}\\ +\includegraphics[scale=0.17]{plots/pool_plots/J2c_500.png}\\ + + +\column{2.5in} +\includegraphics[scale=0.17]{plots/pool_plots/J2c_400E.png}\\ +\includegraphics[scale=0.17]{plots/pool_plots/J2c_500E.png}\\ + + +\end{columns} +\end{frame} + + +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +\begin{frame} +{~} + +\begin{columns} +\column{2.5in} +\includegraphics[scale=0.17]{plots/pool_plots/J3_50.png}\\ +\includegraphics[scale=0.17]{plots/pool_plots/J3_75.png}\\ + + +\column{2.5in} +\includegraphics[scale=0.17]{plots/pool_plots/J3_50E.png}\\ +\includegraphics[scale=0.17]{plots/pool_plots/J3_75E.png} + + +\end{columns} +\end{frame} + +\begin{frame} +{~} + +\begin{columns} +\column{2.5in} +\includegraphics[scale=0.17]{plots/pool_plots/J3_125.png}\\ +\includegraphics[scale=0.17]{plots/pool_plots/J3_175.png}\\ + + +\column{2.5in} +\includegraphics[scale=0.17]{plots/pool_plots/J3_125E.png}\\ +\includegraphics[scale=0.17]{plots/pool_plots/J3_175E.png} + + +\end{columns} +\end{frame} + +\begin{frame} +{~} + +\begin{columns} +\column{2.5in} +\includegraphics[scale=0.17]{plots/pool_plots/J3_225.png}\\ +\includegraphics[scale=0.17]{plots/pool_plots/J3_300.png}\\ + + +\column{2.5in} +\includegraphics[scale=0.17]{plots/pool_plots/J3_225E.png}\\ +\includegraphics[scale=0.17]{plots/pool_plots/J3_300E.png} + + +\end{columns} +\end{frame} + + +\begin{frame} +{~} + +\begin{columns} +\column{2.5in} +\includegraphics[scale=0.17]{plots/pool_plots/J3_400.png}\\ +\includegraphics[scale=0.17]{plots/pool_plots/J3_500.png}\\ + + +\column{2.5in} +\includegraphics[scale=0.17]{plots/pool_plots/J3_400E.png}\\ +\includegraphics[scale=0.17]{plots/pool_plots/J3_500E.png}\\ + + +\end{columns} +\end{frame} + + + +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +\begin{frame} +{~} + +\begin{columns} +\column{2.5in} +\includegraphics[scale=0.17]{plots/pool_plots/J4_50.png}\\ +\includegraphics[scale=0.17]{plots/pool_plots/J4_75.png}\\ + + +\column{2.5in} +\includegraphics[scale=0.17]{plots/pool_plots/J4_50E.png}\\ +\includegraphics[scale=0.17]{plots/pool_plots/J4_75E.png} + + +\end{columns} +\end{frame} + +\begin{frame} +{~} + +\begin{columns} +\column{2.5in} +\includegraphics[scale=0.17]{plots/pool_plots/J4_125.png}\\ +\includegraphics[scale=0.17]{plots/pool_plots/J4_175.png}\\ + + +\column{2.5in} +\includegraphics[scale=0.17]{plots/pool_plots/J4_125E.png}\\ +\includegraphics[scale=0.17]{plots/pool_plots/J4_175E.png} + + +\end{columns} +\end{frame} + +\begin{frame} +{~} + +\begin{columns} +\column{2.5in} +\includegraphics[scale=0.17]{plots/pool_plots/J4_225.png}\\ +\includegraphics[scale=0.17]{plots/pool_plots/J4_300.png}\\ + + +\column{2.5in} +\includegraphics[scale=0.17]{plots/pool_plots/J4_225E.png}\\ +\includegraphics[scale=0.17]{plots/pool_plots/J4_300E.png} + + +\end{columns} +\end{frame} + + +\begin{frame} +{~} + +\begin{columns} +\column{2.5in} +\includegraphics[scale=0.17]{plots/pool_plots/J4_400.png}\\ +\includegraphics[scale=0.17]{plots/pool_plots/J4_500.png}\\ + + +\column{2.5in} +\includegraphics[scale=0.17]{plots/pool_plots/J4_400E.png}\\ 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a/Inflaton/Full_dst_numbers/MMatrix.tex b/Inflaton/Full_dst_numbers/MMatrix.tex new file mode 100644 index 0000000..5216cbf --- /dev/null +++ b/Inflaton/Full_dst_numbers/MMatrix.tex @@ -0,0 +1,88 @@ +\documentclass[xcolor=svgnames]{beamer} +\usepackage[utf8]{inputenc} +\usepackage[english]{babel} +\usepackage{polski} +%\usepackage{amssymb,amsmath} +%\usepackage[latin1]{inputenc} +%\usepackage{amsmath} +%\newcommand\abs[1]{\left|#1\right|} +\usepackage{amsmath} +\newcommand\abs[1]{\left|#1\right|} +\usepackage{hepnicenames} +\usepackage{hepunits} +\usepackage{color} + +\setbeamertemplate{footline}{\insertframenumber/\inserttotalframenumber} +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%5 +\definecolor{mygreen}{cmyk}{0.82,0.11,1,0.25} + + +\usetheme{Sybila} + +\title[Retention numbers]{Retention numbers \\ for Dark Bosons Lines \\ using down stream tracks} +\author{Marcin Chrz\k{a}szcz$^{1,2}$, Andrea Mauri$^{1}$} +\institute{$^1$~University of Zurich,\\ $^2$~Institute of Nuclear Physics, Krakow} +\date{\today} +\begin{document} +% --------------------------- SLIDE -------------------------------------------- +%\frame[plain]{\titlepage} +\author{M.Chrz\k{a}szcz, A.Mauri} +% ------------------------------------------------------------------------------ +% --------------------------- SLIDE -------------------------------------------- + +\institute{~(UZH, IFJ)} + + + + +\begin{frame}\frametitle{Number of events and size} +Assumptions: +\begin{itemize} +\item All events go to FULLDST, ($0.138 \frac{Mb}{event}$)\footnote{Size of FULL dst taken from F.Dettori RD talk on $2^{nd}$ July.}. +\item Some lines are probably correlated, which is not taken into account. +\item $<1\%$ of jobs didn't come back from gird. +\end{itemize} + +\begin{footnotesize} + + + +\begin{table} +\begin{center} + \begin{tabular}{ l | c | c } + \hline + Line name & N. of events~($3fb^{-1}$) & Total \\ \hline + StrippingB2KKX2MuMuDDDarkBosonLine & $19593$ & $2.7~Gb$ \\ \hline + StrippingB2KKX2MuMuDDSSDarkBosonLine & $18969$ & $2.6~Gb$ \\ \hline + StrippingB2KX2MuMuDDDarkBosonLine & $8515$ & $1.2~Gb$ \\ \hline + StrippingB2KX2MuMuDDSSDarkBosonLine & $6658$ & $0.9~Gb$ \\ \hline + StrippingB2KpiX2MuMuDDDarkBosonLine & $82524$& $11.4~Gb$ \\ \hline + StrippingB2KpiX2MuMuDDSSDarkBosonLine & $76738$ & $10.6~Gb$ \\ \hline + TOTAL: & $ 212997$ & $29.4~Gb$ + + \end{tabular} +\end{center} + +\end{table} + +\end{footnotesize} +\end{frame} + +\begin{frame}\frametitle{Futher comments} +\begin{itemize} +\item We are proposing to keep the lines mentioned above in FULLDST. +\item Disk cost will be less then $30~Gb$. +\item There exists also lines with Dark Boson decaying into hadrons. However those lines accept orders of magnitude more events, so we don't want to put it in FULLDST. + +\end{itemize} + + +\end{frame} + + + + + + + +\end{document} diff --git a/Inflaton/Full_dst_numbers/MMatrix.tex~ b/Inflaton/Full_dst_numbers/MMatrix.tex~ new file mode 100644 index 0000000..2fc0e58 --- /dev/null +++ b/Inflaton/Full_dst_numbers/MMatrix.tex~ @@ -0,0 +1,556 @@ +\documentclass[xcolor=svgnames]{beamer} +\usepackage[utf8]{inputenc} +\usepackage[english]{babel} +\usepackage{polski} +%\usepackage{amssymb,amsmath} +%\usepackage[latin1]{inputenc} +%\usepackage{amsmath} +%\newcommand\abs[1]{\left|#1\right|} +\usepackage{amsmath} +\newcommand\abs[1]{\left|#1\right|} +\usepackage{hepnicenames} +\usepackage{hepunits} +\usepackage{color} + + + +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%5 +\definecolor{mygreen}{cmyk}{0.82,0.11,1,0.25} + + +\usetheme{Sybila} + +\title[Unfolding for counting experiments]{Unfolding for counting experiments} +\author{Marcin Chrz\k{a}szcz$^{1,2}$, Nicola Serra$^{1}$} +\institute{$^1$~University of Zurich,\\ $^2$~Institute of Nuclear Physics, Krakow} +\date{\today} + +\begin{document} +% --------------------------- SLIDE -------------------------------------------- +\frame[plain]{\titlepage} +\author{Marcin Chrz\k{a}szcz} +% ------------------------------------------------------------------------------ +% --------------------------- SLIDE -------------------------------------------- + +\begin{frame}\frametitle{Quo vadis $\PBzero \to \PKstar \mu \mu$?} + +\center \includegraphics[width=0.8\paperwidth]{diagram.png}\\ + +\end{frame} +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +\begin{frame}\frametitle{Quo vadis $\PBzero \to \PKstar \mu \mu$?} + +\center \includegraphics[width=0.8\paperwidth]{matrix.png}\\ + +\end{frame} + + +\section{Introduction} + +\begin{frame}\frametitle{Reminder} +For now: +\begin{itemize} +\item We have proven that there has to exists unfolding matrix. +\item Shown how to construct transformation matrix: $Gen \to Reco$. +\item Inverting it we can have transformation matrix of $Reco \to Gen$. +\item For details: \href{https://indico.cern.ch/event/316905/session/1/contribution/18/material/slides/0.pdf}{LINK} + +\end{itemize} + +What is missing? +\begin{columns} +\column{1in} +\begin{enumerate} +\item ERROR! +\end{enumerate} +\column{4in} +\includegraphics[width=0.8\textwidth]{err.jpg}\\ +\end{columns} + +\end{frame} + + + +\begin{frame}\frametitle{How to?} +\begin{itemize} +\item So lets say that transformation matrix:$Gen \to Reco$ is $\epsilon_{i,j}$. +\item Of coz it's easy to write the covariance matrix(error matrix): +\end{itemize} +\begin{equation} +cov(\epsilon_{\alpha, \beta},\epsilon_{a,b}) +\end{equation} +\begin{itemize} +\item Then we can calculate the matrix: $\epsilon_{i,j}^{-1}$(assuming it exists). +\item and the 1M dollar question is: $cov(\epsilon_{\alpha, \beta}^{-1},\epsilon_{a,b}^{-1}) =?$ +\end{itemize} + +\end{frame} + +\begin{frame}\frametitle{Answer to 1M dolar quesion} +\begin{itemize} +\item Solution comes from $\tau$ physics :) +\end{itemize} +\begin{equation} +cov(\epsilon_{\alpha, \beta}^{-1},\epsilon_{a,b}^{-1}) = \epsilon^{-1}_{\alpha,i} \epsilon^{-1}_{j,\beta} \epsilon^{-1}_{a,k} \epsilon^{-1}_{l,b} cov( \epsilon_{ij} \epsilon_{kl}) +\end{equation} +\begin{itemize} +\item It's way to late to latex the prove. For prove see: \href{http://arxiv.org/abs/hep-ex/9909031}{arXiv:hep-ex/9909031} +\item Thanks to orthonormal basis lifes gets simpler: +\end{itemize} +\begin{equation} +cov(\epsilon_{ij},\epsilon_{kl} ) = \sigma_{\epsilon,ij} \delta_{ik} \delta_{jl} ( no correlations) +\end{equation} + +\end{frame} + + +\begin{frame}\frametitle{Total error} +\begin{itemize} +\item So let's say: $B=\epsilon^{-1} f$ +\item Then: +\end{itemize} +\begin{equation} +cov(B_i,B_j) = f_a f_b cov(\epsilon_{i \alpha }^{-1} , \epsilon_{j \beta}^{-1} )+ \epsilon^{-1}_{ ik} \epsilon^{-1}_{jl} cov(f_k,f_l) +\end{equation} +\begin{itemize} +\item Looks easy just need to implement! +\end{itemize} + +\end{frame} + + +\begin{frame}\frametitle{Matrix, $0.1-0.98~GeV$} +\tiny{ +$ A_{reco\rightarrow gen}=\begin{pmatrix} + 0.9495 0.008518 0.01522 -0.007362 0.01496 -0.04544 -0.02468 0.002078 + 0.0002651 0.8261 0.00978 -0.001042 0.004382 0.03191 0.01247 0.01886 + -0.0003391 0.009773 1.03 0.008433 -0.002028 0.003 0.02086 0.001549 + -0.00403 -0.001336 0.01047 0.9215 0.006898 -0.0006023 0.003041 -0.004465 + 0.006557 0.005531 -0.002423 0.00691 1.171 -0.01082 -0.0158 -0.003231 + -0.01931 0.03973 0.00342 -0.0006455 -0.01081 0.9452 0.02232 -0.005304 + .008421 0.0124 0.02071 0.002415 -0.01264 0.01785 1.06 0.001084 + 0.000347 0.01886 0.001555 -0.003568 -0.002591 -0.004226 0.001093 0.8204 + + + + + \end{pmatrix}$ +} + + + + + +\end{frame} + +\begin{frame}\frametitle{Constructing Matrix unfolding} +\begin{itemize} +\item We got first column of the unfolding matrix. +\end{itemize} +\small{ +$ \begin{pmatrix} + 1.06 & \cdots & a_{1,8} \\ + 0.01157 & \cdots & a_{2,8} \\ + -0.003547 & \ddots & \vdots \\ + 0.0007841 & \ddots & \vdots \\ + 0.001126 & \ddots & \vdots \\ + 0.001766 & \ddots & \vdots \\ + 0.001664 & \ddots & \vdots \\ + -0.001937 & \cdots & a_{8,8} + \end{pmatrix}$ + + +} +\begin{itemize} +\item How about the others? +\item We can reweight accordingly to $f_x$. +\end{itemize} + +\end{frame} + +\begin{frame}\frametitle{Constructing Matrix unfolding} +\begin{itemize} +\item To get $S_3$ each event $i^{th}$ has has weight $f_{S_3}(\cos \theta_{k_i},\cos \theta_{l_i},\phi_i) $ +\item One can calculate on MC the reweighed moments in PHPS: +\end{itemize} +\begin{equation} +\int PDF*f_{S_3}=\dfrac{32}{225} +\end{equation} +\begin{itemize} +\item Our base vector now is:$v^{T}_{gen}=(0 ,\frac{32}{225},0,0,0,0,0,0)$ +\item So lets see what do we get as reconstructed vector(after multiplying by $\frac{225}{32}$. +\small{$v^{T}_{rec}=( 0.042, 1.105,-0.005,0.003,-0.0023,-0.005,-0.005,-0.006)$ } +\end{itemize} + +\end{frame} + + +\begin{frame}\frametitle{Constructing Matrix unfolding} +\begin{itemize} +\item Now the matrix looks like: +\end{itemize} +\small{ +$ \begin{pmatrix} + 1.06 & 0.042 & \cdots & a_{1,8} \\ + 0.01157 & 1.105 & \cdots & a_{2,8} \\ + -0.003547 & -0.005 & \ddots & \vdots \\ + 0.0007841 &-0.005 & \ddots & \vdots \\ + 0.001126 & 0.003 &\ddots & \vdots \\ + 0.001766 & -0.0023 &\ddots & \vdots \\ + 0.001664 & -0.005 &\ddots & \vdots \\ + -0.001937 & -0.006 &\cdots & a_{8,8} + \end{pmatrix}$ + + +} +\begin{itemize} +\item The others go in the same way. +\item Repenting this exercise from $1^{st}$ year algebra we can get the full matrix +\end{itemize} + + +\end{frame} +\begin{frame}\frametitle{Constructing Matrix unfolding} +\begin{itemize} +\item The full transformation matrix from generator space to reconstructed space: +\end{itemize} +\tiny{ +$ A_{gen\rightarrow reco}=\begin{pmatrix} + 1.06 & 0.0423 & -0.0081 & 0.0022 & 0.0049 & 0.0037 & 0.0028 & -0.0065 \\ + + 0.0115 & 1.105 & -0.0050 & 0.0027 & -0.0018 & -0.0040 &-0.0054 & -0.0065 \\ + -0.0035 & -0.0050 & 0.981 & 0.0005 & -0.0025 & 0.0002 & -0.0037 & -0.0048\\ + 0.00078 & 0.0034 & 0.0006 & 1.002 & -0.0032 & -0.0040 & 0.0003 & 0.0018\\ + 0.001126 & -0.0023 & -0.0032 & -0.0032 & 1.055 & 0.001& -0.004 & 0.0023\\ + 0.00176 & -0.0050 & 0.00036 & -0.0040 & 0.0011 & 0.96 & -0.0057 & 0.0009 \\ + 0.0016 & -0.005 & -0.003 & 0.00029& -0.003 &-0.004 & 0.9543 & 0.0000\\ + -0.0019 & -0.0065 & -0.004 & 0.001 & 0.0018 & 0.0007 & 0.000 & 1.098 \\ + + + + + + \end{pmatrix}$ + + +} +\begin{itemize} +\item Inverting the matrix is simple, and doable +\end{itemize} +\tiny{ +$ A_{reco\rightarrow gen}=\begin{pmatrix} + 0.9434 & -0.036 & 0.007& -0.0020 & -0.0044& -0.0038 & -0.0030 & 0.0054\\ + -0.009 & 0.90 & 0.0045 & -0.0024& 0.0016 & 0.003873 & 0.00527& 0.005 \\ + 0.003 & 0.00454& 1.019 & -0.00058 & 0.0025& -0.000291 & 0.004 & 0.004 \\ +-0.00071 & -0.0030 & -0.0007 & 0.9977 & 0.0030 & 0.004206 &-0.0003 & -0.0017 \\ + -0.001 & 0.0020 & 0.0031& 0.0030 & 0.9483 & -0.0010 & 0.004626 & -0.0019 \\ + -0.001 & 0.004 & -0.0003 & 0.0042 & -0.001087 & 1.037 & 0.0063 & -0.0009\\ + -0.0017 & 0.0053 & 0.0042 & -0.0002 & 0.00370& 0.0050 & 1.048 & 0.0000 \\ + 0.0016& 0.0053& 0.00452 & -0.001 & -0.001582 & -0.0007213 &0.000 & 0.9105 \\ + + + + + \end{pmatrix}$ +} + +\end{frame} + + + +\begin{frame}\frametitle{Sensitivity to unknowns} +\begin{itemize} +\item We are unfolding based on MC. +\item There are MC/Data differences, which can have impact on the unfolding. +\end{itemize} +Let's put small modification: +\begin{equation} +w_j \to \overline{w_j}= \dfrac{1}{eff(\cos \theta_{l~j}, \cos \theta_{k~j}, \phi_{j})} \times corr(\cos \theta_{l~j}, \cos \theta_{k~j}, \phi_{j}) +\end{equation} +Unfortunately God didn't allowed me sneak peak into his cards so I don't know $corr(\cos \theta_{l}, \cos \theta_{k}, \phi)$, but let's try out some functions and see what happens :) + + +\end{frame} + +\begin{frame}\frametitle{Corr1 functions} +\begin{columns} +\column{2in} +\includegraphics[width=\linewidth]{corr/Corr1_cosk.png}\\ +\includegraphics[width=\linewidth]{corr/Corr1_cosl.png}\\ +\column{2.5in} +$ +corr1(\cos_l, \cos_k,\phi)= 1+ 0.032 \cos_l - 0.032 \cos_k + 0.01 \phi +$ +\includegraphics[width=0.8\linewidth]{corr/Corr1_phi.png}\\ + +\end{columns} + +\end{frame} +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +\begin{frame}\frametitle{Corr2 functions} +\begin{columns} +\column{2in} +\includegraphics[width=0.85\linewidth]{corr/corr21.png}\\ +\includegraphics[width=0.85\linewidth]{corr/corr22.png}\\ +\column{2.5in} +$ +corr2(\cos_l, \cos_k,\phi)= -0.02 \cos_l^2 + 0.02 \cos_k^2 - + 0.015 \phi^2+ 1 +$ +\includegraphics[width=0.75\linewidth]{corr/corr23.png}\\ + +\end{columns} + +\end{frame} + +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +\begin{frame}\frametitle{Corr3 functions} +\begin{columns} +\column{2in} +\includegraphics[width=0.85\linewidth]{corr/corr31.png}\\ +\includegraphics[width=0.85\linewidth]{corr/corr32.png}\\ +\column{2.5in} +$ +corr3(\cos_l, \cos_k,\phi)= 0.02 \cos_l \cos_k + 0.01 \cos_k \phi - 0.01 \phi \cos_l + 1 +$ +\includegraphics[width=0.75\linewidth]{corr/corr33.png}\\ + +\end{columns} + +\end{frame} +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +\begin{frame}\frametitle{Corr4 functions} +\begin{columns} +\column{2in} +\includegraphics[width=0.85\linewidth]{corr/corr41.png}\\ +\includegraphics[width=0.85\linewidth]{corr/corr42.png}\\ +\column{2.5in} +$ +corr3(\cos_l, \cos_k,\phi)= 0.01 \cos_k \cos_l \phi + 1 +$ +\includegraphics[width=0.75\linewidth]{corr/corr43.png}\\ + +\end{columns} + +\end{frame} + + + + +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% + + +\begin{frame}\frametitle{Corr1- MM} + + +\begin{tiny} + +\begin{center} + \begin{tabular}{ l l l l l l l l l } + \hline + \multicolumn{8}{c}{Mean of the pull} \\ \hline +$q^2$ & $S_3$ & $S_4$ & $S_5$ & $S_{6s}$ & $S_{6c}$ & $S_7$ & $S_8$ \\ \hline \hline + +0 & \scalebox{0.5}{$0.0085 \pm 0.026(0.3)$} & \scalebox{0.5}{$0.13 \pm 0.027(4.6)$} & \scalebox{0.5}{$-0.025 \pm 0.027(-0.92)$} & \scalebox{0.5}{$0.46 \pm 0.027(17)$} & \scalebox{0.5}{$-0.13 \pm 0.028(-4.7)$} & \scalebox{0.5}{$0.029 \pm 0.028(1)$} & \scalebox{0.5}{$-0.66 \pm 0.027(-25)$} \\ \hline +1 & \scalebox{0.5}{$0.0094 \pm 0.028(0.33)$} & \scalebox{0.5}{$0.078 \pm 0.028(2.8)$} & \scalebox{0.5}{$-0.02 \pm 0.028(-0.73)$} & \scalebox{0.5}{$0.24 \pm 0.028(8.5)$} & \scalebox{0.5}{$-0.075 \pm 0.028(-2.7)$} & \scalebox{0.5}{$-0.016 \pm 0.026(-0.63)$} & \scalebox{0.5}{$-0.39 \pm 0.028(-14)$} \\ \hline +2 & \scalebox{0.5}{$-0.02 \pm 0.027(-0.72)$} & \scalebox{0.5}{$0.027 \pm 0.026(1)$} & \scalebox{0.5}{$-0.024 \pm 0.027(-0.91)$} & \scalebox{0.5}{$0.18 \pm 0.027(6.8)$} & \scalebox{0.5}{$-0.024 \pm 0.027(-0.89)$} & \scalebox{0.5}{$-0.067 \pm 0.027(-2.5)$} & \scalebox{0.5}{$-0.39 \pm 0.028(-14)$} \\ \hline +3 & \scalebox{0.5}{$0.013 \pm 0.028(0.46)$} & \scalebox{0.5}{$-0.0089 \pm 0.027(-0.32)$} & \scalebox{0.5}{$0.055 \pm 0.026(2.1)$} & \scalebox{0.5}{$0.12 \pm 0.027(4.7)$} & \scalebox{0.5}{$0.11 \pm 0.027(3.9)$} & \scalebox{0.5}{$-0.018 \pm 0.028(-0.63)$} & \scalebox{0.5}{$-0.43 \pm 0.027(-16)$} \\ \hline +4 & \scalebox{0.5}{$-0.0054 \pm 0.029(-0.18)$} & \scalebox{0.5}{$-0.066 \pm 0.027(-2.4)$} & \scalebox{0.5}{$0.037 \pm 0.028(1.3)$} & \scalebox{0.5}{$0.22 \pm 0.027(8.1)$} & \scalebox{0.5}{$0.099 \pm 0.027(3.7)$} & \scalebox{0.5}{$-0.1 \pm 0.026(-3.8)$} & \scalebox{0.5}{$-0.41 \pm 0.026(-15)$} \\ \hline +5 & \scalebox{0.5}{$0.06 \pm 0.027(2.2)$} & \scalebox{0.5}{$-0.069 \pm 0.026(-2.6)$} & \scalebox{0.5}{$-0.013 \pm 0.028(-0.49)$} & \scalebox{0.5}{$0.21 \pm 0.027(7.8)$} & \scalebox{0.5}{$0.093 \pm 0.027(3.5)$} & \scalebox{0.5}{$-0.083 \pm 0.028(-3)$} & \scalebox{0.5}{$-0.41 \pm 0.028(-15)$} \\ \hline +6 & \scalebox{0.5}{$0.0064 \pm 0.026(0.25)$} & \scalebox{0.5}{$-0.051 \pm 0.027(-1.9)$} & \scalebox{0.5}{$-0.029 \pm 0.028(-1)$} & \scalebox{0.5}{$0.26 \pm 0.028(9.2)$} & \scalebox{0.5}{$0.14 \pm 0.027(5.1)$} & \scalebox{0.5}{$-0.081 \pm 0.027(-3)$} & \scalebox{0.5}{$-0.45 \pm 0.028(-16)$} \\ \hline +%7 & \scalebox{0.5}{$0.22 \pm 0.027(8)$} & \scalebox{0.5}{$-0.34 \pm 0.028(-12)$} & \scalebox{0.5}{$-0.43 \pm 0.026(-16)$} & \scalebox{0.5}{$2.4 \pm 0.029(82)$} & \scalebox{0.5}{$0.66 \pm 0.027(24)$} & \scalebox{0.5}{$-0.24 \pm 0.028(-8.6)$} & \scalebox{0.5}{$-0.51 \pm 0.027(-19)$} & +8 & \scalebox{0.5}{$0.023 \pm 0.027(0.85)$} & \scalebox{0.5}{$-0.031 \pm 0.028(-1.1)$} & \scalebox{0.5}{$0.0042 \pm 0.028(0.15)$} & \scalebox{0.5}{$0.21 \pm 0.026(7.8)$} & \scalebox{0.5}{$0.12 \pm 0.028(4.2)$} & \scalebox{0.5}{$-0.13 \pm 0.027(-4.8)$} & \scalebox{0.5}{$-0.48 \pm 0.026(-18)$} \\ \hline +9 & \scalebox{0.5}{$-0.017 \pm 0.027(-0.63)$} & \scalebox{0.5}{$-0.015 \pm 0.026(-0.56)$} & \scalebox{0.5}{$-0.0052 \pm 0.026(-0.2)$} & \scalebox{0.5}{$0.27 \pm 0.027(10)$} & \scalebox{0.5}{$0.046 \pm 0.026(1.7)$} & \scalebox{0.5}{$-0.12 \pm 0.026(-4.4)$} & \scalebox{0.5}{$-0.5 \pm 0.026(-19)$} \\ \hline +10 & \scalebox{0.5}{$-0.054 \pm 0.027(-2)$} & \scalebox{0.5}{$-0.056 \pm 0.026(-2.2)$} & \scalebox{0.5}{$0.036 \pm 0.026(1.4)$} & \scalebox{0.5}{$0.16 \pm 0.028(5.7)$} & \scalebox{0.5}{$0.077 \pm 0.028(2.8)$} & \scalebox{0.5}{$-0.034 \pm 0.027(-1.3)$} & \scalebox{0.5}{$-0.39 \pm 0.028(-14)$} \\ \hline +11 & \scalebox{0.5}{$0.023 \pm 0.027(0.88)$} & \scalebox{0.5}{$0.021 \pm 0.027(0.8)$} & \scalebox{0.5}{$-0.011 \pm 0.027(-0.41)$} & \scalebox{0.5}{$0.14 \pm 0.027(5)$} & \scalebox{0.5}{$0.042 \pm 0.027(1.6)$} & \scalebox{0.5}{$-0.098 \pm 0.028(-3.5)$} & \scalebox{0.5}{$-0.3 \pm 0.027(-11)$} \\ \hline + + + \hline + + + \end{tabular} + +\end{center} + + +\end{tiny} +\end{frame} + +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% + + +\begin{frame}\frametitle{Corr2- MM} + + +\begin{tiny} + +\begin{center} + \begin{tabular}{ l l l l l l l l l } + \hline + \multicolumn{8}{c}{Mean of the pull} \\ \hline +$q^2$ & $S_3$ & $S_4$ & $S_5$ & $S_{6s}$ & $S_{6c}$ & $S_7$ & $S_8$ \\ \hline \hline + +0 & \scalebox{0.5}{$-0.21 \pm 0.026(-8.1)$} & \scalebox{0.5}{$0.061 \pm 0.026(2.3)$} & \scalebox{0.5}{$-0.016 \pm 0.026(-0.63)$} & \scalebox{0.5}{$0.048 \pm 0.026(1.8)$} & \scalebox{0.5}{$-0.0062 \pm 0.027(-0.23)$} & \scalebox{0.5}{$-0.012 \pm 0.028(-0.44)$} & \scalebox{0.5}{$0.0091 \pm 0.026(0.36)$} \\ \hline +1 & \scalebox{0.5}{$-0.12 \pm 0.028(-4.5)$} & \scalebox{0.5}{$0.032 \pm 0.027(1.2)$} & \scalebox{0.5}{$-0.0071 \pm 0.026(-0.27)$} & \scalebox{0.5}{$0.02 \pm 0.027(0.75)$} & \scalebox{0.5}{$-0.086 \pm 0.027(-3.2)$} & \scalebox{0.5}{$-0.03 \pm 0.025(-1.2)$} & \scalebox{0.5}{$0.021 \pm 0.027(0.79)$} \\ \hline +2 & \scalebox{0.5}{$-0.15 \pm 0.027(-5.8)$} & \scalebox{0.5}{$-0.013 \pm 0.026(-0.49)$} & \scalebox{0.5}{$0.011 \pm 0.026(0.44)$} & \scalebox{0.5}{$-0.039 \pm 0.026(-1.5)$} & \scalebox{0.5}{$-0.032 \pm 0.027(-1.2)$} & \scalebox{0.5}{$-0.066 \pm 0.027(-2.5)$} & \scalebox{0.5}{$0.018 \pm 0.028(0.64)$} \\ \hline +3 & \scalebox{0.5}{$-0.15 \pm 0.027(-5.6)$} & \scalebox{0.5}{$0.025 \pm 0.026(0.96)$} & \scalebox{0.5}{$0.016 \pm 0.027(0.58)$} & \scalebox{0.5}{$-0.062 \pm 0.027(-2.3)$} & \scalebox{0.5}{$0.037 \pm 0.026(1.4)$} & \scalebox{0.5}{$0.026 \pm 0.027(0.96)$} & \scalebox{0.5}{$-0.016 \pm 0.027(-0.6)$} \\ \hline +4 & \scalebox{0.5}{$-0.12 \pm 0.028(-4.5)$} & \scalebox{0.5}{$-0.024 \pm 0.026(-0.92)$} & \scalebox{0.5}{$0.045 \pm 0.027(1.6)$} & \scalebox{0.5}{$0.0075 \pm 0.026(0.29)$} & \scalebox{0.5}{$0.015 \pm 0.027(0.53)$} & \scalebox{0.5}{$-0.036 \pm 0.026(-1.4)$} & \scalebox{0.5}{$0.037 \pm 0.026(1.4)$} \\ \hline +5 & \scalebox{0.5}{$-0.095 \pm 0.027(-3.6)$} & \scalebox{0.5}{$-0.032 \pm 0.026(-1.2)$} & \scalebox{0.5}{$0.014 \pm 0.026(0.52)$} & \scalebox{0.5}{$-0.013 \pm 0.026(-0.48)$} & \scalebox{0.5}{$-0.0093 \pm 0.027(-0.35)$} & \scalebox{0.5}{$-0.013 \pm 0.026(-0.51)$} & \scalebox{0.5}{$0.042 \pm 0.027(1.6)$} \\ \hline +6 & \scalebox{0.5}{$-0.17 \pm 0.025(-6.5)$} & \scalebox{0.5}{$0.008 \pm 0.027(0.3)$} & \scalebox{0.5}{$0.012 \pm 0.027(0.45)$} & \scalebox{0.5}{$0.029 \pm 0.027(1.1)$} & \scalebox{0.5}{$0.0072 \pm 0.027(0.27)$} & \scalebox{0.5}{$-0.0012 \pm 0.026(-0.046)$} & \scalebox{0.5}{$0.011 \pm 0.027(0.42)$} \\ \hline +%7 & \scalebox{0.5}{$0.078 \pm 0.026(3)$} & \scalebox{0.5}{$-0.3 \pm 0.026(-11)$} & \scalebox{0.5}{$-0.34 \pm 0.026(-13)$} & \scalebox{0.5}{$2.1 \pm 0.028(73)$} & \scalebox{0.5}{$0.47 \pm 0.026(18)$} & \scalebox{0.5}{$-0.17 \pm 0.027(-6.1)$} & \scalebox{0.5}{$0.0051 \pm 0.027(0.19)$} \\ \hline +8 & \scalebox{0.5}{$-0.13 \pm 0.026(-5.1)$} & \scalebox{0.5}{$-0.0077 \pm 0.027(-0.28)$} & \scalebox{0.5}{$0.05 \pm 0.027(1.9)$} & \scalebox{0.5}{$-0.03 \pm 0.026(-1.2)$} & \scalebox{0.5}{$-0.012 \pm 0.028(-0.44)$} & \scalebox{0.5}{$-0.046 \pm 0.026(-1.7)$} & \scalebox{0.5}{$0.031 \pm 0.026(1.2)$} \\ \hline +9 & \scalebox{0.5}{$-0.15 \pm 0.026(-5.7)$} & \scalebox{0.5}{$-0.0083 \pm 0.026(-0.32)$} & \scalebox{0.5}{$0.03 \pm 0.026(1.2)$} & \scalebox{0.5}{$0.044 \pm 0.027(1.6)$} & \scalebox{0.5}{$-0.07 \pm 0.026(-2.7)$} & \scalebox{0.5}{$-0.022 \pm 0.026(-0.84)$} & \scalebox{0.5}{$-0.045 \pm 0.026(-1.7)$} \\ \hline +10 & \scalebox{0.5}{$-0.15 \pm 0.025(-5.8)$} & \scalebox{0.5}{$-0.032 \pm 0.025(-1.3)$} & \scalebox{0.5}{$0.059 \pm 0.026(2.2)$} & \scalebox{0.5}{$-0.072 \pm 0.028(-2.6)$} & \scalebox{0.5}{$-0.029 \pm 0.027(-1.1)$} & \scalebox{0.5}{$0.064 \pm 0.027(2.4)$} & \scalebox{0.5}{$0.014 \pm 0.027(0.51)$} \\ \hline +11 & \scalebox{0.5}{$-0.067 \pm 0.026(-2.6)$} & \scalebox{0.5}{$0.017 \pm 0.026(0.65)$} & \scalebox{0.5}{$-0.015 \pm 0.026(-0.56)$} & \scalebox{0.5}{$-0.051 \pm 0.026(-1.9)$} & \scalebox{0.5}{$-0.0086 \pm 0.026(-0.33)$} & \scalebox{0.5}{$-0.018 \pm 0.028(-0.67)$} & \scalebox{0.5}{$0.017 \pm 0.027(0.62)$} \\ \hline + + + + + + +\hline + + + \end{tabular} + +\end{center} + + +\end{tiny} +\end{frame} + + +\begin{frame}\frametitle{Corr3- MM} + + +\begin{tiny} + +\begin{center} + \begin{tabular}{ l l l l l l l l l } + \hline + \multicolumn{8}{c}{Mean of the pull} \\ \hline +$q^2$ & $S_3$ & $S_4$ & $S_5$ & $S_{6s}$ & $S_{6c}$ & $S_7$ & $S_8$ \\ \hline \hline + +0 & \scalebox{0.5}{$-0.021 \pm 0.026(-0.81)$} & \scalebox{0.5}{$0.041 \pm 0.026(1.5)$} & \scalebox{0.5}{$0.009 \pm 0.027(0.34)$} & \scalebox{0.5}{$0.043 \pm 0.026(1.6)$} & \scalebox{0.5}{$0.13 \pm 0.028(4.8)$} & \scalebox{0.5}{$-0.0072 \pm 0.028(-0.26)$} & \scalebox{0.5}{$0.044 \pm 0.026(1.7)$} \\ \hline +1 & \scalebox{0.5}{$-0.014 \pm 0.028(-0.51)$} & \scalebox{0.5}{$0.03 \pm 0.027(1.1)$} & \scalebox{0.5}{$0.022 \pm 0.027(0.82)$} & \scalebox{0.5}{$0.015 \pm 0.028(0.53)$} & \scalebox{0.5}{$0.078 \pm 0.028(2.8)$} & \scalebox{0.5}{$-0.037 \pm 0.025(-1.4)$} & \scalebox{0.5}{$0.057 \pm 0.027(2.1)$} \\ \hline +2 & \scalebox{0.5}{$-0.037 \pm 0.027(-1.4)$} & \scalebox{0.5}{$-0.0013 \pm 0.027(-0.048)$} & \scalebox{0.5}{$-0.015 \pm 0.027(-0.54)$} & \scalebox{0.5}{$-0.052 \pm 0.026(-2)$} & \scalebox{0.5}{$0.1 \pm 0.027(3.8)$} & \scalebox{0.5}{$-0.051 \pm 0.026(-1.9)$} & \scalebox{0.5}{$0.022 \pm 0.028(0.78)$} \\ \hline +3 & \scalebox{0.5}{$-0.015 \pm 0.027(-0.55)$} & \scalebox{0.5}{$0.036 \pm 0.028(1.3)$} & \scalebox{0.5}{$-0.039 \pm 0.027(-1.4)$} & \scalebox{0.5}{$-0.072 \pm 0.027(-2.7)$} & \scalebox{0.5}{$0.17 \pm 0.027(6.2)$} & \scalebox{0.5}{$-0.0044 \pm 0.028(-0.15)$} & \scalebox{0.5}{$-0.024 \pm 0.027(-0.9)$} \\ \hline +4 & \scalebox{0.5}{$-0.00047 \pm 0.029(-0.017)$} & \scalebox{0.5}{$-0.012 \pm 0.027(-0.43)$} & \scalebox{0.5}{$0.0099 \pm 0.028(0.35)$} & \scalebox{0.5}{$-0.002 \pm 0.026(-0.076)$} & \scalebox{0.5}{$0.17 \pm 0.028(6.2)$} & \scalebox{0.5}{$-0.062 \pm 0.027(-2.3)$} & \scalebox{0.5}{$0.0086 \pm 0.027(0.32)$} \\ \hline + +5 & \scalebox{0.5}{$0.046 \pm 0.027(1.7)$} & \scalebox{0.5}{$-0.02 \pm 0.026(-0.76)$} & \scalebox{0.5}{$-0.04 \pm 0.027(-1.5)$} & \scalebox{0.5}{$-0.012 \pm 0.027(-0.44)$} & \scalebox{0.5}{$0.13 \pm 0.027(4.8)$} & \scalebox{0.5}{$-0.04 \pm 0.027(-1.5)$} & \scalebox{0.5}{$-0.0056 \pm 0.027(-0.21)$} \\ \hline +6 & \scalebox{0.5}{$-0.013 \pm 0.026(-0.52)$} & \scalebox{0.5}{$0.041 \pm 0.027(1.5)$} & \scalebox{0.5}{$-0.033 \pm 0.028(-1.2)$} & \scalebox{0.5}{$-0.0019 \pm 0.027(-0.068)$} & \scalebox{0.5}{$0.15 \pm 0.027(5.4)$} & \scalebox{0.5}{$-0.034 \pm 0.027(-1.3)$} & \scalebox{0.5}{$-0.021 \pm 0.028(-0.75)$} \\ \hline +%7 & \scalebox{0.5}{$0.25 \pm 0.027(9.1)$} & \scalebox{0.5}{$-0.27 \pm 0.027(-10)$} & \scalebox{0.5}{$-0.41 \pm 0.027(-16)$} & \scalebox{0.5}{$2.1 \pm 0.029(73)$} & \scalebox{0.5}{$0.65 \pm 0.027(24)$} & \scalebox{0.5}{$-0.19 \pm 0.028(-7)$} & \scalebox{0.5}{$-0.053 \pm 0.028(-1.9)$} \\ \hline +8 & \scalebox{0.5}{$0.039 \pm 0.026(1.5)$} & \scalebox{0.5}{$0.01 \pm 0.028(0.36)$} & \scalebox{0.5}{$-0.027 \pm 0.028(-0.96)$} & \scalebox{0.5}{$-0.024 \pm 0.026(-0.9)$} & \scalebox{0.5}{$0.12 \pm 0.027(4.3)$} & \scalebox{0.5}{$-0.092 \pm 0.026(-3.5)$} & \scalebox{0.5}{$-0.036 \pm 0.027(-1.3)$} \\ \hline +9 & \scalebox{0.5}{$-0.01 \pm 0.027(-0.38)$} & \scalebox{0.5}{$0.0024 \pm 0.027(0.09)$} & \scalebox{0.5}{$-0.018 \pm 0.026(-0.68)$} & \scalebox{0.5}{$0.022 \pm 0.028(0.79)$} & \scalebox{0.5}{$0.068 \pm 0.027(2.6)$} & \scalebox{0.5}{$-0.069 \pm 0.026(-2.6)$} & \scalebox{0.5}{$-0.078 \pm 0.026(-3)$} \\ \hline +10 & \scalebox{0.5}{$-0.017 \pm 0.027(-0.62)$} & \scalebox{0.5}{$-0.015 \pm 0.026(-0.57)$} & \scalebox{0.5}{$0.012 \pm 0.027(0.46)$} & \scalebox{0.5}{$-0.074 \pm 0.028(-2.6)$} & \scalebox{0.5}{$0.1 \pm 0.027(3.8)$} & \scalebox{0.5}{$-0.003 \pm 0.027(-0.11)$} & \scalebox{0.5}{$-0.043 \pm 0.029(-1.5)$} \\ \hline +11 & \scalebox{0.5}{$0.032 \pm 0.026(1.2)$} & \scalebox{0.5}{$0.024 \pm 0.026(0.91)$} & \scalebox{0.5}{$-0.04 \pm 0.026(-1.5)$} & \scalebox{0.5}{$-0.066 \pm 0.027(-2.5)$} & \scalebox{0.5}{$0.098 \pm 0.027(3.7)$} & \scalebox{0.5}{$-0.043 \pm 0.028(-1.6)$} & \scalebox{0.5}{$-0.0018 \pm 0.028(-0.064)$} \\ \hline + + + +\hline + + + \end{tabular} + +\end{center} + + +\end{tiny} +\end{frame} + +\begin{frame}\frametitle{Corr4- MM} + + +\begin{tiny} + +\begin{center} + \begin{tabular}{ l l l l l l l l l } + \hline + \multicolumn{8}{c}{Mean of the pull} \\ \hline +$q^2$ & $S_3$ & $S_4$ & $S_5$ & $S_{6s}$ & $S_{6c}$ & $S_7$ & $S_8$ \\ \hline \hline + + +0 & \scalebox{0.5}{$-0.019 \pm 0.026(-0.71)$} & \scalebox{0.5}{$0.048 \pm 0.027(1.8)$} & \scalebox{0.5}{$0.018 \pm 0.027(0.67)$} & \scalebox{0.5}{$0.059 \pm 0.027(2.2)$} & \scalebox{0.5}{$-0.015 \pm 0.028(-0.55)$} & \scalebox{0.5}{$0.061 \pm 0.027(2.2)$} & \scalebox{0.5}{$0.012 \pm 0.027(0.44)$} \\ \hline +1 & \scalebox{0.5}{$-0.014 \pm 0.028(-0.51)$} & \scalebox{0.5}{$0.043 \pm 0.027(1.6)$} & \scalebox{0.5}{$0.013 \pm 0.027(0.49)$} & \scalebox{0.5}{$0.024 \pm 0.028(0.86)$} & \scalebox{0.5}{$-0.038 \pm 0.028(-1.4)$} & \scalebox{0.5}{$0.024 \pm 0.026(0.94)$} & \scalebox{0.5}{$0.037 \pm 0.027(1.3)$} \\ \hline +2 & \scalebox{0.5}{$-0.03 \pm 0.027(-1.1)$} & \scalebox{0.5}{$-0.0021 \pm 0.027(-0.076)$} & \scalebox{0.5}{$-0.01 \pm 0.027(-0.39)$} & \scalebox{0.5}{$-0.017 \pm 0.027(-0.61)$} & \scalebox{0.5}{$-0.016 \pm 0.027(-0.58)$} & \scalebox{0.5}{$0.013 \pm 0.027(0.49)$} & \scalebox{0.5}{$0.027 \pm 0.028(0.98)$} \\ \hline +3 & \scalebox{0.5}{$-0.007 \pm 0.027(-0.26)$} & \scalebox{0.5}{$0.03 \pm 0.028(1.1)$} & \scalebox{0.5}{$-0.036 \pm 0.027(-1.3)$} & \scalebox{0.5}{$-0.074 \pm 0.027(-2.8)$} & \scalebox{0.5}{$0.041 \pm 0.027(1.5)$} & \scalebox{0.5}{$0.08 \pm 0.028(2.9)$} & \scalebox{0.5}{$-0.0083 \pm 0.027(-0.31)$} \\ \hline +4 & \scalebox{0.5}{$0.00089 \pm 0.029(0.031)$} & \scalebox{0.5}{$-0.021 \pm 0.027(-0.77)$} & \scalebox{0.5}{$0.0032 \pm 0.028(0.11)$} & \scalebox{0.5}{$0.0031 \pm 0.026(0.12)$} & \scalebox{0.5}{$0.012 \pm 0.027(0.44)$} & \scalebox{0.5}{$0.019 \pm 0.026(0.71)$} & \scalebox{0.5}{$0.034 \pm 0.027(1.3)$} \\ \hline +5 & \scalebox{0.5}{$0.044 \pm 0.028(1.6)$} & \scalebox{0.5}{$-0.022 \pm 0.026(-0.82)$} & \scalebox{0.5}{$-0.041 \pm 0.027(-1.5)$} & \scalebox{0.5}{$-0.014 \pm 0.027(-0.53)$} & \scalebox{0.5}{$-0.029 \pm 0.027(-1.1)$} & \scalebox{0.5}{$0.041 \pm 0.027(1.5)$} & \scalebox{0.5}{$0.042 \pm 0.028(1.5)$} \\ \hline +6 & \scalebox{0.5}{$-0.011 \pm 0.026(-0.42)$} & \scalebox{0.5}{$0.041 \pm 0.027(1.5)$} & \scalebox{0.5}{$-0.045 \pm 0.028(-1.6)$} & \scalebox{0.5}{$0.011 \pm 0.027(0.41)$} & \scalebox{0.5}{$-0.0089 \pm 0.027(-0.33)$} & \scalebox{0.5}{$0.067 \pm 0.027(2.5)$} & 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\pm 0.027(-0.71)$} & \scalebox{0.5}{$-0.0051 \pm 0.025(-0.2)$} & \scalebox{0.5}{$0.0081 \pm 0.026(0.31)$} & \scalebox{0.5}{$-0.077 \pm 0.028(-2.7)$} & \scalebox{0.5}{$-0.03 \pm 0.027(-1.1)$} & \scalebox{0.5}{$0.11 \pm 0.027(4.1)$} & \scalebox{0.5}{$0.013 \pm 0.028(0.46)$} \\ \hline +11 & \scalebox{0.5}{$0.027 \pm 0.026(1)$} & \scalebox{0.5}{$0.032 \pm 0.027(1.2)$} & \scalebox{0.5}{$-0.038 \pm 0.027(-1.4)$} & \scalebox{0.5}{$-0.048 \pm 0.026(-1.8)$} & \scalebox{0.5}{$-0.021 \pm 0.027(-0.77)$} & \scalebox{0.5}{$0.019 \pm 0.028(0.69)$} & \scalebox{0.5}{$0.035 \pm 0.027(1.3)$} \\ \hline + + + +\hline + + \end{tabular} + +\end{center} + +\end{tiny} +\end{frame} + + + + +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +\section{Reverse Engineering Unfolding} + +\begin{frame}\frametitle{Reverse Engineering- Corr1} +\begin{itemize} +\item Let's try to understand if we can understand why this happens: +\item Let's calculate what should I expect with the unfolding +\item This is up to normalization! +\begin{itemize} +\item $M_5=0.4 S_5 \to M_5=0.00512 S_3 + 0.4 S_5 - 0.002 S_7$ +\item $M_8=0.32 S_8 \to M_8=0.0016 S_4 + 0.00512 S_7 + 0.32 S_8$ +\item $M_7=0.4 S_7 \to M_7=0.002 S_5 + 0.4 S_7 + 0.00512 S_8$ +\item $M_3=0.32 S_3 \to M_3=0.32 S_3 - 0.0008 S_9$ +\end{itemize} +\item The way you can look at this is that i just shown you how our unfolding matrix works like. +\end{itemize} + + + +\end{frame} + +\begin{frame}\frametitle{Reverse Engineering- Corr2} +\begin{itemize} +\item Let's try to understand if we can understand why this happens: +\item Let's calculate what should I expect with the unfolding +\item This is up to normalization! +\begin{itemize} +\item $M_5=0.4 S_5 \to M_5= 0.4 S_5$ +\item $M_8=0.32 S_8 \to M_8=0.32 S_5$ +\item $M_7=0.4 S_7 \to M_7=0.4 S_7$ +\item $M_3=0.32 S_3 \to M_3=-0.0036 + 0.0012 Fl + 0.32 S_3$ +\end{itemize} +\item The way you can look at this is that i just shown you how our unfolding matrix works like. +\end{itemize} + + + +\end{frame} + + + + +\begin{frame}\frametitle{Summary} +\begin{itemize} +\item Developed a systematic way how to get Unfolding matrix +\item Moments are resistant against variety of unfolding discrepancies. +\item This might lead to reduced systematics in the future. +\end{itemize} + + + + +\end{frame} + + + +\end{document} diff --git a/Inflaton/Full_dst_numbers/MMatrix.toc b/Inflaton/Full_dst_numbers/MMatrix.toc new file mode 100644 index 0000000..495658f --- /dev/null +++ b/Inflaton/Full_dst_numbers/MMatrix.toc @@ -0,0 +1,2 @@ +\beamer@endinputifotherversion {3.10pt} +\select@language {english} diff --git a/Inflaton/Full_dst_numbers/P5.png b/Inflaton/Full_dst_numbers/P5.png new file mode 100644 index 0000000..7819eef --- /dev/null +++ b/Inflaton/Full_dst_numbers/P5.png Binary files differ diff --git a/Inflaton/Full_dst_numbers/Q2_4_S8.png b/Inflaton/Full_dst_numbers/Q2_4_S8.png new file mode 100644 index 0000000..9176de4 --- /dev/null +++ b/Inflaton/Full_dst_numbers/Q2_4_S8.png 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`tables.toc'. + +\tf@snm=\write8 +\openout8 = `tables.snm'. + + (./tables.aux) ) +Here is how much of TeX's memory you used: + 14829 strings out of 493848 + 275180 string characters out of 1152823 + 365984 words of memory out of 3000000 + 17729 multiletter control sequences out of 15000+50000 + 7983 words of font info for 23 fonts, out of 3000000 for 9000 + 714 hyphenation exceptions out of 8191 + 49i,14n,53p,419b,545s stack positions out of 5000i,500n,10000p,200000b,50000s +{/usr/share/texmf/fonts/enc/dvips/cm-super/cm-super-t1.enc} + +Output written on tables.pdf (1 page, 44637 bytes). +PDF statistics: + 60 PDF objects out of 1000 (max. 8388607) + 3 named destinations out of 1000 (max. 500000) + 33 words of extra memory for PDF output out of 10000 (max. 10000000) + diff --git a/Inflaton/Full_dst_numbers/tables/tables.nav b/Inflaton/Full_dst_numbers/tables/tables.nav new file mode 100644 index 0000000..230c4a3 --- /dev/null +++ b/Inflaton/Full_dst_numbers/tables/tables.nav @@ -0,0 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0.0182(2.96)$} & \scalebox{0.5}{$-0.0063 \pm 0.0189(-0.334)$} & \scalebox{0.5}{$-0.0297 \pm 0.019(-1.57)$} & \scalebox{0.5}{$-0.00305 \pm 0.0183(-0.166)$} & \scalebox{0.5}{$-0.0503 \pm 0.0183(-2.75)$} & \scalebox{0.5}{$-0.0137 \pm 0.0181(-0.758)$} & \scalebox{0.5}{$0.0169 \pm 0.0187(0.902)$} \\ \hline + + \end{tabular} + } + \end{frame} +\end{document} \ No newline at end of file diff --git a/Inflaton/Full_dst_numbers/tables/tables.toc b/Inflaton/Full_dst_numbers/tables/tables.toc new file mode 100644 index 0000000..e06b51d --- /dev/null +++ b/Inflaton/Full_dst_numbers/tables/tables.toc @@ -0,0 +1 @@ +\beamer@endinputifotherversion {3.10pt} diff --git a/Inflaton/Full_dst_numbers/texput.log b/Inflaton/Full_dst_numbers/texput.log new file mode 100644 index 0000000..f84449f --- /dev/null +++ b/Inflaton/Full_dst_numbers/texput.log @@ -0,0 +1,20 @@ +This is pdfTeX, Version 3.1415926-1.40.10 (TeX Live 2009/Debian) (format=pdflatex 2014.3.24) 24 JUN 2014 18:23 +entering extended mode + %&-line parsing enabled. +**beamerthemeSybila.tex + +! Emergency stop. +<*> beamerthemeSybila.tex + +*** (job aborted, file error in nonstop mode) + + +Here is how much of TeX's memory you used: + 3 strings out of 493848 + 118 string characters out of 1152823 + 47808 words of memory out of 3000000 + 3381 multiletter control sequences out of 15000+50000 + 3640 words of font info for 14 fonts, out of 3000000 for 9000 + 714 hyphenation exceptions out of 8191 + 0i,0n,0p,1b,6s stack positions out of 5000i,500n,10000p,200000b,50000s +! ==> Fatal error occurred, no output PDF file produced! diff --git a/Inflaton/Full_dst_numbers/tmp.png b/Inflaton/Full_dst_numbers/tmp.png new file mode 100644 index 0000000..574cb07 --- /dev/null +++ b/Inflaton/Full_dst_numbers/tmp.png Binary files differ diff --git a/Inflaton/Full_dst_numbers/tmp/beamerthemeSybila.sty b/Inflaton/Full_dst_numbers/tmp/beamerthemeSybila.sty new file mode 100644 index 0000000..5639601 --- /dev/null +++ b/Inflaton/Full_dst_numbers/tmp/beamerthemeSybila.sty @@ -0,0 +1,104 @@ +\mode + +%------------------------------------------------------------------------------- +% Themes +%------------------------------------------------------------------------------- + +\useoutertheme{split} +\useinnertheme{rounded} +\usefonttheme{structurebold} +%\useoutertheme{shadow} + +%------------------------------------------------------------------------------- +% Templates +%------------------------------------------------------------------------------- + +\beamertemplatenavigationsymbolsempty +\beamertemplateheadempty +\beamertemplateshadowblocks + +%------------------------------------------------------------------------------- +% Own templates +%------------------------------------------------------------------------------- + +% Normal title page. +\defbeamertemplate*{title page}{simple}[1][] +{ + \vfill + \begin{centering} + \begin{beamercolorbox}[center, rounded=true]{title} + \usebeamerfont{title}\inserttitle\par% + \ifx\insertsubtitle\@empty% + \else% + \vskip0.25em% + {\usebeamerfont{subtitle}\usebeamercolor[fg]{subtitle}\insertsubtitle\par}% + \fi% + \end{beamercolorbox}% + + \vskip1em + + \begin{beamercolorbox}[sep=8pt,center,#1]{author} + \usebeamerfont{author}\insertauthor + \end{beamercolorbox} + + \vskip1em + + {\usebeamercolor[fg]{titlegraphic}\inserttitlegraphic\par} + \begin{beamercolorbox}[sep=8pt,center,#1]{institute} + \usebeamerfont{date}\insertinstitute + \end{beamercolorbox} + + \vskip1em + + \begin{beamercolorbox}[sep=8pt,center,#1]{date} + \usebeamerfont{date}\insertdate + \end{beamercolorbox} + \end{centering} + \vfill +} + +%------------------------------------------------------------------------------- +% Logo +%------------------------------------------------------------------------------- + +\logo{\hspace*{0.6\textwidth}\includegraphics[width=1.2cm]{sybila-logo-paper-shaded}\hspace*{0.3cm}} + +%------------------------------------------------------------------------------- +% Colors +%------------------------------------------------------------------------------- + +\setbeamercovered{dynamic} + +\setbeamercolor{math text}{fg=green!45!black} +\setbeamercolor{title}{bg=white!30!black} +\setbeamercolor{frametitle}{bg=white!45!black} +\setbeamercolor{footline}{bg=black,fg=white} +\setbeamercolor{author in head/foot}{bg=black,fg=white} +\setbeamercolor{title in head/foot}{bg=white!45!black} +\setbeamercolor{block title}{bg=white!45!black} +\setbeamercolor{block title example}{bg=white!45!black} +\setbeamercolor{block title alerted}{bg=white!15!black} + +\colorlet{redshaded}{red!25!bg} +\colorlet{shaded}{black!25!bg} +\colorlet{shadedshaded}{black!10!bg} +\colorlet{blackshaded}{black!40!bg} + +\usecolortheme{whale} +\usecolortheme{orchid} + +%------------------------------------------------------------------------------- +% Fonts +%------------------------------------------------------------------------------- + +\setbeamerfont{block title}{size={}} +\setbeamerfont{date}{size=\small} + +%------------------------------------------------------------------------------- +% Other +%------------------------------------------------------------------------------- + +\titlegraphic{\includegraphics[width=3.0cm]{sybila-logo-slide-title-shaded.pdf}} + +\mode + diff --git a/Inflaton/Full_dst_numbers/tmp/example.tex b/Inflaton/Full_dst_numbers/tmp/example.tex new file mode 100644 index 0000000..ce0641b --- /dev/null +++ b/Inflaton/Full_dst_numbers/tmp/example.tex @@ -0,0 +1,21 @@ +\documentclass[xcolor=svgnames]{beamer} +\usepackage[utf8]{inputenc} +\usepackage[english]{babel} + +\usetheme{Sybila} + +\title[Parallelization of Methods for Dynamic System Analysis]{Parallelization of Methods for Dynamic System Analysis Using CUDA} +\author{Jan Papou\v{s}ek} +\institute{Masaryk University Brno} +\date{\today} + +\begin{document} +% --------------------------- SLIDE -------------------------------------------- +\frame[plain]{\titlepage} +% ------------------------------------------------------------------------------ +% --------------------------- SLIDE -------------------------------------------- +\begin{frame} + \frametitle{Introduction} +\end{frame} +% ------------------------------------------------------------------------------ +\end{document} diff --git a/Inflaton/Full_dst_numbers/tmp/example/beamerthemeSybila.sty b/Inflaton/Full_dst_numbers/tmp/example/beamerthemeSybila.sty new file mode 100644 index 0000000..5639601 --- /dev/null +++ b/Inflaton/Full_dst_numbers/tmp/example/beamerthemeSybila.sty @@ -0,0 +1,104 @@ +\mode + +%------------------------------------------------------------------------------- +% Themes +%------------------------------------------------------------------------------- + +\useoutertheme{split} +\useinnertheme{rounded} +\usefonttheme{structurebold} +%\useoutertheme{shadow} + +%------------------------------------------------------------------------------- +% Templates +%------------------------------------------------------------------------------- + +\beamertemplatenavigationsymbolsempty +\beamertemplateheadempty +\beamertemplateshadowblocks + +%------------------------------------------------------------------------------- +% Own templates +%------------------------------------------------------------------------------- + +% Normal title page. +\defbeamertemplate*{title page}{simple}[1][] +{ + \vfill + \begin{centering} + \begin{beamercolorbox}[center, rounded=true]{title} + \usebeamerfont{title}\inserttitle\par% + \ifx\insertsubtitle\@empty% + \else% + \vskip0.25em% + {\usebeamerfont{subtitle}\usebeamercolor[fg]{subtitle}\insertsubtitle\par}% + \fi% + \end{beamercolorbox}% + + \vskip1em + + \begin{beamercolorbox}[sep=8pt,center,#1]{author} + \usebeamerfont{author}\insertauthor + \end{beamercolorbox} + + \vskip1em + + {\usebeamercolor[fg]{titlegraphic}\inserttitlegraphic\par} + \begin{beamercolorbox}[sep=8pt,center,#1]{institute} + \usebeamerfont{date}\insertinstitute + \end{beamercolorbox} + + \vskip1em + + \begin{beamercolorbox}[sep=8pt,center,#1]{date} + \usebeamerfont{date}\insertdate + \end{beamercolorbox} + \end{centering} + \vfill +} + +%------------------------------------------------------------------------------- +% Logo +%------------------------------------------------------------------------------- + +\logo{\hspace*{0.6\textwidth}\includegraphics[width=1.2cm]{sybila-logo-paper-shaded}\hspace*{0.3cm}} + +%------------------------------------------------------------------------------- +% Colors +%------------------------------------------------------------------------------- + +\setbeamercovered{dynamic} + +\setbeamercolor{math text}{fg=green!45!black} +\setbeamercolor{title}{bg=white!30!black} +\setbeamercolor{frametitle}{bg=white!45!black} +\setbeamercolor{footline}{bg=black,fg=white} +\setbeamercolor{author in head/foot}{bg=black,fg=white} +\setbeamercolor{title in head/foot}{bg=white!45!black} +\setbeamercolor{block title}{bg=white!45!black} +\setbeamercolor{block title example}{bg=white!45!black} +\setbeamercolor{block title alerted}{bg=white!15!black} + +\colorlet{redshaded}{red!25!bg} +\colorlet{shaded}{black!25!bg} +\colorlet{shadedshaded}{black!10!bg} +\colorlet{blackshaded}{black!40!bg} + +\usecolortheme{whale} +\usecolortheme{orchid} + +%------------------------------------------------------------------------------- +% Fonts +%------------------------------------------------------------------------------- + +\setbeamerfont{block title}{size={}} +\setbeamerfont{date}{size=\small} + +%------------------------------------------------------------------------------- +% Other +%------------------------------------------------------------------------------- + +\titlegraphic{\includegraphics[width=3.0cm]{sybila-logo-slide-title-shaded.pdf}} + +\mode + diff --git a/Inflaton/Full_dst_numbers/tmp/example/example.aux b/Inflaton/Full_dst_numbers/tmp/example/example.aux new file mode 100644 index 0000000..3c3451e --- /dev/null +++ b/Inflaton/Full_dst_numbers/tmp/example/example.aux @@ -0,0 +1,28 @@ +\relax +\ifx\hyper@anchor\@undefined +\global \let \oldcontentsline\contentsline +\gdef \contentsline#1#2#3#4{\oldcontentsline{#1}{#2}{#3}} +\global \let \oldnewlabel\newlabel +\gdef \newlabel#1#2{\newlabelxx{#1}#2} +\gdef \newlabelxx#1#2#3#4#5#6{\oldnewlabel{#1}{{#2}{#3}}} +\AtEndDocument{\let \contentsline\oldcontentsline +\let \newlabel\oldnewlabel} +\else +\global \let \hyper@last\relax +\fi + +\@writefile{toc}{\beamer@endinputifotherversion {3.10pt}} +\@writefile{nav}{\beamer@endinputifotherversion {3.10pt}} +\select@language{english} +\@writefile{toc}{\select@language{english}} +\@writefile{lof}{\select@language{english}} +\@writefile{lot}{\select@language{english}} +\@writefile{nav}{\headcommand {\slideentry {0}{0}{1}{1/1}{}{0}}} +\@writefile{nav}{\headcommand {\beamer@framepages {1}{1}}} +\@writefile{nav}{\headcommand {\slideentry {0}{0}{2}{2/2}{}{0}}} 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-------------------------------------------- +\frame[plain]{\titlepage} +% ------------------------------------------------------------------------------ +% --------------------------- SLIDE -------------------------------------------- +\begin{frame} + \frametitle{Introduction} +\end{frame} +% ------------------------------------------------------------------------------ +\end{document} diff --git a/Inflaton/Full_dst_numbers/tmp/example/example.toc b/Inflaton/Full_dst_numbers/tmp/example/example.toc new file mode 100644 index 0000000..495658f --- /dev/null +++ b/Inflaton/Full_dst_numbers/tmp/example/example.toc @@ -0,0 +1,2 @@ +\beamer@endinputifotherversion {3.10pt} +\select@language {english} diff --git a/Inflaton/Full_dst_numbers/tmp/example/sybila-logo-paper-shaded.png b/Inflaton/Full_dst_numbers/tmp/example/sybila-logo-paper-shaded.png new file mode 100644 index 0000000..f2a2c4e --- /dev/null +++ b/Inflaton/Full_dst_numbers/tmp/example/sybila-logo-paper-shaded.png Binary files 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0000000..670c6a6 --- /dev/null +++ b/Inflaton/Full_dst_numbers/tmp/theme/sybila-logo-slide-title-shaded.pdf Binary files differ diff --git a/Kstmumu/Face2Face_meeting/MMatrix/MMatrix.log b/Kstmumu/Face2Face_meeting/MMatrix/MMatrix.log index 7e9c798..11c0665 100644 --- a/Kstmumu/Face2Face_meeting/MMatrix/MMatrix.log +++ b/Kstmumu/Face2Face_meeting/MMatrix/MMatrix.log @@ -1,4 +1,4 @@ -This is pdfTeX, Version 3.1415926-1.40.10 (TeX Live 2009/Debian) (format=pdflatex 2014.3.24) 25 MAY 2014 01:00 +This is pdfTeX, Version 3.1415926-1.40.10 (TeX Live 2009/Debian) (format=pdflatex 2014.3.24) 24 JUN 2014 17:02 entering extended mode %&-line parsing enabled. **MMatrix.tex @@ -1591,7 +1591,7 @@ Here is how much of TeX's memory you used: 17754 strings out of 493848 307824 string characters out of 1152823 - 404048 words of memory out of 3000000 + 404049 words of memory out of 3000000 20451 multiletter control sequences out of 15000+50000 42311 words of font info for 124 fonts, out of 3000000 for 9000 714 hyphenation exceptions out of 8191 @@ -1614,7 +1614,7 @@ sy10.pfb> -Output written on MMatrix.pdf (23 pages, 545221 bytes). +Output written on MMatrix.pdf (23 pages, 545317 bytes). PDF statistics: 277 PDF objects out of 1000 (max. 8388607) 48 named destinations out of 1000 (max. 500000) diff --git a/Kstmumu/Face2Face_meeting/MMatrix/MMatrix.pdf b/Kstmumu/Face2Face_meeting/MMatrix/MMatrix.pdf index dd08b0e..5cb9b8a 100644 --- a/Kstmumu/Face2Face_meeting/MMatrix/MMatrix.pdf +++ b/Kstmumu/Face2Face_meeting/MMatrix/MMatrix.pdf Binary files differ diff --git a/Kstmumu/Face2Face_meeting/MMatrix/MMatrix.synctex.gz b/Kstmumu/Face2Face_meeting/MMatrix/MMatrix.synctex.gz index 677803d..7b5f21e 100644 --- a/Kstmumu/Face2Face_meeting/MMatrix/MMatrix.synctex.gz +++ b/Kstmumu/Face2Face_meeting/MMatrix/MMatrix.synctex.gz Binary files differ diff --git a/Kstmumu/Face2Face_meeting/MMatrix/beamerthemeSybila.sty b/Kstmumu/Face2Face_meeting/MMatrix/beamerthemeSybila.sty index 934906c..0d037e7 100644 --- a/Kstmumu/Face2Face_meeting/MMatrix/beamerthemeSybila.sty +++ b/Kstmumu/Face2Face_meeting/MMatrix/beamerthemeSybila.sty @@ -7,7 +7,7 @@ \useoutertheme{split} \useinnertheme{rounded} \usefonttheme{structurebold} -%\useoutertheme{shadow} +\useoutertheme{shadow} %------------------------------------------------------------------------------- % Templates @@ -35,7 +35,7 @@ \fi% \end{beamercolorbox}% - \vskip1em + \vskip1emdefbeamertemplate \begin{beamercolorbox}[sep=8pt,center,#1]{author} \usebeamerfont{author}\insertauthor @@ -79,7 +79,7 @@ \setbeamercolor{frametitle}{bg=white!45!black} \setbeamercolor{footline}{bg=black,fg=white} \setbeamercolor{author in head/foot}{bg=black,fg=white} -\setbeamercolor{title in head/foot}{bg=white!45!black} +\setbeamercolor{title in head/foot \insertframenumber\,/\,\inserttotalframenumber}\insertframenumber\,/\,\inserttotalframenumber{bg=white!45!black} \setbeamercolor{block title}{bg=white!45!black} \setbeamercolor{block title example}{bg=white!45!black} \setbeamercolor{block title alerted}{bg=white!15!black} @@ -105,7 +105,7 @@ \titlegraphic{ \includegraphics[width=3.0cm]{images/uzh.jpg}\hspace*{0.3cm} -\includegraphics[height=0.9cm,keepaspectratio]{images/ifj.png}% +\includegraphics[height=0.9cm,keepaspectratio]{images/if2j.png}% } diff --git a/Kstmumu/Face2Face_meeting/MMatrix/texput.log b/Kstmumu/Face2Face_meeting/MMatrix/texput.log index 917e405..c60dc5b 100644 --- a/Kstmumu/Face2Face_meeting/MMatrix/texput.log +++ b/Kstmumu/Face2Face_meeting/MMatrix/texput.log @@ -1,4 +1,4 @@ -This is pdfTeX, Version 3.1415926-1.40.10 (TeX Live 2009/Debian) (format=pdflatex 2014.3.24) 23 MAY 2014 15:20 +This is pdfTeX, Version 3.1415926-1.40.10 (TeX Live 2009/Debian) (format=pdflatex 2014.3.24) 24 JUN 2014 18:11 entering extended mode %&-line parsing enabled. **beamerthemeSybila.tex diff --git a/Kstmumu/Face2Face_meeting/Method_of_moments/MM_v2.log b/Kstmumu/Face2Face_meeting/Method_of_moments/MM_v2.log index 949e066..d6f2697 100644 --- a/Kstmumu/Face2Face_meeting/Method_of_moments/MM_v2.log +++ b/Kstmumu/Face2Face_meeting/Method_of_moments/MM_v2.log @@ -1,4 +1,4 @@ -This is pdfTeX, Version 3.1415926-1.40.10 (TeX Live 2009/Debian) (format=pdflatex 2014.3.24) 23 MAY 2014 21:38 +This is pdfTeX, Version 3.1415926-1.40.10 (TeX Live 2009/Debian) (format=pdflatex 2014.3.24) 25 MAY 2014 20:15 entering extended mode %&-line parsing enabled. **MM_v2.tex @@ -1636,23 +1636,42 @@ LaTeX Font Info: Font shape `OT4/cmss/m/it' in size <9> not available (Font) Font shape `OT4/cmss/m/sl' tried instead on input line 136. + +Overfull \hbox (10.85661pt too wide) detected at line 136 +[][][] \OT4/cmss/m/sl/9 d [] \OML/plm/m/it/9 ^^R[] [][] \OT4/cmss/m/sl/9 d [] \ +OML/plm/m/it/9 ^^R[] [][] \OT4/cmss/m/sl/9 d\OML/plm/m/it/9 ^^^\OT4/cmss/m/sl/9 + PDF\OT1/cmss/m/n/9 ([] \OML/plm/m/it/9 ^^R[]; [] ^^R[]; ^^^\OT1/cmss/m/n/9 ) [ +][] \OML/plm/m/it/9 ^^R[] [] \OT4/cmss/m/n/9 2\OML/plm/m/it/9 ^^R[] \OT1/cmss/m +/n/9 = \OMS/plsy/m/n/9 ^^@[]\OT1/cmss/m/n/9 (\OT4/cmss/m/n/9 2 \OT1/cmss/m/n/9 ++ \OT4/cmss/m/sl/9 F[]\OT1/cmss/m/n/9 ) + [] + + +Overfull \hbox (13.73155pt too wide) detected at line 136 +[][][] \OT4/cmss/m/sl/9 d [] \OML/plm/m/it/9 ^^R[] [][] \OT4/cmss/m/sl/9 d [] \ +OML/plm/m/it/9 ^^R[] [][] \OT4/cmss/m/sl/9 d\OML/plm/m/it/9 ^^^\OT4/cmss/m/sl/9 + PDF\OT1/cmss/m/n/9 ([] \OML/plm/m/it/9 ^^R[]; [] ^^R[]; ^^^\OT1/cmss/m/n/9 ) [ +][] \OML/plm/m/it/9 ^^R[] [] \OT4/cmss/m/n/9 2\OML/plm/m/it/9 ^^R[] \OT1/cmss/m +/n/9 = \OMS/plsy/m/n/9 ^^@[]\OT1/cmss/m/n/9 (\OT4/cmss/m/n/9 1 \OT1/cmss/m/n/9 ++ \OT4/cmss/m/n/9 8\OT4/cmss/m/sl/9 F[]\OT1/cmss/m/n/9 ) + [] + File: images/uzh.jpg Graphic file (type jpg) - -File: images/ifj.png Graphic file (type png) - - [9 - -] -File: images/uzh.jpg Graphic file (type jpg) - -File: images/ifj.png Graphic file (type png) - [10 - -] -File: images/uzh.jpg Graphic file (type jpg) - File: images/ifj.png Graphic file (type png) + [9 + +] +File: images/uzh.jpg Graphic file (type jpg) + +File: images/ifj.png Graphic file (type png) + + [10 + +] +File: images/uzh.jpg Graphic file (type jpg) + +File: images/ifj.png Graphic file (type png) [11 ] @@ -2720,10 +2739,10 @@ (./MM_v2.aux) ) Here is how much of TeX's memory you used: - 18625 strings out of 493848 - 328284 string characters out of 1152823 - 387042 words of memory out of 3000000 - 21092 multiletter control sequences out of 15000+50000 + 18623 strings out of 493848 + 328266 string characters out of 1152823 + 386042 words of memory out of 3000000 + 21090 multiletter control sequences out of 15000+50000 48870 words of font info for 138 fonts, out of 3000000 for 9000 714 hyphenation exceptions out of 8191 49i,32n,60p,594b,630s stack positions out of 5000i,500n,10000p,200000b,50000s @@ -2749,7 +2768,7 @@ re/texmf-texlive/fonts/type1/public/pl/plsy7.pfb> -Output written on MM_v2.pdf (60 pages, 2740984 bytes). +Output written on MM_v2.pdf (60 pages, 2741039 bytes). PDF statistics: 695 PDF objects out of 1000 (max. 8388607) 125 named destinations out of 1000 (max. 500000) diff --git a/Kstmumu/Face2Face_meeting/Method_of_moments/MM_v2.pdf b/Kstmumu/Face2Face_meeting/Method_of_moments/MM_v2.pdf index 72bffb0..fa19ca9 100644 --- a/Kstmumu/Face2Face_meeting/Method_of_moments/MM_v2.pdf +++ b/Kstmumu/Face2Face_meeting/Method_of_moments/MM_v2.pdf Binary files differ diff --git a/Kstmumu/Face2Face_meeting/Method_of_moments/MM_v2.synctex.gz b/Kstmumu/Face2Face_meeting/Method_of_moments/MM_v2.synctex.gz index 3f02cb6..5f8b5db 100644 --- a/Kstmumu/Face2Face_meeting/Method_of_moments/MM_v2.synctex.gz +++ b/Kstmumu/Face2Face_meeting/Method_of_moments/MM_v2.synctex.gz Binary files differ diff --git a/Kstmumu/Face2Face_meeting/Method_of_moments/MM_v2.tex b/Kstmumu/Face2Face_meeting/Method_of_moments/MM_v2.tex index d58eb23..fe0c620 100644 --- a/Kstmumu/Face2Face_meeting/Method_of_moments/MM_v2.tex +++ b/Kstmumu/Face2Face_meeting/Method_of_moments/MM_v2.tex @@ -126,10 +126,10 @@ \int_{-1}^{1}d\cos \theta_l \int_{-1}^{1}d\cos \theta_k \int_{-\pi}^{\pi}d\phi PDF(\cos \theta_k ,\cos \theta_l, \phi) \cos^2 \theta_k =\frac{1}{5} (2F_l+1) \end{equation} \begin{equation} -\int_{-1}^{1}d\cos \theta_l \int_{-1}^{1}d\cos \theta_k \int_{-\pi}^{\pi}d\phi PDF(\cos \theta_k ,\cos \theta_l, \phi) \cos^2 \theta_k =-\dfrac{2}{25}(2 + F_l) +\int_{-1}^{1}d\cos \theta_l \int_{-1}^{1}d\cos \theta_k \int_{-\pi}^{\pi}d\phi PDF(\cos \theta_k ,\cos \theta_l, \phi) \cos^2 \theta_k \cos 2\theta_l =-\dfrac{2}{25}(2 + F_l) \end{equation} \begin{equation} -\int_{-1}^{1}d\cos \theta_l \int_{-1}^{1}d\cos \theta_k \int_{-\pi}^{\pi}d\phi PDF(\cos \theta_k ,\cos \theta_l, \phi) \sin^2 \theta_k =-\dfrac{1}{25}(1+8F_l) +\int_{-1}^{1}d\cos \theta_l \int_{-1}^{1}d\cos \theta_k \int_{-\pi}^{\pi}d\phi PDF(\cos \theta_k ,\cos \theta_l, \phi) \sin^2 \theta_k \cos 2\theta_l=-\dfrac{1}{25}(1+8F_l) \end{equation} \end{footnotesize} @@ -362,7 +362,7 @@ \dfrac{d^3\Gamma}{\Gamma dcos\theta_k dcos\theta_l d\phi} sin \theta_k sin 2 \theta_l sin \phi = \dfrac{4 I_7 }{9} \end{equation} \begin{equation} - \dfrac{d^3\Gamma}{\Gamma dcos\theta_k dcos\theta_l d\phi} sin \theta_k sin2 \theta_l sin \phi = \dfrac{16 S_8 }{45} + \dfrac{d^3\Gamma}{\Gamma dcos\theta_k dcos\theta_l d\phi} sin \theta_k sin2 \theta_l sin \phi = \dfrac{16 I_8 }{45} \end{equation} @@ -382,8 +382,8 @@ \end{itemize} What comes in the next talks(stay tuned): \begin{itemize} +\item Sensitivity will be given tmr. \item This method reduces the error on unfolding. -\item No problem with convergence. \item Systematics easy accessible. \end{itemize} diff --git a/Kstmumu/Face2Face_meeting/Systematics/Systematics.aux b/Kstmumu/Face2Face_meeting/Systematics/Systematics.aux index 75663a0..972daff 100644 --- a/Kstmumu/Face2Face_meeting/Systematics/Systematics.aux +++ b/Kstmumu/Face2Face_meeting/Systematics/Systematics.aux @@ -67,8 +67,10 @@ \@writefile{nav}{\headcommand {\beamer@framepages {22}{22}}} \@writefile{nav}{\headcommand {\slideentry {1}{0}{23}{23/23}{}{0}}} \@writefile{nav}{\headcommand {\beamer@framepages {23}{23}}} -\@writefile{nav}{\headcommand {\beamer@partpages {1}{23}}} -\@writefile{nav}{\headcommand {\beamer@subsectionpages {4}{23}}} -\@writefile{nav}{\headcommand {\beamer@sectionpages {4}{23}}} -\@writefile{nav}{\headcommand {\beamer@documentpages {23}}} -\@writefile{nav}{\headcommand {\def \inserttotalframenumber {23}}} +\@writefile{nav}{\headcommand {\slideentry {1}{0}{24}{24/24}{}{0}}} +\@writefile{nav}{\headcommand {\beamer@framepages {24}{24}}} +\@writefile{nav}{\headcommand {\beamer@partpages {1}{24}}} +\@writefile{nav}{\headcommand {\beamer@subsectionpages {4}{24}}} +\@writefile{nav}{\headcommand {\beamer@sectionpages {4}{24}}} +\@writefile{nav}{\headcommand {\beamer@documentpages {24}}} +\@writefile{nav}{\headcommand {\def \inserttotalframenumber {24}}} diff --git a/Kstmumu/Face2Face_meeting/Systematics/Systematics.log b/Kstmumu/Face2Face_meeting/Systematics/Systematics.log index 2d70483..3d8f45d 100644 --- a/Kstmumu/Face2Face_meeting/Systematics/Systematics.log +++ b/Kstmumu/Face2Face_meeting/Systematics/Systematics.log @@ -1,4 +1,4 @@ -This is pdfTeX, Version 3.1415926-1.40.10 (TeX Live 2009/Debian) (format=pdflatex 2014.3.24) 25 MAY 2014 17:04 +This is pdfTeX, Version 3.1415926-1.40.10 (TeX Live 2009/Debian) (format=pdflatex 2014.3.24) 27 MAY 2014 14:36 entering extended mode %&-line parsing enabled. **Systematics.tex @@ -1357,16 +1357,16 @@ [2 <./diagram.png (PNG copy)>] - 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e69de29..0000000 --- a/Kstmumu/MMatrix2/MM.snm +++ /dev/null diff --git a/Kstmumu/MMatrix2/MM.synctex.gz b/Kstmumu/MMatrix2/MM.synctex.gz deleted file mode 100644 index 78b4daf..0000000 --- a/Kstmumu/MMatrix2/MM.synctex.gz +++ /dev/null Binary files differ diff --git a/Kstmumu/MMatrix2/MM.tex b/Kstmumu/MMatrix2/MM.tex deleted file mode 100644 index 2e9ab92..0000000 --- a/Kstmumu/MMatrix2/MM.tex +++ /dev/null @@ -1,1097 +0,0 @@ -\documentclass[]{beamer} -\setbeamertemplate{navigation symbols}{} -\usepackage{beamerthemesplit} -\useoutertheme{infolines} -\usecolortheme{dolphin} -%\usetheme{Warsaw} -\usetheme{progressbar} -\usecolortheme{progressbar} - -\usefonttheme{progressbar} -\useoutertheme{progressbar} -\useinnertheme{progressbar} -\usepackage{graphicx} -%\usepackage{amssymb,amsmath} -\usepackage[latin1]{inputenc} -\usepackage{amsmath} -\newcommand\abs[1]{\left|#1\right|} -\usepackage{iwona} -\usepackage{hepparticles} -\usepackage{hepnicenames} -\usepackage{hepunits} -\progressbaroptions{imagename=images/lhcb} -%\usetheme{Boadilla}f - -%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%5 -\definecolor{mygreen}{cmyk}{0.82,0.11,1,0.25} -\setbeamertemplate{blocks}[rounded][shadow=false] -\addtobeamertemplate{block begin}{\pgfsetfillopacity{0.8}}{\pgfsetfillopacity{1}} -\setbeamercolor{structure}{fg=mygreen} -\setbeamercolor*{block title example}{fg=mygreen!50, -bg= blue!10} -\setbeamercolor*{block body example}{fg= blue, -bg= blue!5} - - - - - -%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% -%\beamersetuncovermixins{\opaqueness<1>{25}}{\opaqueness<2->{15}} -\title{Method of moments for $\PB \to \PKstar \mu \mu$} -\author{\underline{Marcin Chrzaszcz}$^{1,2}$} -\date{\today} - -\begin{document} - -{ -\institute{$^1$ University of Zurich, $^2$ Institute of Nuclear Physics} -\setbeamertemplate{footline}{} -\begin{frame} -\logo{ -\vspace{2 mm} -\includegraphics[height=1cm,keepaspectratio]{images/uzh.jpg}~ -\includegraphics[width=1cm,keepaspectratio]{images/ifj.png}} - - \titlepage -\end{frame} -} -\institute{UZH,IFJ} - -\section[Outline]{} -\begin{frame} -\tableofcontents -\end{frame} - -\section{Introduction} -\begin{frame}\frametitle{Plan} -Why method of moments: -\begin{enumerate} -\item Complementary approach in performing the fit. -\item Allows to extract info measuring quantities in event basis depending on the angular distribution. -\item Used in $\PB \to \rho \Plepton \nu$(SLAC-386 UC-414),\\ $\PJpsi \to \PK \PK \gamma$(PRD 71, 032005 (2005) ), etc. -\end{enumerate} - - -\end{frame} -\section{Method of Moments - Theory} -\begin{frame}\frametitle{Method of moments} -{~} -Let's assume we have our pdf with $k$ unknown parameters :$PDF(x_i, \alpha)$, $dim(\alpha)=k$. One can calculate $k$ moments, which are the functions of $\alpha_i$: -\begin{equation} -\mu_i=f(\alpha_1,..., \alpha_k) = E[W_i] -\end{equation} -If we have $n$ events in our $q^2$ bin, we can estimate: -\begin{equation} -\widehat{\mu}_i=\dfrac{1}{n}\sum_{j=0}^{j=n-1} w_j -\end{equation} -, where $w_j=g(x_i)$ - -\end{frame} - -\begin{frame}\frametitle{Trivial example} -{~} -Lets see how this works in practice: -\begin{equation} -f(x)=\dfrac{x^{a-1}e^{-x/b}} {b^a \Gamma(a)} -\end{equation} -we measure the moments:\\ -\begin{center} $m_1=\dfrac{X_1+X_2+...+X_n}{n}$,\\ $m_2=\dfrac{X_1^2+X_2^2+...+X_n^2}{n}$.\\\end{center} -and calculate them analytically: -\begin{center} $m_1=ab$, $m_2=b^2a(a+1)$\end{center} -So one just needs to solve this and get the answer: -\center $a=\dfrac{m_1^2}{m_2-m_1^2}$, $b=\dfrac{m_2-m_1^2}{m_1}$ -\end{frame} - -\section{Moments of Ss} - - -\begin{frame}\frametitle{Our PDF} -{~} -The angular terms: -\begin{multline} -\dfrac{d^4\Gamma}{dq^2 dcos\theta_k dcos\theta_l d\phi}=\dfrac{9}{32\pi}( \dfrac{3}{4}(1-F_l)\sin^2 \theta_k + F_l \cos^2 \theta_k + (\dfrac{1}{4}(1-F_l)\sin^2 \theta_k \\ -F_l\cos^2) \cos 2\theta_l + J_3 \sin^2 \theta_k \sin^2 \theta_l cos2\phi + J_4 \sin2 \theta_k \sin \theta_l \cos\phi +\\ J_5 \sin 2 \theta_k \sin \theta_l \cos \phi + (J_{6s} \sin^2 \theta_k + J_{6c} \cos^2 \theta_k) \cos \theta_l + \\ J_7 \sin 2\theta_k \sin \theta_l \sin \phi + J_8 \sin 2 \theta_k \sin 2 \theta_l \sin \phi + J_9 \sin^2 \theta_k \sin^2 \theta_l \sin 2 \phi) -\end{multline} -Since we are fitting a PDF we need to ensure it is normalized: -\begin{equation} -\int_{-\pi}^{\pi} d\phi \int_{-1}^{1} d cos\theta_l \int_{-1}^{1} d cos\theta_k \dfrac{d^4\Gamma}{dq^2 dcos\theta_k dcos\theta_l d\phi}=1 -\end{equation} - - -\end{frame} -\begin{frame}\frametitle{Measuring Js} -{~} -From equation 2 we have the following: - -\begin{equation} -\dfrac{1}{4}(3 J_{1c} + 6 J_{1s} - J_{2c} - 2 J_{2s}) =1 -\end{equation} -For now we will consider the following PDF: -\begin{equation} - \dfrac{d^3\Gamma}{\Gamma dcos\theta_k dcos\theta_l d\phi }(cos\theta_k , cos\theta_l, \phi) -\end{equation} - -Becouse our PDF is not normalized and we are measuring $\Gamma+\overline{\Gamma} -$ we are effectively fitting the $S_i$ (aka $J_i \to S_i$) -\end{frame} - - -\begin{frame}\frametitle{Moments for $\PB \to \PKstar \mu \mu$} -{~} -Let's calculate the moments for Ss: -\begin{equation} - \dfrac{d^3\Gamma}{\Gamma dcos\theta_k dcos\theta_l d\phi }sin^2 \theta_k sin^2 \theta_l cos 2 \phi= \dfrac{8 S_3 }{25} -\end{equation} -\begin{equation} - \dfrac{d^3\Gamma}{\Gamma dcos\theta_k dcos\theta_l d\phi } sin 2 \theta_k sin 2 \theta_k cos\phi= \dfrac{8 S_4 }{25} -\end{equation} -\begin{equation} - \dfrac{d^3\Gamma}{\Gamma dcos\theta_k dcos\theta_l d\phi }sin2\theta_k sin\theta_l cos\phi = \dfrac{2 S_5 }{5} -\end{equation} -\begin{equation} - \dfrac{d^3\Gamma}{\Gamma dcos\theta_k dcos\theta_l d\phi} sin 2 \theta_k sin \theta_l sin \phi = \dfrac{2 S_7 }{5} -\end{equation} -\begin{equation} - \dfrac{d^3\Gamma}{\Gamma dcos\theta_k dcos\theta_l d\phi} sin 2 \theta_k sin2 \theta_l sin \phi = \dfrac{8 S_8 }{25} -\end{equation} - - - -\end{frame} -\begin{frame}\frametitle{Moments for $\PB \to \PKstar \mu \mu$} -{~} -\begin{itemize} -\item The simplest solution one could imagine. -\item We are abusing the fact that the basis is orthogonal. -\item Each of the J doesn't know about other. -\item Only $S_{1s}$, $S_{2s}$, $S_{1c}$, $S_{2c}$ and $S_{6s}$, $S_{6c}$ are not orthogonal, but to get the answer you just need to solve a linear equation system so it's not a tragedy. -\end{itemize} -\begin{equation} - \dfrac{d^3\Gamma}{\Gamma dcos\theta_k dcos\theta_l d\phi} sin^2 \theta_k cos \theta_l = 0.1(S_6c+4S_6s) -\end{equation} -\begin{equation} - \dfrac{d^3\Gamma}{\Gamma dcos\theta_k dcos\theta_l d\phi} cos \theta_l = 0.25(S_{6}c+2S_{6s}) -\end{equation} - -solution: $S_{6c}=2 (4 M_{S_{6c}} - 5 M_{S_{6s}})$, $S_{6s}= -2 M_{S_{6c}} + 5 M_{S_{6s}}$ - - - -\end{frame} - - - -\section{Toy MC study} - -\begin{frame}\frametitle{Moments for $\PB \to \PKstar \mu \mu$} -{~} -Lets see if this method actually works. Let's take some random parameters for the PDF and make a toy. -\begin{columns} -\column{2.5in} -\includegraphics[scale=0.25]{images/J5.png} - - - -\column{2.5in} -\includegraphics[scale=0.25]{images/J7.png} - - -\end{columns} -\begin{itemize} -\item let's take 300 signal events as a working case. -\end{itemize} - -\end{frame} - - - - -\begin{frame}\frametitle{Moments for $\PB \to \PKstar \mu \mu$} -{~} -\small Lets see if this method actually works. Let's take some random parameters for the PDF and make a toy. -\begin{columns} -\column{2.5in} -\includegraphics[scale=0.25]{images/J3.png} - - - -\column{2.5in} -\includegraphics[scale=0.25]{images/J4.png} - - -\end{columns} - - -\begin{itemize} -\item let's take 300 signal events as a working case... we might still change the binning -\end{itemize} - -\end{frame} - - - -\begin{frame}\frametitle{Moments for $\PB \to \PKstar \mu \mu$} -{~} -Lets see if this method actually works. Let's take some random parameters for the PDF and make a toy. -\begin{columns} -\column{2.5in} -\includegraphics[scale=0.25]{images/J8.png} - - - -\column{2.5in} -\includegraphics[scale=0.25]{images/J9.png} - - -\end{columns} - -\begin{itemize} -\item let's take 300 signal events as a working case... we might still change the binning -\end{itemize} - -\end{frame} - -\begin{frame}\frametitle{Error Estimation} -{~} -\begin{itemize} -\item Since moment is the mean of a given distribution the error can be estimated as $mean/RMS$ -\item use TOY MC to check this assumption -\end{itemize} - -\includegraphics[scale=0.3]{plots/conw.png}\\ - - -\end{frame} -%%%%%%%%%%%%%%%%%%%%%%%%5 -\begin{frame}\frametitle{Correlation check} -{~} -\begin{itemize} -\item In theory $S_i$ shouldn't be correlated to $S_j$ in the moment calculation. -\item Lets put this to a test. -\end{itemize} - -\begin{columns} -\column{2.5in} -\includegraphics[scale=0.2]{plots/J9J4.png}\\ - - -\column{2.5in} -\includegraphics[scale=0.2]{plots/J8J5.png}\\ - - -\end{columns} - - -\end{frame} - - -%%%%%%%%%%%%%%%%%%%%%%%%5 -\begin{frame}\frametitle{Correlation check 2} -{~} -\begin{itemize} -\item Let's now FIX $J_x$ and simulate different $J_y$ -\item Again theory would suggest that one J shouldn't know about the other, so $J_x$ shouldn't change with scanning $J_y$ parameter -\end{itemize} - -\begin{columns} -\column{2.5in} -\includegraphics[scale=0.24]{plots/J5_vs_J9_300.png}\\ - - -\column{2.5in} -\includegraphics[scale=0.24]{plots/J3_vs_J9_300.png}\\ - - -\end{columns} - - -\end{frame} - - - -\section{2 am discovery} -\begin{frame}\frametitle{What will happen to our problem with an S-wave?} -{~} -Reminder: -\begin{multline} -\dfrac{d^4\Gamma}{dq^2 dcos\theta_k dcos\theta_l d\phi}=\dfrac{9}{32\pi}( J_{1s}sin^2 \theta_k + J_{1c}cos^2 \theta_k + (J_{2s}sin^2 \theta_k + \\ J_{2c}cos^2) cos 2\theta_l + J_3 sin^2 \theta_k sin^2 \theta_l cos2\phi + J_4 sin2 \theta_k sin \theta_l cos\phi +\\ J_5 sin2 \theta_k sin \theta_l cos \phi + (J_{6s} sin^2 \theta_k + J_{6c} cos^2 \theta_k) cos \theta_l + \\ J_7 sin 2\theta_k sin \theta_l sin \phi + J_8 sin 2 \theta_k sin 2 \theta_l sin phi + J_9 sin^2 \theta_k sin^2 \theta_l sin 2 \phi) -\end{multline} -Let's add a very discussing things that keeps us awake at night: -\begin{multline} -W_s =\dfrac{2}{3} F_s \sin^2 \theta_l + \frac{4}{3} A_s \sin^2 \theta_l \cos \theta_k + I_4 sin \theta_k sin 2 \theta_lcos \phi \\+ I_5 sin \theta_k sin \theta_l cos \phi + I_7 sin \theta_k sin \theta_l + sin \phi + I_8 sin \theta_k sin 2\theta_l sin\phi) -\end{multline} - - -\end{frame} - -\begin{frame}\frametitle{What will happen to our problem with an S-wave?} -{~} -So now our PDF is sum of eq. 15 and 16. Of coz we need to require normalization: -\begin{equation} -\dfrac{1}{12}(32 I_{1a} + 9 J_{1c} + 18 J_{1s} - 3 J_{2c} - 6 J_{2s}) =1 -\end{equation} -No surprises here. If we have a S-wave it has to enter in $\Gamma$. -To build up the preasure, what will happen to our Ss? - - - -\end{frame} - - -\begin{frame}\frametitle{NOTHING!!!!!!!!} -{~} -We are completely insensitive to S-wave: -\begin{equation} - \dfrac{d^3\Gamma}{\Gamma dcos\theta_k dcos\theta_l d\phi }sin^2 \theta_k sin^2 \theta_l cos 2 \phi= \dfrac{8 S_3 }{25} -\end{equation} -\begin{equation} - \dfrac{d^3\Gamma}{\Gamma dcos\theta_k dcos\theta_l d\phi } sin 2 \theta_k sin 2 \theta_k cos\phi= \dfrac{8 S_4 }{25} -\end{equation} -\begin{equation} - \dfrac{d^3\Gamma}{\Gamma dcos\theta_k dcos\theta_l d\phi }sin2\theta_k sin\theta_l cos\phi = \dfrac{2 S_5 }{5} -\end{equation} -\begin{equation} - \dfrac{d^3\Gamma}{\Gamma dcos\theta_k dcos\theta_l d\phi} sin 2 \theta_k sin \theta_l sin \phi = \dfrac{2 S_7 }{5} -\end{equation} -\begin{equation} - \dfrac{d^3\Gamma}{\Gamma dcos\theta_k dcos\theta_l d\phi} sin 2 \theta_k sin2 \theta_l sin \phi = \dfrac{8 S_8 }{25} -\end{equation} - - - -\end{frame} - -\begin{frame}\frametitle{Thins get better :)} -{~} -We can even measure directly the S-wave: -\begin{equation} - \dfrac{d^3\Gamma}{\Gamma dcos\theta_k dcos\theta_l d\phi }sin^2 \theta_l cos \theta_k = \dfrac{32 I_{1b} }{45} -\end{equation} -\begin{equation} - \dfrac{d^3\Gamma}{\Gamma dcos\theta_k dcos\theta_l d\phi } sin \theta_k sin 2 \theta_l cos \phi = \dfrac{16 I_4 }{45} -\end{equation} -\begin{equation} - \dfrac{d^3\Gamma}{\Gamma dcos\theta_k dcos\theta_l d\phi } sin\theta_k sin\theta_l cos\phi = \dfrac{4 I_5 }{9} -\end{equation} -\begin{equation} - \dfrac{d^3\Gamma}{\Gamma dcos\theta_k dcos\theta_l d\phi} sin \theta_k sin 2 \theta_l sin \phi = \dfrac{4 I_7 }{9} -\end{equation} -\begin{equation} - \dfrac{d^3\Gamma}{\Gamma dcos\theta_k dcos\theta_l d\phi} sin \theta_k sin2 \theta_l sin \phi = \dfrac{16 S_8 }{45} -\end{equation} - - - -\end{frame} - - -\begin{frame}\frametitle{Conclusions on S-wave} -{~} -\begin{itemize} -\item S-wave components are transparent to method of moments. -\item If they are orthogonal to others all they toy studies holds for them as well(will reapat for robustness but can bet my house that there is nothing going on there). -\item -\end{itemize} - -\end{frame} - - - -\begin{frame}\frametitle{Conclusions} -{~} -\begin{itemize} -\item Implemented moments method for the K*mm and start testing with toy MC -\item The method converge fast and works for the "simple case", i.e. signal only. -\item Method completely insensitive to S-wave component, thanks to orthogonality. -\item Complementary one can measure in-depended S-wave component. -\end{itemize} -TO DO: -\begin{itemize} -\item add realism: backgrounds -\item Do the unfolding -\item Study binning -\end{itemize} - -\end{frame} -%%%%%%%%%%%%%%%%%%%%%%%%%55 -\begin{frame}\frametitle{~} -{~} -\center \Huge BACKUPS - -\end{frame} - -\begin{frame} -{~} - -\begin{columns} -\column{2.5in} -\includegraphics[scale=0.17]{plots/pool_plots/J1c_50.png}\\ -\includegraphics[scale=0.17]{plots/pool_plots/J1c_75.png}\\ - - -\column{2.5in} -\includegraphics[scale=0.17]{plots/pool_plots/J1c_50E.png}\\ -\includegraphics[scale=0.17]{plots/pool_plots/J1c_75E.png} - - -\end{columns} -\end{frame} - -\begin{frame} -{~} - 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-\setbeamertemplate{footline}{\insertframenumber/\inserttotalframenumber} -%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%5 -\definecolor{mygreen}{cmyk}{0.82,0.11,1,0.25} - - -\usetheme{Sybila} - -\title[Unfolding for counting experiments]{Unfolding for counting experiments} -\author{Marcin Chrz\k{a}szcz$^{1,2}$, Nicola Serra$^{1}$} -\institute{$^1$~University of Zurich,\\ $^2$~Institute of Nuclear Physics, Krakow} -\date{\today} -\begin{document} -% --------------------------- SLIDE -------------------------------------------- -\frame[plain]{\titlepage} -\author{Marcin Chrz\k{a}szcz} -% ------------------------------------------------------------------------------ -% --------------------------- SLIDE -------------------------------------------- - -\institute{~(UZH, IFJ)} - -\section{Introduction} - - -\begin{frame}\frametitle{Reminder 1 - Constructing Matrix unfolding} -\begin{itemize} -\item We don't know explicate -\end{itemize} -\small{ -\begin{equation} -\epsilon(\cos \theta_k, \cos \theta_l,\phi) -\end{equation} -} -\begin{itemize} -\item We don't need to know it, we just need to calculate matrix elements -\item Let's use PHSP MC. -\item Moments for PHSP MC are:\\ -$v^{T}_{gen}=(2/3 ,0,0,0,0,0,0,0)$ -\item After reconstruction we get(full $q^2$ range): -$v^{T}_{rec}=( 0.7069,0.0077,-0.00236466,0.0005,0.0007,0.0011,0.0011,-0.0012)$ -\end{itemize} - - - -\end{frame} - -\begin{frame}\frametitle{Reminder 2 - Constructing Matrix unfolding} -\begin{itemize} -\item We got first column of the unfolding matrix $(\dfrac{3}{2} v_{gen})$. -\end{itemize} -\small{ -$ \begin{pmatrix} - 1.06 & \cdots & a_{1,8} \\ - 0.01157 & \cdots & a_{2,8} \\ - -0.003547 & \ddots & \vdots \\ - 0.0007841 & \ddots & \vdots \\ - 0.001126 & \ddots & \vdots \\ - 0.001766 & \ddots & \vdots \\ - 0.001664 & \ddots & \vdots \\ - -0.001937 & \cdots & a_{8,8} - \end{pmatrix}$ - - -} -\begin{itemize} -\item How about the others? -\item We can reweight accordingly to $f_x$. -\end{itemize} - -\end{frame} - - - -\begin{frame}\frametitle{Reminder 3 - Constructing Matrix unfolding} -\begin{itemize} -\item To get $S_3$ each event $i^{th}$ has has weight $f_{S_3}(\cos \theta_{k_i},\cos \theta_{l_i},\phi_i) $ -\item One can calculate on MC the reweighed moments in PHPS: -\end{itemize} -\begin{equation} -\int PDF*f_{S_3}=\dfrac{32}{225} -\end{equation} -\begin{itemize} -\item Our base vector now is:$v^{T}_{gen}=(0 ,\frac{32}{225},0,0,0,0,0,0)$ -\item So lets see what do we get as reconstructed vector(after multiplying by $\frac{225}{32}$. -\small{$v^{T}_{rec}=( 0.042, 1.105,-0.005,0.003,-0.0023,-0.005,-0.005,-0.006)$ } -\item Please notice that weights are negative, but this is not a problem for the mean. -\item Also we are avoiding the negative PDF problem :) -\end{itemize} - -\end{frame} - - - -\begin{frame}\frametitle{Reminder 4 - Constructing Matrix unfolding} -\begin{itemize} -\item Now the matrix looks like: -\end{itemize} -\small{ -$ \begin{pmatrix} - 1.06 & 0.042 & \cdots & a_{1,8} \\ - 0.01157 & 1.105 & \cdots & a_{2,8} \\ - -0.003547 & -0.005 & \ddots & \vdots \\ - 0.0007841 &-0.005 & \ddots & \vdots \\ - 0.001126 & 0.003 &\ddots & \vdots \\ - 0.001766 & -0.0023 &\ddots & \vdots \\ - 0.001664 & -0.005 &\ddots & \vdots \\ - -0.001937 & -0.006 &\cdots & a_{8,8} - \end{pmatrix}$ - - -} -\begin{itemize} -\item The others go in the same way. -\item Repenting this exercise from $1^{st}$ year algebra we can get the full matrix -\end{itemize} - - -\end{frame} - - - -\begin{frame}\frametitle{Reminder 5} -For now: -\begin{itemize} -\item We have proven that there has to exists unfolding matrix. -\item Shown how to construct transformation matrix: $Gen \to Reco$. -\item Inverting it we can have transformation matrix of $Reco \to Gen$. -\item For details: \href{https://indico.cern.ch/event/316905/session/1/contribution/18/material/slides/0.pdf}{LINK} - -\end{itemize} - -What is missing? -\begin{columns} -\column{1in} -\begin{enumerate} -\item ERROR! -\end{enumerate} -\column{4in} -\includegraphics[width=0.8\textwidth]{err.jpg}\\ -\end{columns} - -\end{frame} - - - - - - -\begin{frame}\frametitle{How to?} -\begin{itemize} -\item So lets say that transformation matrix:$Gen \to Reco$ is $\epsilon_{i,j}$. -\item Each element has an error:$\delta \epsilon_{i,j}$. -\item Then we can calculate the matrix: $\epsilon_{i,j}^{-1}$(assuming it exists). -\item The million dollar question is what is the error on inverted matrix? -\end{itemize} - -\end{frame} - - - -\begin{frame}\frametitle{Answer to 1M dolar quesion} -\only<1>{ -\begin{itemize} -\item One can toy it. -\item But toying is good for kids and Frequentist. -\end{itemize} - -} -\only<2>{ - -\begin{itemize} -\item One can toy it. -\item But toying is good for kids and Frequentist. -\end{itemize} - -\begin{itemize} -\item Solution comes from $\tau$ physics :) \href{http://arxiv.org/abs/hep-ex/9909031}{hep-ex/9909031} -\end{itemize} -\begin{itemize} -\item One can derive(prove in the paper) the general equation: -\end{itemize} -\begin{equation} -\delta \epsilon^{-1}_{\alpha ~ \beta}= [\epsilon^{-1}]^2_{\alpha i}[\delta \epsilon ]^2_{ij} [\epsilon^{-1}]^2_{j \beta} -\end{equation} -} - - -\end{frame} - - - -\begin{frame}\frametitle{Matrix, $0.1-0.98~GeV$} -\tiny{ -$ A_{reco\rightarrow gen}=\begin{pmatrix} -0.9503 & -0.0003394 & -0.01202 & -0.003648 & 0.02225 & -0.04174 & -0.02515 & 0.002239 \\ --0.0009524 & 0.8219 & 0.00187 & 0.003567 & 0.002677 & 0.02974 & 0.006871 & 0.01478\\ --0.008739 & 0.002372 & 1.031 & 0.008389 & -0.001613 & 0.00138 & 0.02255 & 9.205e-05 \\ --0.001247 & 0.003686 & 0.0106 & 0.9235 & -0.004257 & -0.001611 & 0.00106 & -0.004336 \\ -0.008308 & 0.003482 & 0.0003312 & -0.005127 & 1.185 & -0.01059 & -0.01158 & 0.002114\\ --0.01522 & 0.03697 & 0.002679 & -0.002175 & -0.01001 & 0.9441 & 0.02969 & -0.008816 \\ --0.00842 & 0.007239 & 0.02186 & 0.001552 & -0.009282 & 0.02371 & 1.067 & -0.006338 \\ -0.0001436 & 0.01337 & 0.0004291 & -0.00291 & 0.002099 & -0.006733 & -0.006519 & 0.8188 - - - \end{pmatrix}$ -} -{~}\\{~}\\{~}\\ -\tiny{ -$ \delta A_{reco\rightarrow gen}=\begin{pmatrix} -0.005272 & 0.01937 & 0.03246 & 0.02156 & 0.02205 & 0.02222 & 0.03369 & 0.01913 \\ -0.006689 & 0.04713 & 0.03204 & 0.02452 & 0.03633 & 0.02548 & 0.0338 & 0.03364 \\ -0.007514 & 0.03227 & 0.07738 & 0.04294 & 0.04653 & 0.03088 & 0.05652 & 0.03184 \\ -0.007932 & 0.0389 & 0.06793 & 0.04878 & 0.03828 & 0.03536 & 0.04956 & 0.0388 \\ -0.008985 & 0.04197 & 0.06272 & 0.0327 & 0.07225 & 0.03349 & 0.06521 & 0.04161 \\ -0.008064 & 0.03943 & 0.04825 & 0.03506 & 0.0386 & 0.0507 & 0.07108 & 0.03956 \\ -0.00767 & 0.0327 & 0.05558 & 0.03081 & 0.04743 & 0.04477 & 0.08193 & 0.03241 \\ -0.006676 & 0.0336 & 0.03765 & 0.0293 & 0.03582 & 0.03014 & 0.0391 & 0.04682 - - - \end{pmatrix}$ -} - - - -\end{frame} - -\begin{frame}\frametitle{Matrix, $1.1-2~GeV$} -\tiny{ -$ A_{reco\rightarrow gen}=\begin{pmatrix} - 0.9519 & -0.02665 & -0.01432 & 0.002356 & 0.02539 & 0.009878 & -0.01551 & -0.01874 \\ --0.006272 & 0.8122 & -0.00351 & -0.00719 & 0.003585 & 6.784e-05 & 0.02445 & 0.008515 \\ --0.005315 & -0.003716 & 1.048 & 0.01242 & 0.01209 & -0.01478 & -0.001956 & 0.01429 \\ -0.003237 & -0.007177 & 0.01533 & 0.9184 & -0.007548 & -0.0009818 & -0.01874 & 0.009407 \\ -0.01002 & 0.004084 & 0.01391 & -0.006509 & 1.194 & -0.006516 & 0.001536 & -0.02882 \\ -0.002695 & -0.001042 & -0.01721 & -0.001842 & -0.005643 & 0.9264 & 0.02106 & 0.006755 \\ --0.004736 & 0.02346 & -0.002335 & -0.01446 & 0.001169 & 0.01697 & 1.072 & -0.003191 \\ --0.004157 & 0.007576 & 0.01377 & 0.008058 & -0.02219 & 0.005354 & -0.0008608 & 0.8304 - - - \end{pmatrix}$ -} -{~}\\{~}\\{~}\\ -\tiny{ -$ \delta A_{reco\rightarrow gen}=\begin{pmatrix} -0.005202 & 0.01911 & 0.03258 & 0.02103 & 0.02252 & 0.02145 & 0.03366 & 0.01948 \\ -0.006648 & 0.04654 & 0.03227 & 0.02451 & 0.03602 & 0.02464 & 0.03298 & 0.03397 \\ -0.007557 & 0.03197 & 0.07845 & 0.04272 & 0.04744 & 0.03057 & 0.05698 & 0.03287 \\ -0.007902 & 0.03885 & 0.0678 & 0.04839 & 0.0384 & 0.03464 & 0.04925 & 0.03989 \\ -0.009015 & 0.04122 & 0.06374 & 0.03254 & 0.07349 & 0.03269 & 0.0649 & 0.04202 \\ -0.007939 & 0.0389 & 0.04793 & 0.03433 & 0.03828 & 0.04937 & 0.06985 & 0.04023 \\ -0.007651 & 0.03234 & 0.05611 & 0.03062 & 0.04776 & 0.04388 & 0.08157 & 0.03342 \\ -0.006719 & 0.03345 & 0.03868 & 0.02953 & 0.03633 & 0.03002 & 0.03989 & 0.04827 - - - - \end{pmatrix}$ -} - - - -\end{frame} - -\begin{frame}\frametitle{Matrix, $2-3~GeV$} -\tiny{ -$ A_{reco\rightarrow gen}=\begin{pmatrix} -0.9453 & 0.04 & 0.00177 & -0.03031 & 0.04764 & 0.0151 & -0.01258 & -0.04106 \\ -0.01028 & 0.8527 & -5.812e-05 & -0.0136 & 0.005076 & -0.000505 & 0.01096 & 0.006403 \\ --0.0001227 & 0.001005 & 1.093 & -0.001136 & -0.005139 & 0.02279 & -0.01434 & 0.008034 \\ --0.01341 & -0.01719 & -0.001032 & 0.9839 & -0.0002435 & -0.00289 & 0.02836 & 0.01162 \\ -0.01327 & 0.007413 & -0.005841 & 0.0007396 & 1.061 & -0.00545 & 0.01544 & 0.004198 \\ -0.00528 & -0.0006148 & 0.0305 & -0.004015 & -0.00688 & 0.952 & 0.01271 & -0.01459 \\ --0.006055 & 0.01113 & -0.0148 & 0.02406 & 0.01406 & 0.01007 & 1.045 & -0.002972 \\ --0.009041 & 0.004813 & 0.00788 & 0.00857 & 0.004315 & -0.01074 & -0.003336 & 0.8538 - - \end{pmatrix}$ -} -{~}\\{~}\\{~}\\ -\tiny{ -$ \delta A_{reco\rightarrow gen}=\begin{pmatrix} -004924 & 0.01926 & 0.03256 & 0.0219 & 0.01872 & 0.02106 & 0.03102 & 0.01924 \\ -006515 & 0.04928 & 0.03368 & 0.02672 & 0.03054 & 0.02542 & 0.03166 & 0.03499 \\ -007373 & 0.03367 & 0.08093 & 0.04581 & 0.04074 & 0.03073 & 0.05367 & 0.03345 \\ -007823 & 0.04156 & 0.07072 & 0.05291 & 0.03305 & 0.03571 & 0.04708 & 0.04186 \\ -008104 & 0.03815 & 0.05952 & 0.03127 & 0.05851 & 0.03006 & 0.05651 & 0.03821 \\ -007692 & 0.04103 & 0.04888 & 0.03655 & 0.03267 & 0.04975 & 0.06635 & 0.04107 \\ -007215 & 0.03316 & 0.0552 & 0.03129 & 0.03971 & 0.04303 & 0.07527 & 0.03281 \\ -006517 & 0.03465 & 0.03922 & 0.03152 & 0.03039 & 0.03023 & 0.03738 & 0.04986 - - - \end{pmatrix}$ -} - - - -\end{frame} - - -\begin{frame}\frametitle{Matrix, $3-4~GeV$} -\tiny{ -$ A_{reco\rightarrow gen}=\begin{pmatrix} -0.9485 & -0.03531 & 0.03566 & -0.01797 & -0.01638 & 0.01105 & -0.0009454 & 0.01741 \\ --0.0103 & 0.8755 & 0.01175 & -0.0118 & -0.0161 & 0.002323 & -0.0006286 & 0.002953 \\ -0.01246 & 0.01032 & 1.029 & -0.02871 & -0.001326 & -0.0006531 & 0.02134 & -0.001305 \\ --0.009267 & -0.01528 & -0.03585 & 0.983 & 0.01469 & 0.01909 & -0.0007814 & 0.01507 \\ --0.005961 & -0.02135 & -0.0002244 & 0.01444 & 0.9926 & -0.0004736 & -0.002663 & 0.003707 \\ -0.002087 & 0.002114 & -0.001774 & 0.02071 & -0.0001252 & 1.028 & -0.00786 & -0.007389 \\ -0.001439 & -0.0009891 & 0.02285 & -0.001455 & -0.001524 & -0.00625 & 1.095 & 0.008555 \\ -0.005678 & 0.002526 & -0.0023 & 0.01341 & 0.002966 & -0.004732 & 0.007783 & 0.9021 - - - \end{pmatrix}$ -} -{~}\\{~}\\{~}\\ -\tiny{ -$ \delta A_{reco\rightarrow gen}=\begin{pmatrix} -0.005044 & 0.02013 & 0.03103 & 0.02225 & 0.01764 & 0.02351 & 0.03312 & 0.02092 \\ -0.006623 & 0.05256 & 0.03149 & 0.02695 & 0.02883 & 0.02852 & 0.03422 & 0.03844 \\ -0.007229 & 0.03412 & 0.07348 & 0.04506 & 0.03619 & 0.03339 & 0.05534 & 0.03524 \\ -0.007892 & 0.04374 & 0.06735 & 0.05351 & 0.03086 & 0.03969 & 0.0508 & 0.04497 \\ -0.007871 & 0.03822 & 0.05248 & 0.02984 & 0.05276 & 0.03153 & 0.05642 & 0.03947 \\ -0.008018 & 0.04425 & 0.04817 & 0.03854 & 0.03142 & 0.05783 & 0.07315 & 0.0465 \\ -0.007405 & 0.03509 & 0.05327 & 0.03269 & 0.03754 & 0.04886 & 0.08115 & 0.03668 \\ -0.006716 & 0.03761 & 0.03789 & 0.03252 & 0.02902 & 0.03459 & 0.04089 & 0.05595 \\ - \end{pmatrix}$ -} - - - - -\end{frame} - - - -\begin{frame}\frametitle{Matrix, $4-5~GeV$} -\tiny{ -$ A_{reco\rightarrow gen}=\begin{pmatrix} -0.9376 & -0.01202 & 0.01084 & -0.001334 & -0.01096 & -0.007861 & 0.04462 & -0.02943 \\ --0.003862 & 0.8835 & 0.005033 & -0.0009372 & 0.01946 & 0.0005903 & -0.01475 & -0.01096 \\ -0.008222 & 0.005038 & 1.028 & 0.02931 & -0.001236 & 0.002661 & -0.005131 & 0.003024 \\ -0.001399 & 0.0001528 & 0.03615 & 0.999 & 0.003816 & -0.01991 & 0.003867 & -0.004392 \\ --0.00087 & 0.02452 & -0.002084 & 0.003934 & 0.965 & 0.01721 & -0.01357 & 0.001678 \\ --0.001301 & -0.0004482 & 0.003296 & -0.02074 & 0.01785 & 1.025 & 0.01287 & 3.339e-05 \\ -0.0131 & -0.01493 & -0.005807 & 0.002846 & -0.01205 & 0.01028 & 1.067 & -0.005389 \\ --0.007891 & -0.01133 & 0.002935 & -0.002299 & 0.00155 & -0.0001701 & -0.004359 & 0.8885 - - - - \end{pmatrix}$ -} -{~}\\{~}\\{~}\\ -\tiny{ -$ \delta A_{reco\rightarrow gen}=\begin{pmatrix} -0.00485 & 0.01993 & 0.03003 & 0.02205 & 0.01675 & 0.02302 & 0.03184 & 0.02001 \\ -0.006646 & 0.05384 & 0.03241 & 0.02822 & 0.02797 & 0.02913 & 0.03387 & 0.03881 \\ -0.007207 & 0.0349 & 0.07402 & 0.04631 & 0.03544 & 0.03342 & 0.05395 & 0.03486 \\ -0.00793 & 0.04514 & 0.06837 & 0.0555 & 0.0304 & 0.04028 & 0.05 & 0.04548 \\ -0.007778 & 0.038 & 0.05269 & 0.03055 & 0.05035 & 0.03124 & 0.05446 & 0.03809 \\ -0.008046 & 0.04554 & 0.04847 & 0.03966 & 0.03063 & 0.05807 & 0.07187 & 0.04624 \\ -0.007362 & 0.03556 & 0.05265 & 0.03306 & 0.03594 & 0.04858 & 0.07847 & 0.03556 \\ -0.00668 & 0.03834 & 0.03799 & 0.03361 & 0.02794 & 0.03474 & 0.03969 & 0.0549 - - \end{pmatrix}$ -} - - - - -\end{frame} - - -\begin{frame}\frametitle{Matrix, $5-6~GeV$} -\tiny{ -$ A_{reco\rightarrow gen}=\begin{pmatrix} -0.9426 & -0.06054 & -0.01858 & -0.009577 & -0.04448 & 0.01487 & -0.05111 & 0.01211 \\ --0.01507 & 0.9261 & -0.01842 & -0.01486 & 0.007677 & -0.004233 & 0.0158 & 0.014 \\ --0.004885 & -0.01924 & 1.031 & -0.02811 & -0.01966 & -0.01106 & 0.001607 & -0.01568 \\ --0.005543 & -0.01758 & -0.03607 & 1.021 & -0.007365 & 0.003655 & -0.01436 & 0.00549 \\ --0.0161 & 0.009612 & -0.02354 & -0.007301 & 0.9042 & -0.01913 & 0.01151 & -0.005796 \\ -0.00465 & -0.004299 & -0.01486 & 0.003926 & -0.01952 & 1.059 & -0.03643 & 0.01645 \\ --0.01623 & 0.01623 & 0.002113 & -0.01218 & 0.008872 & -0.0291 & 1.07 & 0.006078 \\ -0.002753 & 0.01452 & -0.01636 & 0.004515 & -0.004271 & 0.01376 & 0.006442 & 0.9317 - - \end{pmatrix}$ -} -{~}\\{~}\\{~}\\ -\tiny{ -$ \delta A_{reco\rightarrow gen}=\begin{pmatrix} -0.005003 & 0.02191 & 0.03071 & 0.02325 & 0.01614 & 0.02449 & 0.03247 & 0.02216 \\ -0.006905 & 0.05934 & 0.03295 & 0.02971 & 0.02639 & 0.03158 & 0.0347 & 0.04249 \\ -0.007292 & 0.037 & 0.07401 & 0.04768 & 0.03295 & 0.03528 & 0.05479 & 0.03725 \\ -0.008092 & 0.04885 & 0.06895 & 0.05818 & 0.02831 & 0.04279 & 0.05104 & 0.04891 \\ -0.007625 & 0.03832 & 0.05044 & 0.02997 & 0.04563 & 0.03107 & 0.05238 & 0.03881 \\ -0.008271 & 0.04963 & 0.04961 & 0.04164 & 0.02872 & 0.06191 & 0.07339 & 0.04943 \\ -0.007462 & 0.03732 & 0.05348 & 0.03441 & 0.03342 & 0.05065 & 0.07878 & 0.03779 \\ -0.006902 & 0.0424 & 0.03877 & 0.03522 & 0.02645 & 0.03649 & 0.04033 & 0.06046 - - \end{pmatrix}$ -} - -\end{frame} - -\begin{frame}\frametitle{Matrix, $6-7~GeV$} -\tiny{ -$ A_{reco\rightarrow gen}=\begin{pmatrix} -0.945 & -0.03958 & 0.001374 & 0.009617 & 0.03559 & -0.002808 & 0.02331 & -0.04465 \\ --0.01082 & 0.9286 & 0.002015 & -0.002359 & 0.01392 & -0.01108 & 0.003507 & 0.01705 \\ -0.00141 & 0.002621 & 1.031 & 0.02586 & 0.005218 & -0.01453 & -0.01824 & 0.006611 \\ -0.002335 & -0.003277 & 0.03239 & 1.016 & 0.001427 & -0.004502 & -0.01755 & -0.02446 \\ -0.009841 & 0.01654 & 0.006119 & 0.0005815 & 0.9252 & 0.008913 & 0.01408 & -0.0007158 \\ --0.00144 & -0.01259 & -0.01669 & -0.003164 & 0.007971 & 1.06 & -0.008279 & 0.01129 \\ -0.005264 & 0.003986 & -0.01699 & -0.0127 & 0.01191 & -0.006548 & 1.015 & -0.008087 \\ --0.01037 & 0.01663 & 0.00801 & -0.01934 & -0.001413 & 0.008724 & -0.007422 & 0.9235 - - - \end{pmatrix}$ -} -{~}\\{~}\\{~}\\ -\tiny{ -$ \delta A_{reco\rightarrow gen}=\begin{pmatrix} -0.005032 & 0.02188 & 0.03101 & 0.02328 & 0.01671 & 0.02429 & 0.03088 & 0.022 \\ -0.006931 & 0.06018 & 0.03299 & 0.02969 & 0.02749 & 0.03099 & 0.03255 & 0.04223 \\ -0.007286 & 0.03675 & 0.0738 & 0.04685 & 0.03389 & 0.03559 & 0.05248 & 0.03688 \\ -0.008095 & 0.04878 & 0.06788 & 0.05722 & 0.02884 & 0.04292 & 0.04809 & 0.04844 \\ -0.007711 & 0.03986 & 0.05127 & 0.03021 & 0.04725 & 0.0318 & 0.05043 & 0.03921 \\ -0.008258 & 0.04926 & 0.05066 & 0.04188 & 0.03007 & 0.06099 & 0.0698 & 0.04976 \\ -0.007228 & 0.03647 & 0.05241 & 0.03325 & 0.03342 & 0.04911 & 0.07267 & 0.03646 \\ -0.006913 & 0.04264 & 0.03886 & 0.03505 & 0.02731 & 0.0368 & 0.0384 & 0.05918 - \end{pmatrix}$ -} - -\end{frame} -\begin{frame}\frametitle{Matrix, $7-8~GeV$} -\tiny{ -$ A_{reco\rightarrow gen}=\begin{pmatrix} -0.9439 & -0.008577 & 0.02194 & -0.03527 & 0.02117 & 0.002818 & -0.03045 & 0.03674 \\ --0.00281 & 0.9327 & 0.01528 & -0.01142 & 0.003977 & -0.003849 & 0.005332 & -0.001996 \\ -0.01215 & 0.01497 & 1.049 & 0.02072 & -0.01013 & 0.00439 & 0.0268 & -0.01252 \\ --0.01552 & -0.0141 & 0.0269 & 1.038 & 0.008406 & 0.01559 & 0.006097 & -0.006599 \\ -0.00792 & 0.004397 & -0.01175 & 0.008599 & 0.913 & -0.01238 & 0.01077 & 0.004526 \\ --0.003936 & -0.002701 & 0.006165 & 0.01572 & -0.01315 & 1.056 & 0.005698 & -0.02622 \\ --0.01108 & 0.005669 & 0.02694 & 0.004684 & 0.00747 & 0.004389 & 1.031 & -0.0009495 \\ -0.009494 & -0.001074 & -0.01283 & -0.00596 & 0.00317 & -0.0205 & -0.0007477 & 0.9244 - - \end{pmatrix}$ -} -{~}\\{~}\\{~}\\ -\tiny{ -$ \delta A_{reco\rightarrow gen}=\begin{pmatrix} -0.005117 & 0.02247 & 0.03197 & 0.02424 & 0.01667 & 0.02467 & 0.03167 & 0.0222 \\ -0.007024 & 0.0611 & 0.03411 & 0.03076 & 0.02738 & 0.03196 & 0.03395 & 0.04353 \\ -0.007528 & 0.03781 & 0.07762 & 0.05016 & 0.03419 & 0.03637 & 0.05471 & 0.03789 \\ -0.00836 & 0.05008 & 0.07234 & 0.0615 & 0.02922 & 0.04396 & 0.05051 & 0.04956 \\ -0.007784 & 0.0398 & 0.05285 & 0.03146 & 0.0471 & 0.03192 & 0.05186 & 0.03956 \\ -0.008409 & 0.05064 & 0.0521 & 0.04352 & 0.02981 & 0.06265 & 0.07273 & 0.04945 \\ -0.007446 & 0.03773 & 0.05481 & 0.03522 & 0.03376 & 0.05073 & 0.07631 & 0.03711 \\ -0.007025 & 0.04375 & 0.04004 & 0.03654 & 0.02726 & 0.03676 & 0.03919 & 0.06031 - - \end{pmatrix}$ -} - -\end{frame} - -\begin{frame}\frametitle{Matrix, $15-16~GeV$} -\tiny{ -$ A_{reco\rightarrow gen}=\begin{pmatrix} -0.9339 & 0.00108 & 0.01361 & -0.003327 & 0.02336 & 0.01977 & 0.01204 & 0.06036 \\ --0.002786 & 0.9655 & 0.002191 & -0.01751 & 0.003735 & -0.003235 & -0.01139 & 0.003084 \\ -0.002358 & 0.001539 & 1.044 & 0.0005145 & 0.02315 & 0.01266 & -0.01177 & 0.01238 \\ --0.006399 & -0.02075 & 0.0008438 & 1.065 & 0.003937 & 0.001169 & 0.01186 & 0.007426 \\ -0.005634 & 0.007771 & 0.03177 & 0.005357 & 0.8611 & 0.006598 & 0.02392 & 0.01592 \\ -0.008184 & -0.002466 & 0.01451 & -0.0001025 & 0.005234 & 1.106 & -0.02518 & -0.001139 \\ -0.005487 & -0.01252 & -0.0114 & 0.01094 & 0.01915 & -0.02023 & 1.003 & 0.002107 \\ -0.01222 & -0.0006629 & 0.008504 & 0.003367 & 0.01214 & 0.0004481 & 0.001254 & 0.9418 - - \end{pmatrix}$ -} -{~}\\{~}\\{~}\\ -\tiny{ -$ \delta A_{reco\rightarrow gen}=\begin{pmatrix} -0.007227 & 0.03343 & 0.04627 & 0.03662 & 0.02185 & 0.03722 & 0.04363 & 0.03258 \\ -0.01039 & 0.09654 & 0.05184 & 0.04878 & 0.03787 & 0.05022 & 0.04962 & 0.06603 \\ -0.01081 & 0.05899 & 0.1128 & 0.07597 & 0.04595 & 0.05597 & 0.07601 & 0.05719 \\ -0.0122 & 0.07955 & 0.107 & 0.09418 & 0.04019 & 0.06834 & 0.07171 & 0.07577 \\ -0.01096 & 0.05911 & 0.07402 & 0.04603 & 0.06126 & 0.04891 & 0.07197 & 0.05855 \\ -0.01244 & 0.08032 & 0.07744 & 0.06709 & 0.04246 & 0.09896 & 0.1062 & 0.07742 \\ -0.0106 & 0.05862 & 0.07647 & 0.05126 & 0.04564 & 0.07754 & 0.1063 & 0.05511 \\ -0.0103 & 0.06658 & 0.05991 & 0.05607 & 0.03788 & 0.05824 & 0.05712 & 0.09277 - - - \end{pmatrix}$ -} - -\end{frame} - - -\begin{frame}\frametitle{Matrix, $16-17~GeV$} -\tiny{ -$ A_{reco\rightarrow gen}=\begin{pmatrix} -0.9496 & -0.0144 & -0.04947 & -0.01837 & -0.01716 & 0.03543 & 0.02941 & 0.03469 \\ --0.00478 & 0.9532 & -0.002416 & -0.01565 & -0.002176 & -0.04158 & -0.008659 & 0.008457 \\ --0.02091 & -0.003799 & 1.017 & 0.005475 & -0.002693 & -0.002398 & -0.004536 & 0.004765 \\ --0.01131 & -0.01774 & 0.005349 & 1.036 & -0.01962 & 0.01559 & -0.002843 & -0.0163 \\ --0.003551 & -0.000527 & -0.003863 & -0.01833 & 0.9273 & 0.0113 & 0.0199 & -0.01963 \\ -0.01641 & -0.05085 & -0.003484 & 0.0132 & 0.01329 & 1.057 & 0.005759 & -0.002536 \\ -0.006702 & -0.007821 & -0.007193 & -0.001249 & 0.01617 & 0.004364 & 1.02 & -0.01442\\ -0.008137 & 0.006787 & 0.007275 & -0.01416 & -0.01677 & -0.003623 & -0.01468 & 0.9239 - - - \end{pmatrix}$ -} -{~}\\{~}\\{~}\\ -\tiny{ -$ -delta A_{reco\rightarrow gen}=\begin{pmatrix} -0.008642 & 0.03749 & 0.05212 & 0.03973 & 0.02823 & 0.04084 & 0.05259 & 0.03702 \\ -0.01184 & 0.1057 & 0.05526 & 0.05126 & 0.04746 & 0.05261 & 0.05504 & 0.07191 \\ -0.01242 & 0.0635 & 0.1195 & 0.07948 & 0.05588 & 0.05834 & 0.08514 & 0.06119 \\ -0.01395 & 0.08487 & 0.113 & 0.09802 & 0.04932 & 0.07284 & 0.08126 & 0.08416 \\ -0.0131 & 0.07069 & 0.08419 & 0.05207 & 0.07888 & 0.05367 & 0.08458 & 0.06597 \\ -0.01405 & 0.08461 & 0.08303 & 0.07213 & 0.05018 & 0.102 & 0.1159 & 0.08509 \\ -0.01235 & 0.0632 & 0.08559 & 0.05716 & 0.05601 & 0.08193 & 0.1196 & 0.06223 \\ -0.01171 & 0.07316 & 0.06348 & 0.06076 & 0.04535 & 0.06206 & 0.06367 & 0.101 - \end{pmatrix}$ -} - -\end{frame} - - -\begin{frame}\frametitle{Matrix, $17-18~GeV$} -\tiny{ -$ A_{reco\rightarrow gen}=\begin{pmatrix} -0.9722 & -0.2207 & 0.04866 & 0.03008 & 0.06913 & -0.04369 & 0.006754 & -0.007125 \\ --0.05524 & 1.005 & 0.006893 & 0.001597 & -0.02202 & 0.0168 & 0.01972 & -0.03585 \\ -0.003177 & 0.007009 & 0.9282 & 0.0363 & 0.006305 & -0.01634 & -0.001624 & 0.02907 \\ -0.01302 & 0.001604 & 0.05221 & 0.9617 & 0.01874 & -0.01516 & -0.01685 & -0.00448 \\ -0.02335 & -0.02845 & 0.01286 & 0.02353 & 0.9206 & 0.005032 & -0.02313 & 0.002084 \\ --0.01782 & 0.02651 & -0.02096 & -0.01789 & 0.002636 & 1.073 & 0.05697 & 0.02173 \\ -0.001236 & 0.02227 & 0.001961 & -0.01673 & -0.02081 & 0.04564 & 1.002 & 0.02384 \\ --0.00329 & -0.04029 & 0.03169 & -0.004072 & 0.003657 & 0.02022 & 0.02588 & 0.993 - - - \end{pmatrix}$ -} -{~}\\{~}\\{~}\\ -\tiny{ -$ \delta A_{reco\rightarrow gen}=\begin{pmatrix} -0.01158 & 0.05859 & 0.05715 & 0.04579 & 0.03679 & 0.05273 & 0.06339 & 0.05361 \\ -0.01675 & 0.1375 & 0.06136 & 0.0578 & 0.05652 & 0.06728 & 0.06803 & 0.09741 \\ -0.01504 & 0.07891 & 0.1195 & 0.08187 & 0.06421 & 0.06836 & 0.0968 & 0.07722 \\ -0.01743 & 0.107 & 0.1147 & 0.1026 & 0.05713 & 0.08438 & 0.09246 & 0.104 \\ -0.01671 & 0.08622 & 0.09098 & 0.05799 & 0.09323 & 0.06518 & 0.09928 & 0.08555 \\ -0.01823 & 0.1077 & 0.08822 & 0.07697 & 0.06018 & 0.1254 & 0.1384 & 0.108 \\ -0.01557 & 0.07927 & 0.08985 & 0.06133 & 0.06639 & 0.09943 & 0.1417 & 0.08085 \\ -0.01581 & 0.09842 & 0.07226 & 0.06849 & 0.0572 & 0.07807 & 0.08073 & 0.134 - - \end{pmatrix}$ -} - -\end{frame} - - -\begin{frame}\frametitle{Matrix, $17-18~GeV$} -\tiny{ -$ A_{reco\rightarrow gen}=\begin{pmatrix} -0.9668 & -0.1503 & -0.06883 & -0.03643 & -0.1029 & -0.001732 & 0.02973 & 0.01421 \\ --0.04222 & 1.008 & -0.02683 & -0.00634 & 0.0238 & -0.01704 & -0.02964 & -0.001006 \\ --0.01775 & -0.02415 & 0.9854 & 0.01759 & -0.02388 & -0.02996 & 0.05574 & 0.02075 \\ --0.01405 & -0.001046 & 0.02347 & 0.9961 & -0.03245 & 0.05951 & -0.03554 & -0.03533 \\ --0.02836 & 0.02182 & -0.03202 & -0.02734 & 0.9501 & 0.003661 & -0.005823 & 0.001794 \\ --0.004889 & -0.02396 & -0.03633 & 0.05887 & 0.01071 & 1.14 & 0.02636 & -0.02449 \\ -0.01562 & -0.02848 & 0.05775 & -0.02848 & -0.01448 & 0.0121 & 1.131 & -0.007396 \\ -0.01017 & -0.002444 & 0.02482 & -0.02862 & -0.001555 & -0.02052 & -0.001701 & 0.8984 - - \end{pmatrix}$ -} -{~}\\{~}\\{~}\\ -\tiny{ -$ \delta A_{reco\rightarrow gen}=\begin{pmatrix} -0.01571 & 0.07502 & 0.08616 & 0.06693 & 0.05243 & 0.07755 & 0.1012 & 0.06491 \\ -0.0219 & 0.1898 & 0.08893 & 0.08128 & 0.08134 & 0.1012 & 0.1096 & 0.1178 \\ -0.02111 & 0.1138 & 0.1845 & 0.1207 & 0.09673 & 0.1026 & 0.155 & 0.09628 \\ -0.02383 & 0.1479 & 0.1734 & 0.1504 & 0.08372 & 0.1266 & 0.1453 & 0.1269 \\ -0.02303 & 0.1239 & 0.1389 & 0.0845 & 0.1362 & 0.09892 & 0.1606 & 0.1086 \\ -0.02532 & 0.1566 & 0.1338 & 0.116 & 0.08793 & 0.1951 & 0.2209 & 0.139 \\ -0.02247 & 0.1179 & 0.1425 & 0.0934 & 0.1013 & 0.1557 & 0.2343 & 0.1029 \\ -0.02003 & 0.1234 & 0.09631 & 0.08929 & 0.07676 & 0.1063 & 0.112 & 0.1622 \\ - - - \end{pmatrix}$ -} - -\end{frame} - - -\begin{frame}\frametitle{Summary and plans} -\begin{itemize} -\item WE have all the matrix -\item Error evaluated. -\item In principle, everything is ready for method of moments to be written down and reviewed. -\item I want to play one more trick, using symmetry of $\cos \theta_k$ and $\phi$ we can probably set lot of matrix elements to 0. -\end{itemize} - - -\end{frame} - - - - - - - - -\end{document} diff --git a/Kstmumu/MMatrix2/MMatrix.tex~ b/Kstmumu/MMatrix2/MMatrix.tex~ deleted file mode 100644 index 2fc0e58..0000000 --- a/Kstmumu/MMatrix2/MMatrix.tex~ +++ /dev/null @@ -1,556 +0,0 @@ -\documentclass[xcolor=svgnames]{beamer} -\usepackage[utf8]{inputenc} -\usepackage[english]{babel} -\usepackage{polski} -%\usepackage{amssymb,amsmath} -%\usepackage[latin1]{inputenc} -%\usepackage{amsmath} -%\newcommand\abs[1]{\left|#1\right|} -\usepackage{amsmath} -\newcommand\abs[1]{\left|#1\right|} -\usepackage{hepnicenames} -\usepackage{hepunits} -\usepackage{color} - - - -%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%5 -\definecolor{mygreen}{cmyk}{0.82,0.11,1,0.25} - - -\usetheme{Sybila} - -\title[Unfolding for counting experiments]{Unfolding for counting experiments} -\author{Marcin Chrz\k{a}szcz$^{1,2}$, Nicola Serra$^{1}$} -\institute{$^1$~University of Zurich,\\ $^2$~Institute of Nuclear Physics, Krakow} -\date{\today} - -\begin{document} -% --------------------------- SLIDE -------------------------------------------- -\frame[plain]{\titlepage} -\author{Marcin Chrz\k{a}szcz} -% ------------------------------------------------------------------------------ -% --------------------------- SLIDE -------------------------------------------- - -\begin{frame}\frametitle{Quo vadis $\PBzero \to \PKstar \mu \mu$?} - -\center \includegraphics[width=0.8\paperwidth]{diagram.png}\\ - -\end{frame} -%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% -\begin{frame}\frametitle{Quo vadis $\PBzero \to \PKstar \mu \mu$?} - -\center \includegraphics[width=0.8\paperwidth]{matrix.png}\\ - -\end{frame} - - -\section{Introduction} - -\begin{frame}\frametitle{Reminder} -For now: -\begin{itemize} -\item We have proven that there has to exists unfolding matrix. -\item Shown how to construct transformation matrix: $Gen \to Reco$. -\item Inverting it we can have transformation matrix of $Reco \to Gen$. -\item For details: \href{https://indico.cern.ch/event/316905/session/1/contribution/18/material/slides/0.pdf}{LINK} - -\end{itemize} - -What is missing? -\begin{columns} -\column{1in} -\begin{enumerate} -\item ERROR! -\end{enumerate} -\column{4in} -\includegraphics[width=0.8\textwidth]{err.jpg}\\ -\end{columns} - -\end{frame} - - - -\begin{frame}\frametitle{How to?} -\begin{itemize} -\item So lets say that transformation matrix:$Gen \to Reco$ is $\epsilon_{i,j}$. -\item Of coz it's easy to write the covariance matrix(error matrix): -\end{itemize} -\begin{equation} -cov(\epsilon_{\alpha, \beta},\epsilon_{a,b}) -\end{equation} -\begin{itemize} -\item Then we can calculate the matrix: $\epsilon_{i,j}^{-1}$(assuming it exists). -\item and the 1M dollar question is: $cov(\epsilon_{\alpha, \beta}^{-1},\epsilon_{a,b}^{-1}) =?$ -\end{itemize} - -\end{frame} - -\begin{frame}\frametitle{Answer to 1M dolar quesion} -\begin{itemize} -\item Solution comes from $\tau$ physics :) -\end{itemize} -\begin{equation} -cov(\epsilon_{\alpha, \beta}^{-1},\epsilon_{a,b}^{-1}) = \epsilon^{-1}_{\alpha,i} \epsilon^{-1}_{j,\beta} \epsilon^{-1}_{a,k} \epsilon^{-1}_{l,b} cov( \epsilon_{ij} \epsilon_{kl}) -\end{equation} -\begin{itemize} -\item It's way to late to latex the prove. For prove see: \href{http://arxiv.org/abs/hep-ex/9909031}{arXiv:hep-ex/9909031} -\item Thanks to orthonormal basis lifes gets simpler: -\end{itemize} -\begin{equation} -cov(\epsilon_{ij},\epsilon_{kl} ) = \sigma_{\epsilon,ij} \delta_{ik} \delta_{jl} ( no correlations) -\end{equation} - -\end{frame} - - -\begin{frame}\frametitle{Total error} -\begin{itemize} -\item So let's say: $B=\epsilon^{-1} f$ -\item Then: -\end{itemize} -\begin{equation} -cov(B_i,B_j) = f_a f_b cov(\epsilon_{i \alpha }^{-1} , \epsilon_{j \beta}^{-1} )+ \epsilon^{-1}_{ ik} \epsilon^{-1}_{jl} cov(f_k,f_l) -\end{equation} -\begin{itemize} -\item Looks easy just need to implement! -\end{itemize} - -\end{frame} - - -\begin{frame}\frametitle{Matrix, $0.1-0.98~GeV$} -\tiny{ -$ A_{reco\rightarrow gen}=\begin{pmatrix} - 0.9495 0.008518 0.01522 -0.007362 0.01496 -0.04544 -0.02468 0.002078 - 0.0002651 0.8261 0.00978 -0.001042 0.004382 0.03191 0.01247 0.01886 - -0.0003391 0.009773 1.03 0.008433 -0.002028 0.003 0.02086 0.001549 - -0.00403 -0.001336 0.01047 0.9215 0.006898 -0.0006023 0.003041 -0.004465 - 0.006557 0.005531 -0.002423 0.00691 1.171 -0.01082 -0.0158 -0.003231 - -0.01931 0.03973 0.00342 -0.0006455 -0.01081 0.9452 0.02232 -0.005304 - .008421 0.0124 0.02071 0.002415 -0.01264 0.01785 1.06 0.001084 - 0.000347 0.01886 0.001555 -0.003568 -0.002591 -0.004226 0.001093 0.8204 - - - - - \end{pmatrix}$ -} - - - - - -\end{frame} - -\begin{frame}\frametitle{Constructing Matrix unfolding} -\begin{itemize} -\item We got first column of the unfolding matrix. -\end{itemize} -\small{ -$ \begin{pmatrix} - 1.06 & \cdots & a_{1,8} \\ - 0.01157 & \cdots & a_{2,8} \\ - -0.003547 & \ddots & \vdots \\ - 0.0007841 & \ddots & \vdots \\ - 0.001126 & \ddots & \vdots \\ - 0.001766 & \ddots & \vdots \\ - 0.001664 & \ddots & \vdots \\ - -0.001937 & \cdots & a_{8,8} - \end{pmatrix}$ - - -} -\begin{itemize} -\item How about the others? -\item We can reweight accordingly to $f_x$. -\end{itemize} - -\end{frame} - -\begin{frame}\frametitle{Constructing Matrix unfolding} -\begin{itemize} -\item To get $S_3$ each event $i^{th}$ has has weight $f_{S_3}(\cos \theta_{k_i},\cos \theta_{l_i},\phi_i) $ -\item One can calculate on MC the reweighed moments in PHPS: -\end{itemize} -\begin{equation} -\int PDF*f_{S_3}=\dfrac{32}{225} -\end{equation} -\begin{itemize} -\item Our base vector now is:$v^{T}_{gen}=(0 ,\frac{32}{225},0,0,0,0,0,0)$ -\item So lets see what do we get as reconstructed vector(after multiplying by $\frac{225}{32}$. -\small{$v^{T}_{rec}=( 0.042, 1.105,-0.005,0.003,-0.0023,-0.005,-0.005,-0.006)$ } -\end{itemize} - -\end{frame} - - -\begin{frame}\frametitle{Constructing Matrix unfolding} -\begin{itemize} -\item Now the matrix looks like: -\end{itemize} -\small{ -$ \begin{pmatrix} - 1.06 & 0.042 & \cdots & a_{1,8} \\ - 0.01157 & 1.105 & \cdots & a_{2,8} \\ - -0.003547 & -0.005 & \ddots & \vdots \\ - 0.0007841 &-0.005 & \ddots & \vdots \\ - 0.001126 & 0.003 &\ddots & \vdots \\ - 0.001766 & -0.0023 &\ddots & \vdots \\ - 0.001664 & -0.005 &\ddots & \vdots \\ - -0.001937 & -0.006 &\cdots & a_{8,8} - \end{pmatrix}$ - - -} -\begin{itemize} -\item The others go in the same way. -\item Repenting this exercise from $1^{st}$ year algebra we can get the full matrix -\end{itemize} - - -\end{frame} -\begin{frame}\frametitle{Constructing Matrix unfolding} -\begin{itemize} -\item The full transformation matrix from generator space to reconstructed space: -\end{itemize} -\tiny{ -$ A_{gen\rightarrow reco}=\begin{pmatrix} - 1.06 & 0.0423 & -0.0081 & 0.0022 & 0.0049 & 0.0037 & 0.0028 & -0.0065 \\ - - 0.0115 & 1.105 & -0.0050 & 0.0027 & -0.0018 & -0.0040 &-0.0054 & -0.0065 \\ - -0.0035 & -0.0050 & 0.981 & 0.0005 & -0.0025 & 0.0002 & -0.0037 & -0.0048\\ - 0.00078 & 0.0034 & 0.0006 & 1.002 & -0.0032 & -0.0040 & 0.0003 & 0.0018\\ - 0.001126 & -0.0023 & -0.0032 & -0.0032 & 1.055 & 0.001& -0.004 & 0.0023\\ - 0.00176 & -0.0050 & 0.00036 & -0.0040 & 0.0011 & 0.96 & -0.0057 & 0.0009 \\ - 0.0016 & -0.005 & -0.003 & 0.00029& -0.003 &-0.004 & 0.9543 & 0.0000\\ - -0.0019 & -0.0065 & -0.004 & 0.001 & 0.0018 & 0.0007 & 0.000 & 1.098 \\ - - - - - - \end{pmatrix}$ - - -} -\begin{itemize} -\item Inverting the matrix is simple, and doable -\end{itemize} -\tiny{ -$ A_{reco\rightarrow gen}=\begin{pmatrix} - 0.9434 & -0.036 & 0.007& -0.0020 & -0.0044& -0.0038 & -0.0030 & 0.0054\\ - -0.009 & 0.90 & 0.0045 & -0.0024& 0.0016 & 0.003873 & 0.00527& 0.005 \\ - 0.003 & 0.00454& 1.019 & -0.00058 & 0.0025& -0.000291 & 0.004 & 0.004 \\ --0.00071 & -0.0030 & -0.0007 & 0.9977 & 0.0030 & 0.004206 &-0.0003 & -0.0017 \\ - -0.001 & 0.0020 & 0.0031& 0.0030 & 0.9483 & -0.0010 & 0.004626 & -0.0019 \\ - -0.001 & 0.004 & -0.0003 & 0.0042 & -0.001087 & 1.037 & 0.0063 & -0.0009\\ - -0.0017 & 0.0053 & 0.0042 & -0.0002 & 0.00370& 0.0050 & 1.048 & 0.0000 \\ - 0.0016& 0.0053& 0.00452 & -0.001 & -0.001582 & -0.0007213 &0.000 & 0.9105 \\ - - - - - \end{pmatrix}$ -} - -\end{frame} - - - -\begin{frame}\frametitle{Sensitivity to unknowns} -\begin{itemize} -\item We are unfolding based on MC. -\item There are MC/Data differences, which can have impact on the unfolding. -\end{itemize} -Let's put small modification: -\begin{equation} -w_j \to \overline{w_j}= \dfrac{1}{eff(\cos \theta_{l~j}, \cos \theta_{k~j}, \phi_{j})} \times corr(\cos \theta_{l~j}, \cos \theta_{k~j}, \phi_{j}) -\end{equation} -Unfortunately God didn't allowed me sneak peak into his cards so I don't know $corr(\cos \theta_{l}, \cos \theta_{k}, \phi)$, but let's try out some functions and see what happens :) - - -\end{frame} - -\begin{frame}\frametitle{Corr1 functions} -\begin{columns} -\column{2in} -\includegraphics[width=\linewidth]{corr/Corr1_cosk.png}\\ -\includegraphics[width=\linewidth]{corr/Corr1_cosl.png}\\ -\column{2.5in} -$ -corr1(\cos_l, \cos_k,\phi)= 1+ 0.032 \cos_l - 0.032 \cos_k + 0.01 \phi -$ -\includegraphics[width=0.8\linewidth]{corr/Corr1_phi.png}\\ - -\end{columns} - -\end{frame} -%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% -\begin{frame}\frametitle{Corr2 functions} -\begin{columns} -\column{2in} -\includegraphics[width=0.85\linewidth]{corr/corr21.png}\\ -\includegraphics[width=0.85\linewidth]{corr/corr22.png}\\ -\column{2.5in} -$ -corr2(\cos_l, \cos_k,\phi)= -0.02 \cos_l^2 + 0.02 \cos_k^2 - - 0.015 \phi^2+ 1 -$ -\includegraphics[width=0.75\linewidth]{corr/corr23.png}\\ - -\end{columns} - -\end{frame} - -%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% -\begin{frame}\frametitle{Corr3 functions} -\begin{columns} -\column{2in} -\includegraphics[width=0.85\linewidth]{corr/corr31.png}\\ -\includegraphics[width=0.85\linewidth]{corr/corr32.png}\\ -\column{2.5in} -$ -corr3(\cos_l, \cos_k,\phi)= 0.02 \cos_l \cos_k + 0.01 \cos_k \phi - 0.01 \phi \cos_l + 1 -$ -\includegraphics[width=0.75\linewidth]{corr/corr33.png}\\ - -\end{columns} - -\end{frame} -%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% -\begin{frame}\frametitle{Corr4 functions} -\begin{columns} -\column{2in} -\includegraphics[width=0.85\linewidth]{corr/corr41.png}\\ -\includegraphics[width=0.85\linewidth]{corr/corr42.png}\\ -\column{2.5in} -$ -corr3(\cos_l, \cos_k,\phi)= 0.01 \cos_k \cos_l \phi + 1 -$ -\includegraphics[width=0.75\linewidth]{corr/corr43.png}\\ - -\end{columns} - -\end{frame} - - - - -%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% - - -\begin{frame}\frametitle{Corr1- MM} - - -\begin{tiny} - -\begin{center} - \begin{tabular}{ l l l l l l l l l } - \hline - \multicolumn{8}{c}{Mean of the pull} \\ \hline -$q^2$ & $S_3$ & $S_4$ & $S_5$ & $S_{6s}$ & $S_{6c}$ & $S_7$ & $S_8$ \\ \hline \hline - -0 & \scalebox{0.5}{$0.0085 \pm 0.026(0.3)$} & \scalebox{0.5}{$0.13 \pm 0.027(4.6)$} & \scalebox{0.5}{$-0.025 \pm 0.027(-0.92)$} & \scalebox{0.5}{$0.46 \pm 0.027(17)$} & \scalebox{0.5}{$-0.13 \pm 0.028(-4.7)$} & \scalebox{0.5}{$0.029 \pm 0.028(1)$} & \scalebox{0.5}{$-0.66 \pm 0.027(-25)$} \\ \hline -1 & \scalebox{0.5}{$0.0094 \pm 0.028(0.33)$} & \scalebox{0.5}{$0.078 \pm 0.028(2.8)$} & \scalebox{0.5}{$-0.02 \pm 0.028(-0.73)$} & \scalebox{0.5}{$0.24 \pm 0.028(8.5)$} & \scalebox{0.5}{$-0.075 \pm 0.028(-2.7)$} & \scalebox{0.5}{$-0.016 \pm 0.026(-0.63)$} & \scalebox{0.5}{$-0.39 \pm 0.028(-14)$} \\ \hline -2 & \scalebox{0.5}{$-0.02 \pm 0.027(-0.72)$} & \scalebox{0.5}{$0.027 \pm 0.026(1)$} & \scalebox{0.5}{$-0.024 \pm 0.027(-0.91)$} & \scalebox{0.5}{$0.18 \pm 0.027(6.8)$} & \scalebox{0.5}{$-0.024 \pm 0.027(-0.89)$} & \scalebox{0.5}{$-0.067 \pm 0.027(-2.5)$} & \scalebox{0.5}{$-0.39 \pm 0.028(-14)$} \\ \hline -3 & \scalebox{0.5}{$0.013 \pm 0.028(0.46)$} & \scalebox{0.5}{$-0.0089 \pm 0.027(-0.32)$} & \scalebox{0.5}{$0.055 \pm 0.026(2.1)$} & \scalebox{0.5}{$0.12 \pm 0.027(4.7)$} & \scalebox{0.5}{$0.11 \pm 0.027(3.9)$} & \scalebox{0.5}{$-0.018 \pm 0.028(-0.63)$} & \scalebox{0.5}{$-0.43 \pm 0.027(-16)$} \\ \hline -4 & \scalebox{0.5}{$-0.0054 \pm 0.029(-0.18)$} & \scalebox{0.5}{$-0.066 \pm 0.027(-2.4)$} & \scalebox{0.5}{$0.037 \pm 0.028(1.3)$} & \scalebox{0.5}{$0.22 \pm 0.027(8.1)$} & \scalebox{0.5}{$0.099 \pm 0.027(3.7)$} & \scalebox{0.5}{$-0.1 \pm 0.026(-3.8)$} & \scalebox{0.5}{$-0.41 \pm 0.026(-15)$} \\ \hline -5 & \scalebox{0.5}{$0.06 \pm 0.027(2.2)$} & \scalebox{0.5}{$-0.069 \pm 0.026(-2.6)$} & \scalebox{0.5}{$-0.013 \pm 0.028(-0.49)$} & \scalebox{0.5}{$0.21 \pm 0.027(7.8)$} & \scalebox{0.5}{$0.093 \pm 0.027(3.5)$} & \scalebox{0.5}{$-0.083 \pm 0.028(-3)$} & \scalebox{0.5}{$-0.41 \pm 0.028(-15)$} \\ \hline -6 & \scalebox{0.5}{$0.0064 \pm 0.026(0.25)$} & \scalebox{0.5}{$-0.051 \pm 0.027(-1.9)$} & \scalebox{0.5}{$-0.029 \pm 0.028(-1)$} & \scalebox{0.5}{$0.26 \pm 0.028(9.2)$} & \scalebox{0.5}{$0.14 \pm 0.027(5.1)$} & \scalebox{0.5}{$-0.081 \pm 0.027(-3)$} & \scalebox{0.5}{$-0.45 \pm 0.028(-16)$} \\ \hline -%7 & \scalebox{0.5}{$0.22 \pm 0.027(8)$} & \scalebox{0.5}{$-0.34 \pm 0.028(-12)$} & \scalebox{0.5}{$-0.43 \pm 0.026(-16)$} & \scalebox{0.5}{$2.4 \pm 0.029(82)$} & \scalebox{0.5}{$0.66 \pm 0.027(24)$} & \scalebox{0.5}{$-0.24 \pm 0.028(-8.6)$} & \scalebox{0.5}{$-0.51 \pm 0.027(-19)$} & -8 & \scalebox{0.5}{$0.023 \pm 0.027(0.85)$} & \scalebox{0.5}{$-0.031 \pm 0.028(-1.1)$} & \scalebox{0.5}{$0.0042 \pm 0.028(0.15)$} & \scalebox{0.5}{$0.21 \pm 0.026(7.8)$} & \scalebox{0.5}{$0.12 \pm 0.028(4.2)$} & \scalebox{0.5}{$-0.13 \pm 0.027(-4.8)$} & \scalebox{0.5}{$-0.48 \pm 0.026(-18)$} \\ \hline -9 & \scalebox{0.5}{$-0.017 \pm 0.027(-0.63)$} & \scalebox{0.5}{$-0.015 \pm 0.026(-0.56)$} & \scalebox{0.5}{$-0.0052 \pm 0.026(-0.2)$} & \scalebox{0.5}{$0.27 \pm 0.027(10)$} & \scalebox{0.5}{$0.046 \pm 0.026(1.7)$} & \scalebox{0.5}{$-0.12 \pm 0.026(-4.4)$} & \scalebox{0.5}{$-0.5 \pm 0.026(-19)$} \\ \hline -10 & \scalebox{0.5}{$-0.054 \pm 0.027(-2)$} & \scalebox{0.5}{$-0.056 \pm 0.026(-2.2)$} & \scalebox{0.5}{$0.036 \pm 0.026(1.4)$} & \scalebox{0.5}{$0.16 \pm 0.028(5.7)$} & \scalebox{0.5}{$0.077 \pm 0.028(2.8)$} & \scalebox{0.5}{$-0.034 \pm 0.027(-1.3)$} & \scalebox{0.5}{$-0.39 \pm 0.028(-14)$} \\ \hline -11 & \scalebox{0.5}{$0.023 \pm 0.027(0.88)$} & \scalebox{0.5}{$0.021 \pm 0.027(0.8)$} & \scalebox{0.5}{$-0.011 \pm 0.027(-0.41)$} & \scalebox{0.5}{$0.14 \pm 0.027(5)$} & \scalebox{0.5}{$0.042 \pm 0.027(1.6)$} & \scalebox{0.5}{$-0.098 \pm 0.028(-3.5)$} & \scalebox{0.5}{$-0.3 \pm 0.027(-11)$} \\ \hline - - - \hline - - - \end{tabular} - -\end{center} - - -\end{tiny} -\end{frame} - -%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% - - -\begin{frame}\frametitle{Corr2- MM} - - -\begin{tiny} - -\begin{center} - \begin{tabular}{ l l l l l l l l l } - \hline - \multicolumn{8}{c}{Mean of the pull} \\ \hline -$q^2$ & $S_3$ & $S_4$ & $S_5$ & $S_{6s}$ & $S_{6c}$ & $S_7$ & $S_8$ \\ \hline \hline - -0 & \scalebox{0.5}{$-0.21 \pm 0.026(-8.1)$} & \scalebox{0.5}{$0.061 \pm 0.026(2.3)$} & \scalebox{0.5}{$-0.016 \pm 0.026(-0.63)$} & \scalebox{0.5}{$0.048 \pm 0.026(1.8)$} & \scalebox{0.5}{$-0.0062 \pm 0.027(-0.23)$} & \scalebox{0.5}{$-0.012 \pm 0.028(-0.44)$} & \scalebox{0.5}{$0.0091 \pm 0.026(0.36)$} \\ \hline -1 & \scalebox{0.5}{$-0.12 \pm 0.028(-4.5)$} & \scalebox{0.5}{$0.032 \pm 0.027(1.2)$} & \scalebox{0.5}{$-0.0071 \pm 0.026(-0.27)$} & \scalebox{0.5}{$0.02 \pm 0.027(0.75)$} & \scalebox{0.5}{$-0.086 \pm 0.027(-3.2)$} & \scalebox{0.5}{$-0.03 \pm 0.025(-1.2)$} & \scalebox{0.5}{$0.021 \pm 0.027(0.79)$} \\ \hline -2 & \scalebox{0.5}{$-0.15 \pm 0.027(-5.8)$} & \scalebox{0.5}{$-0.013 \pm 0.026(-0.49)$} & \scalebox{0.5}{$0.011 \pm 0.026(0.44)$} & \scalebox{0.5}{$-0.039 \pm 0.026(-1.5)$} & \scalebox{0.5}{$-0.032 \pm 0.027(-1.2)$} & \scalebox{0.5}{$-0.066 \pm 0.027(-2.5)$} & \scalebox{0.5}{$0.018 \pm 0.028(0.64)$} \\ \hline -3 & \scalebox{0.5}{$-0.15 \pm 0.027(-5.6)$} & \scalebox{0.5}{$0.025 \pm 0.026(0.96)$} & \scalebox{0.5}{$0.016 \pm 0.027(0.58)$} & \scalebox{0.5}{$-0.062 \pm 0.027(-2.3)$} & \scalebox{0.5}{$0.037 \pm 0.026(1.4)$} & \scalebox{0.5}{$0.026 \pm 0.027(0.96)$} & \scalebox{0.5}{$-0.016 \pm 0.027(-0.6)$} \\ \hline -4 & \scalebox{0.5}{$-0.12 \pm 0.028(-4.5)$} & \scalebox{0.5}{$-0.024 \pm 0.026(-0.92)$} & \scalebox{0.5}{$0.045 \pm 0.027(1.6)$} & \scalebox{0.5}{$0.0075 \pm 0.026(0.29)$} & \scalebox{0.5}{$0.015 \pm 0.027(0.53)$} & \scalebox{0.5}{$-0.036 \pm 0.026(-1.4)$} & \scalebox{0.5}{$0.037 \pm 0.026(1.4)$} \\ \hline -5 & \scalebox{0.5}{$-0.095 \pm 0.027(-3.6)$} & \scalebox{0.5}{$-0.032 \pm 0.026(-1.2)$} & \scalebox{0.5}{$0.014 \pm 0.026(0.52)$} & \scalebox{0.5}{$-0.013 \pm 0.026(-0.48)$} & \scalebox{0.5}{$-0.0093 \pm 0.027(-0.35)$} & \scalebox{0.5}{$-0.013 \pm 0.026(-0.51)$} & \scalebox{0.5}{$0.042 \pm 0.027(1.6)$} \\ \hline -6 & \scalebox{0.5}{$-0.17 \pm 0.025(-6.5)$} & \scalebox{0.5}{$0.008 \pm 0.027(0.3)$} & \scalebox{0.5}{$0.012 \pm 0.027(0.45)$} & \scalebox{0.5}{$0.029 \pm 0.027(1.1)$} & \scalebox{0.5}{$0.0072 \pm 0.027(0.27)$} & \scalebox{0.5}{$-0.0012 \pm 0.026(-0.046)$} & \scalebox{0.5}{$0.011 \pm 0.027(0.42)$} \\ \hline -%7 & \scalebox{0.5}{$0.078 \pm 0.026(3)$} & \scalebox{0.5}{$-0.3 \pm 0.026(-11)$} & \scalebox{0.5}{$-0.34 \pm 0.026(-13)$} & \scalebox{0.5}{$2.1 \pm 0.028(73)$} & \scalebox{0.5}{$0.47 \pm 0.026(18)$} & \scalebox{0.5}{$-0.17 \pm 0.027(-6.1)$} & \scalebox{0.5}{$0.0051 \pm 0.027(0.19)$} \\ \hline -8 & \scalebox{0.5}{$-0.13 \pm 0.026(-5.1)$} & \scalebox{0.5}{$-0.0077 \pm 0.027(-0.28)$} & \scalebox{0.5}{$0.05 \pm 0.027(1.9)$} & \scalebox{0.5}{$-0.03 \pm 0.026(-1.2)$} & \scalebox{0.5}{$-0.012 \pm 0.028(-0.44)$} & \scalebox{0.5}{$-0.046 \pm 0.026(-1.7)$} & \scalebox{0.5}{$0.031 \pm 0.026(1.2)$} \\ \hline -9 & \scalebox{0.5}{$-0.15 \pm 0.026(-5.7)$} & \scalebox{0.5}{$-0.0083 \pm 0.026(-0.32)$} & \scalebox{0.5}{$0.03 \pm 0.026(1.2)$} & \scalebox{0.5}{$0.044 \pm 0.027(1.6)$} & \scalebox{0.5}{$-0.07 \pm 0.026(-2.7)$} & \scalebox{0.5}{$-0.022 \pm 0.026(-0.84)$} & \scalebox{0.5}{$-0.045 \pm 0.026(-1.7)$} \\ \hline -10 & \scalebox{0.5}{$-0.15 \pm 0.025(-5.8)$} & \scalebox{0.5}{$-0.032 \pm 0.025(-1.3)$} & \scalebox{0.5}{$0.059 \pm 0.026(2.2)$} & \scalebox{0.5}{$-0.072 \pm 0.028(-2.6)$} & \scalebox{0.5}{$-0.029 \pm 0.027(-1.1)$} & \scalebox{0.5}{$0.064 \pm 0.027(2.4)$} & \scalebox{0.5}{$0.014 \pm 0.027(0.51)$} \\ \hline -11 & \scalebox{0.5}{$-0.067 \pm 0.026(-2.6)$} & \scalebox{0.5}{$0.017 \pm 0.026(0.65)$} & \scalebox{0.5}{$-0.015 \pm 0.026(-0.56)$} & \scalebox{0.5}{$-0.051 \pm 0.026(-1.9)$} & \scalebox{0.5}{$-0.0086 \pm 0.026(-0.33)$} & \scalebox{0.5}{$-0.018 \pm 0.028(-0.67)$} & \scalebox{0.5}{$0.017 \pm 0.027(0.62)$} \\ \hline - - - - - - -\hline - - - \end{tabular} - -\end{center} - - -\end{tiny} -\end{frame} - - -\begin{frame}\frametitle{Corr3- MM} - - -\begin{tiny} - -\begin{center} - \begin{tabular}{ l l l l l l l l l } - \hline - \multicolumn{8}{c}{Mean of the pull} \\ \hline -$q^2$ & $S_3$ & $S_4$ & $S_5$ & $S_{6s}$ & $S_{6c}$ & $S_7$ & $S_8$ \\ \hline \hline - -0 & \scalebox{0.5}{$-0.021 \pm 0.026(-0.81)$} & \scalebox{0.5}{$0.041 \pm 0.026(1.5)$} & \scalebox{0.5}{$0.009 \pm 0.027(0.34)$} & \scalebox{0.5}{$0.043 \pm 0.026(1.6)$} & \scalebox{0.5}{$0.13 \pm 0.028(4.8)$} & \scalebox{0.5}{$-0.0072 \pm 0.028(-0.26)$} & \scalebox{0.5}{$0.044 \pm 0.026(1.7)$} \\ \hline -1 & \scalebox{0.5}{$-0.014 \pm 0.028(-0.51)$} & \scalebox{0.5}{$0.03 \pm 0.027(1.1)$} & \scalebox{0.5}{$0.022 \pm 0.027(0.82)$} & \scalebox{0.5}{$0.015 \pm 0.028(0.53)$} & \scalebox{0.5}{$0.078 \pm 0.028(2.8)$} & \scalebox{0.5}{$-0.037 \pm 0.025(-1.4)$} & \scalebox{0.5}{$0.057 \pm 0.027(2.1)$} \\ \hline -2 & \scalebox{0.5}{$-0.037 \pm 0.027(-1.4)$} & \scalebox{0.5}{$-0.0013 \pm 0.027(-0.048)$} & \scalebox{0.5}{$-0.015 \pm 0.027(-0.54)$} & \scalebox{0.5}{$-0.052 \pm 0.026(-2)$} & \scalebox{0.5}{$0.1 \pm 0.027(3.8)$} & \scalebox{0.5}{$-0.051 \pm 0.026(-1.9)$} & \scalebox{0.5}{$0.022 \pm 0.028(0.78)$} \\ \hline -3 & \scalebox{0.5}{$-0.015 \pm 0.027(-0.55)$} & \scalebox{0.5}{$0.036 \pm 0.028(1.3)$} & \scalebox{0.5}{$-0.039 \pm 0.027(-1.4)$} & \scalebox{0.5}{$-0.072 \pm 0.027(-2.7)$} & \scalebox{0.5}{$0.17 \pm 0.027(6.2)$} & \scalebox{0.5}{$-0.0044 \pm 0.028(-0.15)$} & \scalebox{0.5}{$-0.024 \pm 0.027(-0.9)$} \\ \hline -4 & \scalebox{0.5}{$-0.00047 \pm 0.029(-0.017)$} & \scalebox{0.5}{$-0.012 \pm 0.027(-0.43)$} & \scalebox{0.5}{$0.0099 \pm 0.028(0.35)$} & \scalebox{0.5}{$-0.002 \pm 0.026(-0.076)$} & \scalebox{0.5}{$0.17 \pm 0.028(6.2)$} & \scalebox{0.5}{$-0.062 \pm 0.027(-2.3)$} & \scalebox{0.5}{$0.0086 \pm 0.027(0.32)$} \\ \hline - -5 & \scalebox{0.5}{$0.046 \pm 0.027(1.7)$} & \scalebox{0.5}{$-0.02 \pm 0.026(-0.76)$} & \scalebox{0.5}{$-0.04 \pm 0.027(-1.5)$} & \scalebox{0.5}{$-0.012 \pm 0.027(-0.44)$} & \scalebox{0.5}{$0.13 \pm 0.027(4.8)$} & \scalebox{0.5}{$-0.04 \pm 0.027(-1.5)$} & \scalebox{0.5}{$-0.0056 \pm 0.027(-0.21)$} \\ \hline -6 & \scalebox{0.5}{$-0.013 \pm 0.026(-0.52)$} & \scalebox{0.5}{$0.041 \pm 0.027(1.5)$} & \scalebox{0.5}{$-0.033 \pm 0.028(-1.2)$} & \scalebox{0.5}{$-0.0019 \pm 0.027(-0.068)$} & \scalebox{0.5}{$0.15 \pm 0.027(5.4)$} & \scalebox{0.5}{$-0.034 \pm 0.027(-1.3)$} & \scalebox{0.5}{$-0.021 \pm 0.028(-0.75)$} \\ \hline -%7 & \scalebox{0.5}{$0.25 \pm 0.027(9.1)$} & \scalebox{0.5}{$-0.27 \pm 0.027(-10)$} & \scalebox{0.5}{$-0.41 \pm 0.027(-16)$} & \scalebox{0.5}{$2.1 \pm 0.029(73)$} & \scalebox{0.5}{$0.65 \pm 0.027(24)$} & \scalebox{0.5}{$-0.19 \pm 0.028(-7)$} & \scalebox{0.5}{$-0.053 \pm 0.028(-1.9)$} \\ \hline -8 & \scalebox{0.5}{$0.039 \pm 0.026(1.5)$} & \scalebox{0.5}{$0.01 \pm 0.028(0.36)$} & \scalebox{0.5}{$-0.027 \pm 0.028(-0.96)$} & \scalebox{0.5}{$-0.024 \pm 0.026(-0.9)$} & \scalebox{0.5}{$0.12 \pm 0.027(4.3)$} & \scalebox{0.5}{$-0.092 \pm 0.026(-3.5)$} & \scalebox{0.5}{$-0.036 \pm 0.027(-1.3)$} \\ \hline -9 & \scalebox{0.5}{$-0.01 \pm 0.027(-0.38)$} & \scalebox{0.5}{$0.0024 \pm 0.027(0.09)$} & \scalebox{0.5}{$-0.018 \pm 0.026(-0.68)$} & \scalebox{0.5}{$0.022 \pm 0.028(0.79)$} & \scalebox{0.5}{$0.068 \pm 0.027(2.6)$} & \scalebox{0.5}{$-0.069 \pm 0.026(-2.6)$} & \scalebox{0.5}{$-0.078 \pm 0.026(-3)$} \\ \hline -10 & \scalebox{0.5}{$-0.017 \pm 0.027(-0.62)$} & \scalebox{0.5}{$-0.015 \pm 0.026(-0.57)$} & \scalebox{0.5}{$0.012 \pm 0.027(0.46)$} & \scalebox{0.5}{$-0.074 \pm 0.028(-2.6)$} & \scalebox{0.5}{$0.1 \pm 0.027(3.8)$} & \scalebox{0.5}{$-0.003 \pm 0.027(-0.11)$} & \scalebox{0.5}{$-0.043 \pm 0.029(-1.5)$} \\ \hline -11 & \scalebox{0.5}{$0.032 \pm 0.026(1.2)$} & \scalebox{0.5}{$0.024 \pm 0.026(0.91)$} & \scalebox{0.5}{$-0.04 \pm 0.026(-1.5)$} & \scalebox{0.5}{$-0.066 \pm 0.027(-2.5)$} & \scalebox{0.5}{$0.098 \pm 0.027(3.7)$} & \scalebox{0.5}{$-0.043 \pm 0.028(-1.6)$} & \scalebox{0.5}{$-0.0018 \pm 0.028(-0.064)$} \\ \hline - - - -\hline - - - \end{tabular} - -\end{center} - - -\end{tiny} -\end{frame} - -\begin{frame}\frametitle{Corr4- MM} - - -\begin{tiny} - -\begin{center} - \begin{tabular}{ l l l l l l l l l } - \hline - \multicolumn{8}{c}{Mean of the pull} \\ \hline -$q^2$ & $S_3$ & $S_4$ & $S_5$ & $S_{6s}$ & $S_{6c}$ & $S_7$ & $S_8$ \\ \hline \hline - - -0 & \scalebox{0.5}{$-0.019 \pm 0.026(-0.71)$} & \scalebox{0.5}{$0.048 \pm 0.027(1.8)$} & \scalebox{0.5}{$0.018 \pm 0.027(0.67)$} & \scalebox{0.5}{$0.059 \pm 0.027(2.2)$} & \scalebox{0.5}{$-0.015 \pm 0.028(-0.55)$} & \scalebox{0.5}{$0.061 \pm 0.027(2.2)$} & \scalebox{0.5}{$0.012 \pm 0.027(0.44)$} \\ \hline -1 & \scalebox{0.5}{$-0.014 \pm 0.028(-0.51)$} & \scalebox{0.5}{$0.043 \pm 0.027(1.6)$} & \scalebox{0.5}{$0.013 \pm 0.027(0.49)$} & \scalebox{0.5}{$0.024 \pm 0.028(0.86)$} & \scalebox{0.5}{$-0.038 \pm 0.028(-1.4)$} & \scalebox{0.5}{$0.024 \pm 0.026(0.94)$} & \scalebox{0.5}{$0.037 \pm 0.027(1.3)$} \\ \hline -2 & \scalebox{0.5}{$-0.03 \pm 0.027(-1.1)$} & \scalebox{0.5}{$-0.0021 \pm 0.027(-0.076)$} & \scalebox{0.5}{$-0.01 \pm 0.027(-0.39)$} & \scalebox{0.5}{$-0.017 \pm 0.027(-0.61)$} & \scalebox{0.5}{$-0.016 \pm 0.027(-0.58)$} & \scalebox{0.5}{$0.013 \pm 0.027(0.49)$} & \scalebox{0.5}{$0.027 \pm 0.028(0.98)$} \\ \hline -3 & \scalebox{0.5}{$-0.007 \pm 0.027(-0.26)$} & \scalebox{0.5}{$0.03 \pm 0.028(1.1)$} & \scalebox{0.5}{$-0.036 \pm 0.027(-1.3)$} & \scalebox{0.5}{$-0.074 \pm 0.027(-2.8)$} & \scalebox{0.5}{$0.041 \pm 0.027(1.5)$} & \scalebox{0.5}{$0.08 \pm 0.028(2.9)$} & \scalebox{0.5}{$-0.0083 \pm 0.027(-0.31)$} \\ \hline -4 & \scalebox{0.5}{$0.00089 \pm 0.029(0.031)$} & \scalebox{0.5}{$-0.021 \pm 0.027(-0.77)$} & \scalebox{0.5}{$0.0032 \pm 0.028(0.11)$} & \scalebox{0.5}{$0.0031 \pm 0.026(0.12)$} & \scalebox{0.5}{$0.012 \pm 0.027(0.44)$} & \scalebox{0.5}{$0.019 \pm 0.026(0.71)$} & \scalebox{0.5}{$0.034 \pm 0.027(1.3)$} \\ \hline -5 & \scalebox{0.5}{$0.044 \pm 0.028(1.6)$} & \scalebox{0.5}{$-0.022 \pm 0.026(-0.82)$} & \scalebox{0.5}{$-0.041 \pm 0.027(-1.5)$} & \scalebox{0.5}{$-0.014 \pm 0.027(-0.53)$} & \scalebox{0.5}{$-0.029 \pm 0.027(-1.1)$} & \scalebox{0.5}{$0.041 \pm 0.027(1.5)$} & \scalebox{0.5}{$0.042 \pm 0.028(1.5)$} \\ \hline -6 & \scalebox{0.5}{$-0.011 \pm 0.026(-0.42)$} & \scalebox{0.5}{$0.041 \pm 0.027(1.5)$} & \scalebox{0.5}{$-0.045 \pm 0.028(-1.6)$} & \scalebox{0.5}{$0.011 \pm 0.027(0.41)$} & \scalebox{0.5}{$-0.0089 \pm 0.027(-0.33)$} & \scalebox{0.5}{$0.067 \pm 0.027(2.5)$} & \scalebox{0.5}{$0.036 \pm 0.027(1.3)$} \\ \hline -%7 & \scalebox{0.5}{$0.25 \pm 0.027(9.1)$} & \scalebox{0.5}{$-0.26 \pm 0.027(-9.9)$} & \scalebox{0.5}{$-0.42 \pm 0.027(-16)$} & \scalebox{0.5}{$2.1 \pm 0.029(73)$} & \scalebox{0.5}{$0.47 \pm 0.027(18)$} & \scalebox{0.5}{$-0.077 \pm 0.028(-2.8)$} & \scalebox{0.5}{$0.029 \pm 0.028(1)$} \\ \hline -8 & \scalebox{0.5}{$0.05 \pm 0.026(1.9)$} & \scalebox{0.5}{$0.0021 \pm 0.028(0.074)$} & \scalebox{0.5}{$-0.025 \pm 0.028(-0.91)$} & \scalebox{0.5}{$-0.023 \pm 0.026(-0.87)$} & \scalebox{0.5}{$-0.024 \pm 0.028(-0.85)$} & \scalebox{0.5}{$0.022 \pm 0.026(0.82)$} & \scalebox{0.5}{$0.026 \pm 0.026(0.98)$} \\ \hline -9 & \scalebox{0.5}{$-0.0064 \pm 0.027(-0.23)$} & \scalebox{0.5}{$0.012 \pm 0.027(0.44)$} & \scalebox{0.5}{$-0.0075 \pm 0.026(-0.28)$} & \scalebox{0.5}{$0.029 \pm 0.027(1.1)$} & \scalebox{0.5}{$-0.087 \pm 0.027(-3.2)$} & \scalebox{0.5}{$0.036 \pm 0.027(1.3)$} & \scalebox{0.5}{$-0.02 \pm 0.026(-0.76)$} \\ \hline -10 & \scalebox{0.5}{$-0.019 \pm 0.027(-0.71)$} & \scalebox{0.5}{$-0.0051 \pm 0.025(-0.2)$} & \scalebox{0.5}{$0.0081 \pm 0.026(0.31)$} & \scalebox{0.5}{$-0.077 \pm 0.028(-2.7)$} & \scalebox{0.5}{$-0.03 \pm 0.027(-1.1)$} & \scalebox{0.5}{$0.11 \pm 0.027(4.1)$} & \scalebox{0.5}{$0.013 \pm 0.028(0.46)$} \\ \hline -11 & \scalebox{0.5}{$0.027 \pm 0.026(1)$} & \scalebox{0.5}{$0.032 \pm 0.027(1.2)$} & \scalebox{0.5}{$-0.038 \pm 0.027(-1.4)$} & \scalebox{0.5}{$-0.048 \pm 0.026(-1.8)$} & \scalebox{0.5}{$-0.021 \pm 0.027(-0.77)$} & \scalebox{0.5}{$0.019 \pm 0.028(0.69)$} & \scalebox{0.5}{$0.035 \pm 0.027(1.3)$} \\ \hline - - - -\hline - - \end{tabular} - -\end{center} - -\end{tiny} -\end{frame} - - - - -%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% -\section{Reverse Engineering Unfolding} - -\begin{frame}\frametitle{Reverse Engineering- Corr1} -\begin{itemize} -\item Let's try to understand if we can understand why this happens: -\item Let's calculate what should I expect with the unfolding -\item This is up to normalization! -\begin{itemize} -\item $M_5=0.4 S_5 \to M_5=0.00512 S_3 + 0.4 S_5 - 0.002 S_7$ -\item $M_8=0.32 S_8 \to M_8=0.0016 S_4 + 0.00512 S_7 + 0.32 S_8$ -\item $M_7=0.4 S_7 \to M_7=0.002 S_5 + 0.4 S_7 + 0.00512 S_8$ -\item $M_3=0.32 S_3 \to M_3=0.32 S_3 - 0.0008 S_9$ -\end{itemize} -\item The way you can look at this is that i just shown you how our unfolding matrix works like. -\end{itemize} - - - -\end{frame} - -\begin{frame}\frametitle{Reverse Engineering- Corr2} -\begin{itemize} -\item Let's try to understand if we can understand why this happens: -\item Let's calculate what should I expect with the unfolding -\item This is up to normalization! -\begin{itemize} -\item $M_5=0.4 S_5 \to M_5= 0.4 S_5$ -\item $M_8=0.32 S_8 \to M_8=0.32 S_5$ -\item $M_7=0.4 S_7 \to M_7=0.4 S_7$ -\item $M_3=0.32 S_3 \to M_3=-0.0036 + 0.0012 Fl + 0.32 S_3$ -\end{itemize} -\item The way you can look at this is that i just shown you how our unfolding matrix works like. -\end{itemize} - - - -\end{frame} - - - - -\begin{frame}\frametitle{Summary} -\begin{itemize} -\item Developed a systematic way how to get Unfolding matrix -\item Moments are resistant against variety of unfolding discrepancies. -\item This might lead to reduced systematics in the future. -\end{itemize} - - - - -\end{frame} - - - -\end{document} diff --git a/Kstmumu/MMatrix2/MMatrix.toc b/Kstmumu/MMatrix2/MMatrix.toc deleted file mode 100644 index 1e71ea5..0000000 --- a/Kstmumu/MMatrix2/MMatrix.toc +++ /dev/null @@ -1,3 +0,0 @@ -\beamer@endinputifotherversion {3.10pt} -\select@language {english} -\beamer@sectionintoc {1}{Introduction}{2}{0}{1} diff --git a/Kstmumu/MMatrix2/P5.png b/Kstmumu/MMatrix2/P5.png deleted file mode 100644 index 7819eef..0000000 --- a/Kstmumu/MMatrix2/P5.png +++ /dev/null Binary files differ diff --git a/Kstmumu/MMatrix2/Q2_4_S8.png b/Kstmumu/MMatrix2/Q2_4_S8.png deleted file mode 100644 index 9176de4..0000000 --- a/Kstmumu/MMatrix2/Q2_4_S8.png +++ /dev/null Binary files differ diff 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b/Kstmumu/M_matrix/MM.pdf new file mode 100644 index 0000000..160ac5e --- /dev/null +++ b/Kstmumu/M_matrix/MM.pdf Binary files differ diff --git a/Kstmumu/M_matrix/MM.snm b/Kstmumu/M_matrix/MM.snm new file mode 100644 index 0000000..e69de29 --- /dev/null +++ b/Kstmumu/M_matrix/MM.snm diff --git a/Kstmumu/M_matrix/MM.synctex.gz b/Kstmumu/M_matrix/MM.synctex.gz new file mode 100644 index 0000000..78b4daf --- /dev/null +++ b/Kstmumu/M_matrix/MM.synctex.gz Binary files differ diff --git a/Kstmumu/M_matrix/MM.tex b/Kstmumu/M_matrix/MM.tex new file mode 100644 index 0000000..2e9ab92 --- /dev/null +++ b/Kstmumu/M_matrix/MM.tex @@ -0,0 +1,1097 @@ +\documentclass[]{beamer} +\setbeamertemplate{navigation symbols}{} +\usepackage{beamerthemesplit} +\useoutertheme{infolines} +\usecolortheme{dolphin} +%\usetheme{Warsaw} +\usetheme{progressbar} +\usecolortheme{progressbar} + +\usefonttheme{progressbar} +\useoutertheme{progressbar} +\useinnertheme{progressbar} +\usepackage{graphicx} +%\usepackage{amssymb,amsmath} +\usepackage[latin1]{inputenc} +\usepackage{amsmath} +\newcommand\abs[1]{\left|#1\right|} +\usepackage{iwona} +\usepackage{hepparticles} +\usepackage{hepnicenames} +\usepackage{hepunits} +\progressbaroptions{imagename=images/lhcb} +%\usetheme{Boadilla}f + +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%5 +\definecolor{mygreen}{cmyk}{0.82,0.11,1,0.25} +\setbeamertemplate{blocks}[rounded][shadow=false] +\addtobeamertemplate{block begin}{\pgfsetfillopacity{0.8}}{\pgfsetfillopacity{1}} +\setbeamercolor{structure}{fg=mygreen} +\setbeamercolor*{block title example}{fg=mygreen!50, +bg= blue!10} +\setbeamercolor*{block body example}{fg= blue, +bg= blue!5} + + + + + +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%\beamersetuncovermixins{\opaqueness<1>{25}}{\opaqueness<2->{15}} +\title{Method of moments for $\PB \to \PKstar \mu \mu$} +\author{\underline{Marcin Chrzaszcz}$^{1,2}$} +\date{\today} + +\begin{document} + +{ +\institute{$^1$ University of Zurich, $^2$ Institute of Nuclear Physics} +\setbeamertemplate{footline}{} +\begin{frame} +\logo{ +\vspace{2 mm} +\includegraphics[height=1cm,keepaspectratio]{images/uzh.jpg}~ +\includegraphics[width=1cm,keepaspectratio]{images/ifj.png}} + + \titlepage +\end{frame} +} +\institute{UZH,IFJ} + +\section[Outline]{} +\begin{frame} +\tableofcontents +\end{frame} + +\section{Introduction} +\begin{frame}\frametitle{Plan} +Why method of moments: +\begin{enumerate} +\item Complementary approach in performing the fit. +\item Allows to extract info measuring quantities in event basis depending on the angular distribution. +\item Used in $\PB \to \rho \Plepton \nu$(SLAC-386 UC-414),\\ $\PJpsi \to \PK \PK \gamma$(PRD 71, 032005 (2005) ), etc. +\end{enumerate} + + +\end{frame} +\section{Method of Moments - Theory} +\begin{frame}\frametitle{Method of moments} +{~} +Let's assume we have our pdf with $k$ unknown parameters :$PDF(x_i, \alpha)$, $dim(\alpha)=k$. One can calculate $k$ moments, which are the functions of $\alpha_i$: +\begin{equation} +\mu_i=f(\alpha_1,..., \alpha_k) = E[W_i] +\end{equation} +If we have $n$ events in our $q^2$ bin, we can estimate: +\begin{equation} +\widehat{\mu}_i=\dfrac{1}{n}\sum_{j=0}^{j=n-1} w_j +\end{equation} +, where $w_j=g(x_i)$ + +\end{frame} + +\begin{frame}\frametitle{Trivial example} +{~} +Lets see how this works in practice: +\begin{equation} +f(x)=\dfrac{x^{a-1}e^{-x/b}} {b^a \Gamma(a)} +\end{equation} +we measure the moments:\\ +\begin{center} $m_1=\dfrac{X_1+X_2+...+X_n}{n}$,\\ $m_2=\dfrac{X_1^2+X_2^2+...+X_n^2}{n}$.\\\end{center} +and calculate them analytically: +\begin{center} $m_1=ab$, $m_2=b^2a(a+1)$\end{center} +So one just needs to solve this and get the answer: +\center $a=\dfrac{m_1^2}{m_2-m_1^2}$, $b=\dfrac{m_2-m_1^2}{m_1}$ +\end{frame} + +\section{Moments of Ss} + + +\begin{frame}\frametitle{Our PDF} +{~} +The angular terms: +\begin{multline} +\dfrac{d^4\Gamma}{dq^2 dcos\theta_k dcos\theta_l d\phi}=\dfrac{9}{32\pi}( \dfrac{3}{4}(1-F_l)\sin^2 \theta_k + F_l \cos^2 \theta_k + (\dfrac{1}{4}(1-F_l)\sin^2 \theta_k \\ -F_l\cos^2) \cos 2\theta_l + J_3 \sin^2 \theta_k \sin^2 \theta_l cos2\phi + J_4 \sin2 \theta_k \sin \theta_l \cos\phi +\\ J_5 \sin 2 \theta_k \sin \theta_l \cos \phi + (J_{6s} \sin^2 \theta_k + J_{6c} \cos^2 \theta_k) \cos \theta_l + \\ J_7 \sin 2\theta_k \sin \theta_l \sin \phi + J_8 \sin 2 \theta_k \sin 2 \theta_l \sin \phi + J_9 \sin^2 \theta_k \sin^2 \theta_l \sin 2 \phi) +\end{multline} +Since we are fitting a PDF we need to ensure it is normalized: +\begin{equation} +\int_{-\pi}^{\pi} d\phi \int_{-1}^{1} d cos\theta_l \int_{-1}^{1} d cos\theta_k \dfrac{d^4\Gamma}{dq^2 dcos\theta_k dcos\theta_l d\phi}=1 +\end{equation} + + +\end{frame} +\begin{frame}\frametitle{Measuring Js} +{~} +From equation 2 we have the following: + +\begin{equation} +\dfrac{1}{4}(3 J_{1c} + 6 J_{1s} - J_{2c} - 2 J_{2s}) =1 +\end{equation} +For now we will consider the following PDF: +\begin{equation} + \dfrac{d^3\Gamma}{\Gamma dcos\theta_k dcos\theta_l d\phi }(cos\theta_k , cos\theta_l, \phi) +\end{equation} + +Becouse our PDF is not normalized and we are measuring $\Gamma+\overline{\Gamma} +$ we are effectively fitting the $S_i$ (aka $J_i \to S_i$) +\end{frame} + + +\begin{frame}\frametitle{Moments for $\PB \to \PKstar \mu \mu$} +{~} +Let's calculate the moments for Ss: +\begin{equation} + \dfrac{d^3\Gamma}{\Gamma dcos\theta_k dcos\theta_l d\phi }sin^2 \theta_k sin^2 \theta_l cos 2 \phi= \dfrac{8 S_3 }{25} +\end{equation} +\begin{equation} + \dfrac{d^3\Gamma}{\Gamma dcos\theta_k dcos\theta_l d\phi } sin 2 \theta_k sin 2 \theta_k cos\phi= \dfrac{8 S_4 }{25} +\end{equation} +\begin{equation} + \dfrac{d^3\Gamma}{\Gamma dcos\theta_k dcos\theta_l d\phi }sin2\theta_k sin\theta_l cos\phi = \dfrac{2 S_5 }{5} +\end{equation} +\begin{equation} + \dfrac{d^3\Gamma}{\Gamma dcos\theta_k dcos\theta_l d\phi} sin 2 \theta_k sin \theta_l sin \phi = \dfrac{2 S_7 }{5} +\end{equation} +\begin{equation} + \dfrac{d^3\Gamma}{\Gamma dcos\theta_k dcos\theta_l d\phi} sin 2 \theta_k sin2 \theta_l sin \phi = \dfrac{8 S_8 }{25} +\end{equation} + + + +\end{frame} +\begin{frame}\frametitle{Moments for $\PB \to \PKstar \mu \mu$} +{~} +\begin{itemize} +\item The simplest solution one could imagine. +\item We are abusing the fact that the basis is orthogonal. +\item Each of the J doesn't know about other. +\item Only $S_{1s}$, $S_{2s}$, $S_{1c}$, $S_{2c}$ and $S_{6s}$, $S_{6c}$ are not orthogonal, but to get the answer you just need to solve a linear equation system so it's not a tragedy. +\end{itemize} +\begin{equation} + \dfrac{d^3\Gamma}{\Gamma dcos\theta_k dcos\theta_l d\phi} sin^2 \theta_k cos \theta_l = 0.1(S_6c+4S_6s) +\end{equation} +\begin{equation} + \dfrac{d^3\Gamma}{\Gamma dcos\theta_k dcos\theta_l d\phi} cos \theta_l = 0.25(S_{6}c+2S_{6s}) +\end{equation} + +solution: $S_{6c}=2 (4 M_{S_{6c}} - 5 M_{S_{6s}})$, $S_{6s}= -2 M_{S_{6c}} + 5 M_{S_{6s}}$ + + + +\end{frame} + + + +\section{Toy MC study} + +\begin{frame}\frametitle{Moments for $\PB \to \PKstar \mu \mu$} +{~} +Lets see if this method actually works. Let's take some random parameters for the PDF and make a toy. +\begin{columns} +\column{2.5in} +\includegraphics[scale=0.25]{images/J5.png} + + + +\column{2.5in} +\includegraphics[scale=0.25]{images/J7.png} + + +\end{columns} +\begin{itemize} +\item let's take 300 signal events as a working case. +\end{itemize} + +\end{frame} + + + + +\begin{frame}\frametitle{Moments for $\PB \to \PKstar \mu \mu$} +{~} +\small Lets see if this method actually works. Let's take some random parameters for the PDF and make a toy. +\begin{columns} +\column{2.5in} +\includegraphics[scale=0.25]{images/J3.png} + + + +\column{2.5in} +\includegraphics[scale=0.25]{images/J4.png} + + +\end{columns} + + +\begin{itemize} +\item let's take 300 signal events as a working case... we might still change the binning +\end{itemize} + +\end{frame} + + + +\begin{frame}\frametitle{Moments for $\PB \to \PKstar \mu \mu$} +{~} +Lets see if this method actually works. Let's take some random parameters for the PDF and make a toy. +\begin{columns} +\column{2.5in} +\includegraphics[scale=0.25]{images/J8.png} + + + +\column{2.5in} +\includegraphics[scale=0.25]{images/J9.png} + + +\end{columns} + +\begin{itemize} +\item let's take 300 signal events as a working case... we might still change the binning +\end{itemize} + +\end{frame} + +\begin{frame}\frametitle{Error Estimation} +{~} +\begin{itemize} +\item Since moment is the mean of a given distribution the error can be estimated as $mean/RMS$ +\item use TOY MC to check this assumption +\end{itemize} + +\includegraphics[scale=0.3]{plots/conw.png}\\ + + +\end{frame} +%%%%%%%%%%%%%%%%%%%%%%%%5 +\begin{frame}\frametitle{Correlation check} +{~} +\begin{itemize} +\item In theory $S_i$ shouldn't be correlated to $S_j$ in the moment calculation. +\item Lets put this to a test. +\end{itemize} + +\begin{columns} +\column{2.5in} +\includegraphics[scale=0.2]{plots/J9J4.png}\\ + + +\column{2.5in} +\includegraphics[scale=0.2]{plots/J8J5.png}\\ + + +\end{columns} + + +\end{frame} + + +%%%%%%%%%%%%%%%%%%%%%%%%5 +\begin{frame}\frametitle{Correlation check 2} +{~} +\begin{itemize} +\item Let's now FIX $J_x$ and simulate different $J_y$ +\item Again theory would suggest that one J shouldn't know about the other, so $J_x$ shouldn't change with scanning $J_y$ parameter +\end{itemize} + +\begin{columns} +\column{2.5in} +\includegraphics[scale=0.24]{plots/J5_vs_J9_300.png}\\ + + +\column{2.5in} +\includegraphics[scale=0.24]{plots/J3_vs_J9_300.png}\\ + + +\end{columns} + + +\end{frame} + + + +\section{2 am discovery} +\begin{frame}\frametitle{What will happen to our problem with an S-wave?} +{~} +Reminder: +\begin{multline} +\dfrac{d^4\Gamma}{dq^2 dcos\theta_k dcos\theta_l d\phi}=\dfrac{9}{32\pi}( J_{1s}sin^2 \theta_k + J_{1c}cos^2 \theta_k + (J_{2s}sin^2 \theta_k + \\ J_{2c}cos^2) cos 2\theta_l + J_3 sin^2 \theta_k sin^2 \theta_l cos2\phi + J_4 sin2 \theta_k sin \theta_l cos\phi +\\ J_5 sin2 \theta_k sin \theta_l cos \phi + (J_{6s} sin^2 \theta_k + J_{6c} cos^2 \theta_k) cos \theta_l + \\ J_7 sin 2\theta_k sin \theta_l sin \phi + J_8 sin 2 \theta_k sin 2 \theta_l sin phi + J_9 sin^2 \theta_k sin^2 \theta_l sin 2 \phi) +\end{multline} +Let's add a very discussing things that keeps us awake at night: +\begin{multline} +W_s =\dfrac{2}{3} F_s \sin^2 \theta_l + \frac{4}{3} A_s \sin^2 \theta_l \cos \theta_k + I_4 sin \theta_k sin 2 \theta_lcos \phi \\+ I_5 sin \theta_k sin \theta_l cos \phi + I_7 sin \theta_k sin \theta_l + sin \phi + I_8 sin \theta_k sin 2\theta_l sin\phi) +\end{multline} + + +\end{frame} + +\begin{frame}\frametitle{What will happen to our problem with an S-wave?} +{~} +So now our PDF is sum of eq. 15 and 16. Of coz we need to require normalization: +\begin{equation} +\dfrac{1}{12}(32 I_{1a} + 9 J_{1c} + 18 J_{1s} - 3 J_{2c} - 6 J_{2s}) =1 +\end{equation} +No surprises here. If we have a S-wave it has to enter in $\Gamma$. +To build up the preasure, what will happen to our Ss? + + + +\end{frame} + + +\begin{frame}\frametitle{NOTHING!!!!!!!!} +{~} +We are completely insensitive to S-wave: +\begin{equation} + \dfrac{d^3\Gamma}{\Gamma dcos\theta_k dcos\theta_l d\phi }sin^2 \theta_k sin^2 \theta_l cos 2 \phi= \dfrac{8 S_3 }{25} +\end{equation} +\begin{equation} + \dfrac{d^3\Gamma}{\Gamma dcos\theta_k dcos\theta_l d\phi } sin 2 \theta_k sin 2 \theta_k cos\phi= \dfrac{8 S_4 }{25} +\end{equation} +\begin{equation} + \dfrac{d^3\Gamma}{\Gamma dcos\theta_k dcos\theta_l d\phi }sin2\theta_k sin\theta_l cos\phi = \dfrac{2 S_5 }{5} +\end{equation} +\begin{equation} + \dfrac{d^3\Gamma}{\Gamma dcos\theta_k dcos\theta_l d\phi} sin 2 \theta_k sin \theta_l sin \phi = \dfrac{2 S_7 }{5} +\end{equation} +\begin{equation} + \dfrac{d^3\Gamma}{\Gamma dcos\theta_k dcos\theta_l d\phi} sin 2 \theta_k sin2 \theta_l sin \phi = \dfrac{8 S_8 }{25} +\end{equation} + + + +\end{frame} + +\begin{frame}\frametitle{Thins get better :)} +{~} +We can even measure directly the S-wave: +\begin{equation} + \dfrac{d^3\Gamma}{\Gamma dcos\theta_k dcos\theta_l d\phi }sin^2 \theta_l cos \theta_k = \dfrac{32 I_{1b} }{45} +\end{equation} +\begin{equation} + \dfrac{d^3\Gamma}{\Gamma dcos\theta_k dcos\theta_l d\phi } sin \theta_k sin 2 \theta_l cos \phi = \dfrac{16 I_4 }{45} +\end{equation} +\begin{equation} + \dfrac{d^3\Gamma}{\Gamma dcos\theta_k dcos\theta_l d\phi } sin\theta_k sin\theta_l cos\phi = \dfrac{4 I_5 }{9} +\end{equation} +\begin{equation} + \dfrac{d^3\Gamma}{\Gamma dcos\theta_k dcos\theta_l d\phi} sin \theta_k sin 2 \theta_l sin \phi = \dfrac{4 I_7 }{9} +\end{equation} +\begin{equation} + \dfrac{d^3\Gamma}{\Gamma dcos\theta_k dcos\theta_l d\phi} sin \theta_k sin2 \theta_l sin \phi = \dfrac{16 S_8 }{45} +\end{equation} + + + +\end{frame} + + +\begin{frame}\frametitle{Conclusions on S-wave} +{~} +\begin{itemize} +\item S-wave components are transparent to method of moments. +\item If they are orthogonal to others all they toy studies holds for them as well(will reapat for robustness but can bet my house that there is nothing going on there). +\item +\end{itemize} + +\end{frame} + + + +\begin{frame}\frametitle{Conclusions} +{~} +\begin{itemize} +\item Implemented moments method for the K*mm and start testing with toy MC +\item The method converge fast and works for the "simple case", i.e. signal only. +\item Method completely insensitive to S-wave component, thanks to orthogonality. +\item Complementary one can measure in-depended S-wave component. +\end{itemize} +TO DO: +\begin{itemize} +\item add realism: backgrounds +\item Do the unfolding +\item Study binning +\end{itemize} + +\end{frame} +%%%%%%%%%%%%%%%%%%%%%%%%%55 +\begin{frame}\frametitle{~} +{~} +\center \Huge BACKUPS + +\end{frame} + +\begin{frame} +{~} + +\begin{columns} +\column{2.5in} +\includegraphics[scale=0.17]{plots/pool_plots/J1c_50.png}\\ +\includegraphics[scale=0.17]{plots/pool_plots/J1c_75.png}\\ + + +\column{2.5in} +\includegraphics[scale=0.17]{plots/pool_plots/J1c_50E.png}\\ +\includegraphics[scale=0.17]{plots/pool_plots/J1c_75E.png} + + +\end{columns} +\end{frame} + +\begin{frame} +{~} + +\begin{columns} +\column{2.5in} +\includegraphics[scale=0.17]{plots/pool_plots/J1c_125.png}\\ +\includegraphics[scale=0.17]{plots/pool_plots/J1c_175.png}\\ + + +\column{2.5in} +\includegraphics[scale=0.17]{plots/pool_plots/J1c_125E.png}\\ +\includegraphics[scale=0.17]{plots/pool_plots/J1c_175E.png} + + +\end{columns} +\end{frame} + +\begin{frame} +{~} + +\begin{columns} +\column{2.5in} +\includegraphics[scale=0.17]{plots/pool_plots/J1c_225.png}\\ +\includegraphics[scale=0.17]{plots/pool_plots/J1c_300.png}\\ + + +\column{2.5in} +\includegraphics[scale=0.17]{plots/pool_plots/J1c_225E.png}\\ +\includegraphics[scale=0.17]{plots/pool_plots/J1c_300E.png} + + +\end{columns} +\end{frame} + + +\begin{frame} +{~} + +\begin{columns} +\column{2.5in} +\includegraphics[scale=0.17]{plots/pool_plots/J1c_400.png}\\ + + + +\column{2.5in} +\includegraphics[scale=0.17]{plots/pool_plots/J1c_400E.png}\\ + + + +\end{columns} +\end{frame} + +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%55 +\begin{frame} +{~} + +\begin{columns} +\column{2.5in} +\includegraphics[scale=0.17]{plots/pool_plots/J1s_50.png}\\ +\includegraphics[scale=0.17]{plots/pool_plots/J1s_75.png}\\ + + +\column{2.5in} +\includegraphics[scale=0.17]{plots/pool_plots/J1s_50E.png}\\ +\includegraphics[scale=0.17]{plots/pool_plots/J1s_75E.png} + + +\end{columns} +\end{frame} + +\begin{frame} +{~} + +\begin{columns} +\column{2.5in} +\includegraphics[scale=0.17]{plots/pool_plots/J1s_125.png}\\ +\includegraphics[scale=0.17]{plots/pool_plots/J1s_175.png}\\ + + +\column{2.5in} +\includegraphics[scale=0.17]{plots/pool_plots/J1s_125E.png}\\ +\includegraphics[scale=0.17]{plots/pool_plots/J1s_175E.png} + + +\end{columns} +\end{frame} + +\begin{frame} +{~} + +\begin{columns} +\column{2.5in} +\includegraphics[scale=0.17]{plots/pool_plots/J1s_225.png}\\ +\includegraphics[scale=0.17]{plots/pool_plots/J1s_300.png}\\ + + +\column{2.5in} +\includegraphics[scale=0.17]{plots/pool_plots/J1s_225E.png}\\ +\includegraphics[scale=0.17]{plots/pool_plots/J1s_300E.png} + + +\end{columns} +\end{frame} + + +\begin{frame} +{~} + +\begin{columns} +\column{2.5in} +\includegraphics[scale=0.17]{plots/pool_plots/J1s_400.png}\\ + + + +\column{2.5in} +\includegraphics[scale=0.17]{plots/pool_plots/J1s_400E.png}\\ + + + +\end{columns} +\end{frame} + +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +\begin{frame} +{~} + +\begin{columns} +\column{2.5in} +\includegraphics[scale=0.17]{plots/pool_plots/J2c_50.png}\\ +\includegraphics[scale=0.17]{plots/pool_plots/J2c_75.png}\\ + + +\column{2.5in} +\includegraphics[scale=0.17]{plots/pool_plots/J2c_50E.png}\\ +\includegraphics[scale=0.17]{plots/pool_plots/J2c_75E.png} + + +\end{columns} +\end{frame} + +\begin{frame} +{~} + +\begin{columns} +\column{2.5in} +\includegraphics[scale=0.17]{plots/pool_plots/J2c_125.png}\\ +\includegraphics[scale=0.17]{plots/pool_plots/J2c_175.png}\\ + + +\column{2.5in} +\includegraphics[scale=0.17]{plots/pool_plots/J2c_125E.png}\\ +\includegraphics[scale=0.17]{plots/pool_plots/J2c_175E.png} + + +\end{columns} +\end{frame} + +\begin{frame} +{~} + +\begin{columns} +\column{2.5in} +\includegraphics[scale=0.17]{plots/pool_plots/J2c_225.png}\\ +\includegraphics[scale=0.17]{plots/pool_plots/J2c_300.png}\\ + + +\column{2.5in} +\includegraphics[scale=0.17]{plots/pool_plots/J2c_225E.png}\\ +\includegraphics[scale=0.17]{plots/pool_plots/J2c_300E.png} + + +\end{columns} +\end{frame} + + +\begin{frame} +{~} + +\begin{columns} +\column{2.5in} +\includegraphics[scale=0.17]{plots/pool_plots/J2c_400.png}\\ +\includegraphics[scale=0.17]{plots/pool_plots/J2c_500.png}\\ + + +\column{2.5in} +\includegraphics[scale=0.17]{plots/pool_plots/J2c_400E.png}\\ +\includegraphics[scale=0.17]{plots/pool_plots/J2c_500E.png}\\ + + +\end{columns} +\end{frame} + + +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +\begin{frame} +{~} + +\begin{columns} +\column{2.5in} +\includegraphics[scale=0.17]{plots/pool_plots/J3_50.png}\\ +\includegraphics[scale=0.17]{plots/pool_plots/J3_75.png}\\ + + +\column{2.5in} +\includegraphics[scale=0.17]{plots/pool_plots/J3_50E.png}\\ +\includegraphics[scale=0.17]{plots/pool_plots/J3_75E.png} + + +\end{columns} +\end{frame} + +\begin{frame} +{~} + +\begin{columns} +\column{2.5in} +\includegraphics[scale=0.17]{plots/pool_plots/J3_125.png}\\ +\includegraphics[scale=0.17]{plots/pool_plots/J3_175.png}\\ + + +\column{2.5in} +\includegraphics[scale=0.17]{plots/pool_plots/J3_125E.png}\\ +\includegraphics[scale=0.17]{plots/pool_plots/J3_175E.png} + + +\end{columns} +\end{frame} + +\begin{frame} +{~} + +\begin{columns} +\column{2.5in} +\includegraphics[scale=0.17]{plots/pool_plots/J3_225.png}\\ 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file mode 100644 index 0000000..db097a5 --- /dev/null +++ b/Kstmumu/M_matrix/MMatrix.pdf Binary files differ diff --git a/Kstmumu/M_matrix/MMatrix.snm b/Kstmumu/M_matrix/MMatrix.snm new file mode 100644 index 0000000..e69de29 --- /dev/null +++ b/Kstmumu/M_matrix/MMatrix.snm diff --git a/Kstmumu/M_matrix/MMatrix.synctex.gz b/Kstmumu/M_matrix/MMatrix.synctex.gz new file mode 100644 index 0000000..f6a9845 --- /dev/null +++ b/Kstmumu/M_matrix/MMatrix.synctex.gz Binary files differ diff --git a/Kstmumu/M_matrix/MMatrix.tex b/Kstmumu/M_matrix/MMatrix.tex new file mode 100644 index 0000000..0e1b43f --- /dev/null +++ b/Kstmumu/M_matrix/MMatrix.tex @@ -0,0 +1,77 @@ +\documentclass[xcolor=svgnames]{beamer} +\usepackage[utf8]{inputenc} +\usepackage[english]{babel} +\usepackage{polski} +%\usepackage{amssymb,amsmath} +%\usepackage[latin1]{inputenc} +%\usepackage{amsmath} +%\newcommand\abs[1]{\left|#1\right|} +\usepackage{amsmath} +\newcommand\abs[1]{\left|#1\right|} +\usepackage{hepnicenames} +\usepackage{hepunits} +\usepackage{color} + +\setbeamertemplate{footline}{\insertframenumber/\inserttotalframenumber} +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%5 +\definecolor{mygreen}{cmyk}{0.82,0.11,1,0.25} + + +\usetheme{Sybila} + +\title[Unfolding for counting experiments]{Unfolding for counting experiments} +\author{Marcin Chrz\k{a}szcz$^{1,2}$, Nicola Serra$^{1}$} +\institute{$^1$~University of Zurich,\\ $^2$~Institute of Nuclear Physics, Krakow} +\date{\today} +\begin{document} +% --------------------------- SLIDE -------------------------------------------- +%\frame[plain]{\titlepage} +\author{Marcin Chrz\k{a}szcz} +% ------------------------------------------------------------------------------ +% --------------------------- SLIDE -------------------------------------------- + +\institute{~(UZH, IFJ)} + + + + + + +\begin{frame}\frametitle{Matrix, $1.1-2~GeV$} +\tiny{ +$ A_{gen\rightarrow reco}=\begin{pmatrix} + 1.071 & 0.02887 & -0.004 & -0.0183 & -0.013 & -0.061 & -0.005671 & 0.051 \\ + 0.0050 & 1.259 & 0.0056 & -0.0346 & -0.00018 & 0.018 & 0.004357 & 0.0025 \\ + -0.0036 & 0.0068 & 0.9143 & 0.014 & -0.0145 & 0.0072 & 0.0165 & 0.0005 \\ + -0.0022 & -0.04459 & 0.0177 & 1.068 & -0.0012 & 0.0251 & 0.00909 & -0.04745 \\ + -0.0015 & -0.0005& -0.0177 & -0.0017 & 0.8625 & -0.0023 & -0.0152 & -0.00052\\ + -0.02121 & 0.024 & 0.0093 & 0.026 & -0.0032 & 1.089 & 0.02137 & 0.02941 \\ + 0.0& 0.0049 & 0.017 & 0.0074 & -0.0125 & 0.017 & 0.9125 & -0.004141 \\ + 0.01408 & 0.0048 & 0.0011 & -0.036 &-0.0001 & 0.02308 & -0.00418 & 1.252 + + + + \end{pmatrix}$ +} +{~}\\{~}\\{~}\\ +\tiny{ +$ \delta A_{gen\rightarrow reco}=\begin{pmatrix} + 0.002205 & 0.01055 & 0.006865 & 0.005105 & 0.008786 & 0.008532 & 0.008974 & 0.009591 \\ + 0.002409 & 0.006527 & 0.002872 & 0.004468 & 0.002364 & 0.00476 & 0.004741 & 0.00475 \\ + 0.00251 & 0.002962 & 0.005522 & 0.004635 & 0.003671 & 0.003016 & 0.005282 & 0.003601 \\ + 0.00251 & 0.005359 & 0.005771 & 0.005402 & 0.002848 & 0.004289 & 0.003755 & 0.006318 \\ + 0.002588 & 0.002979 & 0.004702 & 0.002737 & 0.004054 & 0.003591 & 0.003999 & 0.00283 \\ + 0.003039 & 0.00606 & 0.003822 & 0.004242 & 0.003559 & 0.004099 & 0.00676 & 0.005408 \\ + 0.002446 & 0.004826 & 0.005213 & 0.003074 & 0.003114 & 0.005431 & 0.004619 & 0.003198 \\ + 0.002265 & 0.004945 & 0.003555 & 0.005029 & 0.002215 & 0.004251 & 0.003104 & 0.006199 + + \end{pmatrix}$ +} + +\end{frame} + + + + + +\end{document} diff --git a/Kstmumu/M_matrix/MMatrix.tex~ b/Kstmumu/M_matrix/MMatrix.tex~ new file mode 100644 index 0000000..2fc0e58 --- /dev/null +++ b/Kstmumu/M_matrix/MMatrix.tex~ @@ -0,0 +1,556 @@ +\documentclass[xcolor=svgnames]{beamer} +\usepackage[utf8]{inputenc} +\usepackage[english]{babel} +\usepackage{polski} +%\usepackage{amssymb,amsmath} +%\usepackage[latin1]{inputenc} +%\usepackage{amsmath} +%\newcommand\abs[1]{\left|#1\right|} +\usepackage{amsmath} +\newcommand\abs[1]{\left|#1\right|} +\usepackage{hepnicenames} +\usepackage{hepunits} +\usepackage{color} + + + +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%5 +\definecolor{mygreen}{cmyk}{0.82,0.11,1,0.25} + + +\usetheme{Sybila} + +\title[Unfolding for counting experiments]{Unfolding for counting experiments} +\author{Marcin Chrz\k{a}szcz$^{1,2}$, Nicola Serra$^{1}$} +\institute{$^1$~University of Zurich,\\ $^2$~Institute of Nuclear Physics, Krakow} +\date{\today} + +\begin{document} +% --------------------------- SLIDE -------------------------------------------- +\frame[plain]{\titlepage} +\author{Marcin Chrz\k{a}szcz} +% ------------------------------------------------------------------------------ +% --------------------------- SLIDE -------------------------------------------- + +\begin{frame}\frametitle{Quo vadis $\PBzero \to \PKstar \mu \mu$?} + +\center \includegraphics[width=0.8\paperwidth]{diagram.png}\\ + +\end{frame} +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +\begin{frame}\frametitle{Quo vadis $\PBzero \to \PKstar \mu \mu$?} + +\center \includegraphics[width=0.8\paperwidth]{matrix.png}\\ + +\end{frame} + + +\section{Introduction} + +\begin{frame}\frametitle{Reminder} +For now: +\begin{itemize} +\item We have proven that there has to exists unfolding matrix. +\item Shown how to construct transformation matrix: $Gen \to Reco$. +\item Inverting it we can have transformation matrix of $Reco \to Gen$. +\item For details: \href{https://indico.cern.ch/event/316905/session/1/contribution/18/material/slides/0.pdf}{LINK} + +\end{itemize} + +What is missing? +\begin{columns} +\column{1in} +\begin{enumerate} +\item ERROR! +\end{enumerate} +\column{4in} +\includegraphics[width=0.8\textwidth]{err.jpg}\\ +\end{columns} + +\end{frame} + + + +\begin{frame}\frametitle{How to?} +\begin{itemize} +\item So lets say that transformation matrix:$Gen \to Reco$ is $\epsilon_{i,j}$. +\item Of coz it's easy to write the covariance matrix(error matrix): +\end{itemize} +\begin{equation} +cov(\epsilon_{\alpha, \beta},\epsilon_{a,b}) +\end{equation} +\begin{itemize} +\item Then we can calculate the matrix: $\epsilon_{i,j}^{-1}$(assuming it exists). +\item and the 1M dollar question is: $cov(\epsilon_{\alpha, \beta}^{-1},\epsilon_{a,b}^{-1}) =?$ +\end{itemize} + +\end{frame} + +\begin{frame}\frametitle{Answer to 1M dolar quesion} +\begin{itemize} +\item Solution comes from $\tau$ physics :) +\end{itemize} +\begin{equation} +cov(\epsilon_{\alpha, \beta}^{-1},\epsilon_{a,b}^{-1}) = \epsilon^{-1}_{\alpha,i} \epsilon^{-1}_{j,\beta} \epsilon^{-1}_{a,k} \epsilon^{-1}_{l,b} cov( \epsilon_{ij} \epsilon_{kl}) +\end{equation} +\begin{itemize} +\item It's way to late to latex the prove. For prove see: \href{http://arxiv.org/abs/hep-ex/9909031}{arXiv:hep-ex/9909031} +\item Thanks to orthonormal basis lifes gets simpler: +\end{itemize} +\begin{equation} +cov(\epsilon_{ij},\epsilon_{kl} ) = \sigma_{\epsilon,ij} \delta_{ik} \delta_{jl} ( no correlations) +\end{equation} + +\end{frame} + + +\begin{frame}\frametitle{Total error} +\begin{itemize} +\item So let's say: $B=\epsilon^{-1} f$ +\item Then: +\end{itemize} +\begin{equation} +cov(B_i,B_j) = f_a f_b cov(\epsilon_{i \alpha }^{-1} , \epsilon_{j \beta}^{-1} )+ \epsilon^{-1}_{ ik} \epsilon^{-1}_{jl} cov(f_k,f_l) +\end{equation} +\begin{itemize} +\item Looks easy just need to implement! +\end{itemize} + +\end{frame} + + +\begin{frame}\frametitle{Matrix, $0.1-0.98~GeV$} +\tiny{ +$ A_{reco\rightarrow gen}=\begin{pmatrix} + 0.9495 0.008518 0.01522 -0.007362 0.01496 -0.04544 -0.02468 0.002078 + 0.0002651 0.8261 0.00978 -0.001042 0.004382 0.03191 0.01247 0.01886 + -0.0003391 0.009773 1.03 0.008433 -0.002028 0.003 0.02086 0.001549 + -0.00403 -0.001336 0.01047 0.9215 0.006898 -0.0006023 0.003041 -0.004465 + 0.006557 0.005531 -0.002423 0.00691 1.171 -0.01082 -0.0158 -0.003231 + -0.01931 0.03973 0.00342 -0.0006455 -0.01081 0.9452 0.02232 -0.005304 + .008421 0.0124 0.02071 0.002415 -0.01264 0.01785 1.06 0.001084 + 0.000347 0.01886 0.001555 -0.003568 -0.002591 -0.004226 0.001093 0.8204 + + + + + \end{pmatrix}$ +} + + + + + +\end{frame} + +\begin{frame}\frametitle{Constructing Matrix unfolding} +\begin{itemize} +\item We got first column of the unfolding matrix. +\end{itemize} +\small{ +$ \begin{pmatrix} + 1.06 & \cdots & a_{1,8} \\ + 0.01157 & \cdots & a_{2,8} \\ + -0.003547 & \ddots & \vdots \\ + 0.0007841 & \ddots & \vdots \\ + 0.001126 & \ddots & \vdots \\ + 0.001766 & \ddots & \vdots \\ + 0.001664 & \ddots & \vdots \\ + -0.001937 & \cdots & a_{8,8} + \end{pmatrix}$ + + +} +\begin{itemize} +\item How about the others? +\item We can reweight accordingly to $f_x$. +\end{itemize} + +\end{frame} + +\begin{frame}\frametitle{Constructing Matrix unfolding} +\begin{itemize} +\item To get $S_3$ each event $i^{th}$ has has weight $f_{S_3}(\cos \theta_{k_i},\cos \theta_{l_i},\phi_i) $ +\item One can calculate on MC the reweighed moments in PHPS: +\end{itemize} +\begin{equation} +\int PDF*f_{S_3}=\dfrac{32}{225} +\end{equation} +\begin{itemize} +\item Our base vector now is:$v^{T}_{gen}=(0 ,\frac{32}{225},0,0,0,0,0,0)$ +\item So lets see what do we get as reconstructed vector(after multiplying by $\frac{225}{32}$. +\small{$v^{T}_{rec}=( 0.042, 1.105,-0.005,0.003,-0.0023,-0.005,-0.005,-0.006)$ } +\end{itemize} + +\end{frame} + + +\begin{frame}\frametitle{Constructing Matrix unfolding} +\begin{itemize} +\item Now the matrix looks like: +\end{itemize} +\small{ +$ \begin{pmatrix} + 1.06 & 0.042 & \cdots & a_{1,8} \\ + 0.01157 & 1.105 & \cdots & a_{2,8} \\ + -0.003547 & -0.005 & \ddots & \vdots \\ + 0.0007841 &-0.005 & \ddots & \vdots \\ + 0.001126 & 0.003 &\ddots & \vdots \\ + 0.001766 & -0.0023 &\ddots & \vdots \\ + 0.001664 & -0.005 &\ddots & \vdots \\ + -0.001937 & -0.006 &\cdots & a_{8,8} + \end{pmatrix}$ + + +} +\begin{itemize} +\item The others go in the same way. +\item Repenting this exercise from $1^{st}$ year algebra we can get the full matrix +\end{itemize} + + +\end{frame} +\begin{frame}\frametitle{Constructing Matrix unfolding} +\begin{itemize} +\item The full transformation matrix from generator space to reconstructed space: +\end{itemize} +\tiny{ +$ A_{gen\rightarrow reco}=\begin{pmatrix} + 1.06 & 0.0423 & -0.0081 & 0.0022 & 0.0049 & 0.0037 & 0.0028 & -0.0065 \\ + + 0.0115 & 1.105 & -0.0050 & 0.0027 & -0.0018 & -0.0040 &-0.0054 & -0.0065 \\ + -0.0035 & -0.0050 & 0.981 & 0.0005 & -0.0025 & 0.0002 & -0.0037 & -0.0048\\ + 0.00078 & 0.0034 & 0.0006 & 1.002 & -0.0032 & -0.0040 & 0.0003 & 0.0018\\ + 0.001126 & -0.0023 & -0.0032 & -0.0032 & 1.055 & 0.001& -0.004 & 0.0023\\ + 0.00176 & -0.0050 & 0.00036 & -0.0040 & 0.0011 & 0.96 & -0.0057 & 0.0009 \\ + 0.0016 & -0.005 & -0.003 & 0.00029& -0.003 &-0.004 & 0.9543 & 0.0000\\ + -0.0019 & -0.0065 & -0.004 & 0.001 & 0.0018 & 0.0007 & 0.000 & 1.098 \\ + + + + + + \end{pmatrix}$ + + +} +\begin{itemize} +\item Inverting the matrix is simple, and doable +\end{itemize} +\tiny{ +$ A_{reco\rightarrow gen}=\begin{pmatrix} + 0.9434 & -0.036 & 0.007& -0.0020 & -0.0044& -0.0038 & -0.0030 & 0.0054\\ + -0.009 & 0.90 & 0.0045 & -0.0024& 0.0016 & 0.003873 & 0.00527& 0.005 \\ + 0.003 & 0.00454& 1.019 & -0.00058 & 0.0025& -0.000291 & 0.004 & 0.004 \\ +-0.00071 & -0.0030 & -0.0007 & 0.9977 & 0.0030 & 0.004206 &-0.0003 & -0.0017 \\ + -0.001 & 0.0020 & 0.0031& 0.0030 & 0.9483 & -0.0010 & 0.004626 & -0.0019 \\ + -0.001 & 0.004 & -0.0003 & 0.0042 & -0.001087 & 1.037 & 0.0063 & -0.0009\\ + -0.0017 & 0.0053 & 0.0042 & -0.0002 & 0.00370& 0.0050 & 1.048 & 0.0000 \\ + 0.0016& 0.0053& 0.00452 & -0.001 & -0.001582 & -0.0007213 &0.000 & 0.9105 \\ + + + + + \end{pmatrix}$ +} + +\end{frame} + + + +\begin{frame}\frametitle{Sensitivity to unknowns} +\begin{itemize} +\item We are unfolding based on MC. +\item There are MC/Data differences, which can have impact on the unfolding. +\end{itemize} +Let's put small modification: +\begin{equation} +w_j \to \overline{w_j}= \dfrac{1}{eff(\cos \theta_{l~j}, \cos \theta_{k~j}, \phi_{j})} \times corr(\cos \theta_{l~j}, \cos \theta_{k~j}, \phi_{j}) +\end{equation} +Unfortunately God didn't allowed me sneak peak into his cards so I don't know $corr(\cos \theta_{l}, \cos \theta_{k}, \phi)$, but let's try out some functions and see what happens :) + + +\end{frame} + +\begin{frame}\frametitle{Corr1 functions} +\begin{columns} +\column{2in} +\includegraphics[width=\linewidth]{corr/Corr1_cosk.png}\\ +\includegraphics[width=\linewidth]{corr/Corr1_cosl.png}\\ +\column{2.5in} +$ +corr1(\cos_l, \cos_k,\phi)= 1+ 0.032 \cos_l - 0.032 \cos_k + 0.01 \phi +$ +\includegraphics[width=0.8\linewidth]{corr/Corr1_phi.png}\\ + +\end{columns} + +\end{frame} +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +\begin{frame}\frametitle{Corr2 functions} +\begin{columns} +\column{2in} +\includegraphics[width=0.85\linewidth]{corr/corr21.png}\\ +\includegraphics[width=0.85\linewidth]{corr/corr22.png}\\ +\column{2.5in} +$ +corr2(\cos_l, \cos_k,\phi)= -0.02 \cos_l^2 + 0.02 \cos_k^2 - + 0.015 \phi^2+ 1 +$ +\includegraphics[width=0.75\linewidth]{corr/corr23.png}\\ + +\end{columns} + +\end{frame} + +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +\begin{frame}\frametitle{Corr3 functions} +\begin{columns} +\column{2in} +\includegraphics[width=0.85\linewidth]{corr/corr31.png}\\ +\includegraphics[width=0.85\linewidth]{corr/corr32.png}\\ +\column{2.5in} +$ +corr3(\cos_l, \cos_k,\phi)= 0.02 \cos_l \cos_k + 0.01 \cos_k \phi - 0.01 \phi \cos_l + 1 +$ +\includegraphics[width=0.75\linewidth]{corr/corr33.png}\\ + +\end{columns} + +\end{frame} +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +\begin{frame}\frametitle{Corr4 functions} +\begin{columns} +\column{2in} +\includegraphics[width=0.85\linewidth]{corr/corr41.png}\\ +\includegraphics[width=0.85\linewidth]{corr/corr42.png}\\ +\column{2.5in} +$ +corr3(\cos_l, \cos_k,\phi)= 0.01 \cos_k \cos_l \phi + 1 +$ +\includegraphics[width=0.75\linewidth]{corr/corr43.png}\\ + +\end{columns} + +\end{frame} + + + + +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% + + +\begin{frame}\frametitle{Corr1- MM} + + +\begin{tiny} + +\begin{center} + \begin{tabular}{ l l l l l l l l l } + \hline + \multicolumn{8}{c}{Mean of the pull} \\ \hline +$q^2$ & $S_3$ & $S_4$ & $S_5$ & $S_{6s}$ & $S_{6c}$ & $S_7$ & $S_8$ \\ \hline \hline + +0 & \scalebox{0.5}{$0.0085 \pm 0.026(0.3)$} & \scalebox{0.5}{$0.13 \pm 0.027(4.6)$} & \scalebox{0.5}{$-0.025 \pm 0.027(-0.92)$} & \scalebox{0.5}{$0.46 \pm 0.027(17)$} & \scalebox{0.5}{$-0.13 \pm 0.028(-4.7)$} & \scalebox{0.5}{$0.029 \pm 0.028(1)$} & \scalebox{0.5}{$-0.66 \pm 0.027(-25)$} \\ \hline +1 & \scalebox{0.5}{$0.0094 \pm 0.028(0.33)$} & \scalebox{0.5}{$0.078 \pm 0.028(2.8)$} & \scalebox{0.5}{$-0.02 \pm 0.028(-0.73)$} & \scalebox{0.5}{$0.24 \pm 0.028(8.5)$} & \scalebox{0.5}{$-0.075 \pm 0.028(-2.7)$} & \scalebox{0.5}{$-0.016 \pm 0.026(-0.63)$} & \scalebox{0.5}{$-0.39 \pm 0.028(-14)$} \\ \hline +2 & \scalebox{0.5}{$-0.02 \pm 0.027(-0.72)$} & \scalebox{0.5}{$0.027 \pm 0.026(1)$} & \scalebox{0.5}{$-0.024 \pm 0.027(-0.91)$} & \scalebox{0.5}{$0.18 \pm 0.027(6.8)$} & \scalebox{0.5}{$-0.024 \pm 0.027(-0.89)$} & \scalebox{0.5}{$-0.067 \pm 0.027(-2.5)$} & \scalebox{0.5}{$-0.39 \pm 0.028(-14)$} \\ \hline +3 & \scalebox{0.5}{$0.013 \pm 0.028(0.46)$} & \scalebox{0.5}{$-0.0089 \pm 0.027(-0.32)$} & \scalebox{0.5}{$0.055 \pm 0.026(2.1)$} & \scalebox{0.5}{$0.12 \pm 0.027(4.7)$} & \scalebox{0.5}{$0.11 \pm 0.027(3.9)$} & \scalebox{0.5}{$-0.018 \pm 0.028(-0.63)$} & \scalebox{0.5}{$-0.43 \pm 0.027(-16)$} \\ \hline +4 & \scalebox{0.5}{$-0.0054 \pm 0.029(-0.18)$} & \scalebox{0.5}{$-0.066 \pm 0.027(-2.4)$} & \scalebox{0.5}{$0.037 \pm 0.028(1.3)$} & \scalebox{0.5}{$0.22 \pm 0.027(8.1)$} & \scalebox{0.5}{$0.099 \pm 0.027(3.7)$} & \scalebox{0.5}{$-0.1 \pm 0.026(-3.8)$} & \scalebox{0.5}{$-0.41 \pm 0.026(-15)$} \\ \hline +5 & \scalebox{0.5}{$0.06 \pm 0.027(2.2)$} & \scalebox{0.5}{$-0.069 \pm 0.026(-2.6)$} & \scalebox{0.5}{$-0.013 \pm 0.028(-0.49)$} & \scalebox{0.5}{$0.21 \pm 0.027(7.8)$} & \scalebox{0.5}{$0.093 \pm 0.027(3.5)$} & \scalebox{0.5}{$-0.083 \pm 0.028(-3)$} & \scalebox{0.5}{$-0.41 \pm 0.028(-15)$} \\ \hline +6 & \scalebox{0.5}{$0.0064 \pm 0.026(0.25)$} & \scalebox{0.5}{$-0.051 \pm 0.027(-1.9)$} & \scalebox{0.5}{$-0.029 \pm 0.028(-1)$} & \scalebox{0.5}{$0.26 \pm 0.028(9.2)$} & \scalebox{0.5}{$0.14 \pm 0.027(5.1)$} & \scalebox{0.5}{$-0.081 \pm 0.027(-3)$} & \scalebox{0.5}{$-0.45 \pm 0.028(-16)$} \\ \hline +%7 & \scalebox{0.5}{$0.22 \pm 0.027(8)$} & \scalebox{0.5}{$-0.34 \pm 0.028(-12)$} & \scalebox{0.5}{$-0.43 \pm 0.026(-16)$} & \scalebox{0.5}{$2.4 \pm 0.029(82)$} & \scalebox{0.5}{$0.66 \pm 0.027(24)$} & \scalebox{0.5}{$-0.24 \pm 0.028(-8.6)$} & \scalebox{0.5}{$-0.51 \pm 0.027(-19)$} & +8 & \scalebox{0.5}{$0.023 \pm 0.027(0.85)$} & \scalebox{0.5}{$-0.031 \pm 0.028(-1.1)$} & \scalebox{0.5}{$0.0042 \pm 0.028(0.15)$} & \scalebox{0.5}{$0.21 \pm 0.026(7.8)$} & \scalebox{0.5}{$0.12 \pm 0.028(4.2)$} & \scalebox{0.5}{$-0.13 \pm 0.027(-4.8)$} & \scalebox{0.5}{$-0.48 \pm 0.026(-18)$} \\ \hline +9 & \scalebox{0.5}{$-0.017 \pm 0.027(-0.63)$} & \scalebox{0.5}{$-0.015 \pm 0.026(-0.56)$} & \scalebox{0.5}{$-0.0052 \pm 0.026(-0.2)$} & \scalebox{0.5}{$0.27 \pm 0.027(10)$} & \scalebox{0.5}{$0.046 \pm 0.026(1.7)$} & \scalebox{0.5}{$-0.12 \pm 0.026(-4.4)$} & \scalebox{0.5}{$-0.5 \pm 0.026(-19)$} \\ \hline +10 & \scalebox{0.5}{$-0.054 \pm 0.027(-2)$} & \scalebox{0.5}{$-0.056 \pm 0.026(-2.2)$} & \scalebox{0.5}{$0.036 \pm 0.026(1.4)$} & \scalebox{0.5}{$0.16 \pm 0.028(5.7)$} & \scalebox{0.5}{$0.077 \pm 0.028(2.8)$} & \scalebox{0.5}{$-0.034 \pm 0.027(-1.3)$} & \scalebox{0.5}{$-0.39 \pm 0.028(-14)$} \\ \hline +11 & \scalebox{0.5}{$0.023 \pm 0.027(0.88)$} & \scalebox{0.5}{$0.021 \pm 0.027(0.8)$} & \scalebox{0.5}{$-0.011 \pm 0.027(-0.41)$} & \scalebox{0.5}{$0.14 \pm 0.027(5)$} & \scalebox{0.5}{$0.042 \pm 0.027(1.6)$} & \scalebox{0.5}{$-0.098 \pm 0.028(-3.5)$} & \scalebox{0.5}{$-0.3 \pm 0.027(-11)$} \\ \hline + + + \hline + + + \end{tabular} + +\end{center} + + +\end{tiny} +\end{frame} + +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% + + +\begin{frame}\frametitle{Corr2- MM} + + +\begin{tiny} + +\begin{center} + \begin{tabular}{ l l l l l l l l l } + \hline + \multicolumn{8}{c}{Mean of the pull} \\ \hline +$q^2$ & $S_3$ & $S_4$ & $S_5$ & $S_{6s}$ & $S_{6c}$ & $S_7$ & $S_8$ \\ \hline \hline + +0 & \scalebox{0.5}{$-0.21 \pm 0.026(-8.1)$} & \scalebox{0.5}{$0.061 \pm 0.026(2.3)$} & \scalebox{0.5}{$-0.016 \pm 0.026(-0.63)$} & \scalebox{0.5}{$0.048 \pm 0.026(1.8)$} & \scalebox{0.5}{$-0.0062 \pm 0.027(-0.23)$} & \scalebox{0.5}{$-0.012 \pm 0.028(-0.44)$} & \scalebox{0.5}{$0.0091 \pm 0.026(0.36)$} \\ \hline +1 & \scalebox{0.5}{$-0.12 \pm 0.028(-4.5)$} & \scalebox{0.5}{$0.032 \pm 0.027(1.2)$} & \scalebox{0.5}{$-0.0071 \pm 0.026(-0.27)$} & \scalebox{0.5}{$0.02 \pm 0.027(0.75)$} & \scalebox{0.5}{$-0.086 \pm 0.027(-3.2)$} & \scalebox{0.5}{$-0.03 \pm 0.025(-1.2)$} & \scalebox{0.5}{$0.021 \pm 0.027(0.79)$} \\ \hline +2 & \scalebox{0.5}{$-0.15 \pm 0.027(-5.8)$} & \scalebox{0.5}{$-0.013 \pm 0.026(-0.49)$} & \scalebox{0.5}{$0.011 \pm 0.026(0.44)$} & \scalebox{0.5}{$-0.039 \pm 0.026(-1.5)$} & \scalebox{0.5}{$-0.032 \pm 0.027(-1.2)$} & \scalebox{0.5}{$-0.066 \pm 0.027(-2.5)$} & \scalebox{0.5}{$0.018 \pm 0.028(0.64)$} \\ \hline +3 & \scalebox{0.5}{$-0.15 \pm 0.027(-5.6)$} & \scalebox{0.5}{$0.025 \pm 0.026(0.96)$} & \scalebox{0.5}{$0.016 \pm 0.027(0.58)$} & \scalebox{0.5}{$-0.062 \pm 0.027(-2.3)$} & \scalebox{0.5}{$0.037 \pm 0.026(1.4)$} & \scalebox{0.5}{$0.026 \pm 0.027(0.96)$} & \scalebox{0.5}{$-0.016 \pm 0.027(-0.6)$} \\ \hline +4 & \scalebox{0.5}{$-0.12 \pm 0.028(-4.5)$} & \scalebox{0.5}{$-0.024 \pm 0.026(-0.92)$} & \scalebox{0.5}{$0.045 \pm 0.027(1.6)$} & \scalebox{0.5}{$0.0075 \pm 0.026(0.29)$} & \scalebox{0.5}{$0.015 \pm 0.027(0.53)$} & \scalebox{0.5}{$-0.036 \pm 0.026(-1.4)$} & \scalebox{0.5}{$0.037 \pm 0.026(1.4)$} \\ \hline +5 & \scalebox{0.5}{$-0.095 \pm 0.027(-3.6)$} & \scalebox{0.5}{$-0.032 \pm 0.026(-1.2)$} & \scalebox{0.5}{$0.014 \pm 0.026(0.52)$} & \scalebox{0.5}{$-0.013 \pm 0.026(-0.48)$} & \scalebox{0.5}{$-0.0093 \pm 0.027(-0.35)$} & \scalebox{0.5}{$-0.013 \pm 0.026(-0.51)$} & \scalebox{0.5}{$0.042 \pm 0.027(1.6)$} \\ \hline +6 & \scalebox{0.5}{$-0.17 \pm 0.025(-6.5)$} & \scalebox{0.5}{$0.008 \pm 0.027(0.3)$} & \scalebox{0.5}{$0.012 \pm 0.027(0.45)$} & \scalebox{0.5}{$0.029 \pm 0.027(1.1)$} & \scalebox{0.5}{$0.0072 \pm 0.027(0.27)$} & \scalebox{0.5}{$-0.0012 \pm 0.026(-0.046)$} & \scalebox{0.5}{$0.011 \pm 0.027(0.42)$} \\ \hline +%7 & \scalebox{0.5}{$0.078 \pm 0.026(3)$} & \scalebox{0.5}{$-0.3 \pm 0.026(-11)$} & \scalebox{0.5}{$-0.34 \pm 0.026(-13)$} & \scalebox{0.5}{$2.1 \pm 0.028(73)$} & \scalebox{0.5}{$0.47 \pm 0.026(18)$} & \scalebox{0.5}{$-0.17 \pm 0.027(-6.1)$} & \scalebox{0.5}{$0.0051 \pm 0.027(0.19)$} \\ \hline +8 & \scalebox{0.5}{$-0.13 \pm 0.026(-5.1)$} & \scalebox{0.5}{$-0.0077 \pm 0.027(-0.28)$} & \scalebox{0.5}{$0.05 \pm 0.027(1.9)$} & \scalebox{0.5}{$-0.03 \pm 0.026(-1.2)$} & \scalebox{0.5}{$-0.012 \pm 0.028(-0.44)$} & \scalebox{0.5}{$-0.046 \pm 0.026(-1.7)$} & \scalebox{0.5}{$0.031 \pm 0.026(1.2)$} \\ \hline +9 & \scalebox{0.5}{$-0.15 \pm 0.026(-5.7)$} & \scalebox{0.5}{$-0.0083 \pm 0.026(-0.32)$} & \scalebox{0.5}{$0.03 \pm 0.026(1.2)$} & \scalebox{0.5}{$0.044 \pm 0.027(1.6)$} & \scalebox{0.5}{$-0.07 \pm 0.026(-2.7)$} & \scalebox{0.5}{$-0.022 \pm 0.026(-0.84)$} & \scalebox{0.5}{$-0.045 \pm 0.026(-1.7)$} \\ \hline +10 & \scalebox{0.5}{$-0.15 \pm 0.025(-5.8)$} & \scalebox{0.5}{$-0.032 \pm 0.025(-1.3)$} & \scalebox{0.5}{$0.059 \pm 0.026(2.2)$} & \scalebox{0.5}{$-0.072 \pm 0.028(-2.6)$} & \scalebox{0.5}{$-0.029 \pm 0.027(-1.1)$} & \scalebox{0.5}{$0.064 \pm 0.027(2.4)$} & \scalebox{0.5}{$0.014 \pm 0.027(0.51)$} \\ \hline +11 & \scalebox{0.5}{$-0.067 \pm 0.026(-2.6)$} & \scalebox{0.5}{$0.017 \pm 0.026(0.65)$} & \scalebox{0.5}{$-0.015 \pm 0.026(-0.56)$} & \scalebox{0.5}{$-0.051 \pm 0.026(-1.9)$} & \scalebox{0.5}{$-0.0086 \pm 0.026(-0.33)$} & \scalebox{0.5}{$-0.018 \pm 0.028(-0.67)$} & \scalebox{0.5}{$0.017 \pm 0.027(0.62)$} \\ \hline + + + + + + +\hline + + + \end{tabular} + +\end{center} + + +\end{tiny} +\end{frame} + + +\begin{frame}\frametitle{Corr3- MM} + + +\begin{tiny} + +\begin{center} + \begin{tabular}{ l l l l l l l l l } + \hline + \multicolumn{8}{c}{Mean of the pull} \\ \hline +$q^2$ & $S_3$ & $S_4$ & $S_5$ & $S_{6s}$ & $S_{6c}$ & $S_7$ & $S_8$ \\ \hline \hline + +0 & \scalebox{0.5}{$-0.021 \pm 0.026(-0.81)$} & \scalebox{0.5}{$0.041 \pm 0.026(1.5)$} & \scalebox{0.5}{$0.009 \pm 0.027(0.34)$} & \scalebox{0.5}{$0.043 \pm 0.026(1.6)$} & \scalebox{0.5}{$0.13 \pm 0.028(4.8)$} & \scalebox{0.5}{$-0.0072 \pm 0.028(-0.26)$} & \scalebox{0.5}{$0.044 \pm 0.026(1.7)$} \\ \hline +1 & \scalebox{0.5}{$-0.014 \pm 0.028(-0.51)$} & \scalebox{0.5}{$0.03 \pm 0.027(1.1)$} & \scalebox{0.5}{$0.022 \pm 0.027(0.82)$} & \scalebox{0.5}{$0.015 \pm 0.028(0.53)$} & \scalebox{0.5}{$0.078 \pm 0.028(2.8)$} & \scalebox{0.5}{$-0.037 \pm 0.025(-1.4)$} & \scalebox{0.5}{$0.057 \pm 0.027(2.1)$} \\ \hline +2 & \scalebox{0.5}{$-0.037 \pm 0.027(-1.4)$} & \scalebox{0.5}{$-0.0013 \pm 0.027(-0.048)$} & \scalebox{0.5}{$-0.015 \pm 0.027(-0.54)$} & \scalebox{0.5}{$-0.052 \pm 0.026(-2)$} & \scalebox{0.5}{$0.1 \pm 0.027(3.8)$} & \scalebox{0.5}{$-0.051 \pm 0.026(-1.9)$} & \scalebox{0.5}{$0.022 \pm 0.028(0.78)$} \\ \hline +3 & \scalebox{0.5}{$-0.015 \pm 0.027(-0.55)$} & \scalebox{0.5}{$0.036 \pm 0.028(1.3)$} & \scalebox{0.5}{$-0.039 \pm 0.027(-1.4)$} & \scalebox{0.5}{$-0.072 \pm 0.027(-2.7)$} & \scalebox{0.5}{$0.17 \pm 0.027(6.2)$} & \scalebox{0.5}{$-0.0044 \pm 0.028(-0.15)$} & \scalebox{0.5}{$-0.024 \pm 0.027(-0.9)$} \\ \hline +4 & \scalebox{0.5}{$-0.00047 \pm 0.029(-0.017)$} & \scalebox{0.5}{$-0.012 \pm 0.027(-0.43)$} & \scalebox{0.5}{$0.0099 \pm 0.028(0.35)$} & \scalebox{0.5}{$-0.002 \pm 0.026(-0.076)$} & \scalebox{0.5}{$0.17 \pm 0.028(6.2)$} & \scalebox{0.5}{$-0.062 \pm 0.027(-2.3)$} & \scalebox{0.5}{$0.0086 \pm 0.027(0.32)$} \\ \hline + +5 & \scalebox{0.5}{$0.046 \pm 0.027(1.7)$} & \scalebox{0.5}{$-0.02 \pm 0.026(-0.76)$} & \scalebox{0.5}{$-0.04 \pm 0.027(-1.5)$} & \scalebox{0.5}{$-0.012 \pm 0.027(-0.44)$} & \scalebox{0.5}{$0.13 \pm 0.027(4.8)$} & \scalebox{0.5}{$-0.04 \pm 0.027(-1.5)$} & \scalebox{0.5}{$-0.0056 \pm 0.027(-0.21)$} \\ \hline +6 & \scalebox{0.5}{$-0.013 \pm 0.026(-0.52)$} & \scalebox{0.5}{$0.041 \pm 0.027(1.5)$} & \scalebox{0.5}{$-0.033 \pm 0.028(-1.2)$} & \scalebox{0.5}{$-0.0019 \pm 0.027(-0.068)$} & \scalebox{0.5}{$0.15 \pm 0.027(5.4)$} & \scalebox{0.5}{$-0.034 \pm 0.027(-1.3)$} & \scalebox{0.5}{$-0.021 \pm 0.028(-0.75)$} \\ \hline +%7 & \scalebox{0.5}{$0.25 \pm 0.027(9.1)$} & \scalebox{0.5}{$-0.27 \pm 0.027(-10)$} & \scalebox{0.5}{$-0.41 \pm 0.027(-16)$} & \scalebox{0.5}{$2.1 \pm 0.029(73)$} & \scalebox{0.5}{$0.65 \pm 0.027(24)$} & \scalebox{0.5}{$-0.19 \pm 0.028(-7)$} & \scalebox{0.5}{$-0.053 \pm 0.028(-1.9)$} \\ \hline +8 & \scalebox{0.5}{$0.039 \pm 0.026(1.5)$} & \scalebox{0.5}{$0.01 \pm 0.028(0.36)$} & \scalebox{0.5}{$-0.027 \pm 0.028(-0.96)$} & \scalebox{0.5}{$-0.024 \pm 0.026(-0.9)$} & \scalebox{0.5}{$0.12 \pm 0.027(4.3)$} & \scalebox{0.5}{$-0.092 \pm 0.026(-3.5)$} & \scalebox{0.5}{$-0.036 \pm 0.027(-1.3)$} \\ \hline +9 & \scalebox{0.5}{$-0.01 \pm 0.027(-0.38)$} & \scalebox{0.5}{$0.0024 \pm 0.027(0.09)$} & \scalebox{0.5}{$-0.018 \pm 0.026(-0.68)$} & \scalebox{0.5}{$0.022 \pm 0.028(0.79)$} & \scalebox{0.5}{$0.068 \pm 0.027(2.6)$} & \scalebox{0.5}{$-0.069 \pm 0.026(-2.6)$} & \scalebox{0.5}{$-0.078 \pm 0.026(-3)$} \\ \hline +10 & \scalebox{0.5}{$-0.017 \pm 0.027(-0.62)$} & \scalebox{0.5}{$-0.015 \pm 0.026(-0.57)$} & \scalebox{0.5}{$0.012 \pm 0.027(0.46)$} & \scalebox{0.5}{$-0.074 \pm 0.028(-2.6)$} & \scalebox{0.5}{$0.1 \pm 0.027(3.8)$} & \scalebox{0.5}{$-0.003 \pm 0.027(-0.11)$} & \scalebox{0.5}{$-0.043 \pm 0.029(-1.5)$} \\ \hline +11 & \scalebox{0.5}{$0.032 \pm 0.026(1.2)$} & \scalebox{0.5}{$0.024 \pm 0.026(0.91)$} & \scalebox{0.5}{$-0.04 \pm 0.026(-1.5)$} & \scalebox{0.5}{$-0.066 \pm 0.027(-2.5)$} & \scalebox{0.5}{$0.098 \pm 0.027(3.7)$} & \scalebox{0.5}{$-0.043 \pm 0.028(-1.6)$} & \scalebox{0.5}{$-0.0018 \pm 0.028(-0.064)$} \\ \hline + + + +\hline + + + \end{tabular} + +\end{center} + + +\end{tiny} +\end{frame} + +\begin{frame}\frametitle{Corr4- MM} + + +\begin{tiny} + +\begin{center} + \begin{tabular}{ l l l l l l l l l } + \hline + \multicolumn{8}{c}{Mean of the pull} \\ \hline +$q^2$ & $S_3$ & $S_4$ & $S_5$ & $S_{6s}$ & $S_{6c}$ & $S_7$ & $S_8$ \\ \hline \hline + + +0 & \scalebox{0.5}{$-0.019 \pm 0.026(-0.71)$} & \scalebox{0.5}{$0.048 \pm 0.027(1.8)$} & \scalebox{0.5}{$0.018 \pm 0.027(0.67)$} & \scalebox{0.5}{$0.059 \pm 0.027(2.2)$} & \scalebox{0.5}{$-0.015 \pm 0.028(-0.55)$} & \scalebox{0.5}{$0.061 \pm 0.027(2.2)$} & \scalebox{0.5}{$0.012 \pm 0.027(0.44)$} \\ \hline +1 & \scalebox{0.5}{$-0.014 \pm 0.028(-0.51)$} & \scalebox{0.5}{$0.043 \pm 0.027(1.6)$} & \scalebox{0.5}{$0.013 \pm 0.027(0.49)$} & \scalebox{0.5}{$0.024 \pm 0.028(0.86)$} & \scalebox{0.5}{$-0.038 \pm 0.028(-1.4)$} & \scalebox{0.5}{$0.024 \pm 0.026(0.94)$} & \scalebox{0.5}{$0.037 \pm 0.027(1.3)$} \\ \hline +2 & \scalebox{0.5}{$-0.03 \pm 0.027(-1.1)$} & \scalebox{0.5}{$-0.0021 \pm 0.027(-0.076)$} & \scalebox{0.5}{$-0.01 \pm 0.027(-0.39)$} & \scalebox{0.5}{$-0.017 \pm 0.027(-0.61)$} & \scalebox{0.5}{$-0.016 \pm 0.027(-0.58)$} & \scalebox{0.5}{$0.013 \pm 0.027(0.49)$} & \scalebox{0.5}{$0.027 \pm 0.028(0.98)$} \\ \hline +3 & \scalebox{0.5}{$-0.007 \pm 0.027(-0.26)$} & \scalebox{0.5}{$0.03 \pm 0.028(1.1)$} & \scalebox{0.5}{$-0.036 \pm 0.027(-1.3)$} & \scalebox{0.5}{$-0.074 \pm 0.027(-2.8)$} & \scalebox{0.5}{$0.041 \pm 0.027(1.5)$} & \scalebox{0.5}{$0.08 \pm 0.028(2.9)$} & \scalebox{0.5}{$-0.0083 \pm 0.027(-0.31)$} \\ \hline +4 & \scalebox{0.5}{$0.00089 \pm 0.029(0.031)$} & \scalebox{0.5}{$-0.021 \pm 0.027(-0.77)$} & \scalebox{0.5}{$0.0032 \pm 0.028(0.11)$} & \scalebox{0.5}{$0.0031 \pm 0.026(0.12)$} & \scalebox{0.5}{$0.012 \pm 0.027(0.44)$} & \scalebox{0.5}{$0.019 \pm 0.026(0.71)$} & \scalebox{0.5}{$0.034 \pm 0.027(1.3)$} \\ \hline +5 & \scalebox{0.5}{$0.044 \pm 0.028(1.6)$} & \scalebox{0.5}{$-0.022 \pm 0.026(-0.82)$} & \scalebox{0.5}{$-0.041 \pm 0.027(-1.5)$} & \scalebox{0.5}{$-0.014 \pm 0.027(-0.53)$} & \scalebox{0.5}{$-0.029 \pm 0.027(-1.1)$} & \scalebox{0.5}{$0.041 \pm 0.027(1.5)$} & \scalebox{0.5}{$0.042 \pm 0.028(1.5)$} \\ \hline +6 & \scalebox{0.5}{$-0.011 \pm 0.026(-0.42)$} & \scalebox{0.5}{$0.041 \pm 0.027(1.5)$} & \scalebox{0.5}{$-0.045 \pm 0.028(-1.6)$} & \scalebox{0.5}{$0.011 \pm 0.027(0.41)$} & \scalebox{0.5}{$-0.0089 \pm 0.027(-0.33)$} & \scalebox{0.5}{$0.067 \pm 0.027(2.5)$} & 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\pm 0.027(-0.71)$} & \scalebox{0.5}{$-0.0051 \pm 0.025(-0.2)$} & \scalebox{0.5}{$0.0081 \pm 0.026(0.31)$} & \scalebox{0.5}{$-0.077 \pm 0.028(-2.7)$} & \scalebox{0.5}{$-0.03 \pm 0.027(-1.1)$} & \scalebox{0.5}{$0.11 \pm 0.027(4.1)$} & \scalebox{0.5}{$0.013 \pm 0.028(0.46)$} \\ \hline +11 & \scalebox{0.5}{$0.027 \pm 0.026(1)$} & \scalebox{0.5}{$0.032 \pm 0.027(1.2)$} & \scalebox{0.5}{$-0.038 \pm 0.027(-1.4)$} & \scalebox{0.5}{$-0.048 \pm 0.026(-1.8)$} & \scalebox{0.5}{$-0.021 \pm 0.027(-0.77)$} & \scalebox{0.5}{$0.019 \pm 0.028(0.69)$} & \scalebox{0.5}{$0.035 \pm 0.027(1.3)$} \\ \hline + + + +\hline + + \end{tabular} + +\end{center} + +\end{tiny} +\end{frame} + + + + +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +\section{Reverse Engineering Unfolding} + +\begin{frame}\frametitle{Reverse Engineering- Corr1} +\begin{itemize} +\item Let's try to understand if we can understand why this happens: +\item Let's calculate what should I expect with the unfolding +\item This is up to normalization! +\begin{itemize} +\item $M_5=0.4 S_5 \to M_5=0.00512 S_3 + 0.4 S_5 - 0.002 S_7$ +\item $M_8=0.32 S_8 \to M_8=0.0016 S_4 + 0.00512 S_7 + 0.32 S_8$ +\item $M_7=0.4 S_7 \to M_7=0.002 S_5 + 0.4 S_7 + 0.00512 S_8$ +\item $M_3=0.32 S_3 \to M_3=0.32 S_3 - 0.0008 S_9$ +\end{itemize} +\item The way you can look at this is that i just shown you how our unfolding matrix works like. +\end{itemize} + + + +\end{frame} + +\begin{frame}\frametitle{Reverse Engineering- Corr2} +\begin{itemize} +\item Let's try to understand if we can understand why this happens: +\item Let's calculate what should I expect with the unfolding +\item This is up to normalization! +\begin{itemize} +\item $M_5=0.4 S_5 \to M_5= 0.4 S_5$ +\item $M_8=0.32 S_8 \to M_8=0.32 S_5$ +\item $M_7=0.4 S_7 \to M_7=0.4 S_7$ +\item $M_3=0.32 S_3 \to M_3=-0.0036 + 0.0012 Fl + 0.32 S_3$ +\end{itemize} +\item The way you can look at this is that i just shown you how our unfolding matrix works like. +\end{itemize} + + + +\end{frame} + + + + +\begin{frame}\frametitle{Summary} +\begin{itemize} +\item Developed a systematic way how to get Unfolding matrix +\item Moments are resistant against variety of unfolding discrepancies. +\item This might lead to reduced systematics in the future. +\end{itemize} + + + + +\end{frame} + + + +\end{document} diff --git a/Kstmumu/M_matrix/MMatrix.toc b/Kstmumu/M_matrix/MMatrix.toc new file mode 100644 index 0000000..495658f --- /dev/null +++ b/Kstmumu/M_matrix/MMatrix.toc @@ -0,0 +1,2 @@ +\beamer@endinputifotherversion {3.10pt} +\select@language {english} diff --git a/Kstmumu/M_matrix/P5.png b/Kstmumu/M_matrix/P5.png new file mode 100644 index 0000000..7819eef --- /dev/null +++ b/Kstmumu/M_matrix/P5.png Binary files differ diff --git a/Kstmumu/M_matrix/Q2_4_S8.png b/Kstmumu/M_matrix/Q2_4_S8.png new file mode 100644 index 0000000..9176de4 --- /dev/null +++ b/Kstmumu/M_matrix/Q2_4_S8.png Binary files differ diff --git a/Kstmumu/M_matrix/Q2_5_6_S5.eps 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b/Kstmumu/M_matrix/tables/tables.toc new file mode 100644 index 0000000..e06b51d --- /dev/null +++ b/Kstmumu/M_matrix/tables/tables.toc @@ -0,0 +1 @@ +\beamer@endinputifotherversion {3.10pt} diff --git a/Kstmumu/M_matrix/texput.log b/Kstmumu/M_matrix/texput.log new file mode 100644 index 0000000..f84449f --- /dev/null +++ b/Kstmumu/M_matrix/texput.log @@ -0,0 +1,20 @@ +This is pdfTeX, Version 3.1415926-1.40.10 (TeX Live 2009/Debian) (format=pdflatex 2014.3.24) 24 JUN 2014 18:23 +entering extended mode + %&-line parsing enabled. +**beamerthemeSybila.tex + +! Emergency stop. +<*> beamerthemeSybila.tex + +*** (job aborted, file error in nonstop mode) + + +Here is how much of TeX's memory you used: + 3 strings out of 493848 + 118 string characters out of 1152823 + 47808 words of memory out of 3000000 + 3381 multiletter control sequences out of 15000+50000 + 3640 words of font info for 14 fonts, out of 3000000 for 9000 + 714 hyphenation exceptions out of 8191 + 0i,0n,0p,1b,6s stack positions out of 5000i,500n,10000p,200000b,50000s +! ==> Fatal error occurred, no output PDF file produced! diff --git a/Kstmumu/M_matrix/tmp.png b/Kstmumu/M_matrix/tmp.png new file mode 100644 index 0000000..574cb07 --- /dev/null +++ b/Kstmumu/M_matrix/tmp.png Binary files differ diff --git a/Kstmumu/M_matrix/tmp/beamerthemeSybila.sty b/Kstmumu/M_matrix/tmp/beamerthemeSybila.sty new file mode 100644 index 0000000..5639601 --- /dev/null +++ b/Kstmumu/M_matrix/tmp/beamerthemeSybila.sty @@ -0,0 +1,104 @@ +\mode + 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{\usebeamerfont{subtitle}\usebeamercolor[fg]{subtitle}\insertsubtitle\par}% + \fi% + \end{beamercolorbox}% + + \vskip1em + + \begin{beamercolorbox}[sep=8pt,center,#1]{author} + \usebeamerfont{author}\insertauthor + \end{beamercolorbox} + + \vskip1em + + {\usebeamercolor[fg]{titlegraphic}\inserttitlegraphic\par} + \begin{beamercolorbox}[sep=8pt,center,#1]{institute} + \usebeamerfont{date}\insertinstitute + \end{beamercolorbox} + + \vskip1em + + \begin{beamercolorbox}[sep=8pt,center,#1]{date} + \usebeamerfont{date}\insertdate + \end{beamercolorbox} + \end{centering} + \vfill +} + +%------------------------------------------------------------------------------- +% Logo +%------------------------------------------------------------------------------- + +\logo{\hspace*{0.6\textwidth}\includegraphics[width=1.2cm]{sybila-logo-paper-shaded}\hspace*{0.3cm}} + +%------------------------------------------------------------------------------- +% Colors +%------------------------------------------------------------------------------- + +\setbeamercovered{dynamic} + +\setbeamercolor{math text}{fg=green!45!black} +\setbeamercolor{title}{bg=white!30!black} +\setbeamercolor{frametitle}{bg=white!45!black} +\setbeamercolor{footline}{bg=black,fg=white} +\setbeamercolor{author in head/foot}{bg=black,fg=white} +\setbeamercolor{title in head/foot}{bg=white!45!black} +\setbeamercolor{block title}{bg=white!45!black} +\setbeamercolor{block title example}{bg=white!45!black} +\setbeamercolor{block title alerted}{bg=white!15!black} + +\colorlet{redshaded}{red!25!bg} +\colorlet{shaded}{black!25!bg} +\colorlet{shadedshaded}{black!10!bg} +\colorlet{blackshaded}{black!40!bg} + +\usecolortheme{whale} +\usecolortheme{orchid} + +%------------------------------------------------------------------------------- +% Fonts +%------------------------------------------------------------------------------- + +\setbeamerfont{block title}{size={}} +\setbeamerfont{date}{size=\small} + +%------------------------------------------------------------------------------- +% Other +%------------------------------------------------------------------------------- + +\titlegraphic{\includegraphics[width=3.0cm]{sybila-logo-slide-title-shaded.pdf}} + +\mode + diff --git a/Kstmumu/M_matrix/tmp/example.tex b/Kstmumu/M_matrix/tmp/example.tex new file mode 100644 index 0000000..ce0641b --- /dev/null +++ b/Kstmumu/M_matrix/tmp/example.tex @@ -0,0 +1,21 @@ +\documentclass[xcolor=svgnames]{beamer} +\usepackage[utf8]{inputenc} +\usepackage[english]{babel} + +\usetheme{Sybila} + +\title[Parallelization of Methods for Dynamic System Analysis]{Parallelization of Methods for Dynamic System Analysis Using CUDA} +\author{Jan Papou\v{s}ek} +\institute{Masaryk University Brno} +\date{\today} + +\begin{document} +% --------------------------- SLIDE -------------------------------------------- +\frame[plain]{\titlepage} +% ------------------------------------------------------------------------------ +% --------------------------- SLIDE -------------------------------------------- +\begin{frame} + \frametitle{Introduction} +\end{frame} +% ------------------------------------------------------------------------------ +\end{document} diff --git a/Kstmumu/M_matrix/tmp/example/beamerthemeSybila.sty b/Kstmumu/M_matrix/tmp/example/beamerthemeSybila.sty new file mode 100644 index 0000000..5639601 --- /dev/null +++ b/Kstmumu/M_matrix/tmp/example/beamerthemeSybila.sty @@ -0,0 +1,104 @@ +\mode + +%------------------------------------------------------------------------------- +% Themes +%------------------------------------------------------------------------------- + +\useoutertheme{split} +\useinnertheme{rounded} +\usefonttheme{structurebold} +%\useoutertheme{shadow} + +%------------------------------------------------------------------------------- +% Templates +%------------------------------------------------------------------------------- + +\beamertemplatenavigationsymbolsempty +\beamertemplateheadempty +\beamertemplateshadowblocks + +%------------------------------------------------------------------------------- +% Own templates +%------------------------------------------------------------------------------- + +% Normal title page. +\defbeamertemplate*{title page}{simple}[1][] +{ + \vfill + \begin{centering} + \begin{beamercolorbox}[center, rounded=true]{title} + \usebeamerfont{title}\inserttitle\par% + \ifx\insertsubtitle\@empty% + \else% + \vskip0.25em% + {\usebeamerfont{subtitle}\usebeamercolor[fg]{subtitle}\insertsubtitle\par}% + \fi% + \end{beamercolorbox}% + + \vskip1em + + \begin{beamercolorbox}[sep=8pt,center,#1]{author} + \usebeamerfont{author}\insertauthor + \end{beamercolorbox} + + \vskip1em + + {\usebeamercolor[fg]{titlegraphic}\inserttitlegraphic\par} + \begin{beamercolorbox}[sep=8pt,center,#1]{institute} + 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a/Kstmumu/RECO12_14/MMatrix.synctex.gz b/Kstmumu/RECO12_14/MMatrix.synctex.gz new file mode 100644 index 0000000..f6a9845 --- /dev/null +++ b/Kstmumu/RECO12_14/MMatrix.synctex.gz Binary files differ diff --git a/Kstmumu/RECO12_14/MMatrix.tex~ b/Kstmumu/RECO12_14/MMatrix.tex~ new file mode 100644 index 0000000..2fc0e58 --- /dev/null +++ b/Kstmumu/RECO12_14/MMatrix.tex~ @@ -0,0 +1,556 @@ +\documentclass[xcolor=svgnames]{beamer} +\usepackage[utf8]{inputenc} +\usepackage[english]{babel} +\usepackage{polski} +%\usepackage{amssymb,amsmath} +%\usepackage[latin1]{inputenc} +%\usepackage{amsmath} +%\newcommand\abs[1]{\left|#1\right|} +\usepackage{amsmath} +\newcommand\abs[1]{\left|#1\right|} +\usepackage{hepnicenames} +\usepackage{hepunits} +\usepackage{color} + + + +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%5 +\definecolor{mygreen}{cmyk}{0.82,0.11,1,0.25} + + +\usetheme{Sybila} + +\title[Unfolding for counting experiments]{Unfolding for counting experiments} +\author{Marcin Chrz\k{a}szcz$^{1,2}$, Nicola Serra$^{1}$} +\institute{$^1$~University of Zurich,\\ $^2$~Institute of Nuclear Physics, Krakow} +\date{\today} + +\begin{document} +% --------------------------- SLIDE -------------------------------------------- +\frame[plain]{\titlepage} +\author{Marcin Chrz\k{a}szcz} +% ------------------------------------------------------------------------------ +% --------------------------- SLIDE -------------------------------------------- + +\begin{frame}\frametitle{Quo vadis $\PBzero \to \PKstar \mu \mu$?} + +\center \includegraphics[width=0.8\paperwidth]{diagram.png}\\ + +\end{frame} +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +\begin{frame}\frametitle{Quo vadis $\PBzero \to \PKstar \mu \mu$?} + +\center \includegraphics[width=0.8\paperwidth]{matrix.png}\\ + +\end{frame} + + +\section{Introduction} + +\begin{frame}\frametitle{Reminder} +For now: +\begin{itemize} +\item We have proven that there has to exists unfolding matrix. +\item Shown how to construct transformation matrix: $Gen \to Reco$. +\item Inverting it we can have transformation matrix of $Reco \to Gen$. +\item For details: \href{https://indico.cern.ch/event/316905/session/1/contribution/18/material/slides/0.pdf}{LINK} + +\end{itemize} + +What is missing? +\begin{columns} +\column{1in} +\begin{enumerate} +\item ERROR! +\end{enumerate} +\column{4in} +\includegraphics[width=0.8\textwidth]{err.jpg}\\ +\end{columns} + +\end{frame} + + + +\begin{frame}\frametitle{How to?} +\begin{itemize} +\item So lets say that transformation matrix:$Gen \to Reco$ is $\epsilon_{i,j}$. +\item Of coz it's easy to write the covariance matrix(error matrix): +\end{itemize} +\begin{equation} +cov(\epsilon_{\alpha, \beta},\epsilon_{a,b}) +\end{equation} +\begin{itemize} +\item Then we can calculate the matrix: $\epsilon_{i,j}^{-1}$(assuming it exists). +\item and the 1M dollar question is: $cov(\epsilon_{\alpha, \beta}^{-1},\epsilon_{a,b}^{-1}) =?$ +\end{itemize} + +\end{frame} + +\begin{frame}\frametitle{Answer to 1M dolar quesion} +\begin{itemize} +\item Solution comes from $\tau$ physics :) +\end{itemize} +\begin{equation} +cov(\epsilon_{\alpha, \beta}^{-1},\epsilon_{a,b}^{-1}) = \epsilon^{-1}_{\alpha,i} \epsilon^{-1}_{j,\beta} \epsilon^{-1}_{a,k} \epsilon^{-1}_{l,b} cov( \epsilon_{ij} \epsilon_{kl}) +\end{equation} +\begin{itemize} +\item It's way to late to latex the prove. For prove see: \href{http://arxiv.org/abs/hep-ex/9909031}{arXiv:hep-ex/9909031} +\item Thanks to orthonormal basis lifes gets simpler: +\end{itemize} +\begin{equation} +cov(\epsilon_{ij},\epsilon_{kl} ) = \sigma_{\epsilon,ij} \delta_{ik} \delta_{jl} ( no correlations) +\end{equation} + +\end{frame} + + +\begin{frame}\frametitle{Total error} +\begin{itemize} +\item So let's say: $B=\epsilon^{-1} f$ +\item Then: +\end{itemize} +\begin{equation} +cov(B_i,B_j) = f_a f_b cov(\epsilon_{i \alpha }^{-1} , \epsilon_{j \beta}^{-1} )+ \epsilon^{-1}_{ ik} \epsilon^{-1}_{jl} cov(f_k,f_l) +\end{equation} +\begin{itemize} +\item Looks easy just need to implement! +\end{itemize} + +\end{frame} + + +\begin{frame}\frametitle{Matrix, $0.1-0.98~GeV$} +\tiny{ +$ A_{reco\rightarrow gen}=\begin{pmatrix} + 0.9495 0.008518 0.01522 -0.007362 0.01496 -0.04544 -0.02468 0.002078 + 0.0002651 0.8261 0.00978 -0.001042 0.004382 0.03191 0.01247 0.01886 + -0.0003391 0.009773 1.03 0.008433 -0.002028 0.003 0.02086 0.001549 + -0.00403 -0.001336 0.01047 0.9215 0.006898 -0.0006023 0.003041 -0.004465 + 0.006557 0.005531 -0.002423 0.00691 1.171 -0.01082 -0.0158 -0.003231 + -0.01931 0.03973 0.00342 -0.0006455 -0.01081 0.9452 0.02232 -0.005304 + .008421 0.0124 0.02071 0.002415 -0.01264 0.01785 1.06 0.001084 + 0.000347 0.01886 0.001555 -0.003568 -0.002591 -0.004226 0.001093 0.8204 + + + + + \end{pmatrix}$ +} + + + + + +\end{frame} + +\begin{frame}\frametitle{Constructing Matrix unfolding} +\begin{itemize} +\item We got first column of the unfolding matrix. +\end{itemize} +\small{ +$ \begin{pmatrix} + 1.06 & \cdots & a_{1,8} \\ + 0.01157 & \cdots & a_{2,8} \\ + -0.003547 & \ddots & \vdots \\ + 0.0007841 & \ddots & \vdots \\ + 0.001126 & \ddots & \vdots \\ + 0.001766 & \ddots & \vdots \\ + 0.001664 & \ddots & \vdots \\ + -0.001937 & \cdots & a_{8,8} + \end{pmatrix}$ + + +} +\begin{itemize} +\item How about the others? +\item We can reweight accordingly to $f_x$. +\end{itemize} + +\end{frame} + +\begin{frame}\frametitle{Constructing Matrix unfolding} +\begin{itemize} +\item To get $S_3$ each event $i^{th}$ has has weight $f_{S_3}(\cos \theta_{k_i},\cos \theta_{l_i},\phi_i) $ +\item One can calculate on MC the reweighed moments in PHPS: +\end{itemize} +\begin{equation} +\int PDF*f_{S_3}=\dfrac{32}{225} +\end{equation} +\begin{itemize} +\item Our base vector now is:$v^{T}_{gen}=(0 ,\frac{32}{225},0,0,0,0,0,0)$ +\item So lets see what do we get as reconstructed vector(after multiplying by $\frac{225}{32}$. +\small{$v^{T}_{rec}=( 0.042, 1.105,-0.005,0.003,-0.0023,-0.005,-0.005,-0.006)$ } +\end{itemize} + +\end{frame} + + +\begin{frame}\frametitle{Constructing Matrix unfolding} +\begin{itemize} +\item Now the matrix looks like: +\end{itemize} +\small{ +$ \begin{pmatrix} + 1.06 & 0.042 & \cdots & a_{1,8} \\ + 0.01157 & 1.105 & \cdots & a_{2,8} \\ + -0.003547 & -0.005 & \ddots & \vdots \\ + 0.0007841 &-0.005 & \ddots & \vdots \\ + 0.001126 & 0.003 &\ddots & \vdots \\ + 0.001766 & -0.0023 &\ddots & \vdots \\ + 0.001664 & -0.005 &\ddots & \vdots \\ + -0.001937 & -0.006 &\cdots & a_{8,8} + \end{pmatrix}$ + + +} +\begin{itemize} +\item The others go in the same way. +\item Repenting this exercise from $1^{st}$ year algebra we can get the full matrix +\end{itemize} + + +\end{frame} +\begin{frame}\frametitle{Constructing Matrix unfolding} +\begin{itemize} +\item The full transformation matrix from generator space to reconstructed space: +\end{itemize} +\tiny{ +$ A_{gen\rightarrow reco}=\begin{pmatrix} + 1.06 & 0.0423 & -0.0081 & 0.0022 & 0.0049 & 0.0037 & 0.0028 & -0.0065 \\ + + 0.0115 & 1.105 & -0.0050 & 0.0027 & -0.0018 & -0.0040 &-0.0054 & -0.0065 \\ + -0.0035 & -0.0050 & 0.981 & 0.0005 & -0.0025 & 0.0002 & -0.0037 & -0.0048\\ + 0.00078 & 0.0034 & 0.0006 & 1.002 & -0.0032 & -0.0040 & 0.0003 & 0.0018\\ + 0.001126 & -0.0023 & -0.0032 & -0.0032 & 1.055 & 0.001& -0.004 & 0.0023\\ + 0.00176 & -0.0050 & 0.00036 & -0.0040 & 0.0011 & 0.96 & -0.0057 & 0.0009 \\ + 0.0016 & -0.005 & -0.003 & 0.00029& -0.003 &-0.004 & 0.9543 & 0.0000\\ + -0.0019 & -0.0065 & -0.004 & 0.001 & 0.0018 & 0.0007 & 0.000 & 1.098 \\ + + + + + + \end{pmatrix}$ + + +} +\begin{itemize} +\item Inverting the matrix is simple, and doable +\end{itemize} +\tiny{ +$ A_{reco\rightarrow gen}=\begin{pmatrix} + 0.9434 & -0.036 & 0.007& -0.0020 & -0.0044& -0.0038 & -0.0030 & 0.0054\\ + -0.009 & 0.90 & 0.0045 & -0.0024& 0.0016 & 0.003873 & 0.00527& 0.005 \\ + 0.003 & 0.00454& 1.019 & -0.00058 & 0.0025& -0.000291 & 0.004 & 0.004 \\ +-0.00071 & -0.0030 & -0.0007 & 0.9977 & 0.0030 & 0.004206 &-0.0003 & -0.0017 \\ + -0.001 & 0.0020 & 0.0031& 0.0030 & 0.9483 & -0.0010 & 0.004626 & -0.0019 \\ + -0.001 & 0.004 & -0.0003 & 0.0042 & -0.001087 & 1.037 & 0.0063 & -0.0009\\ + -0.0017 & 0.0053 & 0.0042 & -0.0002 & 0.00370& 0.0050 & 1.048 & 0.0000 \\ + 0.0016& 0.0053& 0.00452 & -0.001 & -0.001582 & -0.0007213 &0.000 & 0.9105 \\ + + + + + \end{pmatrix}$ +} + +\end{frame} + + + +\begin{frame}\frametitle{Sensitivity to unknowns} +\begin{itemize} +\item We are unfolding based on MC. +\item There are MC/Data differences, which can have impact on the unfolding. +\end{itemize} +Let's put small modification: +\begin{equation} +w_j \to \overline{w_j}= \dfrac{1}{eff(\cos \theta_{l~j}, \cos \theta_{k~j}, \phi_{j})} \times corr(\cos \theta_{l~j}, \cos \theta_{k~j}, \phi_{j}) +\end{equation} +Unfortunately God didn't allowed me sneak peak into his cards so I don't know $corr(\cos \theta_{l}, \cos \theta_{k}, \phi)$, but let's try out some functions and see what happens :) + + +\end{frame} + +\begin{frame}\frametitle{Corr1 functions} +\begin{columns} +\column{2in} +\includegraphics[width=\linewidth]{corr/Corr1_cosk.png}\\ +\includegraphics[width=\linewidth]{corr/Corr1_cosl.png}\\ +\column{2.5in} +$ +corr1(\cos_l, \cos_k,\phi)= 1+ 0.032 \cos_l - 0.032 \cos_k + 0.01 \phi +$ +\includegraphics[width=0.8\linewidth]{corr/Corr1_phi.png}\\ + +\end{columns} + +\end{frame} +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +\begin{frame}\frametitle{Corr2 functions} +\begin{columns} +\column{2in} +\includegraphics[width=0.85\linewidth]{corr/corr21.png}\\ +\includegraphics[width=0.85\linewidth]{corr/corr22.png}\\ +\column{2.5in} +$ +corr2(\cos_l, \cos_k,\phi)= -0.02 \cos_l^2 + 0.02 \cos_k^2 - + 0.015 \phi^2+ 1 +$ +\includegraphics[width=0.75\linewidth]{corr/corr23.png}\\ + +\end{columns} + +\end{frame} + +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +\begin{frame}\frametitle{Corr3 functions} +\begin{columns} +\column{2in} +\includegraphics[width=0.85\linewidth]{corr/corr31.png}\\ +\includegraphics[width=0.85\linewidth]{corr/corr32.png}\\ +\column{2.5in} +$ +corr3(\cos_l, \cos_k,\phi)= 0.02 \cos_l \cos_k + 0.01 \cos_k \phi - 0.01 \phi \cos_l + 1 +$ +\includegraphics[width=0.75\linewidth]{corr/corr33.png}\\ + +\end{columns} + +\end{frame} +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +\begin{frame}\frametitle{Corr4 functions} +\begin{columns} +\column{2in} +\includegraphics[width=0.85\linewidth]{corr/corr41.png}\\ +\includegraphics[width=0.85\linewidth]{corr/corr42.png}\\ +\column{2.5in} +$ +corr3(\cos_l, \cos_k,\phi)= 0.01 \cos_k \cos_l \phi + 1 +$ +\includegraphics[width=0.75\linewidth]{corr/corr43.png}\\ + +\end{columns} + +\end{frame} + + + + +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% + + +\begin{frame}\frametitle{Corr1- MM} + + +\begin{tiny} + +\begin{center} + \begin{tabular}{ l l l l l l l l l } + \hline + \multicolumn{8}{c}{Mean of the pull} \\ \hline +$q^2$ & $S_3$ & $S_4$ & $S_5$ & $S_{6s}$ & $S_{6c}$ & $S_7$ & $S_8$ \\ \hline \hline + +0 & \scalebox{0.5}{$0.0085 \pm 0.026(0.3)$} & \scalebox{0.5}{$0.13 \pm 0.027(4.6)$} & \scalebox{0.5}{$-0.025 \pm 0.027(-0.92)$} & \scalebox{0.5}{$0.46 \pm 0.027(17)$} & \scalebox{0.5}{$-0.13 \pm 0.028(-4.7)$} & \scalebox{0.5}{$0.029 \pm 0.028(1)$} & \scalebox{0.5}{$-0.66 \pm 0.027(-25)$} \\ \hline +1 & \scalebox{0.5}{$0.0094 \pm 0.028(0.33)$} & \scalebox{0.5}{$0.078 \pm 0.028(2.8)$} & \scalebox{0.5}{$-0.02 \pm 0.028(-0.73)$} & \scalebox{0.5}{$0.24 \pm 0.028(8.5)$} & \scalebox{0.5}{$-0.075 \pm 0.028(-2.7)$} & \scalebox{0.5}{$-0.016 \pm 0.026(-0.63)$} & \scalebox{0.5}{$-0.39 \pm 0.028(-14)$} \\ \hline +2 & \scalebox{0.5}{$-0.02 \pm 0.027(-0.72)$} & \scalebox{0.5}{$0.027 \pm 0.026(1)$} & \scalebox{0.5}{$-0.024 \pm 0.027(-0.91)$} & \scalebox{0.5}{$0.18 \pm 0.027(6.8)$} & \scalebox{0.5}{$-0.024 \pm 0.027(-0.89)$} & \scalebox{0.5}{$-0.067 \pm 0.027(-2.5)$} & \scalebox{0.5}{$-0.39 \pm 0.028(-14)$} \\ \hline +3 & \scalebox{0.5}{$0.013 \pm 0.028(0.46)$} & \scalebox{0.5}{$-0.0089 \pm 0.027(-0.32)$} & \scalebox{0.5}{$0.055 \pm 0.026(2.1)$} & \scalebox{0.5}{$0.12 \pm 0.027(4.7)$} & \scalebox{0.5}{$0.11 \pm 0.027(3.9)$} & \scalebox{0.5}{$-0.018 \pm 0.028(-0.63)$} & \scalebox{0.5}{$-0.43 \pm 0.027(-16)$} \\ \hline +4 & \scalebox{0.5}{$-0.0054 \pm 0.029(-0.18)$} & \scalebox{0.5}{$-0.066 \pm 0.027(-2.4)$} & \scalebox{0.5}{$0.037 \pm 0.028(1.3)$} & \scalebox{0.5}{$0.22 \pm 0.027(8.1)$} & \scalebox{0.5}{$0.099 \pm 0.027(3.7)$} & \scalebox{0.5}{$-0.1 \pm 0.026(-3.8)$} & \scalebox{0.5}{$-0.41 \pm 0.026(-15)$} \\ \hline +5 & \scalebox{0.5}{$0.06 \pm 0.027(2.2)$} & \scalebox{0.5}{$-0.069 \pm 0.026(-2.6)$} & \scalebox{0.5}{$-0.013 \pm 0.028(-0.49)$} & \scalebox{0.5}{$0.21 \pm 0.027(7.8)$} & \scalebox{0.5}{$0.093 \pm 0.027(3.5)$} & \scalebox{0.5}{$-0.083 \pm 0.028(-3)$} & \scalebox{0.5}{$-0.41 \pm 0.028(-15)$} \\ \hline +6 & \scalebox{0.5}{$0.0064 \pm 0.026(0.25)$} & \scalebox{0.5}{$-0.051 \pm 0.027(-1.9)$} & \scalebox{0.5}{$-0.029 \pm 0.028(-1)$} & \scalebox{0.5}{$0.26 \pm 0.028(9.2)$} & \scalebox{0.5}{$0.14 \pm 0.027(5.1)$} & \scalebox{0.5}{$-0.081 \pm 0.027(-3)$} & \scalebox{0.5}{$-0.45 \pm 0.028(-16)$} \\ \hline +%7 & \scalebox{0.5}{$0.22 \pm 0.027(8)$} & \scalebox{0.5}{$-0.34 \pm 0.028(-12)$} & \scalebox{0.5}{$-0.43 \pm 0.026(-16)$} & \scalebox{0.5}{$2.4 \pm 0.029(82)$} & \scalebox{0.5}{$0.66 \pm 0.027(24)$} & \scalebox{0.5}{$-0.24 \pm 0.028(-8.6)$} & \scalebox{0.5}{$-0.51 \pm 0.027(-19)$} & +8 & \scalebox{0.5}{$0.023 \pm 0.027(0.85)$} & \scalebox{0.5}{$-0.031 \pm 0.028(-1.1)$} & \scalebox{0.5}{$0.0042 \pm 0.028(0.15)$} & \scalebox{0.5}{$0.21 \pm 0.026(7.8)$} & \scalebox{0.5}{$0.12 \pm 0.028(4.2)$} & \scalebox{0.5}{$-0.13 \pm 0.027(-4.8)$} & \scalebox{0.5}{$-0.48 \pm 0.026(-18)$} \\ \hline +9 & \scalebox{0.5}{$-0.017 \pm 0.027(-0.63)$} & \scalebox{0.5}{$-0.015 \pm 0.026(-0.56)$} & \scalebox{0.5}{$-0.0052 \pm 0.026(-0.2)$} & \scalebox{0.5}{$0.27 \pm 0.027(10)$} & \scalebox{0.5}{$0.046 \pm 0.026(1.7)$} & \scalebox{0.5}{$-0.12 \pm 0.026(-4.4)$} & \scalebox{0.5}{$-0.5 \pm 0.026(-19)$} \\ \hline +10 & \scalebox{0.5}{$-0.054 \pm 0.027(-2)$} & \scalebox{0.5}{$-0.056 \pm 0.026(-2.2)$} & \scalebox{0.5}{$0.036 \pm 0.026(1.4)$} & \scalebox{0.5}{$0.16 \pm 0.028(5.7)$} & \scalebox{0.5}{$0.077 \pm 0.028(2.8)$} & \scalebox{0.5}{$-0.034 \pm 0.027(-1.3)$} & \scalebox{0.5}{$-0.39 \pm 0.028(-14)$} \\ \hline +11 & \scalebox{0.5}{$0.023 \pm 0.027(0.88)$} & \scalebox{0.5}{$0.021 \pm 0.027(0.8)$} & \scalebox{0.5}{$-0.011 \pm 0.027(-0.41)$} & \scalebox{0.5}{$0.14 \pm 0.027(5)$} & \scalebox{0.5}{$0.042 \pm 0.027(1.6)$} & \scalebox{0.5}{$-0.098 \pm 0.028(-3.5)$} & \scalebox{0.5}{$-0.3 \pm 0.027(-11)$} \\ \hline + + + \hline + + + \end{tabular} + +\end{center} + + +\end{tiny} +\end{frame} + +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% + + +\begin{frame}\frametitle{Corr2- MM} + + +\begin{tiny} + +\begin{center} + \begin{tabular}{ l l l l l l l l l } + \hline + \multicolumn{8}{c}{Mean of the pull} \\ \hline +$q^2$ & $S_3$ & $S_4$ & $S_5$ & $S_{6s}$ & $S_{6c}$ & $S_7$ & $S_8$ \\ \hline \hline + +0 & \scalebox{0.5}{$-0.21 \pm 0.026(-8.1)$} & \scalebox{0.5}{$0.061 \pm 0.026(2.3)$} & \scalebox{0.5}{$-0.016 \pm 0.026(-0.63)$} & \scalebox{0.5}{$0.048 \pm 0.026(1.8)$} & \scalebox{0.5}{$-0.0062 \pm 0.027(-0.23)$} & \scalebox{0.5}{$-0.012 \pm 0.028(-0.44)$} & \scalebox{0.5}{$0.0091 \pm 0.026(0.36)$} \\ \hline +1 & \scalebox{0.5}{$-0.12 \pm 0.028(-4.5)$} & \scalebox{0.5}{$0.032 \pm 0.027(1.2)$} & \scalebox{0.5}{$-0.0071 \pm 0.026(-0.27)$} & \scalebox{0.5}{$0.02 \pm 0.027(0.75)$} & \scalebox{0.5}{$-0.086 \pm 0.027(-3.2)$} & \scalebox{0.5}{$-0.03 \pm 0.025(-1.2)$} & \scalebox{0.5}{$0.021 \pm 0.027(0.79)$} \\ \hline +2 & \scalebox{0.5}{$-0.15 \pm 0.027(-5.8)$} & \scalebox{0.5}{$-0.013 \pm 0.026(-0.49)$} & \scalebox{0.5}{$0.011 \pm 0.026(0.44)$} & \scalebox{0.5}{$-0.039 \pm 0.026(-1.5)$} & \scalebox{0.5}{$-0.032 \pm 0.027(-1.2)$} & \scalebox{0.5}{$-0.066 \pm 0.027(-2.5)$} & \scalebox{0.5}{$0.018 \pm 0.028(0.64)$} \\ \hline +3 & \scalebox{0.5}{$-0.15 \pm 0.027(-5.6)$} & \scalebox{0.5}{$0.025 \pm 0.026(0.96)$} & \scalebox{0.5}{$0.016 \pm 0.027(0.58)$} & \scalebox{0.5}{$-0.062 \pm 0.027(-2.3)$} & \scalebox{0.5}{$0.037 \pm 0.026(1.4)$} & \scalebox{0.5}{$0.026 \pm 0.027(0.96)$} & \scalebox{0.5}{$-0.016 \pm 0.027(-0.6)$} \\ \hline +4 & \scalebox{0.5}{$-0.12 \pm 0.028(-4.5)$} & \scalebox{0.5}{$-0.024 \pm 0.026(-0.92)$} & \scalebox{0.5}{$0.045 \pm 0.027(1.6)$} & \scalebox{0.5}{$0.0075 \pm 0.026(0.29)$} & \scalebox{0.5}{$0.015 \pm 0.027(0.53)$} & \scalebox{0.5}{$-0.036 \pm 0.026(-1.4)$} & \scalebox{0.5}{$0.037 \pm 0.026(1.4)$} \\ \hline +5 & \scalebox{0.5}{$-0.095 \pm 0.027(-3.6)$} & \scalebox{0.5}{$-0.032 \pm 0.026(-1.2)$} & \scalebox{0.5}{$0.014 \pm 0.026(0.52)$} & \scalebox{0.5}{$-0.013 \pm 0.026(-0.48)$} & \scalebox{0.5}{$-0.0093 \pm 0.027(-0.35)$} & \scalebox{0.5}{$-0.013 \pm 0.026(-0.51)$} & \scalebox{0.5}{$0.042 \pm 0.027(1.6)$} \\ \hline +6 & \scalebox{0.5}{$-0.17 \pm 0.025(-6.5)$} & \scalebox{0.5}{$0.008 \pm 0.027(0.3)$} & \scalebox{0.5}{$0.012 \pm 0.027(0.45)$} & \scalebox{0.5}{$0.029 \pm 0.027(1.1)$} & \scalebox{0.5}{$0.0072 \pm 0.027(0.27)$} & \scalebox{0.5}{$-0.0012 \pm 0.026(-0.046)$} & \scalebox{0.5}{$0.011 \pm 0.027(0.42)$} \\ \hline +%7 & \scalebox{0.5}{$0.078 \pm 0.026(3)$} & \scalebox{0.5}{$-0.3 \pm 0.026(-11)$} & \scalebox{0.5}{$-0.34 \pm 0.026(-13)$} & \scalebox{0.5}{$2.1 \pm 0.028(73)$} & \scalebox{0.5}{$0.47 \pm 0.026(18)$} & \scalebox{0.5}{$-0.17 \pm 0.027(-6.1)$} & \scalebox{0.5}{$0.0051 \pm 0.027(0.19)$} \\ \hline +8 & \scalebox{0.5}{$-0.13 \pm 0.026(-5.1)$} & \scalebox{0.5}{$-0.0077 \pm 0.027(-0.28)$} & \scalebox{0.5}{$0.05 \pm 0.027(1.9)$} & \scalebox{0.5}{$-0.03 \pm 0.026(-1.2)$} & \scalebox{0.5}{$-0.012 \pm 0.028(-0.44)$} & \scalebox{0.5}{$-0.046 \pm 0.026(-1.7)$} & \scalebox{0.5}{$0.031 \pm 0.026(1.2)$} \\ \hline +9 & \scalebox{0.5}{$-0.15 \pm 0.026(-5.7)$} & \scalebox{0.5}{$-0.0083 \pm 0.026(-0.32)$} & \scalebox{0.5}{$0.03 \pm 0.026(1.2)$} & \scalebox{0.5}{$0.044 \pm 0.027(1.6)$} & \scalebox{0.5}{$-0.07 \pm 0.026(-2.7)$} & \scalebox{0.5}{$-0.022 \pm 0.026(-0.84)$} & \scalebox{0.5}{$-0.045 \pm 0.026(-1.7)$} \\ \hline +10 & \scalebox{0.5}{$-0.15 \pm 0.025(-5.8)$} & \scalebox{0.5}{$-0.032 \pm 0.025(-1.3)$} & \scalebox{0.5}{$0.059 \pm 0.026(2.2)$} & \scalebox{0.5}{$-0.072 \pm 0.028(-2.6)$} & \scalebox{0.5}{$-0.029 \pm 0.027(-1.1)$} & \scalebox{0.5}{$0.064 \pm 0.027(2.4)$} & \scalebox{0.5}{$0.014 \pm 0.027(0.51)$} \\ \hline +11 & \scalebox{0.5}{$-0.067 \pm 0.026(-2.6)$} & \scalebox{0.5}{$0.017 \pm 0.026(0.65)$} & \scalebox{0.5}{$-0.015 \pm 0.026(-0.56)$} & \scalebox{0.5}{$-0.051 \pm 0.026(-1.9)$} & \scalebox{0.5}{$-0.0086 \pm 0.026(-0.33)$} & \scalebox{0.5}{$-0.018 \pm 0.028(-0.67)$} & \scalebox{0.5}{$0.017 \pm 0.027(0.62)$} \\ \hline + + + + + + +\hline + + + \end{tabular} + +\end{center} + + +\end{tiny} +\end{frame} + + +\begin{frame}\frametitle{Corr3- MM} + + +\begin{tiny} + +\begin{center} + \begin{tabular}{ l l l l l l l l l } + \hline + \multicolumn{8}{c}{Mean of the pull} \\ \hline +$q^2$ & $S_3$ & $S_4$ & $S_5$ & $S_{6s}$ & $S_{6c}$ & $S_7$ & $S_8$ \\ \hline \hline + +0 & \scalebox{0.5}{$-0.021 \pm 0.026(-0.81)$} & \scalebox{0.5}{$0.041 \pm 0.026(1.5)$} & \scalebox{0.5}{$0.009 \pm 0.027(0.34)$} & \scalebox{0.5}{$0.043 \pm 0.026(1.6)$} & \scalebox{0.5}{$0.13 \pm 0.028(4.8)$} & \scalebox{0.5}{$-0.0072 \pm 0.028(-0.26)$} & \scalebox{0.5}{$0.044 \pm 0.026(1.7)$} \\ \hline +1 & \scalebox{0.5}{$-0.014 \pm 0.028(-0.51)$} & \scalebox{0.5}{$0.03 \pm 0.027(1.1)$} & \scalebox{0.5}{$0.022 \pm 0.027(0.82)$} & \scalebox{0.5}{$0.015 \pm 0.028(0.53)$} & \scalebox{0.5}{$0.078 \pm 0.028(2.8)$} & \scalebox{0.5}{$-0.037 \pm 0.025(-1.4)$} & \scalebox{0.5}{$0.057 \pm 0.027(2.1)$} \\ \hline +2 & \scalebox{0.5}{$-0.037 \pm 0.027(-1.4)$} & \scalebox{0.5}{$-0.0013 \pm 0.027(-0.048)$} & \scalebox{0.5}{$-0.015 \pm 0.027(-0.54)$} & \scalebox{0.5}{$-0.052 \pm 0.026(-2)$} & \scalebox{0.5}{$0.1 \pm 0.027(3.8)$} & \scalebox{0.5}{$-0.051 \pm 0.026(-1.9)$} & \scalebox{0.5}{$0.022 \pm 0.028(0.78)$} \\ \hline +3 & \scalebox{0.5}{$-0.015 \pm 0.027(-0.55)$} & \scalebox{0.5}{$0.036 \pm 0.028(1.3)$} & \scalebox{0.5}{$-0.039 \pm 0.027(-1.4)$} & \scalebox{0.5}{$-0.072 \pm 0.027(-2.7)$} & \scalebox{0.5}{$0.17 \pm 0.027(6.2)$} & \scalebox{0.5}{$-0.0044 \pm 0.028(-0.15)$} & \scalebox{0.5}{$-0.024 \pm 0.027(-0.9)$} \\ \hline +4 & \scalebox{0.5}{$-0.00047 \pm 0.029(-0.017)$} & \scalebox{0.5}{$-0.012 \pm 0.027(-0.43)$} & \scalebox{0.5}{$0.0099 \pm 0.028(0.35)$} & \scalebox{0.5}{$-0.002 \pm 0.026(-0.076)$} & \scalebox{0.5}{$0.17 \pm 0.028(6.2)$} & \scalebox{0.5}{$-0.062 \pm 0.027(-2.3)$} & \scalebox{0.5}{$0.0086 \pm 0.027(0.32)$} \\ \hline + +5 & \scalebox{0.5}{$0.046 \pm 0.027(1.7)$} & \scalebox{0.5}{$-0.02 \pm 0.026(-0.76)$} & \scalebox{0.5}{$-0.04 \pm 0.027(-1.5)$} & \scalebox{0.5}{$-0.012 \pm 0.027(-0.44)$} & \scalebox{0.5}{$0.13 \pm 0.027(4.8)$} & \scalebox{0.5}{$-0.04 \pm 0.027(-1.5)$} & \scalebox{0.5}{$-0.0056 \pm 0.027(-0.21)$} \\ \hline +6 & \scalebox{0.5}{$-0.013 \pm 0.026(-0.52)$} & \scalebox{0.5}{$0.041 \pm 0.027(1.5)$} & \scalebox{0.5}{$-0.033 \pm 0.028(-1.2)$} & \scalebox{0.5}{$-0.0019 \pm 0.027(-0.068)$} & \scalebox{0.5}{$0.15 \pm 0.027(5.4)$} & \scalebox{0.5}{$-0.034 \pm 0.027(-1.3)$} & \scalebox{0.5}{$-0.021 \pm 0.028(-0.75)$} \\ \hline +%7 & \scalebox{0.5}{$0.25 \pm 0.027(9.1)$} & \scalebox{0.5}{$-0.27 \pm 0.027(-10)$} & \scalebox{0.5}{$-0.41 \pm 0.027(-16)$} & \scalebox{0.5}{$2.1 \pm 0.029(73)$} & \scalebox{0.5}{$0.65 \pm 0.027(24)$} & \scalebox{0.5}{$-0.19 \pm 0.028(-7)$} & \scalebox{0.5}{$-0.053 \pm 0.028(-1.9)$} \\ \hline +8 & \scalebox{0.5}{$0.039 \pm 0.026(1.5)$} & \scalebox{0.5}{$0.01 \pm 0.028(0.36)$} & \scalebox{0.5}{$-0.027 \pm 0.028(-0.96)$} & \scalebox{0.5}{$-0.024 \pm 0.026(-0.9)$} & \scalebox{0.5}{$0.12 \pm 0.027(4.3)$} & \scalebox{0.5}{$-0.092 \pm 0.026(-3.5)$} & \scalebox{0.5}{$-0.036 \pm 0.027(-1.3)$} \\ \hline +9 & \scalebox{0.5}{$-0.01 \pm 0.027(-0.38)$} & \scalebox{0.5}{$0.0024 \pm 0.027(0.09)$} & \scalebox{0.5}{$-0.018 \pm 0.026(-0.68)$} & \scalebox{0.5}{$0.022 \pm 0.028(0.79)$} & \scalebox{0.5}{$0.068 \pm 0.027(2.6)$} & \scalebox{0.5}{$-0.069 \pm 0.026(-2.6)$} & \scalebox{0.5}{$-0.078 \pm 0.026(-3)$} \\ \hline +10 & \scalebox{0.5}{$-0.017 \pm 0.027(-0.62)$} & \scalebox{0.5}{$-0.015 \pm 0.026(-0.57)$} & \scalebox{0.5}{$0.012 \pm 0.027(0.46)$} & \scalebox{0.5}{$-0.074 \pm 0.028(-2.6)$} & \scalebox{0.5}{$0.1 \pm 0.027(3.8)$} & \scalebox{0.5}{$-0.003 \pm 0.027(-0.11)$} & \scalebox{0.5}{$-0.043 \pm 0.029(-1.5)$} \\ \hline +11 & \scalebox{0.5}{$0.032 \pm 0.026(1.2)$} & \scalebox{0.5}{$0.024 \pm 0.026(0.91)$} & \scalebox{0.5}{$-0.04 \pm 0.026(-1.5)$} & \scalebox{0.5}{$-0.066 \pm 0.027(-2.5)$} & \scalebox{0.5}{$0.098 \pm 0.027(3.7)$} & \scalebox{0.5}{$-0.043 \pm 0.028(-1.6)$} & \scalebox{0.5}{$-0.0018 \pm 0.028(-0.064)$} \\ \hline + + + +\hline + + + \end{tabular} + +\end{center} + + +\end{tiny} +\end{frame} + +\begin{frame}\frametitle{Corr4- MM} + + +\begin{tiny} + +\begin{center} + \begin{tabular}{ l l l l l l l l l } + \hline + \multicolumn{8}{c}{Mean of the pull} \\ \hline +$q^2$ & $S_3$ & $S_4$ & $S_5$ & $S_{6s}$ & $S_{6c}$ & $S_7$ & $S_8$ \\ \hline \hline + + +0 & \scalebox{0.5}{$-0.019 \pm 0.026(-0.71)$} & \scalebox{0.5}{$0.048 \pm 0.027(1.8)$} & \scalebox{0.5}{$0.018 \pm 0.027(0.67)$} & \scalebox{0.5}{$0.059 \pm 0.027(2.2)$} & \scalebox{0.5}{$-0.015 \pm 0.028(-0.55)$} & \scalebox{0.5}{$0.061 \pm 0.027(2.2)$} & \scalebox{0.5}{$0.012 \pm 0.027(0.44)$} \\ \hline +1 & \scalebox{0.5}{$-0.014 \pm 0.028(-0.51)$} & \scalebox{0.5}{$0.043 \pm 0.027(1.6)$} & \scalebox{0.5}{$0.013 \pm 0.027(0.49)$} & \scalebox{0.5}{$0.024 \pm 0.028(0.86)$} & \scalebox{0.5}{$-0.038 \pm 0.028(-1.4)$} & \scalebox{0.5}{$0.024 \pm 0.026(0.94)$} & \scalebox{0.5}{$0.037 \pm 0.027(1.3)$} \\ \hline +2 & \scalebox{0.5}{$-0.03 \pm 0.027(-1.1)$} & \scalebox{0.5}{$-0.0021 \pm 0.027(-0.076)$} & \scalebox{0.5}{$-0.01 \pm 0.027(-0.39)$} & \scalebox{0.5}{$-0.017 \pm 0.027(-0.61)$} & \scalebox{0.5}{$-0.016 \pm 0.027(-0.58)$} & \scalebox{0.5}{$0.013 \pm 0.027(0.49)$} & \scalebox{0.5}{$0.027 \pm 0.028(0.98)$} \\ \hline +3 & \scalebox{0.5}{$-0.007 \pm 0.027(-0.26)$} & \scalebox{0.5}{$0.03 \pm 0.028(1.1)$} & \scalebox{0.5}{$-0.036 \pm 0.027(-1.3)$} & \scalebox{0.5}{$-0.074 \pm 0.027(-2.8)$} & \scalebox{0.5}{$0.041 \pm 0.027(1.5)$} & \scalebox{0.5}{$0.08 \pm 0.028(2.9)$} & \scalebox{0.5}{$-0.0083 \pm 0.027(-0.31)$} \\ \hline +4 & \scalebox{0.5}{$0.00089 \pm 0.029(0.031)$} & \scalebox{0.5}{$-0.021 \pm 0.027(-0.77)$} & \scalebox{0.5}{$0.0032 \pm 0.028(0.11)$} & \scalebox{0.5}{$0.0031 \pm 0.026(0.12)$} & \scalebox{0.5}{$0.012 \pm 0.027(0.44)$} & \scalebox{0.5}{$0.019 \pm 0.026(0.71)$} & \scalebox{0.5}{$0.034 \pm 0.027(1.3)$} \\ \hline +5 & \scalebox{0.5}{$0.044 \pm 0.028(1.6)$} & \scalebox{0.5}{$-0.022 \pm 0.026(-0.82)$} & \scalebox{0.5}{$-0.041 \pm 0.027(-1.5)$} & \scalebox{0.5}{$-0.014 \pm 0.027(-0.53)$} & \scalebox{0.5}{$-0.029 \pm 0.027(-1.1)$} & \scalebox{0.5}{$0.041 \pm 0.027(1.5)$} & \scalebox{0.5}{$0.042 \pm 0.028(1.5)$} \\ \hline +6 & \scalebox{0.5}{$-0.011 \pm 0.026(-0.42)$} & \scalebox{0.5}{$0.041 \pm 0.027(1.5)$} & \scalebox{0.5}{$-0.045 \pm 0.028(-1.6)$} & \scalebox{0.5}{$0.011 \pm 0.027(0.41)$} & \scalebox{0.5}{$-0.0089 \pm 0.027(-0.33)$} & \scalebox{0.5}{$0.067 \pm 0.027(2.5)$} & \scalebox{0.5}{$0.036 \pm 0.027(1.3)$} \\ \hline +%7 & \scalebox{0.5}{$0.25 \pm 0.027(9.1)$} & \scalebox{0.5}{$-0.26 \pm 0.027(-9.9)$} & \scalebox{0.5}{$-0.42 \pm 0.027(-16)$} & \scalebox{0.5}{$2.1 \pm 0.029(73)$} & \scalebox{0.5}{$0.47 \pm 0.027(18)$} & \scalebox{0.5}{$-0.077 \pm 0.028(-2.8)$} & \scalebox{0.5}{$0.029 \pm 0.028(1)$} \\ \hline +8 & \scalebox{0.5}{$0.05 \pm 0.026(1.9)$} & \scalebox{0.5}{$0.0021 \pm 0.028(0.074)$} & \scalebox{0.5}{$-0.025 \pm 0.028(-0.91)$} & \scalebox{0.5}{$-0.023 \pm 0.026(-0.87)$} & \scalebox{0.5}{$-0.024 \pm 0.028(-0.85)$} & \scalebox{0.5}{$0.022 \pm 0.026(0.82)$} & \scalebox{0.5}{$0.026 \pm 0.026(0.98)$} \\ \hline +9 & \scalebox{0.5}{$-0.0064 \pm 0.027(-0.23)$} & \scalebox{0.5}{$0.012 \pm 0.027(0.44)$} & \scalebox{0.5}{$-0.0075 \pm 0.026(-0.28)$} & \scalebox{0.5}{$0.029 \pm 0.027(1.1)$} & \scalebox{0.5}{$-0.087 \pm 0.027(-3.2)$} & \scalebox{0.5}{$0.036 \pm 0.027(1.3)$} & \scalebox{0.5}{$-0.02 \pm 0.026(-0.76)$} \\ \hline +10 & \scalebox{0.5}{$-0.019 \pm 0.027(-0.71)$} & \scalebox{0.5}{$-0.0051 \pm 0.025(-0.2)$} & \scalebox{0.5}{$0.0081 \pm 0.026(0.31)$} & \scalebox{0.5}{$-0.077 \pm 0.028(-2.7)$} & \scalebox{0.5}{$-0.03 \pm 0.027(-1.1)$} & \scalebox{0.5}{$0.11 \pm 0.027(4.1)$} & \scalebox{0.5}{$0.013 \pm 0.028(0.46)$} \\ \hline +11 & \scalebox{0.5}{$0.027 \pm 0.026(1)$} & \scalebox{0.5}{$0.032 \pm 0.027(1.2)$} & \scalebox{0.5}{$-0.038 \pm 0.027(-1.4)$} & \scalebox{0.5}{$-0.048 \pm 0.026(-1.8)$} & \scalebox{0.5}{$-0.021 \pm 0.027(-0.77)$} & \scalebox{0.5}{$0.019 \pm 0.028(0.69)$} & \scalebox{0.5}{$0.035 \pm 0.027(1.3)$} \\ \hline + + + +\hline + + \end{tabular} + +\end{center} + +\end{tiny} +\end{frame} + + + + +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +\section{Reverse Engineering Unfolding} + +\begin{frame}\frametitle{Reverse Engineering- Corr1} +\begin{itemize} +\item Let's try to understand if we can understand why this happens: +\item Let's calculate what should I expect with the unfolding +\item This is up to normalization! +\begin{itemize} +\item $M_5=0.4 S_5 \to M_5=0.00512 S_3 + 0.4 S_5 - 0.002 S_7$ +\item $M_8=0.32 S_8 \to M_8=0.0016 S_4 + 0.00512 S_7 + 0.32 S_8$ +\item $M_7=0.4 S_7 \to M_7=0.002 S_5 + 0.4 S_7 + 0.00512 S_8$ +\item $M_3=0.32 S_3 \to M_3=0.32 S_3 - 0.0008 S_9$ +\end{itemize} +\item The way you can look at this is that i just shown you how our unfolding matrix works like. +\end{itemize} + + + +\end{frame} + +\begin{frame}\frametitle{Reverse Engineering- Corr2} +\begin{itemize} +\item Let's try to understand if we can understand why this happens: +\item Let's calculate what should I expect with the unfolding +\item This is up to normalization! +\begin{itemize} +\item $M_5=0.4 S_5 \to M_5= 0.4 S_5$ +\item $M_8=0.32 S_8 \to M_8=0.32 S_5$ +\item $M_7=0.4 S_7 \to M_7=0.4 S_7$ +\item $M_3=0.32 S_3 \to M_3=-0.0036 + 0.0012 Fl + 0.32 S_3$ +\end{itemize} +\item The way you can look at this is that i just shown you how our unfolding matrix works like. +\end{itemize} + + + +\end{frame} + + + + +\begin{frame}\frametitle{Summary} +\begin{itemize} +\item Developed a systematic way how to get Unfolding matrix +\item Moments are resistant against variety of unfolding discrepancies. +\item This might lead to reduced systematics in the future. +\end{itemize} + + + + +\end{frame} + + + +\end{document} diff --git a/Kstmumu/RECO12_14/MMatrix.toc b/Kstmumu/RECO12_14/MMatrix.toc new file mode 100644 index 0000000..495658f --- /dev/null +++ b/Kstmumu/RECO12_14/MMatrix.toc @@ -0,0 +1,2 @@ +\beamer@endinputifotherversion {3.10pt} +\select@language {english} diff --git a/Kstmumu/RECO12_14/P5.png b/Kstmumu/RECO12_14/P5.png new file mode 100644 index 0000000..7819eef --- /dev/null +++ b/Kstmumu/RECO12_14/P5.png Binary files differ diff --git a/Kstmumu/RECO12_14/Q2_4_S8.png b/Kstmumu/RECO12_14/Q2_4_S8.png new file mode 100644 index 0000000..9176de4 --- /dev/null +++ b/Kstmumu/RECO12_14/Q2_4_S8.png Binary files differ diff --git a/Kstmumu/RECO12_14/Q2_5_6_S5.eps 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defining Unicode char U+00F2 (decimal 242) + defining Unicode char U+00F3 (decimal 243) + defining Unicode char U+00F4 (decimal 244) + defining Unicode char U+00F5 (decimal 245) + defining Unicode char U+00F6 (decimal 246) + defining Unicode char U+00F8 (decimal 248) + defining Unicode char U+00F9 (decimal 249) + defining Unicode char U+00FA (decimal 250) + defining Unicode char U+00FB (decimal 251) + defining Unicode char U+00FC (decimal 252) + defining Unicode char U+00FD (decimal 253) + defining Unicode char U+00FE (decimal 254) + defining Unicode char U+00FF (decimal 255) + defining Unicode char U+0102 (decimal 258) + defining Unicode char U+0103 (decimal 259) + defining Unicode char U+0104 (decimal 260) + defining Unicode char U+0105 (decimal 261) + defining Unicode char U+0106 (decimal 262) + defining Unicode char U+0107 (decimal 263) + defining Unicode char U+010C (decimal 268) + defining Unicode char U+010D (decimal 269) + defining Unicode char U+010E (decimal 270) + defining Unicode char U+010F (decimal 271) + defining Unicode char U+0110 (decimal 272) + defining Unicode char U+0111 (decimal 273) + defining Unicode char U+0118 (decimal 280) + defining Unicode char U+0119 (decimal 281) + defining Unicode char U+011A (decimal 282) + defining Unicode char U+011B (decimal 283) + defining Unicode char U+011E (decimal 286) + defining Unicode char U+011F (decimal 287) + defining Unicode char U+0130 (decimal 304) + defining Unicode char U+0131 (decimal 305) + defining Unicode char U+0132 (decimal 306) + defining Unicode char U+0133 (decimal 307) + defining Unicode char U+0139 (decimal 313) + defining Unicode char U+013A (decimal 314) + defining Unicode char U+013D (decimal 317) + defining Unicode char U+013E (decimal 318) + defining Unicode char U+0141 (decimal 321) + defining Unicode char U+0142 (decimal 322) + defining Unicode char U+0143 (decimal 323) + defining Unicode char U+0144 (decimal 324) + defining Unicode char U+0147 (decimal 327) + defining Unicode char U+0148 (decimal 328) + defining Unicode char U+014A (decimal 330) + defining Unicode char U+014B (decimal 331) + defining Unicode char U+0150 (decimal 336) + defining Unicode char U+0151 (decimal 337) + defining Unicode char U+0152 (decimal 338) + defining Unicode char U+0153 (decimal 339) + defining Unicode char U+0154 (decimal 340) + defining Unicode char U+0155 (decimal 341) + defining Unicode char U+0158 (decimal 344) + defining Unicode char U+0159 (decimal 345) + defining Unicode char U+015A (decimal 346) + defining Unicode char U+015B (decimal 347) + defining Unicode char U+015E (decimal 350) + defining Unicode char U+015F (decimal 351) + defining Unicode char U+0160 (decimal 352) + defining Unicode char U+0161 (decimal 353) + defining Unicode char U+0162 (decimal 354) + defining Unicode char U+0163 (decimal 355) + defining Unicode char U+0164 (decimal 356) + defining Unicode char U+0165 (decimal 357) + defining Unicode char U+016E (decimal 366) + defining Unicode char 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321) + defining Unicode char U+0142 (decimal 322) + defining Unicode char U+0152 (decimal 338) + defining Unicode char U+0153 (decimal 339) + defining Unicode char U+2013 (decimal 8211) + defining Unicode char U+2014 (decimal 8212) + defining Unicode char U+2018 (decimal 8216) + defining Unicode char U+2019 (decimal 8217) + defining Unicode char U+201C (decimal 8220) + defining Unicode char U+201D (decimal 8221) +) +Now handling font encoding OMS ... +... processing UTF-8 mapping file for font encoding OMS + +(/usr/share/texmf-texlive/tex/latex/base/omsenc.dfu +File: omsenc.dfu 2008/04/05 v1.1m UTF-8 support for inputenc + defining Unicode char U+00A7 (decimal 167) + defining Unicode char U+00B6 (decimal 182) + defining Unicode char U+00B7 (decimal 183) + defining Unicode char U+2020 (decimal 8224) + defining Unicode char U+2021 (decimal 8225) + defining Unicode char U+2022 (decimal 8226) +) +Now handling font encoding OMX ... +... no UTF-8 mapping file for font encoding OMX +Now 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a/Kstmumu/RECO12_14/RECO.out b/Kstmumu/RECO12_14/RECO.out new file mode 100644 index 0000000..e69de29 --- /dev/null +++ b/Kstmumu/RECO12_14/RECO.out diff --git a/Kstmumu/RECO12_14/RECO.pdf b/Kstmumu/RECO12_14/RECO.pdf new file mode 100644 index 0000000..18258b5 --- /dev/null +++ b/Kstmumu/RECO12_14/RECO.pdf Binary files differ diff --git a/Kstmumu/RECO12_14/RECO.snm b/Kstmumu/RECO12_14/RECO.snm new file mode 100644 index 0000000..e69de29 --- /dev/null +++ b/Kstmumu/RECO12_14/RECO.snm diff --git a/Kstmumu/RECO12_14/RECO.synctex.gz b/Kstmumu/RECO12_14/RECO.synctex.gz new file mode 100644 index 0000000..b129b71 --- /dev/null +++ b/Kstmumu/RECO12_14/RECO.synctex.gz Binary files differ diff --git a/Kstmumu/RECO12_14/RECO.tex b/Kstmumu/RECO12_14/RECO.tex new file mode 100644 index 0000000..f8d4042 --- /dev/null +++ b/Kstmumu/RECO12_14/RECO.tex @@ -0,0 +1,200 @@ +\documentclass[xcolor=svgnames]{beamer} +\usepackage[utf8]{inputenc} +\usepackage[english]{babel} +\usepackage{polski} +%\usepackage{amssymb,amsmath} +%\usepackage[latin1]{inputenc} +%\usepackage{amsmath} +%\newcommand\abs[1]{\left|#1\right|} +\usepackage{amsmath} +\newcommand\abs[1]{\left|#1\right|} +\usepackage{hepnicenames} +\usepackage{hepunits} +\usepackage{color} +\usepackage{mathrsfs} +\setbeamertemplate{footline}{\insertframenumber/\inserttotalframenumber} +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%5 +\definecolor{mygreen}{cmyk}{0.82,0.11,1,0.25} + + +\usetheme{Sybila} + +\title[RECO 12 vs 14, vol 1]{RECO 12 vs 14, vol 1} +\author{Tom Blake$^{1}$,~Marcin Chrz\k{a}szcz$^{2,3}$} +\institute{$^1$~University of Warwick,\\ $^2$~University of Zurich,\\ $^3$~Institute of Nuclear Physics, Krakow} +\date{\today} +\begin{document} +% --------------------------- SLIDE -------------------------------------------- +\frame[plain]{\titlepage} +\author{Tom Blake, Marcin Chrz\k{a}szcz} +% ------------------------------------------------------------------------------ +% --------------------------- SLIDE -------------------------------------------- + +\institute{~(UW, UZH, IFJ)} + + +\begin{frame}\frametitle{Basics} +As you should now from email exchange: +\begin{itemize} +\item $\PBzero \to \PKstar \mu \mu$ PHPS MC was produced. +\item We also have SM MC. +\item $\PJpsi \PKstar$ on way(later today we should have it). +\item All are SIM08 +\item For now $4~TeV$ data, $3.5~TeV$ in queue. +\item The same events(common, Gauss, Boole, Moore) are processed by 2 different Brunel versions(one for RECO12, other for RECO14). +\item Since I don't have full selection, I am studying the events that pass our stripping 20. +\item Events are truth matched between two ntuples using EVENTNUMBER. +\end{itemize} + + +\end{frame} +\begin{frame}\frametitle{Results/Plots 1} + +\begin{itemize} +\item RECO 12 and STRIPPING 20 selected 5054 +\item Among those 4667 are also selected by RECO 14 and our stripping. +\item The over lap is about $92.3 \pm 0.4 \%$. +\item A bit higher compared to what we saw in data.... +\end{itemize} + + +\end{frame} + + +\begin{frame}\frametitle{Results/Plots $\PBzero$} +\begin{columns} +\column{2.5in} + +\includegraphics[width=0.7\textwidth]{RECO/B0_DIRA.png} +\column{2.5in} +\includegraphics[width=0.7\textwidth]{RECO/B0_FD.png} +\end{columns} +\begin{columns} +\column{2.5in} + +\includegraphics[width=0.7\textwidth]{RECO/B0_FDCHI2.png} +\column{2.5in} +\includegraphics[width=0.7\textwidth]{RECO/B0_IP.png} +\end{columns} + +\end{frame} + + +\begin{frame}\frametitle{Results/Plots $\PBzero$} +\begin{columns} +\column{2.5in} + +\includegraphics[width=0.7\textwidth]{RECO/B0_IPCHI2.png} +\column{2.5in} +\includegraphics[width=0.7\textwidth]{RECO/B0_MM.png} +\end{columns} +\begin{columns} +\column{2.5in} + +\includegraphics[width=0.7\textwidth]{RECO/B0_P.png} +\column{2.5in} +\includegraphics[width=0.7\textwidth]{RECO/B0_PT.png} +\end{columns} + +\end{frame} + +\begin{frame}\frametitle{Results/Plots $\PBzero$} +\begin{columns} +\column{2.5in} + +\includegraphics[width=0.7\textwidth]{RECO/B0_tau.png} +\column{2.5in} +\includegraphics[width=0.7\textwidth]{RECO/B0_VRTXCHI2.png} +\end{columns} + +\end{frame} + + + + +\begin{frame}\frametitle{Results/Plots $\PK$} +\begin{columns} +\column{2.5in} + +\includegraphics[width=0.7\textwidth]{RECO/K_P.png} +\column{2.5in} +\includegraphics[width=0.7\textwidth]{RECO/K_PT.png} +\end{columns} +\begin{columns} +\column{2.5in} +\includegraphics[width=0.7\textwidth]{RECO/K_TRK_CHI2.png} +\column{2.5in} +{~} +\end{columns} +\end{frame} + + +\begin{frame}\frametitle{Results/Plots $\Ppi$} +\begin{columns} +\column{2.5in} + +\includegraphics[width=0.7\textwidth]{RECO/Pi_P.png} +\column{2.5in} +\includegraphics[width=0.7\textwidth]{RECO/Pi_PT.png} +\end{columns} +\begin{columns} +\column{2.5in} +\includegraphics[width=0.7\textwidth]{RECO/Pi_TRK_CHI2.png} +\column{2.5in} +{~} +\end{columns} +\end{frame} + + + +\begin{frame}\frametitle{Results/Plots $\Pmuon$} +\begin{columns} +\column{2.5in} + +\includegraphics[width=0.7\textwidth]{RECO/Mum_P.png} +\column{2.5in} +\includegraphics[width=0.7\textwidth]{RECO/Mum_PT.png} +\end{columns} +\begin{columns} +\column{2.5in} +\includegraphics[width=0.7\textwidth]{RECO/Mum_TRK_CHI2.png} +\column{2.5in} +{~} +\end{columns} +\end{frame} + + +\begin{frame}\frametitle{Results/Plots $\APmuon$} +\begin{columns} +\column{2.5in} + +\includegraphics[width=0.7\textwidth]{RECO/Mup_P.png} +\column{2.5in} +\includegraphics[width=0.7\textwidth]{RECO/Mup_PT.png} +\end{columns} +\begin{columns} +\column{2.5in} +\includegraphics[width=0.7\textwidth]{RECO/Mup_TRK_CHI2.png} +\column{2.5in} +{~} +\end{columns} +\end{frame} + +\begin{frame}\frametitle{Conclusions} +\begin{enumerate} +\item The spread of the variables looks smaller then in data. +\item This needs further investigations: $\PJpsi \PKstar$, full selection, $3.5~TeV$,(more suggestions?) +\item What else should I compare? PID? other? Let me know. +\item The thing that comes to my mind when I look at those plots is: +\end{enumerate} + +\begin{center} +"The truth is rarely pure and never simple." +\end{center} + + + + +\end{frame} + +\end{document} diff --git a/Kstmumu/RECO12_14/RECO.toc b/Kstmumu/RECO12_14/RECO.toc new file mode 100644 index 0000000..495658f --- /dev/null +++ b/Kstmumu/RECO12_14/RECO.toc @@ -0,0 +1,2 @@ +\beamer@endinputifotherversion {3.10pt} +\select@language {english} diff --git a/Kstmumu/RECO12_14/RECO/B0_DIRA.png b/Kstmumu/RECO12_14/RECO/B0_DIRA.png new file mode 100644 index 0000000..506d161 --- /dev/null +++ b/Kstmumu/RECO12_14/RECO/B0_DIRA.png Binary files differ diff --git a/Kstmumu/RECO12_14/RECO/B0_FD.png b/Kstmumu/RECO12_14/RECO/B0_FD.png new file mode 100644 index 0000000..e3f8a60 --- /dev/null +++ b/Kstmumu/RECO12_14/RECO/B0_FD.png Binary files differ diff --git a/Kstmumu/RECO12_14/RECO/B0_FDCHI2.png b/Kstmumu/RECO12_14/RECO/B0_FDCHI2.png new file mode 100644 index 0000000..589b9b8 --- 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+\setbeamerfont{date}{size=\small} + +%------------------------------------------------------------------------------- +% Other +%------------------------------------------------------------------------------- + +\titlegraphic{\includegraphics[width=3.0cm]{sybila-logo-slide-title-shaded.pdf}} + +\mode + diff --git a/Kstmumu/RECO12_14/tmp/example.tex b/Kstmumu/RECO12_14/tmp/example.tex new file mode 100644 index 0000000..ce0641b --- /dev/null +++ b/Kstmumu/RECO12_14/tmp/example.tex @@ -0,0 +1,21 @@ +\documentclass[xcolor=svgnames]{beamer} +\usepackage[utf8]{inputenc} +\usepackage[english]{babel} + +\usetheme{Sybila} + +\title[Parallelization of Methods for Dynamic System Analysis]{Parallelization of Methods for Dynamic System Analysis Using CUDA} +\author{Jan Papou\v{s}ek} +\institute{Masaryk University Brno} +\date{\today} + +\begin{document} +% --------------------------- SLIDE -------------------------------------------- +\frame[plain]{\titlepage} +% ------------------------------------------------------------------------------ +% --------------------------- SLIDE -------------------------------------------- +\begin{frame} + \frametitle{Introduction} +\end{frame} +% ------------------------------------------------------------------------------ +\end{document} diff --git a/Kstmumu/RECO12_14/tmp/example/beamerthemeSybila.sty b/Kstmumu/RECO12_14/tmp/example/beamerthemeSybila.sty new file mode 100644 index 0000000..5639601 --- /dev/null +++ b/Kstmumu/RECO12_14/tmp/example/beamerthemeSybila.sty @@ -0,0 +1,104 @@ +\mode + +%------------------------------------------------------------------------------- +% Themes +%------------------------------------------------------------------------------- + +\useoutertheme{split} +\useinnertheme{rounded} +\usefonttheme{structurebold} +%\useoutertheme{shadow} + +%------------------------------------------------------------------------------- +% Templates +%------------------------------------------------------------------------------- + +\beamertemplatenavigationsymbolsempty +\beamertemplateheadempty +\beamertemplateshadowblocks + +%------------------------------------------------------------------------------- +% Own templates +%------------------------------------------------------------------------------- + +% Normal title page. +\defbeamertemplate*{title page}{simple}[1][] +{ + \vfill + \begin{centering} + \begin{beamercolorbox}[center, rounded=true]{title} + \usebeamerfont{title}\inserttitle\par% + \ifx\insertsubtitle\@empty% + \else% + \vskip0.25em% + {\usebeamerfont{subtitle}\usebeamercolor[fg]{subtitle}\insertsubtitle\par}% + \fi% + \end{beamercolorbox}% + + \vskip1em + + \begin{beamercolorbox}[sep=8pt,center,#1]{author} + \usebeamerfont{author}\insertauthor + \end{beamercolorbox} + + \vskip1em + + {\usebeamercolor[fg]{titlegraphic}\inserttitlegraphic\par} + \begin{beamercolorbox}[sep=8pt,center,#1]{institute} + \usebeamerfont{date}\insertinstitute + \end{beamercolorbox} + + \vskip1em + + \begin{beamercolorbox}[sep=8pt,center,#1]{date} + \usebeamerfont{date}\insertdate + \end{beamercolorbox} + \end{centering} + \vfill +} + +%------------------------------------------------------------------------------- +% Logo +%------------------------------------------------------------------------------- + +\logo{\hspace*{0.6\textwidth}\includegraphics[width=1.2cm]{sybila-logo-paper-shaded}\hspace*{0.3cm}} + +%------------------------------------------------------------------------------- +% Colors +%------------------------------------------------------------------------------- + +\setbeamercovered{dynamic} + +\setbeamercolor{math text}{fg=green!45!black} +\setbeamercolor{title}{bg=white!30!black} +\setbeamercolor{frametitle}{bg=white!45!black} +\setbeamercolor{footline}{bg=black,fg=white} +\setbeamercolor{author in head/foot}{bg=black,fg=white} +\setbeamercolor{title in head/foot}{bg=white!45!black} 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a/Kstmumu/RECO12_14/tmp/example/example.synctex.gz b/Kstmumu/RECO12_14/tmp/example/example.synctex.gz new file mode 100644 index 0000000..5bccdb3 --- /dev/null +++ b/Kstmumu/RECO12_14/tmp/example/example.synctex.gz Binary files differ diff --git a/Kstmumu/RECO12_14/tmp/example/example.tex b/Kstmumu/RECO12_14/tmp/example/example.tex new file mode 100644 index 0000000..ce0641b --- /dev/null +++ b/Kstmumu/RECO12_14/tmp/example/example.tex @@ -0,0 +1,21 @@ +\documentclass[xcolor=svgnames]{beamer} +\usepackage[utf8]{inputenc} +\usepackage[english]{babel} + +\usetheme{Sybila} + +\title[Parallelization of Methods for Dynamic System Analysis]{Parallelization of Methods for Dynamic System Analysis Using CUDA} +\author{Jan Papou\v{s}ek} +\institute{Masaryk University Brno} +\date{\today} + +\begin{document} +% --------------------------- SLIDE -------------------------------------------- +\frame[plain]{\titlepage} +% ------------------------------------------------------------------------------ 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/y2 y2 y1 sub def + clip + newpath + 2 setlinecap + systemdict + /setstrokeadjust known { true setstrokeadjust } if + x2 x1 sub 1 add { + x1 a mul y1 moveto 0 y2 rlineto stroke + /x1 x1 1 add + hatchWidthInc 0 gt { CLW add } if + def + hatchSepInc 0 gt hatchWidthInc 0 gt or { + /a a hatchSepInc add def + CLW hatchWidthInc add SLW + } if + } repeat + grestore + pop pop } def +% +/PenroseFill {% on stack: scaling factor + dup dup scale + 1 exch div round /penroseFactor ED + a 0 dtransform round exch round exch + 2 copy idtransform + exch Atan rotate + idtransform pop /a ED + .25 .25 itransform pathbbox + /y2 ED + a Div ceiling cvi /x2 ED /y1 ED + a Div cvi /x1 ED /y2 y2 y1 sub def + clip + newpath + systemdict + /setstrokeadjust known { true setstrokeadjust } if + /I/S/L/W/G/+/Z/F/E/D[/def/exch/for{E D}/add{s E get mul} + { Z -36.2001 1 33 }{25 E S rlineto}{/q Z dup q G E q 1 + G}{Z 2 2}]{cvx def}forall + [0 72 1008 {dup sin E cos }F ]1 setlinejoin/s W{/a W{/b I 10{/i I 4{/m I moveto + i m +/j I 10{/l Z b m l + G a l G sub s m get div .2 + floor .3 + 25 + mul j l + S rmoveto}F i L j L stroke }F}F}F}F + grestore + pop pop +} def +% +%gsave abs CLW add /a ED a 0 dtransform round exch round exch +%2 copy idtransform exch Atan rotate idtransform pop /a ED .25 .25 +%% DG/SR modification begin - Dec. 12, 1997 - Patch 2 +%%itransform translate pathbbox /y2 ED a Div ceiling cvi /x2 ED /y1 ED a +%itransform pathbbox /y2 ED a Div ceiling cvi /x2 ED /y1 ED a +%% DG/SR modification end +%Div cvi /x1 ED /y2 y2 y1 sub def clip newpath 2 setlinecap systemdict +%/setstrokeadjust known { true setstrokeadjust } if x2 x1 sub 1 add { x1 +%% DG/SR modification begin - Jun. 1, 1998 - Patch 3 (from Michael Vulis) +%% a mul y1 moveto 0 y2 rlineto stroke /x1 x1 1 add def } repeat grestore } +%% def +%a mul y1 moveto 0 y2 rlineto stroke /x1 x1 1 add def } repeat grestore +%pop pop } def +%% DG/SR modification end +% +/BeginArrow { + ADict begin % hold it local, for end see EndArrow + /@mtrx CM def + gsave + 2 copy T + 2 index sub neg exch + 3 index sub exch Atan + rotate newpath +} def +% +/EndArrow { @mtrx setmatrix CP grestore end } def % end the ADict +% +/Arrow { + CLW mul add dup + 2 div /w ED + mul dup /h ED + mul /a ED + { 0 h T 1 -1 scale } if + w neg h moveto + 0 0 L w h L w neg a neg rlineto + gsave fill grestore +} def +% +/ArrowD { % the sides are drawn as curves (hv 20071211) + CLW mul add dup + 2 div /w ED + mul dup /h ED + mul /Inset ED + { 0 h T 1 -1 scale } if % changes the direction +% we use y=w/h^2 * x^2 as equation for the control points +% for the coordinates the arrow is seen from top to bottom +% the bottom (tip) is (0;0) + w neg h moveto % lower left of > + w 9 div 4 mul neg h 3 div 2 mul + w 9 div neg h 3 div + 0 0 curveto % tip of > + w 9 div h 3 div + w 9 div 4 mul h 3 div 2 mul + w h curveto % upper left of > + w neg Inset neg rlineto % move to x=0 and inset + gsave fill grestore +} def +% +/Tbar { + CLW mul add /z ED + z -2 div CLW 2 div moveto + z 0 rlineto stroke + 0 CLW moveto +} def +% +/Bracket { + CLW mul add dup CLW sub 2 div + /x ED mul CLW add /y ED /z CLW 2 div def + x neg y moveto + x neg CLW 2 div L x CLW 2 div L x y L stroke + 0 CLW moveto +} def +% +/RoundBracket { + CLW mul add dup 2 div + /x ED mul /y ED /mtrx CM def + 0 CLW 2 div T x y mul 0 ne { x y scale } if + 1 1 moveto + .85 .5 .35 0 0 0 curveto + -.35 0 -.85 .5 -1 1 curveto + mtrx setmatrix stroke 0 CLW moveto +} def +% +/SD { 0 360 arc fill } def +% +/EndDot { % DS is the dot size + { /z DS def } { /z 0 def } ifelse + /b ED 0 z DS SD b { 0 z DS CLW sub SD } if + 0 DS z add CLW 4 div sub moveto } def +% +/Shadow { [ { /moveto load } { /lineto load } { /curveto load } { + /closepath load } /pathforall load stopped { pop pop pop pop CP /moveto + load } if ] cvx newpath 3 1 roll T exec } def +% +%/NArray { +% aload length 2 div dup dup cvi eq not { exch pop } if /n exch +% cvi def +%} def +% +/NArray { % holds the coordinates and on top of stack the showpoints boolean + /showpoints ED + counttomark 2 div dup cvi /n ED + n eq not { exch pop } if + showpoints { ] aload /Points ED } { n 2 mul 1 add -1 roll pop } ifelse +} def +% +/Line { + NArray n 0 eq not + { n 1 eq { 0 0 /n 2 def } if ArrowA /n n 2 sub def + n { Lineto } repeat + CP 4 2 roll ArrowB L pop pop + } if +} def +% +/Arcto { + /a [ 6 -2 roll ] cvx def + a r + /arcto load stopped { 5 } { 4 } ifelse { pop } repeat + a +} def +% +/CheckClosed { dup n 2 mul 1 sub index eq 2 index n 2 mul 1 add index eq + and { pop pop /n n 1 sub def } if } def +/Polygon { NArray n 2 eq { 0 0 /n 3 def } if n 3 lt { n { pop pop } + repeat } { n 3 gt { CheckClosed } if n 2 mul -2 roll /y0 ED /x0 ED /y1 + ED /x1 ED x1 y1 /x1 x0 x1 add 2 div def /y1 y0 y1 add 2 div def x1 y1 + moveto /n n 2 sub def n { Lineto } repeat x1 y1 x0 y0 6 4 roll Lineto + Lineto pop pop closepath } ifelse } def +/Diamond { + /mtrx CM def + T rotate + /h ED + /w ED + dup 0 eq { pop } { CLW mul neg + /d ED + /a w h Atan def + /h d a sin Div h add def + /w d a cos Div w add def } ifelse + mark w 2 div h 2 div w 0 0 h neg w neg 0 0 h w 2 div h 2 div + /ArrowA { moveto } def + /ArrowB { } def + false Line + closepath mtrx setmatrix } def +% DG modification begin - Jan. 15, 1997 +%/Triangle { /mtrx CM def translate rotate /h ED 2 div /w ED dup 0 eq { +%pop } { CLW mul /d ED /h h d w h Atan sin Div sub def /w w d h w Atan 2 +%div dup cos exch sin Div mul sub def } ifelse mark 0 d w neg d 0 h w d 0 +%d /ArrowA { moveto } def /ArrowB { } def false Line closepath mtrx +%setmatrix } def +% +/Triangle { + /mtrx CM def + translate + rotate /h ED 2 div /w ED + dup CLW mul /d ED + /h h d w h Atan sin Div sub def + /w w d h w Atan 2 div dup cos exch sin Div mul sub def + mark + 0 d w neg d 0 h w d 0 d + /ArrowA { moveto } def + /ArrowB { } def + false + Line + closepath + mtrx +% DG/SR modification begin - Jun. 1, 1998 - Patch 3 (from Michael Vulis) +% setmatrix } def + setmatrix pop +} def +% DG/SR modification end +% +/CCA { + /y ED /x ED + 2 copy y sub /dy1 ED + x sub /dx1 ED + /l1 dx1 dy1 Pyth def +} def +% +/CC { + /l0 l1 def + /x1 x dx sub def + /y1 y dy sub def + /dx0 dx1 def + /dy0 dy1 def + CCA + /dx dx0 l1 c exp mul dx1 l0 c exp mul add def + /dy dy0 l1 c exp mul dy1 l0 c exp mul add def + /m dx0 dy0 Atan dx1 dy1 Atan sub 2 div cos abs b exp a mul dx dy Pyth Div 2 div def + /x2 x l0 dx mul m mul sub def + /y2 y l0 dy mul m mul sub def + /dx l1 dx mul m mul neg def + /dy l1 dy mul m mul neg def +} def +% +/IC { + /c c 1 add def + c 0 lt { /c 0 def } { c 3 gt { /c 3 def } if } ifelse + /a a 2 mul 3 div 45 cos b exp div def + CCA + /dx 0 def + /dy 0 def +} def +% +/BOC { IC CC x2 y2 x1 y1 ArrowA CP 4 2 roll x y curveto } def +/NC { CC x1 y1 x2 y2 x y curveto } def +/EOC { x dx sub y dy sub 4 2 roll ArrowB 2 copy curveto } def +/BAC { IC CC x y moveto CC x1 y1 CP ArrowA } def +/NAC { x2 y2 x y curveto CC x1 y1 } def +/EAC { x2 y2 x y ArrowB curveto pop pop } def +% +/OpenCurve { + NArray n 3 lt + { n { pop pop } repeat } + { BOC /n n 3 sub def n { NC } repeat EOC } ifelse +} def +% +/AltCurve { + { false NArray n 2 mul 2 roll + [ n 2 mul 3 sub 1 roll ] aload + /Points ED + n 2 mul -2 roll } + { false NArray } ifelse + n 4 lt { n { pop pop } repeat } { BAC /n n 4 sub def n { NAC } repeat EAC } ifelse +} def +% +/ClosedCurve { + NArray n 3 lt + { n { pop pop } repeat } + { n 3 gt { CheckClosed } if + 6 copy n 2 mul 6 add 6 roll + IC CC x y moveto n { NC } repeat + closepath pop pop + } ifelse +} def +% +/SQ { /r ED r r moveto r r neg L r neg r neg L r neg r L fill } def +/ST { /y ED /x ED x y moveto x neg y L 0 x L fill } def +/SP { /r ED gsave 0 r moveto 4 { 72 rotate 0 r L } repeat fill grestore } def +% +/FontDot { + DS 2 mul dup + matrix scale matrix concatmatrix exch matrix + rotate matrix concatmatrix exch + findfont exch makefont setfont +} def +% +/Rect { + x1 y1 y2 add 2 div moveto + x1 y2 lineto + x2 y2 lineto + x2 y1 lineto + x1 y1 lineto + closepath +} def +% +/OvalFrame { + x1 x2 eq y1 y2 eq or + { pop pop x1 y1 moveto x2 y2 L } + { y1 y2 sub abs x1 x2 sub abs 2 copy gt + { exch pop } { pop } ifelse + 2 div exch { dup 3 1 roll mul exch } if + 2 copy lt { pop } { exch pop } ifelse + /b ED + x1 y1 y2 add 2 div moveto + x1 y2 x2 y2 b arcto + x2 y2 x2 y1 b arcto + x2 y1 x1 y1 b arcto + x1 y1 x1 y2 b arcto + 16 { pop } repeat + closepath + } ifelse +} def +% +/Frame { + CLW mul /a ED + 3 -1 roll + 2 copy gt { exch } if + a sub /y2 ED + a add /y1 ED + 2 copy gt { exch } if + a sub /x2 ED + a add /x1 ED + 1 index 0 eq { pop pop Rect } { OvalFrame } ifelse +} def +% +/BezierNArray { + /f ED + counttomark 2 div dup cvi /n ED + n eq not { exch pop } if + n 1 sub neg 3 mod 3 add 3 mod { 0 0 /n n 1 add def } repeat + f { ] aload /Points ED } { n 2 mul 1 add -1 roll pop } ifelse +} def +% +/OpenBezier { + BezierNArray + n 1 eq + { pop pop } + { ArrowA n 4 sub 3 idiv + { 6 2 roll 4 2 roll curveto } repeat + 6 2 roll 4 2 roll ArrowB curveto } ifelse +} def +% +/ClosedBezier { + BezierNArray + n 1 eq + { pop pop } + { moveto n 1 sub 3 idiv + { 6 2 roll 4 2 roll curveto } repeat + closepath } ifelse +} def +% +/BezierShowPoints { + gsave + Points aload length 2 div cvi /n ED + moveto + n 1 sub { lineto } repeat + CLW 2 div SLW [ 4 4 ] 0 setdash stroke + grestore +} def +% +/Parab { + /y0 ED /x0 ED /y1 ED /x1 ED + /dx x0 x1 sub 3 div def + /dy y0 y1 sub 3 div def + x0 dx sub y0 dy add x1 y1 ArrowA + x0 dx add y0 dy add x0 2 mul x1 sub y1 ArrowB + curveto + /Points [ x1 y1 x0 y0 x0 2 mul x1 sub y1 ] def +} def +% +/Grid { + newpath + /a 4 string def + /b ED /c ED /n ED + cvi dup 1 lt { pop 1 } if + /s ED + s div dup 0 eq { pop 1 } if + /dy ED s div dup 0 eq { pop 1 } if + /dx ED dy div round dy mul + /y0 ED dx div round dx mul + /x0 ED dy div round cvi + /y2 ED dx div round cvi + /x2 ED dy div round cvi + /y1 ED dx div round cvi + /x1 ED + /h y2 y1 sub 0 gt { 1 } { -1 } ifelse def + /w x2 x1 sub 0 gt { 1 } { -1 } ifelse def + b 0 gt { + /z1 b 4 div CLW 2 div add def +% /Helvetica findfont b scalefont setfont + /b b .95 mul CLW 2 div add def } if + systemdict /setstrokeadjust known + { true setstrokeadjust /t { } def } + { /t { transform 0.25 sub round 0.25 add exch 0.25 sub round 0.25 add + exch itransform } bind def } ifelse + gsave n 0 gt { 1 setlinecap [ 0 dy n div ] dy n div 2 div setdash } { 2 setlinecap } ifelse + /i x1 def + /f y1 dy mul n 0 gt { dy n div 2 div h mul sub } if def + /g y2 dy mul n 0 gt { dy n div 2 div h mul add } if def + x2 x1 sub w mul 1 add dup 1000 gt { pop 1000 } if + { i dx mul dup y0 moveto + b 0 gt + { gsave c i a cvs dup stringwidth pop + /z2 ED w 0 gt {z1} {z1 z2 add neg} ifelse + h 0 gt {b neg}{z1} ifelse + rmoveto show grestore } if + dup t f moveto + g t L stroke + /i i w add def + } repeat + grestore + gsave + n 0 gt + % DG/SR modification begin - Nov. 7, 1997 - Patch 1 + %{ 1 setlinecap [ 0 dx n div ] dy n div 2 div setdash } + { 1 setlinecap [ 0 dx n div ] dx n div 2 div setdash } + % DG/SR modification end + { 2 setlinecap } ifelse + /i y1 def + /f x1 dx mul n 0 gt { dx n div 2 div w mul sub } if def + /g x2 dx mul n 0 gt { dx n div 2 div w mul add } if def + y2 y1 sub h mul 1 add dup 1000 gt { pop 1000 } if + { newpath i dy mul dup x0 exch moveto + b 0 gt { gsave c i a cvs dup stringwidth pop + /z2 ED + w 0 gt {z1 z2 add neg} {z1} ifelse + h 0 gt {z1} {b neg} ifelse + rmoveto show grestore } if + dup f exch t moveto + g exch t L stroke + /i i h add def + } repeat + grestore +} def +% +/ArcArrow { + /d ED /b ED /a ED + gsave + newpath 0 -1000 moveto clip + newpath + 0 1 0 0 b + grestore + c mul + /e ED + pop pop pop r a e d PtoC y add exch x add + exch r a PtoC y add exch x add exch b pop pop pop pop a e d CLW 8 div c + mul neg d +} def +% +/Ellipse { /mtrx CM def T scale 0 0 1 5 3 roll arc mtrx setmatrix } def +% +/ArcAdjust { %%%% Vincent Guirardel +% given a target length (targetLength) and an initial angle (angle0) [in the stack], +% let M(angle0)=(rx*cos(angle0),ry*sin(angle0))=(x0,y0). +% This computes an angle t such that (x0,y0) is at distance +% targetLength from the point M(t)=(rx*cos(t),ry*sin(t)). +% NOTE: this an absolute angle, it does not have to be added or substracted to angle0 +% contrary to TvZ's code. +% To achieve, this, one iterates the following process: start with some angle t, +% compute the point M' at distance targetLength of (x0,y0) on the semi-line [(x0,y0) M(t)]. +% Now take t' (= new angle) so that (0,0) M(t') and M' are aligned. +% +% Another difference with TvZ's code is that we need d (=add/sub) to be defined. +% the value of d = add/sub is used to know on which side we have to move. +% It is only used in the initialisation of the angle before the iteration. +% +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +% Input stack: 1: target length 2: initial angle +% variables used : rx, ry, d (=add/sub) +% + /targetLength ED /angle0 ED + /x0 rx angle0 cos mul def + /y0 ry angle0 sin mul def +% we are looking for an angle t such that (x0,y0) is at distance targetLength +% from the point M(t)=(rx*cos(t),ry*sin(t))) +%initialisation of angle (using 1st order approx = TvZ's code) + targetLength 57.2958 mul + angle0 sin rx mul dup mul + angle0 cos ry mul dup mul + add sqrt div +% if initialisation angle is two large (more than 90 degrees) set it to 90 degrees +% (if the ellipse is very curved at the point where we draw the arrow, % +% the value can be much more than 360 degrees !) +% this should avoid going on the wrong side (more than 180 degrees) or go near +% a bad attractive point (at 180 degrees) + dup 90 ge { pop 90 } if + angle0 exch d % add or sub +% maximum number of times to iterate the iterative procedure: +% iterative procedure: takes an angle t on top of stack, computes a +% better angle (and put it on top of stack) + 30 { dup +% compute distance D between (x0,y0) and M(t) + dup cos rx mul x0 sub dup mul exch sin ry mul y0 sub dup mul add sqrt +% if D almost equals targetLength, we stop + dup targetLength sub abs 1e-5 le { pop exit } if +% stack now contains D t +% compute the point M(t') at distance targetLength of (x0,y0) on the semi-line [(x0,y0) M(t)]: +% M(t')= ( (x(t)-x0)*targetLength/d+x0 , (y(t)-y0)*targetLength/d+y0 ) + exch dup cos rx mul x0 sub exch sin ry mul y0 sub +% stack contains: y(t)-y0, x(t)-x0, d + 2 index Div targetLength mul y0 add ry Div exch + 2 index Div targetLength mul x0 add rx Div +% stack contains x(t')/rx , y(t')/ry , d +% now compute t', and remove D from stack + atan exch pop + } repeat +% we don't look at what happened... in particular, if targetLength is greater +% than the diameter of the ellipse... +% the final angle will be around /angle0 + 180. maybe we should treat this pathological case... +% after iteration, stack contains an angle t such that M(t) is the tail of the arrow +% to give back the result as a an angle relative to angle0 we could add the following line: +% angle0 sub 0 exch d +% +% begin bug fix 2006-01-11 +% we want to adjust the new angle t' by a multiple of 360 so that | t'-angle0 | <= 180 +%(we don't want to make the ellipse turn more or less than it should)... +dup angle0 sub dup abs 180 gt { 180 add 360 div floor 360 mul sub } { pop } ifelse +% end bug fix +} def +% +/EllipticArcArrow { + /d ED % is add or sub + /b ED % arrow procedure + /a1 ED % angle + gsave + newpath + 0 -1000 moveto + clip % Set clippath far from arrow. + newpath + 0 1 0 0 b % Draw arrow to determine length. + grestore +% Length of arrow is on top of stack. Next 3 numbers are junk. +% + a1 exch ArcAdjust % Angular position of base of arrow. + /a2 ED + pop pop pop + a2 cos rx mul xOrig add % hv 2007-08-29 x->xOrig + a2 sin ry mul yOrig add % hv 2007-08-29 y->yOrig + a1 cos rx mul xOrig add % + a1 sin ry mul yOrig add % +% Now arrow tip coor and base coor are on stack. + b pop pop pop pop % Draw arrow, and discard coordinates. + a2 CLW 8 div +% change value of d (test it by looking if `` 1 1 d '' gives 2 or not ) + 1 1 d 2 eq { /d { sub } def } { /d { add } def } ifelse + ArcAdjust +% resets original value of d + 1 1 d 2 eq { /d { sub } def } { /d { add } def } ifelse % Adjust angle to give overlap. +} def +%%------------------ tvz/DG/hv (2004-05-10) end -------------------%% +% +/Rot { CP CP translate 3 -1 roll neg rotate NET } def +% +/RotBegin { + tx@Dict /TMatrix known not { /TMatrix { } def /RAngle { 0 } def } if + /TMatrix [ TMatrix CM ] cvx def + /a ED + a Rot /RAngle [ RAngle dup a add ] cvx def +} def +% +/RotEnd { + /TMatrix [ TMatrix setmatrix ] cvx def + /RAngle [ RAngle pop ] cvx def +} def +% +/PutCoor { gsave CP T CM STV exch exec moveto setmatrix CP grestore } def +/PutBegin { /TMatrix [ TMatrix CM ] cvx def CP 4 2 roll T moveto } def +/PutEnd { CP /TMatrix [ TMatrix setmatrix ] cvx def moveto } def +% +/Uput { + /a ED + add 2 div /h ED 2 + div /w ED + /s a sin def + /c a cos def + /b s abs c abs 2 copy gt dup + /q ED + { pop } { exch pop } ifelse def + /w1 c b div w mul def + /h1 s b div h mul def + q { w1 abs w sub dup c mul abs }{ h1 abs h sub dup s mul abs } ifelse +} def +% +/UUput { + /z ED + abs /y ED + /x ED + q { x s div c mul abs y gt }{ x c div s mul abs y gt } ifelse + { x x mul y y mul sub z z mul add sqrt z add } + { q { x s div } { x c div } ifelse abs + } ifelse + a PtoC + h1 add exch + w1 add exch +} def +% +/BeginOL { + dup (all) eq exch TheOL eq or + { IfVisible not { Visible /IfVisible true def } if } + { IfVisible { Invisible /IfVisible false def } if } ifelse +} def +% +/InitOL { + /OLUnit [ 3000 3000 matrix defaultmatrix dtransform ] cvx def + /Visible { CP OLUnit idtransform T moveto } def + /Invisible { CP OLUnit neg exch neg exch idtransform T moveto } def + /BOL { BeginOL } def + /IfVisible true def +} def +% +end +%-----------------------------------------------------------------------------% +% +% END pstricks.pro + +%%EndProcSet +%%BeginProcSet: pst-algparser.pro 0 0 +% $Id: pst-algparser.pro 26 2008-06-14 11:50:02Z herbert $ +%% +%% PostScript prologue for PSTricks algorithm parser +%% Version 0.01, 2008/01/01 +%% +%% This program can be redistributed and/or modified under the terms +%% of the LaTeX Project Public License Distributed from CTAN archives +%% in directory macros/latex/base/lppl.txt. +%% +%%-----------------------------------------------------------------------------% +% +/AlgParser { tx@AlgToPs begin AlgToPs end } def % Dominique Rodriguez +% +/tx@CoreAnalyzerDict 100 dict def tx@CoreAnalyzerDict begin +% +% PS ANALYZER FOR ALGEBRAIC EXPRESSION V1.12 +% E->T|E+T +% T->FS|T*FS +% FS -> F | +FS | -FS +% F->P|F^SF +% P->(E)|literal +% literal->number|var|var[E]|func(params) +% params->E|E,param +% number->TOBEFINISHED +% +%% E expression, T term, SF signed factor, F factor, P power +% +%% parser +% +%% str +% +%% C->EE +%% STR index -> STR index+lenExpr +/AnalyzeCond { AnalyzeExpr ReadCondOp AnalyzeExpr EvalCondOp } def +% +%% analyze Expression List (separator , or | ) +%% STR index -> STR index+lenExpr +%% /AnalyzeListOfE { +%% { NextNonBlankChar pop AnalyzeExpr%%dup Strlen eq { exit } if NextNonBlankChar +%% NextNonBlankChar dup 0 eq { pop exit } if +%% dup 44 ne 1 index 124 ne and { dup 41 ne { PROBLEMCONTACTBILLOU } { pop exit } ifelse } if +%% pop NextNonBlankChar dup 0 eq { exit } if 124 ne { PROBLEMCONTACTBILLOU } if 1 add NextNonBlankChar 0 eq {toto} if } loop +%% AnalyzeListOfEPostHook +%% } def +/AnalyzeListOfE { + /NotFirst false def + { NextNonBlankChar pop AnalyzeExpr + NotFirst { EvalListOfExpr } { /NotFirst true def } ifelse + dup Strlen eq { exit } if NextNonBlankChar + dup 44 ne 1 index 124 ne and + { dup 41 ne { PROBLEMCONTACTBILLOU } { pop exit } ifelse } + if pop 1 add } loop + AnalyzeListOfEPostHook +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% E->T|E+T +%% STR index -> STR index+lenExpr +/AnalyzeExpr { + AnalyzePreHook AnalyzeTerm IsEndingExpr + { dup 0 ne { 32 eq { NextNonBlankChar } if } { pop } ifelse } + { { RollOp 1 add NextNonBlankChar pop AnalyzeTerm PreEvalHook EvalAddSub IsEndingExpr { pop exit } if } loop } + ifelse + AnalyzePostHook +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% T->FS|T*FS +%% STR index +/AnalyzeTerm { + AnalyzePreHook AnalyzeSignedFactor IsEndingTerm + { dup 0 ne { 32 eq { NextNonBlankChar } if } { pop } ifelse } + { { RollOp 1 add NextNonBlankChar pop AnalyzeSignedFactor PreEvalHook EvalMulDiv IsEndingTerm { pop exit } if} loop } + ifelse + AnalyzePostHook +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% FS -> F | +FS | -FS +%% STR index +/AnalyzeSignedFactor { + AnalyzePreHook 2 copy get dup IsUnaryOp + { RollOp 1 add NextNonBlankChar pop AnalyzeSignedFactor EvalUnaryOp } + { pop AnalyzeFactor } + ifelse AnalyzePostHook +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% F->P|F^P +%% STR index +/AnalyzeFactor { + AnalyzePreHook AnalyzePower IsEndingFactor + { dup 0 ne { 32 eq { NextNonBlankChar } if } { pop } ifelse } + { { RollOp 1 add NextNonBlankChar pop AnalyzePower PreEvalHook EvalPower IsEndingFactor { pop exit } if} loop } + ifelse AnalyzePostHook +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% P->(E)|literal +%% STR index +/AnalyzePower { + %% depending of first char either a number, or a literal + 2 copy get dup 40 eq%%an open par + { pop 1 add NextNonBlankChar pop AnalyzeExpr 1 add NextNonBlankChar pop } + { AnalyzeLiteral } + ifelse +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% STR index STR[index] -> STR index +%/AnalyzeLiteral { IsNumber { EvalNumber } { EvalLiteral } ifelse } def +/AnalyzeLiteral { dup IsUnaryOp exch IsNumber or { EvalNumber } { EvalLiteral } ifelse } def%%dr 09102006 +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% recognize + or - +%% chr -> T/F +/IsUnaryOp { dup 43 eq exch 45 eq or } bind def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% a number can contain only : 0123456789. +%% chr -> T/F +/IsNumber { dup 48 ge exch dup 57 le 3 -1 roll and exch 46 eq or } bind def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% STR index -> STR index number +%% a number can be of the form [0-9]*.[0-9]*\([eE][+-]?[0-9]+\)? +%% STR index -> STR index' number +/ReadNumber { + exch dup 3 -1 roll dup 3 1 roll + %%read mantissa + { 1 add 2 copy dup Strlen eq { pop pop 0 exit } if get dup IsNumber not { exit } if pop } loop + dup 101 eq exch 69 eq or + %%% there is a "e" or "E" -> read exponant + { 1 add 2 copy get dup IsUnaryOp + { pop 1 add 2 copy get } if + { IsNumber not { exit } if 1 add 2 copy get } loop } + if + dup 4 1 roll + 3 -1 roll exch 1 index sub getinterval +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% a number can contain only : 0123456789. +%% chr -> T/F +/IsCondOp { dup 30 eq exch dup 60 ge exch 62 le and or } bind def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% STR index -> STR index number +%% a number can be of the form [0-9]*.[0-9]*\([eE][+-]?[0-9]+\)? +%% STR index -> STR index' number +/ReadCondOp { + NextNonBlankChar 1 index 4 1 roll + { IsCondOp not { exit } if 1 add 2 copy get } loop + 2 copy 5 -1 roll + exch 1 index sub getinterval 3 1 roll +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% a literal can contain only : 0123456789. +%% chr -> T/F +/IsLiteral {% + dup 48 ge exch dup 57 le 3 -1 roll and exch + dup 65 ge exch dup 90 le 3 -1 roll and 3 -1 roll or exch + dup 97 ge exch 122 le and or } bind def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% a literal can be of the form [a-zA-Z][a-zA-Z0-9]*\(\((Expression)\)|\(\[Expression\]\)\)? +%% STR index -> literal STR index' nextchr +/ReadLiteral { + exch dup 3 -1 roll dup 3 1 roll + %%read literal core + { 2 copy dup Strlen eq { pop pop 0 exit } if get dup IsLiteral not { exit } if pop 1 add } loop + 4 1 roll dup 5 1 roll 3 -1 roll exch 1 index sub getinterval 4 1 roll +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% expr is ended by end of str or a clpar +%% STR index -> STR index STR[index] T/F +/IsEndingExpr {% + 2 copy dup Strlen eq + %% if end of str is reached -> end ! + { pop pop 0 true } + %% ending chr -> clpar, comma, |, <, >, =, !, + {get dup dup 41 eq + exch dup 124 eq + exch dup 93 eq + exch dup 44 eq + exch dup 30 eq + exch dup 60 ge exch 62 le and or or or or or} + ifelse } def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% expr is ended by end of str or a +- +%% STR index -> STR index STR[index] T/F +/IsEndingTerm { IsEndingExpr { true } { dup dup 43 eq exch 45 eq or } ifelse } def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% expr is ended by end of str or */ +%% STR index -> STR index STR[index] T/F +/IsEndingFactor { IsEndingTerm { true } { dup dup 42 eq exch 47 eq or } ifelse } def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% expr is ended by end of str or ^ +%% STR index -> STR index STR[index] T/F +/IsEndingPower { IsEndingFactor { true } { dup 94 eq } ifelse } def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% STR index -> STR index STR[index] +/NextNonBlankChar { { dup Strlen eq { 0 exit } if 2 copy get dup neBlkChar { exit } if pop 1 add } loop } bind def +/neBlkChar { dup 32 ne exch dup 10 ne exch 9 ne and and } bind def +%%%%%%%%%%%%%%%%%%%%%%%% +%% DEBUG +/BRK {false} def +/BRKtrue {/BRK true def} def +/BRKStop {BRK {BRKtoto} if } def +/BRKEvalStop {BRK exch if } def +/BRKBRK2true {BRK {BRK2true} if } def +/BRK2 {false} def +/BRK2true {/BRK2 true def} def +/BRK2Stop {BRK2 {BRK2toto} if } def/BRK {false} def +end +% +%-------------------------------------------------------------------------------% +% +/tx@AlgToPs 12 dict def tx@AlgToPs begin +% +%% algExpr -> PSVector +/AlgToPs { tx@CoreAnalyzerDict begin InitParser AnalyzeListOfE pop pop EndingSequence end } def +/EndingSequence { ExpressionVector aload length /end cvx exch 1 add array astore } def +/InitParser { /ExpressionVector [ /tx@AddMathFunc cvx /begin cvx ] def dup length /Strlen exch def 0 } def +/Strlen 0 def +/EvalListOfExpr {} def% +/EvalNumber {% + ReadNumber cvr /ExpressionVector ExpressionVector aload length dup 3 add -1 roll cvx + exch 1 add array astore def NextNonBlankChar pop } def +/EvalAddSub {% + /ExpressionVector ExpressionVector aload length dup 5 add -1 roll + 43 eq { /add } { /sub } ifelse cvx exch 1 add array astore def +} def +/EvalMulDiv {% + /ExpressionVector ExpressionVector aload length dup 5 add -1 roll + 42 eq { /mul } { /div } ifelse cvx exch 1 add array astore def +} def +/EvalPower {% + /ExpressionVector ExpressionVector aload length dup 5 add -1 roll + pop /exp cvx exch 1 add array astore def +} def +/EvalLiteral {% + ReadLiteral + dup 40 eq%%% there is an open par -> function call + { pop 2 index + dup (Sum) eq { EvalSum } + { dup (IfTE) eq { EvalCond } + { dup (Derive) eq { pop EvalDerive } + { pop 1 add NextNonBlankChar pop AnalyzeListOfE 2 index TrigoFunc + /ExpressionVector ExpressionVector aload length dup 5 add -1 roll cvn cvx + exch 1 add array astore def 1 add NextNonBlankChar pop } ifelse } ifelse} ifelse } + { /ExpressionVector ExpressionVector aload length dup 6 add -1 roll cvn cvx exch 1 add array astore def + dup 91 eq%%% there is an open bracket -> vector element + { pop 1 add NextNonBlankChar pop AnalyzeExpr + /ExpressionVector ExpressionVector aload length /cvi cvx exch /get cvx exch 2 add array astore def 1 add } + { pop NextNonBlankChar pop } + ifelse} + ifelse +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% the derive function : Derive(n,f(x)) +%% firstparindex lastparindex -> +/EvalDerive { + %% manage the function descripiton + 1 add ReadNumber 3 1 roll NextNonBlankChar + 44 ne { ANALYZER_ERROR_missing_second_comma_in_Sum } if + 1 add NextNonBlankChar pop + 3 -1 roll cvi + dup 0 eq + { pop AnalyzeExpr 3 -1 roll pop 1 add } + { 1 sub 3 1 roll (x) exch tx@Derive begin DeriveIndexed end 4 -1 roll + { (x) tx@Derive begin Derive end } repeat + ExpressionVector exch /ExpressionVector [] def + AlgToPs aload length + /ExpressionVector 1 index 3 add -1 roll aload length dup 3 add -1 roll /l2 exch def /l1 exch def + l1 l2 add 1 add l2 neg roll l1 l2 add array astore def 3 -1 roll pop 1 add + 1 index length /Strlen exch def } ifelse +} def +/EvalSum {% + pop 1 add NextNonBlankChar pop + %% read the variable name + ReadLiteral pop NextNonBlankChar + 44 ne { ANALYZER_ERROR_missing_first_comma_in_Sum } if + %% read the initial value + 1 add NextNonBlankChar pop ReadNumber cvi 3 1 roll + 2 copy get 44 ne { ANALYZER_ERROR_missing_second_comma_in_Sum } if + %% read the increment value + 1 add NextNonBlankChar pop ReadNumber cvi 3 1 roll + 2 copy get 44 ne { ANALYZER_ERROR_missing_second_comma_in_Sum } if + %% read the limit value + 1 add NextNonBlankChar pop ReadNumber cvi 3 1 roll + 2 copy get 44 ne { ANALYZER_ERROR_missing_second_comma_in_Sum } if + /ExpressionVector ExpressionVector aload length dup 7 add -3 roll 0 4 1 roll + 5 -1 roll 4 add array astore def + %% keep ExpressionVector for later and create a new one for internal Sum computation + ExpressionVector 3 1 roll /ExpressionVector [ 6 -1 roll cvn /exch cvx /def cvx ] def + 1 add NextNonBlankChar pop AnalyzeExpr + %% add each term + /ExpressionVector ExpressionVector aload length 1 add /add cvx exch array astore def + /ExpressionVector 4 -1 roll aload length ExpressionVector cvx /for cvx 3 -1 roll 2 add + array astore def 3 -1 roll pop 1 add +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% Convert to radians if trigo function call +%% (name) -> +/TrigoFunc { + dup (cos) eq 1 index (sin) eq or exch (tan) eq or + { /ExpressionVector ExpressionVector aload length Pi /div cvx 180 /mul cvx 5 -1 roll 4 add + array astore def + } if +} def +/EvalCond {% + pop 1 add AnalyzeCond NextNonBlankChar + 44 ne { ANALYZER_ERROR_missing_first_comma_in_IfTE } if + ExpressionVector 3 1 roll /ExpressionVector [] def + 1 add AnalyzeExpr ExpressionVector 3 1 roll /ExpressionVector [] def + NextNonBlankChar 44 ne { ANALYZER_ERROR_missing_second_comma_in_IfTE } if + 1 add AnalyzeExpr + NextNonBlankChar 41 ne { ANALYZER_ERROR_missing_ending parenthesis_in_IfTE } if + ExpressionVector + /ExpressionVector 6 -1 roll aload length dup + 6 add -1 roll cvx exch dup 4 add -1 roll cvx /ifelse cvx 3 -1 roll 3 add array astore def + 1 add 3 -1 roll pop +} def +%% CondOp STR index +/EvalCondOp {% + 3 -1 roll + dup (=) eq { /eq } {% + dup (<) eq { /lt } {% + dup (>) eq { /gt } {% + dup (>=) eq { /ge } {% + dup (<=) eq { /ge } {% + dup (!=) eq { /ne } { ERROR_non_valid_conditional_operator } + ifelse } ifelse } ifelse } ifelse } ifelse } ifelse + cvx exch pop + /ExpressionVector ExpressionVector aload length dup 3 add -1 roll exch 1 add array astore def } def +/EvalUnaryOp { + 3 -1 roll 45 eq { /ExpressionVector ExpressionVector aload length /neg cvx exch 1 add array astore def } if +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% H O O K S +/AnalyzePreHook {} bind def +/PreEvalHook {} bind def +/AnalyzeListOfEPostHook {} bind def +/AnalyzePostHook {} def +/RollOp { 3 1 roll } bind def +end %tx@CoreAnalyzerDict +% +%--------------------------------------------------------------------% +% +/tx@Derive 41 dict def tx@Derive begin +%%increase ^^ for each function added +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% algExpr variable -> PSVector +/Derive {% + 10240 string 3 1 roll 0 3 1 roll + /Variable exch def + tx@CoreAnalyzerDict begin InitParser AnalyzeListOfE end +} def +/Strlen 0 def +/InitParser { dup length /Strlen exch def 0 } def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% algExpr variable index -> PSVector +/DeriveIndexed {% + 3 1 roll 10240 string 3 1 roll 0 3 1 roll + /Variable exch def + tx@CoreAnalyzerDict begin InitParser pop 4 -1 roll AnalyzeExpr 4 -2 roll pop pop 4 -2 roll exch pop end +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% (u,v)'=-(u',v') +/EvalListOfExpr {% + 4 2 roll 2 copy 9 -1 roll dup length 4 1 roll putinterval add AddPipe + 2 copy 7 -1 roll dup length 4 1 roll putinterval add + 6 -2 roll pop pop + 2 copy pop 0 6 2 roll GetIntervalNewStr 5 1 roll 2 copy 0 exch getinterval 6 1 roll } def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% (-u)'=-(u') +/EvalUnaryOp { + 4 -2 roll 4 index (0) eq + { (0) StrConcat 7 -1 roll pop } + { 7 -1 roll 45 eq + { AddSub AddOpPar true } { false } ifelse + 3 1 roll 5 index StrConcat 3 -1 roll { AddClPar } if } ifelse + 2 copy pop 0 6 2 roll GetIntervalNewStr + 7 -2 roll pop pop 2 index 6 index dup 4 index exch sub getinterval exch 6 2 roll +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% (number)'=0 +/EvalNumber { ReadNumber (0) 6 2 roll } def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% (u+v)'=u'+v' +/EvalAddSub {% + 7 index dup (0) eq + { pop true }%% du=0 nothing added + { dup length exch 5 index 5 index 3 -1 roll putinterval 4 -1 roll add 3 1 roll false } + ifelse + 5 index dup (0) eq + { pop { (0) } { 4 -2 roll 2 copy pop 0 6 2 roll GetIntervalNewStr } ifelse }%%dv=0 + { exch + { 5 -2 roll 7 index 45 eq { AddSub } if false } %%nothing yet added + { 5 -2 roll 7 index 43 eq%%something yet added + { AddAdd false } { AddSub AddOpPar true } ifelse } + ifelse 11 1 roll + 3 -1 roll StrConcat 10 -1 roll { AddClPar } if + 2 copy pop 0 6 2 roll GetIntervalNewStr } + ifelse + mark 11 -5 roll cleartomark 2 index 6 index dup 4 index exch sub getinterval exch 6 2 roll +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% (u*v)' or (u/v)' +/EvalMulDiv { 6 index 42 eq {EvalMul} {EvalDiv} ifelse } def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% (u*v)'=u'*v+u*v' +/EvalMul {% + 4 -2 roll 7 index dup (0) eq + { pop false }%%du=0 + { (1) eq%%du=1 + { false } + { AddOpPar 7 index StrConcat AddClPar AddMul AddOpPar true } ifelse + 3 1 roll 6 index StrConcat 3 -1 roll { AddClPar } if + true }%%du!=0 + ifelse + 5 1 roll 5 index (0) eq + { 5 -1 roll not { (0) StrConcat } if }%%dv=0 + { 5 -1 roll { AddAdd } if + 4 index (1) eq + { 8 index StrConcat } + { AddOpPar 8 index StrConcat AddClPar AddMul AddOpPar 4 index StrConcat AddClPar } + ifelse + }%%dv!=0 + ifelse + 2 copy pop 0 6 2 roll GetIntervalNewStr + mark 11 -5 roll cleartomark 2 index 6 index dup 4 index exch sub getinterval exch 6 2 roll +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% (u/v)'=(u'*v-u*v')/v^2 +/EvalDiv {% + 4 -2 roll + 4 index (0) eq%%dv=0 -> u'/v + { 7 index (0) eq { (0) StrConcat } { AddOpPar 7 index StrConcat AddClPar AddDiv 5 index StrConcat } ifelse } + { 7 index dup (0) eq + { pop }%%du=0 + { (1) eq%%du=1 + { false } + { AddOpPar 7 index StrConcat AddClPar AddMul AddOpPar true } ifelse + 3 1 roll 6 index StrConcat 3 -1 roll { AddClPar } if}%%du!=0 + ifelse + AddSub + 4 index (1) eq + { 8 index StrConcat } + { AddOpPar 8 index StrConcat AddClPar AddMul AddOpPar 4 index StrConcat AddClPar } + ifelse + %}%%dv!=0 + 2 copy GetIntervalNewStr 3 1 roll pop 0 AddOpPar 3 -1 roll StrConcat AddClPar + AddDiv AddOpPar 5 index StrConcat AddClPar 2 copy (^2) putinterval 2 add } + ifelse + 2 copy pop 0 6 2 roll GetIntervalNewStr + mark 11 -5 roll cleartomark 2 index 6 index dup 4 index exch sub getinterval exch 6 2 roll +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% str1 index str2 -> str1 index +/StrConcat { dup length 4 2 roll 2 copy 6 -1 roll putinterval 3 -1 roll add } bind def +/GetIntervalNewStr { 0 exch getinterval dup length string copy } bind def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% (u^v)'=(u^v)'=u'vu^(v-1)+v'u^(v)ln(u) +/EvalPower {% + 4 -2 roll 7 index (0) eq + {%%if du=0 then (u^v)'=v'ln(u)u^v + 4 index (0) eq + { (0) StrConcat }%%if dv=0 then (u^v)'=0 + { 4 index (1) ne { AddOpPar 4 index StrConcat (\)*) StrConcat } if + 8 index (e) ne { (ln\() StrConcat 8 index StrConcat (\)*) StrConcat } if + AddOpPar 8 index StrConcat (\)^\() StrConcat 5 index StrConcat AddClPar } ifelse + } + {%%du!=0 + 4 index (0) eq + {%%if dv=0 then (u^v)'=vu'u^(v-1) + 5 index dup IsStrNumber + { dup (0) eq + { StrConcat } + { dup dup (1) eq exch (1.0) eq or + { StrConcat } + { StrConcat + 7 index dup (1) ne exch (1.0) ne and%%%dr 09102006 insert du if <> 1 + { (*\() StrConcat 7 index StrConcat (\)) StrConcat } if%%%dr 09102006 + (*\() StrConcat 8 index StrConcat (\)) StrConcat + 5 index dup dup (2) eq exch (2.0) eq or + { pop } { cvr 1 sub 20 string cvs 3 1 roll (^) StrConcat 3 -1 roll StrConcat } ifelse } ifelse } ifelse } + { pop AddOpPar 5 index StrConcat (\)*\() StrConcat 8 index StrConcat (\)^\() StrConcat + 5 index StrConcat (-1\)) StrConcat } ifelse + } + {%%if dv!=0 and du!=0 then (u^v)'=u'vu^(v-1)+v'u^(v)ln(u) + 7 index (1) ne { AddOpPar 7 index StrConcat (\)*) StrConcat } if + AddOpPar 5 index StrConcat (\)*\() StrConcat + 8 index StrConcat (\)^\() StrConcat + 5 index StrConcat (-1\)+\() StrConcat + 4 index (1) ne { 4 index StrConcat (\)*\() StrConcat } if + 8 index StrConcat (\)^\() StrConcat + 5 index StrConcat (\)*ln\() StrConcat + 8 index StrConcat AddClPar + } ifelse + } ifelse + 2 copy pop 0 6 2 roll GetIntervalNewStr + mark 11 -5 roll cleartomark 2 index 6 index dup 4 index exch sub getinterval exch 6 2 roll +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% str -> true/false +/IsStrNumber {% + true exch + { dup 48 lt exch dup 57 gt 3 -1 roll or + exch dup 46 ne%%. + exch dup 43 ne%%+ + exch 45 ne%%- + and and and { pop false } if } forall +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% literal switch -> func call, vector, variables +/EvalLiteral {% + ReadLiteral dup 40 eq%%% there is an open par -> function call + { pop (EvalFunc_ ) 9 4 index StrConcat 0 exch getinterval cvn cvx exec } + { dup 91 eq%%% there is an open bracket -> vector element + { ERROR_vector_not_yet_implemented } + { pop EvalVariable } + ifelse } + ifelse +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% first last parpos Expr[first:parpos-1] -> +/EvalVariable { 2 index Variable eq { (1) } { (0) } ifelse 4 -1 roll exch 6 2 roll } def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% (f(u))'=u'f'(u) +/EvalFunc { + 4 2 roll 4 index (1) ne + { AddOpPar 4 index StrConcat (\)*) StrConcat } if + (Eval ) 4 8 index StrConcat 0 exch getinterval cvn cvx exec + 2 copy pop 0 6 2 roll GetIntervalNewStr + mark 9 -3 roll cleartomark 2 index 6 index dup 4 index exch sub getinterval exch 6 2 roll +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% Func derivative -> Eval +/EvalFunc_sin {% + PreCommonFunc + { (cos\() StrConcat 5 index StrConcat AddClPar } if + PostCommonFunc } def +/EvalFunc_cos {% + PreCommonFunc + { (\(-sin\() StrConcat 5 index StrConcat (\)\)) StrConcat } if + PostCommonFunc } def +/EvalFunc_tan {% + PreCommonFunc + { dup 0 eq { (1) StrConcat } { 1 sub } ifelse (/cos\() StrConcat 5 index StrConcat (\)^2) StrConcat } if + PostCommonFunc } def +/EvalFunc_asin {% + PreCommonFunc + { (1/sqrt\(1-\() StrConcat 5 index StrConcat (\)^2\)\)) StrConcat } if + PostCommonFunc } def +/EvalFunc_acos {% + PreCommonFunc + { (-1/sqrt\(1-\() StrConcat 5 index StrConcat (\)^2\)\)) StrConcat } if + PostCommonFunc } def +/EvalFunc_atg {% + PreCommonFunc + { (1/\(1+\() StrConcat 5 index StrConcat (\)^2\)\)) StrConcat } if + PostCommonFunc } def +/EvalFunc_ln {% + PreCommonFunc + { dup 0 eq { (1) StrConcat } { 1 sub } ifelse (/\() StrConcat 5 index StrConcat AddClPar } if + PostCommonFunc } def +/EvalFunc_exp {% + PreCommonFunc + { (exp\() StrConcat 5 index StrConcat AddClPar } if + PostCommonFunc } def +/EvalFunc_sqrt {% + PreCommonFunc + { dup 0 eq { (1) StrConcat } { 1 sub } ifelse (/\(2*sqrt\() StrConcat 5 index StrConcat (\)\)) StrConcat } if + PostCommonFunc } def +/EvalFunc_Fact {% + PreCommonFunc { ERROR_no_variable_expression_in_Fact } if + PostCommonFunc } def +/EvalFunc_sh {% + PreCommonFunc + { (ch\() StrConcat 5 index StrConcat AddClPar } if + PostCommonFunc } def +/EvalFunc_ch {% + PreCommonFunc + { (sh\() StrConcat 5 index StrConcat AddClPar } if + PostCommonFunc } def +/EvalFunc_th {% + PreCommonFunc + { dup 0 eq { (1) StrConcat } { 1 sub } ifelse (/ch\() StrConcat 5 index StrConcat (\)^2) StrConcat } if + PostCommonFunc } def +/EvalFunc_Argsh {% + PreCommonFunc + { (1/sqrt\(1+\() StrConcat 5 index StrConcat (\)^2\)\)) StrConcat } if + PostCommonFunc } def +/EvalFunc_Argch {% + PreCommonFunc + { (1/sqrt\(\() StrConcat 5 index StrConcat (\)^2-1\)\)) StrConcat } if + PostCommonFunc } def +/EvalFunc_Argth {% + PreCommonFunc + { (1/\(1-\() StrConcat 5 index StrConcat (\)^2\)\)) StrConcat } if + PostCommonFunc } def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +/PreCommonFunc { + 1 add NextNonBlankChar pop 3 -1 roll 5 1 roll AnalyzeExpr 1 add NextNonBlankChar pop + 4 2 roll 4 index (0) eq + { (0) StrConcat false } + { 4 index (1) ne { AddOpPar 4 index StrConcat (\)*) StrConcat } if true } ifelse +} def +/PostCommonFunc { + 2 copy pop 0 6 2 roll GetIntervalNewStr + mark 9 -3 roll cleartomark 2 index 6 index dup 4 index exch sub getinterval exch 6 2 roll +} def +/EvalFunc_Derive {% + 1 add ReadNumber cvi 1 add dup cvr log 1 add cvi string cvs + 4 -1 roll pop 5 1 roll 1 add NextNonBlankChar pop AnalyzeExpr 1 add + 4 -2 roll (Derive\() StrConcat 7 -1 roll StrConcat (,) StrConcat 6 -1 roll StrConcat AddClPar + 2 copy pop 0 6 2 roll GetIntervalNewStr 6 -1 roll pop 2 index 6 index dup 4 index exch sub getinterval + exch 6 2 roll } def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% literal switch -> func call, vector, variables +/EvalFunc_Sum {% + 1 add NextNonBlankChar pop + %% read the variable name + ReadLiteral pop 3 -1 roll pop NextNonBlankChar + 44 ne { ANALYZER_ERROR_missing_first_comma_in_Sum } if + %% read the initial value + 1 add NextNonBlankChar pop ReadNumber pop + 2 copy get 44 ne { ANALYZER_ERROR_missing_second_comma_in_Sum } if + %% read the increment value + 1 add NextNonBlankChar pop ReadNumber pop + 2 copy get 44 ne { ANALYZER_ERROR_missing_third_comma_in_Sum } if + %% read the limit value + 1 add NextNonBlankChar pop ReadNumber pop + 2 copy get 44 ne { ANALYZER_ERROR_missing_fourth_comma_in_Sum } if + 1 add NextNonBlankChar pop dup 6 1 roll 3 -1 roll pop AnalyzeExpr 1 add NextNonBlankChar pop + 4 -2 roll 3 index 8 index dup 9 index exch sub getinterval StrConcat + 4 index StrConcat AddClPar + 2 copy pop 0 6 2 roll GetIntervalNewStr + mark 9 -3 roll cleartomark 2 index 6 index dup 4 index exch sub getinterval exch 6 2 roll +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% literal switch -> func call, vector, variables +/EvalFunc_IfTE {% + 3 -1 roll pop 1 add NextNonBlankChar pop SkipCond + NextNonBlankChar + 44 ne { ANALYZER_ERROR_missing_first_comma_in_IfTE } if + 1 add NextNonBlankChar pop dup 5 1 roll + AnalyzeExpr NextNonBlankChar + 44 ne { ANALYZER_ERROR_missing_second_comma_in_IfTE } if + 1 add NextNonBlankChar pop + AnalyzeExpr 1 add NextNonBlankChar pop + 4 -2 roll 3 index 10 index dup 11 index exch sub getinterval StrConcat + 6 index StrConcat (,) StrConcat 4 index StrConcat AddClPar + 2 copy pop 0 6 2 roll GetIntervalNewStr + mark 11 -5 roll cleartomark 2 index 6 index dup 4 index exch sub getinterval exch 6 2 roll +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% advance in str until a comma is found (no error detection!) +%% str index -> str index' +/SkipCond { { 1 add 2 copy get 44 eq {exit } if } loop } bind def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% Convert to radians if trigo function call +%% (name) -> +/TrigoFunc { + dup (cos) eq 1 index (sin) eq or exch (tan) eq or + { /ExpressionVector ExpressionVector aload length Pi /div cvx 180 /mul cvx 5 -1 roll 4 add + array astore def + } if +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% No derivative for condition.... +/EvalCondOp { 3 -1 roll pop } bind def +/PutIntervalOneAdd {putinterval 1 add} bind def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% Add open parenthesis in string at the given index +%% str index -> str index+1 +/AddOpPar {2 copy (\() PutIntervalOneAdd} bind def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% Add close parenthesis in string at the given index +%% str index -> str index+1 +/AddClPar {2 copy (\)) PutIntervalOneAdd} bind def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% Add 0 in string at the given index +%% str index -> str index+1 +/AddZero {2 copy (0) PutIntervalOneAdd} bind def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% Add open parenthesis in string at the given index +%% str index -> str index+1 +/AddMul {2 copy (*) PutIntervalOneAdd} bind def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% Add open parenthesis in string at the given index +%% str index -> str index+1 +/AddDiv {2 copy (/) PutIntervalOneAdd} bind def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% Add a plus sign in string at the given index +%% str index -> str index+1 +/AddAdd {2 copy (+) PutIntervalOneAdd} bind def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% Add a minus sign in string at the given index +%% str index -> str index+1 +/AddSub {2 copy (-) PutIntervalOneAdd} bind def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% Add a pipe sign in string at the given index +%% str index -> str index+1 +/AddPipe {2 copy (|) PutIntervalOneAdd} bind def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% H O O K S +/AnalyzePreHook { dup 5 1 roll } bind def +/PreEvalHook {} def +/AnalyzePostHook { 7 -1 roll pop } bind def +/AnalyzeListOfEPostHook { 6 -1 roll mark 6 1 roll cleartomark } bind def +/RollOp { 5 1 roll } bind def +end%%%tx@CoreAnalyzerDict +/tx@AddMathFunc 12 dict def tx@AddMathFunc begin +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% NEW FUNC +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% function arcsine in radians asin(x)=atan(x/sqrt(1-x^2)) +%% x -> theta +/asin {% + dup abs 1 gt { EQDFasinrangeerror } if + dup dup dup mul 1 exch sub sqrt atan exch 0 lt { 360 sub } if DegtoRad +} def +%% function arccosine in radians acos(x)=atan(sqrt(1-x^2)/x) +%% x -> theta +/acos {% + dup abs 1 gt { EQDFacosrangeerror } if + dup dup mul 1 exch sub sqrt exch atan DegtoRad +} def +%% function arctangent in radians +%% x -> theta +/atg { 1 atan dup 90 gt { 360 sub } if DegtoRad } bind def +%% HYPERBOLIC FUNCTIONS +/sh { dup Ex exch neg Ex sub 2 div } def +/ch { dup Ex exch neg Ex add 2 div } def +/th { dup sh exch ch div } def +/Argsh { dup dup mul 1 add sqrt add ln } def +/Argch { dup dup mul 1 sub sqrt add ln } def +/Argth { dup 1 add exch 1 exch sub div ln 2 div } def +%% modified exponential funtion for 0 +%% x n -> x^n +/Exp { dup 0 eq { pop pop 1 } { exp } ifelse } bind def +%% modified exponential funtion for 0 +%% x -> e^x +/Ex { Euler exch exp } bind def +%% +%% factorial function +%% n -> n! +/Fact { 1 exch 2 exch 1 exch { mul } for } bind def +/fact { Fact } bind def +end + +% END pstricks.pro + +%%EndProcSet +%%BeginProcSet: pst-dots.pro 0 0 +% $Id: pst-dots.pro 26 2008-06-14 11:50:02Z herbert $ +% +%% PostScript prologue for pstricks.tex. +%% Version 2.02, 2008/04/18 +%% +%% For distribution, see pstricks.tex. +%% +%% Timothy Van Zandt +%% +%% This program can be redistributed and/or modified under the terms +%% of the LaTeX Project Public License Distributed from CTAN archives +%% in directory macros/latex/base/lppl.txt. +%% 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+\title[$\Ptau \to \Pmu \Pmu \Pmu$ ]{$\Ptau \to \Pmu \Pmu \Pmu$ } +\author{ Marcin Chrz\k{a}szcz$^{1,2}$ , Nicola Serra$^{1}$ } +\institute[UTH, IFJ] + +\date{\today} +\begin{document} +% --------------------------- SLIDE -------------------------------------------- +\frame[plain]{\titlepage} +\author{Marcin Chrz\k{a}szcz} +% ------------------------------------------------------------------------------ +% --------------------------- SLIDE -------------------------------------------- + +\institute{~(UZH, IFJ)} + + + % \begin{frame}\frametitle{Outline} + % \begin{enumerate} + % \item introduction\vspace{.5em} + % \item multivariate technique\vspace{.5em} + % \item normalisation\vspace{.5em} + % % \item backgrounds\vspace{.5em} + % \item expected sensitivity\vspace{.5em} + % \item model dependence\vspace{.5em} data from Reco14Stripping20(r1) + % \end{enumerate} + % Major news wrt.\ the $1~fb^{-1}$ analysis are highlighted in \textcolor{mygreen}{green} + % \end{frame} + + \section{Unblinded results} + + \begin{frame} + \frametitle{Unblinding 1} +\begin{columns} +\column{1in}{~} +\column{3in} +'' +THERE came a day at summer’s full \\ +Entirely for us \\ +I thought that such were for the saints, \\ +Where revelations be. ''\footnote{E.Dickinson} \\ + \column{1in}{~} +\end{columns} +{~}\\ +{~}\\ +\begin{Large} +On Monday $4^{th}$ of August we were given the permission to unblind. +\end{Large} + + + \end{frame} + + + + \begin{frame} + \frametitle{Unblinding 2} +\begin{itemize} +\item Unfortunately no big ''revelations'' were there: +\item 2011 numbers: +\end{itemize} + \includegraphics[width=1.\textwidth]{2011.png} + + \end{frame} + + \begin{frame} + \frametitle{Unblinding 3} +\begin{itemize} +\item Unfortunately no big ''revelations'' were also in 2012 data: + +\end{itemize} + \includegraphics[width=1.1\textwidth]{2012.png} + + \end{frame} + + + + \begin{frame} + \frametitle{Unblinding 4} + + \begin{center} + \includegraphics[width=0.7\textwidth]{banana_line.pdf} + \end{center} +\begin{columns} + +\column{0.2in}{~} +\column{2in} +Limits(PHSP):\\ +Observed(Expected)\\ +$4.6~(5.0)\times 10^{-8}$ at $90\%$ CL\\ +$5.6~(6.1)\times 10^{-8}$ at $95\%$ CL\\ + + \column{3in} + \includegraphics[width=0.5\textwidth]{model.png} +\end{columns} + \end{frame} + + \begin{frame} + \frametitle{Conclusions} + \begin{columns} + \column{2.5in} + \begin{itemize} + \item We didn't find NP (yet). + \item Limits set with full LHCb dataset. + \item Awaiting for the future data! + \end{itemize} +\column{2.5in} + + \includegraphics[width=1\textwidth]{TauLFV_UL_2013001.pdf} + + + + \end{columns} + \begin{itemize} + \item We would like to thank our referees for very friendly,thorough and fruitful review. + \item With this presentation we ask collaboration for approval. + \end{itemize} + + + \end{frame} + + + +\end{document} diff --git a/Zurich_group/11.10.2014/mchrzasz.toc b/Zurich_group/11.10.2014/mchrzasz.toc new file mode 100644 index 0000000..9d9db62 --- /dev/null +++ b/Zurich_group/11.10.2014/mchrzasz.toc @@ -0,0 +1,3 @@ +\beamer@endinputifotherversion {3.10pt} +\select@language {english} +\beamer@sectionintoc {1}{Unblinded results}{2}{0}{1} diff --git 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diff --git a/Zurich_group/11.10.2014/texput.log b/Zurich_group/11.10.2014/texput.log new file mode 100644 index 0000000..1a9ab65 --- /dev/null +++ b/Zurich_group/11.10.2014/texput.log @@ -0,0 +1,21 @@ +This is pdfTeX, Version 3.1415926-2.4-1.40.13 (TeX Live 2012/Debian) (format=pdflatex 2013.3.11) 14 APR 2014 16:37 +entering extended mode + restricted \write18 enabled. + %&-line parsing enabled. +**p + +! Emergency stop. +<*> p + +End of file on the terminal! + + +Here is how much of TeX's memory you used: + 3 strings out of 494673 + 102 string characters out of 3173157 + 47775 words of memory out of 3000000 + 3323 multiletter control sequences out of 15000+200000 + 3640 words of font info for 14 fonts, out of 3000000 for 9000 + 243 hyphenation exceptions out of 8191 + 0i,0n,0p,1b,6s stack positions out of 5000i,500n,10000p,200000b,50000s +! ==> Fatal error occurred, no output PDF file produced! diff --git a/Zurich_group/11.10.2014/tmp.tex b/Zurich_group/11.10.2014/tmp.tex new file mode 100644 index 0000000..b78638c --- /dev/null +++ b/Zurich_group/11.10.2014/tmp.tex @@ -0,0 +1,701 @@ +\documentclass[xcolor=dvipsnames,table]{beamer} + + + + + + \author[Paul Seyfert]{ + Johannes Albrecht\inst{1}, Marta Calvi\inst{2}, Marcin Chrz\k{a}szcz\inst{3,4}, Laura Gavardi\inst{1}, Jon Harrison\inst{5}, Basem Khanji\inst{2}, George Lafferty\inst{5}, Tatiana Likhomanenko\inst{6}, Eduardo Rodrigues\inst{5}, Nicola Serra\inst{4}, \underline{Paul Seyfert\inst{7}}} + + \institute[Uni Heidelberg]{ + \inst{1}Dortmund, + \inst{2}Milano Bicocca, + \inst{3}Cracow, \inst{4}Zurich, \inst{5}Manchester, \inst{6}Yandex, \inst{7}Heidelberg University + } + + \date{\today} + \subject{} + + + \AtBeginSection[] + { + \begin{frame}{} + \tableofcontents[currentsection,currentsubsection] + \end{frame} + } + + + \begin{document} + \begin{frame} + \titlepage + \end{frame} + + + \begin{frame} + \begin{enumerate} + \item introduction\vspace{.5em} + \item multivariate technique\vspace{.5em} + \item choice of triggers\vspace{.5em} + \item normalisation\vspace{.5em} + \item backgrounds\vspace{.5em} + \item expected sensitivity\vspace{.5em} + \item model dependence\vspace{.5em} + \end{enumerate} + Major news wrt.\ the previous analysis rounds highlighted in \textcolor{darkgreen}{green} + \end{frame} + + \section{introduction} + + \begin{frame} + \frametitle{Status $\Ptau\to\Pmu\Pmu\Pmu$} + \begin{columns} + \begin{column}{.62\textwidth} + \begin{fmffile}{sm} + \begin{fmfgraph*}(200,150) + \fmfstraight + \fmfleft{is3,is2,is1,i1,i2,i3,i4,i5,i6} + \fmfright{os3,os2,os1,o1,o2,o3,o4,o5,o6} + + + \fmf{phantom}{o1,g1} + \fmf{phantom,tension=1.5}{g1,i1} + + \fmffreeze + + \fmf{photon, tension=2.,lab.side=left, lab=$\Pphoton$}{g1,g2} + \fmf{fermion,lab.side=left,label=$\APmuon$}{o3,g2} + \fmf{fermion,lab.side=left,label=$\Pmuon$}{g2,o5} + \fmf{phantom,tension=1.5}{i6,g2} + + \fmffreeze + + + \fmf{fermion,lab.side=left,label=$\Pgtm$}{i1,w1} + \fmf{dashes,lab.side=right,label=$\PWminus$}{w1,w2} + \fmf{fermion,lab.side=left,label=$\Pmuon$}{w2,o1} + + + \fmfipath{p[]} + \fmf{plain,tension=0,right,label={$\Pgngt\to\Pgngm$},tag=1}{w1,w2} + \fmffreeze + \fmfiset{p1}{vpath1(__w1,__w2)} + \fmfiv{d.sh=cross,d.ang=0,d.size=5thick}{point length(p1)/2 of p1} + + + \end{fmfgraph*} + + \end{fmffile} + {\footnotesize{ + \begin{itemize} + \item charged Lepton Flavour Violation process + \item possible as penguin with neutrino oscillation + \item unmeasurable small + \end{itemize} + }} + \end{column} + \begin{column}{.37\textwidth} + \begin{block}{current limits ($ 90\,\%$ CL)} + + \begin{description} + \item[BaBar] $3.3\times 10^{-8}$ + \item[Belle] $2.1\times 10^{-8}$ + \item[LHCb] $8.0\times 10^{-8}$ + \end{description} + \end{block} + \begin{block}{BSM predictions} + \begin{description} + \item[var.\ SUSY] $10^{-10}$ + \item[non universal $\PZprime$] $10^{-8}$ + \item[mSUGRA+seesaw] $10^{-9}$ + \end{description} + \end{block} + \end{column} + \end{columns} + \end{frame} + + \begin{frame} + \frametitle{$\Ptau$ production} + \begin{itemize} + \item consider five production channels (fractions at $\unit{8}{\TeV}$):\begin{itemize} + \item prompt $\PDs\to\Ptau$ ($73.1\pm3.9\,\%$) + \item prompt $\PDplus\to\Ptau$ ($0.42\pm0.43\,\%$) + \item non-prompt $\PDs\to\Ptau$ ($9.7\pm2.1\,\%$) + \item non-prompt $\PDplus\to\Ptau$ ($0.02\pm0.02\,\%$) + \item $X_{\Pbottom}\to\Ptau$ (meson or baryon) ($16.8\pm3.0\,\%$) + \end{itemize} + \item \textcolor{darkgreen}{use $\sigma(\Pbottom\APbottom)$ at $\unit{8}{\TeV}$ from LHCb} + \item \textcolor{darkgreen}{use Pythia scaling for $\sigma(\Pcharm\APcharm)$ at $\unit{8}{\TeV}$} + \end{itemize} + \begin{exampleblock}{$\mathcal{B}(\PDplus\to\Ptau)$} + \begin{itemize} + \item old analysis: used upper limit + \item now: $\mathcal{B}(\PDplus\to\Pmu\Pnum)$ + helicity suppression + phase space + \item \texttt{hep-ex:0604043} + \item $\mathcal{B}(\PDplus\to\Ptau\Pnut)=1\pm1\times10^{-4}$ + \end{itemize} + \end{exampleblock} + \end{frame} + + \begin{frame} + \frametitle{Strategy} + \begin{itemize} + \item mostly as in many rare decay searches: + \item loose stripping selection + \item multivariate classification in: mass, PID, ``geometry/topology'' + \item relative normalisation ($\PDs\to\Pphi(\Pmu\Pmu)\Ppi$) + \item invariant mass fit for expected background in each likelihood bin\newline fit in $m-m_{\Ptau}>\unit{30}{\MeV}$ + \item ``middle sidebands'' for classifier evaluation ($\unit{20}{\MeV}300\MeV$} \\ +Track $\chi^2$/ndf &\multicolumn{2}{c|}{$<3 $} \\ +IP $\chi^2$/ndf &\multicolumn{2}{c|}{$>9 $} \\ +\textcolor{darkgreen}{track ghost probability} &\multicolumn{2}{c|}{\textcolor{darkgreen}{$<0.3 $}} \\ +\hline +$\mu$ pairs &\multicolumn{2}{c|}{} \\ +$m_{\mu^+\mu^-} - m_{\phi}$ & $>20\MeV$ & $<20\MeV$\\ +$m_{\mu^+\mu^-}$ & $> 450\MeV$ & - \\ +$m_{\mu^+\mu^+}$ & $> 250\MeV$ & - \\ +\hline +$\tau^\pm$ and \PDs &\multicolumn{2}{c|}{} \\ +$\Delta m$ & $<400\MeV$ & $<50\MeV$\\ +Vertex $\chi^2$ &\multicolumn{2}{c|}{$<15$} \\ +\textcolor{darkgreen}{IP $\chi^2$} &\multicolumn{2}{c|}{$<225^1 $} \\ +$\cos\alpha$ &\multicolumn{2}{c|}{$>0.99$} \\ +$c\tau$ (stripping) &\multicolumn{2}{c|}{$>\unit{100}{\mu m}$} \\ + &\multicolumn{2}{c|}{no PV refitting}\\ +decay time (offline) &\multicolumn{2}{c|}{$> -0.01$ ns \& $< 0.025$ ns}\\ + &\multicolumn{2}{c|}{PV refitting}\\ +\hline +\end{tabular} +}} + +{\footnotesize{$^1$ different LoKi functor}} + \end{frame} + + \section{multivariate technique} + + \begin{frame} + \frametitle{``geometric likelihood''} + \begin{itemize} + \item classify the displaced 3-body decay properties of a signal candidate + \item revisit variable choice + \item revisit classification technique + \item \textcolor{darkgreen}{more toolkits tried: MatrixNet, NeuroBayes}, TMVA + \item \textcolor{darkgreen}{retune input variables\newline($\PBs\to\Pmu\Pmu$ isolation $\rightarrow$ Laura's BDT isolation: CERN-THESIS-2013-259)} + \end{itemize} + + \end{frame} + \begin{frame} + \frametitle{setup} + \begin{itemize} + \item train $1/3$ signal MC against $1/2$ background MC + \item variables \begin{itemize} + \item $3\times$ DOCA + \item vertex $\chi^2$ + \item $\tau$ decay time + \item $\tau$ IP$\chi^2$ + \item min.\ $\mu$ IP$\chi^2$ + \item $\Ptau$ pointing angle + \item $\tau$ $p_T$ + \item max.\ track $\chi^2$ + \item $\PBs\to\Pmu\Pmu$ track isolation + \item cone isolation + \item \textcolor{darkgreen}{BDT isolation} + \end{itemize} + \end{itemize} + \end{frame} + \begin{frame} + \frametitle{futher tweaking} + \begin{itemize} + \item \textcolor{darkgreen}{remove fully reconstructed 3-body decays from background sample\newline (don't expect to be able to discriminate these)} + \item don't apply trigger prior to training + \end{itemize} + + \begin{exampleblock}{``blending'' technique} + \begin{itemize} + \item for each signal channel we train: one BDT, three Fisher classifier, four MLPs, one FDA, and one LD classifier + \item[$\Rightarrow$] 50 classifiers + \item one final MatrixNet classifier using the 13 base variables and the 50 classifiers as input + \newline(trained on the second $1/3$ of signal MC and the second $1/2$ of background MC) + \end{itemize} + \end{exampleblock} + \end{frame} + + \begin{frame} + \frametitle{performance} + \begin{itemize} + \item classifier prefers $\Ptau$ from prompt $\PDs$ + \end{itemize} + \begin{columns} + \begin{column}{.48\textwidth} + \begin{block}{MC response for different\newline $\Ptau$ production channels} + \includegraphics[width=.95\textwidth]{./for_paul.png} + \end{block} + \end{column} + \begin{column}{.48\textwidth} + \begin{block}{response for $\PDs\to\Pphi\Ppi$\newline data and MC} + \includegraphics[width=.95\textwidth]{./MN_BLEND_FLAT.png} + \end{block} + \end{column} + \end{columns} + \end{frame} + + \begin{frame} + \frametitle{calibration} + \begin{itemize} + \item assume all differences between $\Ptau\to\Pmu\Pmu\Pmu$ and $\PDs\to\Pphi\Ppi$ come from kinematics (mass, resonance, decay time) + \item get correction $\PDs\leadsto\Ptau$ from MC + \item apply corrections to $\PDs\to\Pphi\Ppi$ on data + \end{itemize} + \begin{block}{validation} + \begin{itemize} + \item done for 2011 analysis, treating smeared MC as data + \end{itemize} + \end{block} + \begin{columns} + \begin{column}{.45\textwidth} + \begin{itemize} + \item $\PDs\to\Pphi\Ppi$ well modelled in MC + \item until the very low likelihood end of the distribution + \item[$\rightarrow$] i.e.\ also badly pointing non-prompt $\PDs$ + \end{itemize} + \end{column} + \begin{column}{.45\textwidth} + \includegraphics[width=.95\textwidth]{MN_BLEND_FLAT.png} + \end{column} + \end{columns} + \end{frame} + + \begin{frame} + \frametitle{PID} + \begin{itemize} + \item we used ProbNNmu already in the previous round of the analysis + \item now use MC12TuneV2 (latest) + \item two-fold reason:\begin{itemize} + \item expect better performance than CombDLL variables + \item ``one variable for everything'':\newline with CombDLL we needed both CombDLL($\mu-\pi$) and CombDLL($\mu-K$) + \end{itemize} + \end{itemize} + \end{frame} + + \begin{frame} + \frametitle{PIDCalib} + \begin{itemize} + \item calibration strategy: use PIDCalib + \item confirm with $\PDs\to\Pphi\Ppi$ if everything is fine + \end{itemize} + \begin{columns} + \begin{column}{.45\textwidth} + cut\&fit: + \begin{itemize} + \item fit $\PDs\to\Pphi\Ppi$ with a TIS muon in data + \item cut on ProbNNmu of one muon + \item fit again + \item[$\rightarrow$] ratio is ``true'' cut efficiency + \end{itemize} + \begin{block}{ProbNNmu>0.4} + $\varepsilon=86.3\,\%$ + \end{block} + \end{column} + \begin{column}{.45\textwidth} + PIDCalib + \begin{itemize} + \item apply full selection (incl. trigger) to $\PDs\to\Pphi\Ppi$ MC reference sample + \item avoid IsMuon bias + \end{itemize} + \begin{block}{ProbNNmu>0.4} + $\varepsilon=89.8\,\%$ + \end{block} + \end{column} + \end{columns} + \end{frame} + + \begin{frame} + \frametitle{?} + \begin{itemize} + \item first shown at \myhref{https://indico.cern.ch/event/291727/}{charming VRD meeting} + \item also mentionned at last \myhref{https://indico.cern.ch/event/298021/}{LHCb week} + \item many emails exchanged with Barbara Sciascia + \item mistakes on user side found + \item still no agreement + \end{itemize} + \begin{exampleblock}{phenomenologic treatment} + \begin{itemize} + \item correlations are small in $\PDs\to\Pphi\Ppi$ data and MC + \newline $\varepsilon(\text{cut on one muon})^2 = \varepsilon(\text{cut on two muons})$ + \item[$\Rightarrow$] use $c^3=(\varepsilon(\text{cut and fit})/\varepsilon(\text{PIDCalib}))^3$ as correction to PIDCalib for $\Ptau\to\Pmu\Pmu\Pmu$ + \item assign error of $0.02$ for $c$ + \end{itemize} + \end{exampleblock} + \begin{itemize} + \item planned: investigate further (usage/bug/samples) + \item planned: use muons from $\PDs\to\Pphi\Ppi$ directly + \end{itemize} + \end{frame} + + \begin{frame} + \frametitle{binning optimisation} + \begin{itemize} + \item how to optimise the binning in two classifiers? + \item $\unit{1}{\reciprocal\femtobarn}$ CONF note: two one-dimensional optimisations as in $\PBs\to\Pmu\Pmu$ + \item $\unit{1}{\reciprocal\femtobarn}$ PAPER: iterative loop of one-dimensional optimisations\newline optimising one classifier on the sensitive range of the other classifier + \item \textcolor{darkgreen}{now: optimise two-dimensions (optimise bin boundaries in both dimensions at the same time)} + \item unchanged: don't use lowest likelihood bins\newline(reflection backgrounds, no sensitivity gain) + \end{itemize} + \end{frame} + \begin{frame} + \frametitle{impact of new binning optimisation} + \begin{itemize} + \item removal of tiny bins which contribute negligible sensitivity + \item colour: limit obtained, using only this particular bin + \item number: rank of that bin (1=best sensitivity bin) + \end{itemize} + + ~ + + \begin{columns} + \begin{column}{.5\textwidth} + old analysis + + ~ + + \includegraphics[width=.95\textwidth]{./90CLonebinlimit.eps} + \end{column} + \begin{column}{.5\textwidth} + new analysis + + (2011 data, not final calibration) + \includegraphics[width=.95\textwidth]{./rank.eps} + \end{column} + \end{columns} + \end{frame} + + + \begin{frame} + \frametitle{mass shape} + \begin{itemize} + \item double-Gaussian with fixed fraction ($70\,\%$ inner Gaussian) + \item fix fraction to ease calibration:\newline + $\sigma_{data}^{\Ptau} = \frac{\sigma_{MC}^{\Ptau}}{\sigma_{MC}^{\PDs}}\times\sigma_{data}^{\PDs}$ + \end{itemize} + \includegraphics[width=.44\textwidth]{./Ds_data_2011.pdf} + \includegraphics[width=.44\textwidth]{./Ds_data_2012.pdf} + + {\footnotesize{ + \begin{tabular}{|c|c|c|} + \hline + calibrated $\Ptau$ mass shape & 7~TeV & 8~TeV\\ + \hline + Mean ($\MeV$) & $1779.1 \pm 0.1$ & $1779.0 \pm 0.1$\\ + \hline + $\sigma_1$ ($\MeV$) & $7.7 \pm 0.1$ & $7.6 \pm 0.1$\\ + \hline + $\sigma_2$ ($\MeV$) & $12.0 \pm 0.8$ & $11.5 \pm 0.5$\\ + \hline + \end{tabular} + } + } + \end{frame} + +\beamertemplateshadingbackground{darkgreen!30}{PineGreen!30} + \section{choice of triggers} + \begin{frame} + \frametitle{the story} + \begin{itemize} + \item first look at $\PDs\to\Pphi\Ppi$ revealed: signal/background much worse in 2012 + \item[$\rightarrow$] charm got more bandwidth in 2012 + \item taking all events quite unsatisfactory:\begin{itemize} + \item strictly speaking: we don't know why the events ended up on tape + \item trigger efficiencies unstable (TIS/TPS/TOS efficiencies for lots of lines and TCKs) + \item signal anyhow mostly TOS in a muon trigger + \end{itemize} + \item[$\Rightarrow$] if an event was background in the trigger, then don't consider it signal afterwards. + \end{itemize} + \end{frame} + + \begin{frame} + \frametitle{strategy} + \begin{itemize} + \item back of the envelope: limit scales with $1/\varepsilon_\text{sig}$ + \item back of the envelope: limit scales with $\sqrt{\varepsilon_\text{bkg}}$ + \item[$\Rightarrow$] minimise $FOM=\frac{\sqrt{\varepsilon_\text{bkg}}}{\varepsilon_\text{sig}}$ + \item running TCKsh and some combinatorics: $\mathcal{O}(2^{256}\approx 10^{75})$ possibilities of using HLT2 line (ignoring that there are different TCKs, TIS/TOS/TPS/DEC, \dots) + \item[$\rightarrow$] be more pragmatic! + \end{itemize} + \begin{exampleblock}{trigger optimisation} + \begin{itemize} + \item sort trigger lines (Punzi FoM) + \item start with events from the best trigger line and compute $FOM$ + \item add events from the next trigger and recompute $FOM$ + \item iterate and converge to $FOM(\text{all triggers})$ + \item use all triggers until $FOM$ starts rising. + \end{itemize} + \end{exampleblock} + \end{frame} + + \begin{frame} + \frametitle{our triggers} + {\footnotesize{ + \begin{tabular}{l|c|c} + & signal & normalisation \\\hline\hline + L0$^1$ & \multicolumn{2}{c}{L0Muon TOS}\\\hline + Hlt1$^1$ & \multicolumn{2}{c}{Hlt1TrackMuon TOS}\\\hline + Hlt2 2011 & Hlt2CharmSemilepD2HMuMu TOS & Hlt2DiMuonDetached$^2$ TOS \\ + & || Hlt2TriMuonTau TOS & \\\hline + Hlt2 2012 & Hlt2TriMuonTau$^1$ TOS & Hlt2DiMuonDetached$^2$ TOS\\\hline + \end{tabular} + } + } + \only<1>{ + \begin{block}{$^1$ triggers in 2012} + \begin{itemize} + \item cuts changed through 2012 + \item[$\rightarrow$] \textcolor{darkgreen}{emulated two different TCKs for 2012} + \end{itemize} + \end{block}} + \only<2>{ + \begin{block}{$^2$ word on Hlt2DiMuonDetached} + \begin{itemize} + \item keep it simple here + \item line unchanged in 2012 + \item[$\rightarrow$] choice keeps Hlt2 trigger efficiency stable + \item $\PDs\to\Pphi\Ppi$ anyhow doesn't behave like $\Ptau\to\Pmu\Pmu\Pmu$ in the TriMuon trigger (requires misidentification) + \end{itemize} + \end{block}} + + \end{frame} + + \begin{frame} + \frametitle{cross check (not in the note)} + \begin{itemize} + \item shouldn't the multivariate classifier do better than any trigger? + \item back-of-the-envelope overestimates the improvement (expect $\sim 9\,\%$ improvement) + \item[$\rightarrow$] add events back to the ntuple, recalculate normalisation, redid fits + \item[$\Rightarrow$] \textcolor{darkgreen}{restricting the triggers gains $\sim 3\,\%$ sensitivity wrt.\ previous round} + \end{itemize} + \end{frame} +\beamertemplateshadingbackground{White}{White} + + \section{normalisation} + + \begin{frame} + \frametitle{relative normalisation} + $\mathcal{B}(\Ptau\to\Pmu\Pmu\Pmu) = \frac{\mathcal{B}(\PDs\to\Pphi\Ppi)}{\mathcal{B}(\PDs\to\Ptau\Pnut)} \times f_{\PDs}^{\Ptau} \times \frac{\varepsilon_\text{norm} }{\varepsilon_\text{sig} } \times \frac{N_\text{sig}}{N_\text{norm}} = \alpha\times N_\text{sig}$ + \begin{itemize} + \item where $\varepsilon$ stands for trigger, reconstruction, selection + \item $\text{norm}$ = normalisation channel $\PDs\to\Pphi\Ppi$ + \item $f_{\PDs}^{\Ptau}$ is the fraction of $\Ptau$ coming from $\PDs$ + \newline i.e.\ $(83\pm3)\,\%$ for 2012 + \end{itemize} + \includegraphics[width=.47\textwidth]{./Ds_data_2011.pdf} + \includegraphics[width=.47\textwidth]{./Ds_data_2012.pdf} + \end{frame} + + \begin{frame}[allowframebreaks] + \frametitle{normalisation in numbers} + {\footnotesize{ +$\begin{array}{c|c|c} +& \rm{7~TeV} & \rm{8~TeV}\\ +\hline +\rm{\epsilon\mathstrut_{sig}}^{GEN} & 8.98 \pm 0.41 & 9.20 \pm 0.36\\ +\hline +\rm{\epsilon_{cal}}^{GEN} & 11.19 \pm 0.34 & 11.53 \pm 0.32\\ +\hline +\rm{\epsilon_{sig}}^{REC,isMuon,SEL} & 9.794 \pm 0.028 & 9.134 \pm 0.023 \\ +\hline +\rm{\epsilon_{cal}}^{REC,isMuon,SEL} & 7.187 \pm 0.022 & 6.690 \pm 0.022 \\ +\hline +\frac{\rm{c_{cal}}^{track}}{\rm{c_{sig}}^{track}} & 0.997 \pm 0.009 \pm 0.026 & 0.996 \pm 0.009 \pm 0.026 \\ +\hline +\frac{\rm{c_{cal}}^{\mu ID}}{\rm{c_{sig}}^{\mu ID}} & 0.9731 \pm 0.0031 \pm 0.0264 & 1.0071 \pm 0.0022 \pm 0.0204 \\ +\hline +\rm{c}^{\Pphi} & \multicolumn{2}{c}{0.98 \pm 0.01} \\ +\hline +\rm{c}^{\Ptau} & 1.032 \pm 0.006 & 1.026 \pm 0.006\\ +\hline +\rm{c}^{trash} & 1.95 \pm 0.12 & 2.05 \pm 0.12\\ +\hline +\rm{\epsilon\mathstrut_{sig}}^{TRIG} & 35.45 \pm 0.11 \pm 0.14 & 39.1 \pm 1.7 \pm 2.0 \\ +\hline +\rm{\epsilon\mathstrut_{cal}}^{TRIG} & 23.42 \pm 0.14 \pm 0.09 & 20.62 \pm 0.76 \pm 1.07 \\ +\end{array}$ + }} + +\framebreak + + {\footnotesize{ +$\begin{array}{c|c|c} +& \rm{7~TeV} & \rm{8~TeV}\\ +\hline +\mathcal{B}(\PDs\to\Pphi\Ppi) & \multicolumn{2}{c}{(1.317 \pm 0.099) \times 10^{-5}}\\ +\hline +f^{\Ptau}_{\PDs} & 0.82 \pm 0.03 & 0.83 \pm 0.03 \\ +\hline +\mathcal{B}(\PDs\to\Ptau\Pnut) & \multicolumn{2}{c}{0.0561 \pm 0.0024}\\ +\hline +\rm{\epsilon\mathstrut_{norm}}^{REC\&SEL}/ +\rm{\epsilon\mathstrut_{sig}}^{REC\&SEL} +& 0.897 \pm 0.061 & 0.926 \pm 0.056 \\ +\hline +\rm{\epsilon\mathstrut_{norm}}^{TRIG}/ +\rm{\epsilon\mathstrut_{sig}}^{TRIG} +& 0.6606 \pm 0.0059 & 0.527 \pm 0.041\\ +\hline +N_{norm} & 28,162 \pm 434 & 51,998 \pm 684\\ +\hline & \\[-1.5em]\hline +\alpha & (4.05 \pm 0.48) \times 10^{-9} & (1.83 \pm 0.25) \times 10^{-9}\\ +\alpha^{trash} & (7.90 \pm 0.49) \times 10^{-9} & (3.75 \pm 0.27) \times 10^{-9}\\ +\end{array}$ +}} + \end{frame} + + + \section{backgrounds} + + \begin{frame} + \frametitle{misidentification} + \begin{itemize} + \item most dominant: $\PDplus\to\PK\Ppi\Ppi$ + \item experience from last round: cut away low ProbNNmu range + \item check remaining data under $\PK\Ppi\Ppi$ hypothesis for $\PDplus$ peak + \item[$\Rightarrow$] misid safely contained in ``trash'' bin + \item \textcolor{darkgreen}{$\PDplus\to\Ppi\Ppi\Ppi$ and $\PDs\to\Ppi\Ppi\Ppi$ start to become visible in 2012} + \end{itemize} + \includegraphics[width=.45\textwidth]{./Dp2Kpipi_all_2012_senseBins.pdf} + \includegraphics[width=.45\textwidth]{./FittoD23pi_2012.pdf} + \end{frame} + + \begin{frame} + \frametitle{evil backgrounds} + \begin{itemize} + \item $\Pphi\to\Pmu\Pmu + X$: narrow veto on dimuon mass + \item $\PDs\to\Peta(\Pmu\Pmu\Pphoton)\Pmu\Pnum$: not so easy + \begin{itemize} + \item modelled in CONF note + \item optimised veto in PAPER + \item right now: both versions in the ANA note + \end{itemize} + \item baseline: veto $m_{\APmuon\Pmuon} < \unit{450}{\MeV}$ + \begin{itemize} + \item fits better understood + \item sensitivity unchanged when removing veto + \item smaller uncertainty on expected background + \end{itemize} + \end{itemize} + \end{frame} + + \begin{frame} + \frametitle{remaining backgrounds} + \begin{itemize} + \item fit exponential to invariant mass spectrum in each likelihood bin + \item don't use $\pm \unit{30}{\MeV}$ in the fit + \item[$\rightarrow$] compatible results blinding only $\pm \unit{20}{\MeV}$\footnote{partially used in classifier developement} + \end{itemize} + {\begin{center} + most sensitive bins in 2011 and 2012 + \includegraphics[width=.4\textwidth]{./fit2011.png} + \includegraphics[width=.4\textwidth]{./fit2012.png} + \end{center}} + \end{frame} + + \section{results} + + \begin{frame} + \frametitle{expected limit} + \begin{itemize} + \item still blinded + \item consider nuisance parameters from background fit, signal pdf calibration, normalisation + \item nuisance parameters due to $\Ptau$ production not included in signal pdf shape, yet + \item limit for combined 2011+2012 analysis + \end{itemize} + \end{frame} + + \begin{frame} + \frametitle{sensitivity} + $\mathcal{B}(\Ptau\to\Pmu\Pmu\Pmu)<5.6 \times 10^{-8}$ at 90\% CL + + \includegraphics[width=.8\textwidth]{./banana.png} + \end{frame} + +\beamertemplateshadingbackground{PineGreen!30}{White} + \section{model dependence} + + \begin{frame} + \frametitle{model dependence} + \begin{itemize} + \item $\Peta$ veto $\Rightarrow$ our limit not applicable to New Physics with small $m_{\APmuon\Pmuon}$ + \item model independent description in \texttt{arXiv:0707.0988} + \item 5 relevant Dalitz distributions: 2 four-point operators, 1 radiative operator, 2 interference terms + \end{itemize} + \only<2->{ + \begin{itemize} + \item with radiative distribution limit gets worse by $51\,\%$ (dominantly from the $\Peta$ veto) + \item the other four Dalitz distributions behave nicely (within $7\,\%$) + \end{itemize} + } + \only<1>{ + \includegraphics[width=.331\textwidth]{./gammallll.eps} + \includegraphics[width=.331\textwidth]{./gammallrr.eps} + \includegraphics[width=.331\textwidth]{./gammarad.eps} + + \includegraphics[width=.331\textwidth]{./gammarad-llll.eps} + \includegraphics[width=.331\textwidth]{./gammarad-llrr.eps} +} + + \end{frame} + +\beamertemplateshadingbackground{White}{White} + + \begin{frame} + \frametitle{Conclusion} + \begin{columns} + \begin{column}{.55\textwidth} + \begin{itemize} + \item finally all pieces put together + \item model (in)dependence of $\Peta$ veto investigated + \item expected sensitivity computed\newline $5.6\times 10^{-8}$ + \end{itemize} + \end{column} + \begin{column}{.45\textwidth} + \includegraphics[width=\textwidth]{party-music-hd-wallpaper-1920x1200-3850.jpg} + \end{column} + \end{columns} + + \end{frame} + \end{document} diff --git a/Zurich_group/11.10.2014/xwindow.png b/Zurich_group/11.10.2014/xwindow.png new file mode 100644 index 0000000..f43cc7e --- /dev/null +++ b/Zurich_group/11.10.2014/xwindow.png Binary files differ diff --git a/Zurich_group/14_07_2014/MM.aux b/Zurich_group/14_07_2014/MM.aux new file mode 100644 index 0000000..b7fa3c4 --- /dev/null +++ b/Zurich_group/14_07_2014/MM.aux @@ -0,0 +1,163 @@ +\relax +\ifx\hyper@anchor\@undefined +\global \let 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a/Zurich_group/14_07_2014/MM.pdf b/Zurich_group/14_07_2014/MM.pdf new file mode 100644 index 0000000..160ac5e --- /dev/null +++ b/Zurich_group/14_07_2014/MM.pdf Binary files differ diff --git a/Zurich_group/14_07_2014/MM.snm b/Zurich_group/14_07_2014/MM.snm new file mode 100644 index 0000000..e69de29 --- /dev/null +++ b/Zurich_group/14_07_2014/MM.snm diff --git a/Zurich_group/14_07_2014/MM.synctex.gz b/Zurich_group/14_07_2014/MM.synctex.gz new file mode 100644 index 0000000..78b4daf --- /dev/null +++ b/Zurich_group/14_07_2014/MM.synctex.gz Binary files differ diff --git a/Zurich_group/14_07_2014/MM.tex b/Zurich_group/14_07_2014/MM.tex new file mode 100644 index 0000000..2e9ab92 --- /dev/null +++ b/Zurich_group/14_07_2014/MM.tex @@ -0,0 +1,1097 @@ +\documentclass[]{beamer} +\setbeamertemplate{navigation symbols}{} +\usepackage{beamerthemesplit} +\useoutertheme{infolines} +\usecolortheme{dolphin} +%\usetheme{Warsaw} +\usetheme{progressbar} +\usecolortheme{progressbar} + +\usefonttheme{progressbar} +\useoutertheme{progressbar} +\useinnertheme{progressbar} +\usepackage{graphicx} +%\usepackage{amssymb,amsmath} +\usepackage[latin1]{inputenc} +\usepackage{amsmath} +\newcommand\abs[1]{\left|#1\right|} +\usepackage{iwona} +\usepackage{hepparticles} +\usepackage{hepnicenames} +\usepackage{hepunits} +\progressbaroptions{imagename=images/lhcb} +%\usetheme{Boadilla}f + +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%5 +\definecolor{mygreen}{cmyk}{0.82,0.11,1,0.25} +\setbeamertemplate{blocks}[rounded][shadow=false] +\addtobeamertemplate{block begin}{\pgfsetfillopacity{0.8}}{\pgfsetfillopacity{1}} +\setbeamercolor{structure}{fg=mygreen} +\setbeamercolor*{block title example}{fg=mygreen!50, +bg= blue!10} +\setbeamercolor*{block body example}{fg= blue, +bg= blue!5} + + + + + +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%\beamersetuncovermixins{\opaqueness<1>{25}}{\opaqueness<2->{15}} +\title{Method of moments for $\PB \to \PKstar \mu \mu$} +\author{\underline{Marcin Chrzaszcz}$^{1,2}$} +\date{\today} + +\begin{document} + +{ +\institute{$^1$ University of Zurich, $^2$ Institute of Nuclear Physics} +\setbeamertemplate{footline}{} +\begin{frame} +\logo{ +\vspace{2 mm} +\includegraphics[height=1cm,keepaspectratio]{images/uzh.jpg}~ +\includegraphics[width=1cm,keepaspectratio]{images/ifj.png}} + + \titlepage +\end{frame} +} +\institute{UZH,IFJ} + +\section[Outline]{} +\begin{frame} +\tableofcontents +\end{frame} + +\section{Introduction} +\begin{frame}\frametitle{Plan} +Why method of moments: +\begin{enumerate} +\item Complementary approach in performing the fit. +\item Allows to extract info measuring quantities in event basis depending on the angular distribution. +\item Used in $\PB \to \rho \Plepton \nu$(SLAC-386 UC-414),\\ $\PJpsi \to \PK \PK \gamma$(PRD 71, 032005 (2005) ), etc. +\end{enumerate} + + +\end{frame} +\section{Method of Moments - Theory} +\begin{frame}\frametitle{Method of moments} +{~} +Let's assume we have our pdf with $k$ unknown parameters :$PDF(x_i, \alpha)$, $dim(\alpha)=k$. One can calculate $k$ moments, which are the functions of $\alpha_i$: +\begin{equation} +\mu_i=f(\alpha_1,..., \alpha_k) = E[W_i] +\end{equation} +If we have $n$ events in our $q^2$ bin, we can estimate: +\begin{equation} +\widehat{\mu}_i=\dfrac{1}{n}\sum_{j=0}^{j=n-1} w_j +\end{equation} +, where $w_j=g(x_i)$ + +\end{frame} + +\begin{frame}\frametitle{Trivial example} +{~} +Lets see how this works in practice: +\begin{equation} +f(x)=\dfrac{x^{a-1}e^{-x/b}} {b^a \Gamma(a)} +\end{equation} +we measure the moments:\\ +\begin{center} $m_1=\dfrac{X_1+X_2+...+X_n}{n}$,\\ $m_2=\dfrac{X_1^2+X_2^2+...+X_n^2}{n}$.\\\end{center} +and calculate them analytically: +\begin{center} $m_1=ab$, $m_2=b^2a(a+1)$\end{center} +So one just needs to solve this and get the answer: +\center $a=\dfrac{m_1^2}{m_2-m_1^2}$, $b=\dfrac{m_2-m_1^2}{m_1}$ +\end{frame} + +\section{Moments of Ss} + + +\begin{frame}\frametitle{Our PDF} +{~} +The angular terms: +\begin{multline} +\dfrac{d^4\Gamma}{dq^2 dcos\theta_k dcos\theta_l d\phi}=\dfrac{9}{32\pi}( \dfrac{3}{4}(1-F_l)\sin^2 \theta_k + F_l \cos^2 \theta_k + (\dfrac{1}{4}(1-F_l)\sin^2 \theta_k \\ -F_l\cos^2) \cos 2\theta_l + J_3 \sin^2 \theta_k \sin^2 \theta_l cos2\phi + J_4 \sin2 \theta_k \sin \theta_l \cos\phi +\\ J_5 \sin 2 \theta_k \sin \theta_l \cos \phi + (J_{6s} \sin^2 \theta_k + J_{6c} \cos^2 \theta_k) \cos \theta_l + \\ J_7 \sin 2\theta_k \sin \theta_l \sin \phi + J_8 \sin 2 \theta_k \sin 2 \theta_l \sin \phi + J_9 \sin^2 \theta_k \sin^2 \theta_l \sin 2 \phi) +\end{multline} +Since we are fitting a PDF we need to ensure it is normalized: +\begin{equation} +\int_{-\pi}^{\pi} d\phi \int_{-1}^{1} d cos\theta_l \int_{-1}^{1} d cos\theta_k \dfrac{d^4\Gamma}{dq^2 dcos\theta_k dcos\theta_l d\phi}=1 +\end{equation} + + +\end{frame} +\begin{frame}\frametitle{Measuring Js} +{~} +From equation 2 we have the following: + +\begin{equation} +\dfrac{1}{4}(3 J_{1c} + 6 J_{1s} - J_{2c} - 2 J_{2s}) =1 +\end{equation} +For now we will consider the following PDF: +\begin{equation} + \dfrac{d^3\Gamma}{\Gamma dcos\theta_k dcos\theta_l d\phi }(cos\theta_k , cos\theta_l, \phi) +\end{equation} + +Becouse our PDF is not normalized and we are measuring $\Gamma+\overline{\Gamma} +$ we are effectively fitting the $S_i$ (aka $J_i \to S_i$) +\end{frame} + + +\begin{frame}\frametitle{Moments for $\PB \to \PKstar \mu \mu$} +{~} +Let's calculate the moments for Ss: +\begin{equation} + \dfrac{d^3\Gamma}{\Gamma dcos\theta_k dcos\theta_l d\phi }sin^2 \theta_k sin^2 \theta_l cos 2 \phi= \dfrac{8 S_3 }{25} +\end{equation} +\begin{equation} + \dfrac{d^3\Gamma}{\Gamma dcos\theta_k dcos\theta_l d\phi } sin 2 \theta_k sin 2 \theta_k cos\phi= \dfrac{8 S_4 }{25} +\end{equation} +\begin{equation} + \dfrac{d^3\Gamma}{\Gamma dcos\theta_k dcos\theta_l d\phi }sin2\theta_k sin\theta_l cos\phi = \dfrac{2 S_5 }{5} +\end{equation} +\begin{equation} + \dfrac{d^3\Gamma}{\Gamma dcos\theta_k dcos\theta_l d\phi} sin 2 \theta_k sin \theta_l sin \phi = \dfrac{2 S_7 }{5} +\end{equation} +\begin{equation} + \dfrac{d^3\Gamma}{\Gamma dcos\theta_k dcos\theta_l d\phi} sin 2 \theta_k sin2 \theta_l sin \phi = \dfrac{8 S_8 }{25} +\end{equation} + + + +\end{frame} +\begin{frame}\frametitle{Moments for $\PB \to \PKstar \mu \mu$} +{~} +\begin{itemize} +\item The simplest solution one could imagine. +\item We are abusing the fact that the basis is orthogonal. +\item Each of the J doesn't know about other. +\item Only $S_{1s}$, $S_{2s}$, $S_{1c}$, $S_{2c}$ and $S_{6s}$, $S_{6c}$ are not orthogonal, but to get the answer you just need to solve a linear equation system so it's not a tragedy. +\end{itemize} +\begin{equation} + \dfrac{d^3\Gamma}{\Gamma dcos\theta_k dcos\theta_l d\phi} sin^2 \theta_k cos \theta_l = 0.1(S_6c+4S_6s) +\end{equation} +\begin{equation} + \dfrac{d^3\Gamma}{\Gamma dcos\theta_k dcos\theta_l d\phi} cos \theta_l = 0.25(S_{6}c+2S_{6s}) +\end{equation} + +solution: $S_{6c}=2 (4 M_{S_{6c}} - 5 M_{S_{6s}})$, $S_{6s}= -2 M_{S_{6c}} + 5 M_{S_{6s}}$ + + + +\end{frame} + + + +\section{Toy MC study} + +\begin{frame}\frametitle{Moments for $\PB \to \PKstar \mu \mu$} +{~} +Lets see if this method actually works. Let's take some random parameters for the PDF and make a toy. +\begin{columns} +\column{2.5in} +\includegraphics[scale=0.25]{images/J5.png} + + + +\column{2.5in} +\includegraphics[scale=0.25]{images/J7.png} + + +\end{columns} +\begin{itemize} +\item let's take 300 signal events as a working case. +\end{itemize} + +\end{frame} + + + + +\begin{frame}\frametitle{Moments for $\PB \to \PKstar \mu \mu$} +{~} +\small Lets see if this method actually works. Let's take some random parameters for the PDF and make a toy. +\begin{columns} +\column{2.5in} +\includegraphics[scale=0.25]{images/J3.png} + + + +\column{2.5in} +\includegraphics[scale=0.25]{images/J4.png} + + +\end{columns} + + +\begin{itemize} +\item let's take 300 signal events as a working case... we might still change the binning +\end{itemize} + +\end{frame} + + + +\begin{frame}\frametitle{Moments for $\PB \to \PKstar \mu \mu$} +{~} +Lets see if this method actually works. Let's take some random parameters for the PDF and make a toy. +\begin{columns} +\column{2.5in} +\includegraphics[scale=0.25]{images/J8.png} + + + +\column{2.5in} +\includegraphics[scale=0.25]{images/J9.png} + + +\end{columns} + +\begin{itemize} +\item let's take 300 signal events as a working case... we might still change the binning +\end{itemize} + +\end{frame} + +\begin{frame}\frametitle{Error Estimation} +{~} +\begin{itemize} +\item Since moment is the mean of a given distribution the error can be estimated as $mean/RMS$ +\item use TOY MC to check this assumption +\end{itemize} + +\includegraphics[scale=0.3]{plots/conw.png}\\ + + +\end{frame} +%%%%%%%%%%%%%%%%%%%%%%%%5 +\begin{frame}\frametitle{Correlation check} +{~} +\begin{itemize} +\item In theory $S_i$ shouldn't be correlated to $S_j$ in the moment calculation. +\item Lets put this to a test. +\end{itemize} + +\begin{columns} +\column{2.5in} +\includegraphics[scale=0.2]{plots/J9J4.png}\\ + + +\column{2.5in} +\includegraphics[scale=0.2]{plots/J8J5.png}\\ + + +\end{columns} + + +\end{frame} + + +%%%%%%%%%%%%%%%%%%%%%%%%5 +\begin{frame}\frametitle{Correlation check 2} +{~} +\begin{itemize} +\item Let's now FIX $J_x$ and simulate different $J_y$ +\item Again theory would suggest that one J shouldn't know about the other, so $J_x$ shouldn't change with scanning $J_y$ parameter +\end{itemize} + +\begin{columns} +\column{2.5in} +\includegraphics[scale=0.24]{plots/J5_vs_J9_300.png}\\ + + +\column{2.5in} +\includegraphics[scale=0.24]{plots/J3_vs_J9_300.png}\\ + + +\end{columns} + + +\end{frame} + + + +\section{2 am discovery} +\begin{frame}\frametitle{What will happen to our problem with an S-wave?} +{~} +Reminder: +\begin{multline} +\dfrac{d^4\Gamma}{dq^2 dcos\theta_k dcos\theta_l d\phi}=\dfrac{9}{32\pi}( J_{1s}sin^2 \theta_k + J_{1c}cos^2 \theta_k + (J_{2s}sin^2 \theta_k + \\ J_{2c}cos^2) cos 2\theta_l + J_3 sin^2 \theta_k sin^2 \theta_l cos2\phi + J_4 sin2 \theta_k sin \theta_l cos\phi +\\ J_5 sin2 \theta_k sin \theta_l cos \phi + (J_{6s} sin^2 \theta_k + J_{6c} cos^2 \theta_k) cos \theta_l + \\ J_7 sin 2\theta_k sin \theta_l sin \phi + J_8 sin 2 \theta_k sin 2 \theta_l sin phi + J_9 sin^2 \theta_k sin^2 \theta_l sin 2 \phi) +\end{multline} +Let's add a very discussing things that keeps us awake at night: +\begin{multline} +W_s =\dfrac{2}{3} F_s \sin^2 \theta_l + \frac{4}{3} A_s \sin^2 \theta_l \cos \theta_k + I_4 sin \theta_k sin 2 \theta_lcos \phi \\+ I_5 sin \theta_k sin \theta_l cos \phi + I_7 sin \theta_k sin \theta_l + sin \phi + I_8 sin \theta_k sin 2\theta_l sin\phi) +\end{multline} + + +\end{frame} + +\begin{frame}\frametitle{What will happen to our problem with an S-wave?} +{~} +So now our PDF is sum of eq. 15 and 16. Of coz we need to require normalization: +\begin{equation} +\dfrac{1}{12}(32 I_{1a} + 9 J_{1c} + 18 J_{1s} - 3 J_{2c} - 6 J_{2s}) =1 +\end{equation} +No surprises here. If we have a S-wave it has to enter in $\Gamma$. +To build up the preasure, what will happen to our Ss? + + + +\end{frame} + + +\begin{frame}\frametitle{NOTHING!!!!!!!!} +{~} +We are completely insensitive to S-wave: +\begin{equation} + \dfrac{d^3\Gamma}{\Gamma dcos\theta_k dcos\theta_l d\phi }sin^2 \theta_k sin^2 \theta_l cos 2 \phi= \dfrac{8 S_3 }{25} +\end{equation} +\begin{equation} + \dfrac{d^3\Gamma}{\Gamma dcos\theta_k dcos\theta_l d\phi } sin 2 \theta_k sin 2 \theta_k cos\phi= \dfrac{8 S_4 }{25} +\end{equation} +\begin{equation} + \dfrac{d^3\Gamma}{\Gamma dcos\theta_k dcos\theta_l d\phi }sin2\theta_k sin\theta_l cos\phi = \dfrac{2 S_5 }{5} +\end{equation} +\begin{equation} + \dfrac{d^3\Gamma}{\Gamma dcos\theta_k dcos\theta_l d\phi} sin 2 \theta_k sin \theta_l sin \phi = \dfrac{2 S_7 }{5} +\end{equation} +\begin{equation} + \dfrac{d^3\Gamma}{\Gamma dcos\theta_k dcos\theta_l d\phi} sin 2 \theta_k sin2 \theta_l sin \phi = \dfrac{8 S_8 }{25} +\end{equation} + + + +\end{frame} + +\begin{frame}\frametitle{Thins get better :)} +{~} +We can even measure directly the S-wave: +\begin{equation} + \dfrac{d^3\Gamma}{\Gamma dcos\theta_k dcos\theta_l d\phi }sin^2 \theta_l cos \theta_k = \dfrac{32 I_{1b} }{45} +\end{equation} +\begin{equation} + \dfrac{d^3\Gamma}{\Gamma dcos\theta_k dcos\theta_l d\phi } sin \theta_k sin 2 \theta_l cos \phi = \dfrac{16 I_4 }{45} +\end{equation} +\begin{equation} + \dfrac{d^3\Gamma}{\Gamma dcos\theta_k dcos\theta_l d\phi } sin\theta_k sin\theta_l cos\phi = \dfrac{4 I_5 }{9} +\end{equation} +\begin{equation} + \dfrac{d^3\Gamma}{\Gamma dcos\theta_k dcos\theta_l d\phi} sin \theta_k sin 2 \theta_l sin \phi = \dfrac{4 I_7 }{9} +\end{equation} +\begin{equation} + \dfrac{d^3\Gamma}{\Gamma dcos\theta_k dcos\theta_l d\phi} sin \theta_k sin2 \theta_l sin \phi = \dfrac{16 S_8 }{45} +\end{equation} + + + +\end{frame} + + +\begin{frame}\frametitle{Conclusions on S-wave} +{~} +\begin{itemize} +\item S-wave components are transparent to method of moments. +\item If they are orthogonal to others all they toy studies holds for them as well(will reapat for robustness but can bet my house that there is nothing going on there). +\item +\end{itemize} + +\end{frame} + + + +\begin{frame}\frametitle{Conclusions} +{~} +\begin{itemize} +\item Implemented moments method for the K*mm and start testing with toy MC +\item The method converge fast and works for the "simple case", i.e. signal only. +\item Method completely insensitive to S-wave component, thanks to orthogonality. +\item Complementary one can measure in-depended S-wave component. +\end{itemize} +TO DO: +\begin{itemize} +\item add realism: backgrounds +\item Do the unfolding +\item Study binning +\end{itemize} + +\end{frame} +%%%%%%%%%%%%%%%%%%%%%%%%%55 +\begin{frame}\frametitle{~} +{~} +\center \Huge BACKUPS + +\end{frame} + +\begin{frame} +{~} + +\begin{columns} +\column{2.5in} +\includegraphics[scale=0.17]{plots/pool_plots/J1c_50.png}\\ +\includegraphics[scale=0.17]{plots/pool_plots/J1c_75.png}\\ + + +\column{2.5in} +\includegraphics[scale=0.17]{plots/pool_plots/J1c_50E.png}\\ +\includegraphics[scale=0.17]{plots/pool_plots/J1c_75E.png} + + +\end{columns} +\end{frame} + +\begin{frame} +{~} + +\begin{columns} +\column{2.5in} +\includegraphics[scale=0.17]{plots/pool_plots/J1c_125.png}\\ +\includegraphics[scale=0.17]{plots/pool_plots/J1c_175.png}\\ + + +\column{2.5in} +\includegraphics[scale=0.17]{plots/pool_plots/J1c_125E.png}\\ +\includegraphics[scale=0.17]{plots/pool_plots/J1c_175E.png} + + +\end{columns} +\end{frame} + +\begin{frame} +{~} + +\begin{columns} +\column{2.5in} +\includegraphics[scale=0.17]{plots/pool_plots/J1c_225.png}\\ +\includegraphics[scale=0.17]{plots/pool_plots/J1c_300.png}\\ + + +\column{2.5in} +\includegraphics[scale=0.17]{plots/pool_plots/J1c_225E.png}\\ +\includegraphics[scale=0.17]{plots/pool_plots/J1c_300E.png} + + +\end{columns} +\end{frame} + + +\begin{frame} +{~} + +\begin{columns} +\column{2.5in} +\includegraphics[scale=0.17]{plots/pool_plots/J1c_400.png}\\ + + + +\column{2.5in} +\includegraphics[scale=0.17]{plots/pool_plots/J1c_400E.png}\\ + + + +\end{columns} +\end{frame} + +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%55 +\begin{frame} +{~} + +\begin{columns} +\column{2.5in} +\includegraphics[scale=0.17]{plots/pool_plots/J1s_50.png}\\ +\includegraphics[scale=0.17]{plots/pool_plots/J1s_75.png}\\ + + +\column{2.5in} +\includegraphics[scale=0.17]{plots/pool_plots/J1s_50E.png}\\ +\includegraphics[scale=0.17]{plots/pool_plots/J1s_75E.png} + + +\end{columns} +\end{frame} + +\begin{frame} +{~} + +\begin{columns} +\column{2.5in} +\includegraphics[scale=0.17]{plots/pool_plots/J1s_125.png}\\ +\includegraphics[scale=0.17]{plots/pool_plots/J1s_175.png}\\ + + +\column{2.5in} +\includegraphics[scale=0.17]{plots/pool_plots/J1s_125E.png}\\ +\includegraphics[scale=0.17]{plots/pool_plots/J1s_175E.png} + + +\end{columns} +\end{frame} + +\begin{frame} +{~} + +\begin{columns} +\column{2.5in} +\includegraphics[scale=0.17]{plots/pool_plots/J1s_225.png}\\ +\includegraphics[scale=0.17]{plots/pool_plots/J1s_300.png}\\ + + +\column{2.5in} +\includegraphics[scale=0.17]{plots/pool_plots/J1s_225E.png}\\ +\includegraphics[scale=0.17]{plots/pool_plots/J1s_300E.png} + + +\end{columns} +\end{frame} + + +\begin{frame} +{~} + +\begin{columns} +\column{2.5in} +\includegraphics[scale=0.17]{plots/pool_plots/J1s_400.png}\\ + + + +\column{2.5in} +\includegraphics[scale=0.17]{plots/pool_plots/J1s_400E.png}\\ + + + +\end{columns} +\end{frame} + +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +\begin{frame} +{~} + +\begin{columns} +\column{2.5in} +\includegraphics[scale=0.17]{plots/pool_plots/J2c_50.png}\\ +\includegraphics[scale=0.17]{plots/pool_plots/J2c_75.png}\\ + + +\column{2.5in} +\includegraphics[scale=0.17]{plots/pool_plots/J2c_50E.png}\\ +\includegraphics[scale=0.17]{plots/pool_plots/J2c_75E.png} + + +\end{columns} +\end{frame} + +\begin{frame} +{~} + +\begin{columns} +\column{2.5in} +\includegraphics[scale=0.17]{plots/pool_plots/J2c_125.png}\\ +\includegraphics[scale=0.17]{plots/pool_plots/J2c_175.png}\\ + + +\column{2.5in} +\includegraphics[scale=0.17]{plots/pool_plots/J2c_125E.png}\\ +\includegraphics[scale=0.17]{plots/pool_plots/J2c_175E.png} + + +\end{columns} +\end{frame} + +\begin{frame} +{~} + +\begin{columns} +\column{2.5in} +\includegraphics[scale=0.17]{plots/pool_plots/J2c_225.png}\\ +\includegraphics[scale=0.17]{plots/pool_plots/J2c_300.png}\\ + + +\column{2.5in} +\includegraphics[scale=0.17]{plots/pool_plots/J2c_225E.png}\\ +\includegraphics[scale=0.17]{plots/pool_plots/J2c_300E.png} + + +\end{columns} +\end{frame} + + +\begin{frame} +{~} + +\begin{columns} +\column{2.5in} +\includegraphics[scale=0.17]{plots/pool_plots/J2c_400.png}\\ +\includegraphics[scale=0.17]{plots/pool_plots/J2c_500.png}\\ + + +\column{2.5in} +\includegraphics[scale=0.17]{plots/pool_plots/J2c_400E.png}\\ +\includegraphics[scale=0.17]{plots/pool_plots/J2c_500E.png}\\ + + +\end{columns} +\end{frame} + + +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +\begin{frame} +{~} + +\begin{columns} +\column{2.5in} +\includegraphics[scale=0.17]{plots/pool_plots/J3_50.png}\\ +\includegraphics[scale=0.17]{plots/pool_plots/J3_75.png}\\ + + +\column{2.5in} +\includegraphics[scale=0.17]{plots/pool_plots/J3_50E.png}\\ +\includegraphics[scale=0.17]{plots/pool_plots/J3_75E.png} + + +\end{columns} +\end{frame} + +\begin{frame} +{~} + +\begin{columns} +\column{2.5in} +\includegraphics[scale=0.17]{plots/pool_plots/J3_125.png}\\ +\includegraphics[scale=0.17]{plots/pool_plots/J3_175.png}\\ + + +\column{2.5in} +\includegraphics[scale=0.17]{plots/pool_plots/J3_125E.png}\\ +\includegraphics[scale=0.17]{plots/pool_plots/J3_175E.png} + + +\end{columns} +\end{frame} + +\begin{frame} +{~} + +\begin{columns} +\column{2.5in} +\includegraphics[scale=0.17]{plots/pool_plots/J3_225.png}\\ +\includegraphics[scale=0.17]{plots/pool_plots/J3_300.png}\\ + + +\column{2.5in} +\includegraphics[scale=0.17]{plots/pool_plots/J3_225E.png}\\ +\includegraphics[scale=0.17]{plots/pool_plots/J3_300E.png} + + +\end{columns} +\end{frame} + + +\begin{frame} +{~} + +\begin{columns} +\column{2.5in} +\includegraphics[scale=0.17]{plots/pool_plots/J3_400.png}\\ +\includegraphics[scale=0.17]{plots/pool_plots/J3_500.png}\\ + + +\column{2.5in} +\includegraphics[scale=0.17]{plots/pool_plots/J3_400E.png}\\ +\includegraphics[scale=0.17]{plots/pool_plots/J3_500E.png}\\ + + +\end{columns} +\end{frame} + + + +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +\begin{frame} +{~} + +\begin{columns} +\column{2.5in} +\includegraphics[scale=0.17]{plots/pool_plots/J4_50.png}\\ +\includegraphics[scale=0.17]{plots/pool_plots/J4_75.png}\\ + + +\column{2.5in} +\includegraphics[scale=0.17]{plots/pool_plots/J4_50E.png}\\ +\includegraphics[scale=0.17]{plots/pool_plots/J4_75E.png} + + +\end{columns} 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+\newcommand\abs[1]{\left|#1\right|} +\usepackage{hepnicenames} +\usepackage{hepunits} +\usepackage{color} + + + +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%5 +\definecolor{mygreen}{cmyk}{0.82,0.11,1,0.25} + + +\usetheme{Sybila} + +\title[Unfolding for counting experiments]{Unfolding for counting experiments} +\author{Marcin Chrz\k{a}szcz$^{1,2}$, Nicola Serra$^{1}$} +\institute{$^1$~University of Zurich,\\ $^2$~Institute of Nuclear Physics, Krakow} +\date{\today} + +\begin{document} +% --------------------------- SLIDE -------------------------------------------- +\frame[plain]{\titlepage} +\author{Marcin Chrz\k{a}szcz} +% ------------------------------------------------------------------------------ +% --------------------------- SLIDE -------------------------------------------- + +\begin{frame}\frametitle{Quo vadis $\PBzero \to \PKstar \mu \mu$?} + +\center \includegraphics[width=0.8\paperwidth]{diagram.png}\\ + +\end{frame} +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +\begin{frame}\frametitle{Quo vadis $\PBzero \to \PKstar \mu \mu$?} + +\center \includegraphics[width=0.8\paperwidth]{matrix.png}\\ + +\end{frame} + + +\section{Introduction} + +\begin{frame}\frametitle{Reminder} +For now: +\begin{itemize} +\item We have proven that there has to exists unfolding matrix. +\item Shown how to construct transformation matrix: $Gen \to Reco$. +\item Inverting it we can have transformation matrix of $Reco \to Gen$. +\item For details: \href{https://indico.cern.ch/event/316905/session/1/contribution/18/material/slides/0.pdf}{LINK} + +\end{itemize} + +What is missing? +\begin{columns} +\column{1in} +\begin{enumerate} +\item ERROR! +\end{enumerate} +\column{4in} +\includegraphics[width=0.8\textwidth]{err.jpg}\\ +\end{columns} + +\end{frame} + + + +\begin{frame}\frametitle{How to?} +\begin{itemize} +\item So lets say that transformation matrix:$Gen \to Reco$ is $\epsilon_{i,j}$. +\item Of coz it's easy to write the covariance matrix(error matrix): +\end{itemize} +\begin{equation} +cov(\epsilon_{\alpha, \beta},\epsilon_{a,b}) +\end{equation} +\begin{itemize} +\item Then we can calculate the matrix: $\epsilon_{i,j}^{-1}$(assuming it exists). +\item and the 1M dollar question is: $cov(\epsilon_{\alpha, \beta}^{-1},\epsilon_{a,b}^{-1}) =?$ +\end{itemize} + +\end{frame} + +\begin{frame}\frametitle{Answer to 1M dolar quesion} +\begin{itemize} +\item Solution comes from $\tau$ physics :) +\end{itemize} +\begin{equation} +cov(\epsilon_{\alpha, \beta}^{-1},\epsilon_{a,b}^{-1}) = \epsilon^{-1}_{\alpha,i} \epsilon^{-1}_{j,\beta} \epsilon^{-1}_{a,k} \epsilon^{-1}_{l,b} cov( \epsilon_{ij} \epsilon_{kl}) +\end{equation} +\begin{itemize} +\item It's way to late to latex the prove. For prove see: \href{http://arxiv.org/abs/hep-ex/9909031}{arXiv:hep-ex/9909031} +\item Thanks to orthonormal basis lifes gets simpler: +\end{itemize} +\begin{equation} +cov(\epsilon_{ij},\epsilon_{kl} ) = \sigma_{\epsilon,ij} \delta_{ik} \delta_{jl} ( no correlations) +\end{equation} + +\end{frame} + + +\begin{frame}\frametitle{Total error} +\begin{itemize} +\item So let's say: $B=\epsilon^{-1} f$ +\item Then: +\end{itemize} +\begin{equation} +cov(B_i,B_j) = f_a f_b cov(\epsilon_{i \alpha }^{-1} , \epsilon_{j \beta}^{-1} )+ \epsilon^{-1}_{ ik} \epsilon^{-1}_{jl} cov(f_k,f_l) +\end{equation} +\begin{itemize} +\item Looks easy just need to implement! +\end{itemize} + +\end{frame} + + +\begin{frame}\frametitle{Matrix, $0.1-0.98~GeV$} +\tiny{ +$ A_{reco\rightarrow gen}=\begin{pmatrix} + 0.9495 0.008518 0.01522 -0.007362 0.01496 -0.04544 -0.02468 0.002078 + 0.0002651 0.8261 0.00978 -0.001042 0.004382 0.03191 0.01247 0.01886 + -0.0003391 0.009773 1.03 0.008433 -0.002028 0.003 0.02086 0.001549 + -0.00403 -0.001336 0.01047 0.9215 0.006898 -0.0006023 0.003041 -0.004465 + 0.006557 0.005531 -0.002423 0.00691 1.171 -0.01082 -0.0158 -0.003231 + -0.01931 0.03973 0.00342 -0.0006455 -0.01081 0.9452 0.02232 -0.005304 + .008421 0.0124 0.02071 0.002415 -0.01264 0.01785 1.06 0.001084 + 0.000347 0.01886 0.001555 -0.003568 -0.002591 -0.004226 0.001093 0.8204 + + + + + \end{pmatrix}$ +} + + + + + +\end{frame} + +\begin{frame}\frametitle{Constructing Matrix unfolding} +\begin{itemize} +\item We got first column of the unfolding matrix. +\end{itemize} +\small{ +$ \begin{pmatrix} + 1.06 & \cdots & a_{1,8} \\ + 0.01157 & \cdots & a_{2,8} \\ + -0.003547 & \ddots & \vdots \\ + 0.0007841 & \ddots & \vdots \\ + 0.001126 & \ddots & \vdots \\ + 0.001766 & \ddots & \vdots \\ + 0.001664 & \ddots & \vdots \\ + -0.001937 & \cdots & a_{8,8} + \end{pmatrix}$ + + +} +\begin{itemize} +\item How about the others? +\item We can reweight accordingly to $f_x$. +\end{itemize} + +\end{frame} + +\begin{frame}\frametitle{Constructing Matrix unfolding} +\begin{itemize} +\item To get $S_3$ each event $i^{th}$ has has weight $f_{S_3}(\cos \theta_{k_i},\cos \theta_{l_i},\phi_i) $ +\item One can calculate on MC the reweighed moments in PHPS: +\end{itemize} +\begin{equation} +\int PDF*f_{S_3}=\dfrac{32}{225} +\end{equation} +\begin{itemize} +\item Our base vector now is:$v^{T}_{gen}=(0 ,\frac{32}{225},0,0,0,0,0,0)$ +\item So lets see what do we get as reconstructed vector(after multiplying by $\frac{225}{32}$. +\small{$v^{T}_{rec}=( 0.042, 1.105,-0.005,0.003,-0.0023,-0.005,-0.005,-0.006)$ } +\end{itemize} + +\end{frame} + + +\begin{frame}\frametitle{Constructing Matrix unfolding} +\begin{itemize} +\item Now the matrix looks like: +\end{itemize} +\small{ +$ \begin{pmatrix} + 1.06 & 0.042 & \cdots & a_{1,8} \\ + 0.01157 & 1.105 & \cdots & a_{2,8} \\ + -0.003547 & -0.005 & \ddots & \vdots \\ + 0.0007841 &-0.005 & \ddots & \vdots \\ + 0.001126 & 0.003 &\ddots & \vdots \\ + 0.001766 & -0.0023 &\ddots & \vdots \\ + 0.001664 & -0.005 &\ddots & \vdots \\ + -0.001937 & -0.006 &\cdots & a_{8,8} + \end{pmatrix}$ + + +} +\begin{itemize} +\item The others go in the same way. +\item Repenting this exercise from $1^{st}$ year algebra we can get the full matrix +\end{itemize} + + +\end{frame} +\begin{frame}\frametitle{Constructing Matrix unfolding} +\begin{itemize} +\item The full transformation matrix from generator space to reconstructed space: +\end{itemize} +\tiny{ +$ A_{gen\rightarrow reco}=\begin{pmatrix} + 1.06 & 0.0423 & -0.0081 & 0.0022 & 0.0049 & 0.0037 & 0.0028 & -0.0065 \\ + + 0.0115 & 1.105 & -0.0050 & 0.0027 & -0.0018 & -0.0040 &-0.0054 & -0.0065 \\ + -0.0035 & -0.0050 & 0.981 & 0.0005 & -0.0025 & 0.0002 & -0.0037 & -0.0048\\ + 0.00078 & 0.0034 & 0.0006 & 1.002 & -0.0032 & -0.0040 & 0.0003 & 0.0018\\ + 0.001126 & -0.0023 & -0.0032 & -0.0032 & 1.055 & 0.001& -0.004 & 0.0023\\ + 0.00176 & -0.0050 & 0.00036 & -0.0040 & 0.0011 & 0.96 & -0.0057 & 0.0009 \\ + 0.0016 & -0.005 & -0.003 & 0.00029& -0.003 &-0.004 & 0.9543 & 0.0000\\ + -0.0019 & -0.0065 & -0.004 & 0.001 & 0.0018 & 0.0007 & 0.000 & 1.098 \\ + + + + + + \end{pmatrix}$ + + +} +\begin{itemize} +\item Inverting the matrix is simple, and doable +\end{itemize} +\tiny{ +$ A_{reco\rightarrow gen}=\begin{pmatrix} + 0.9434 & -0.036 & 0.007& -0.0020 & -0.0044& -0.0038 & -0.0030 & 0.0054\\ + -0.009 & 0.90 & 0.0045 & -0.0024& 0.0016 & 0.003873 & 0.00527& 0.005 \\ + 0.003 & 0.00454& 1.019 & -0.00058 & 0.0025& -0.000291 & 0.004 & 0.004 \\ +-0.00071 & -0.0030 & -0.0007 & 0.9977 & 0.0030 & 0.004206 &-0.0003 & -0.0017 \\ + -0.001 & 0.0020 & 0.0031& 0.0030 & 0.9483 & -0.0010 & 0.004626 & -0.0019 \\ + -0.001 & 0.004 & -0.0003 & 0.0042 & -0.001087 & 1.037 & 0.0063 & -0.0009\\ + -0.0017 & 0.0053 & 0.0042 & -0.0002 & 0.00370& 0.0050 & 1.048 & 0.0000 \\ + 0.0016& 0.0053& 0.00452 & -0.001 & -0.001582 & -0.0007213 &0.000 & 0.9105 \\ + + + + + \end{pmatrix}$ +} + +\end{frame} + + + +\begin{frame}\frametitle{Sensitivity to unknowns} +\begin{itemize} +\item We are unfolding based on MC. +\item There are MC/Data differences, which can have impact on the unfolding. +\end{itemize} +Let's put small modification: +\begin{equation} +w_j \to \overline{w_j}= \dfrac{1}{eff(\cos \theta_{l~j}, \cos \theta_{k~j}, \phi_{j})} \times corr(\cos \theta_{l~j}, \cos \theta_{k~j}, \phi_{j}) +\end{equation} +Unfortunately God didn't allowed me sneak peak into his cards so I don't know $corr(\cos \theta_{l}, \cos \theta_{k}, \phi)$, but let's try out some functions and see what happens :) + + +\end{frame} + +\begin{frame}\frametitle{Corr1 functions} +\begin{columns} +\column{2in} +\includegraphics[width=\linewidth]{corr/Corr1_cosk.png}\\ +\includegraphics[width=\linewidth]{corr/Corr1_cosl.png}\\ +\column{2.5in} +$ +corr1(\cos_l, \cos_k,\phi)= 1+ 0.032 \cos_l - 0.032 \cos_k + 0.01 \phi +$ +\includegraphics[width=0.8\linewidth]{corr/Corr1_phi.png}\\ + +\end{columns} + +\end{frame} +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +\begin{frame}\frametitle{Corr2 functions} +\begin{columns} +\column{2in} +\includegraphics[width=0.85\linewidth]{corr/corr21.png}\\ +\includegraphics[width=0.85\linewidth]{corr/corr22.png}\\ +\column{2.5in} +$ +corr2(\cos_l, \cos_k,\phi)= -0.02 \cos_l^2 + 0.02 \cos_k^2 - + 0.015 \phi^2+ 1 +$ +\includegraphics[width=0.75\linewidth]{corr/corr23.png}\\ + +\end{columns} + +\end{frame} + +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +\begin{frame}\frametitle{Corr3 functions} +\begin{columns} +\column{2in} +\includegraphics[width=0.85\linewidth]{corr/corr31.png}\\ +\includegraphics[width=0.85\linewidth]{corr/corr32.png}\\ +\column{2.5in} +$ +corr3(\cos_l, \cos_k,\phi)= 0.02 \cos_l \cos_k + 0.01 \cos_k \phi - 0.01 \phi \cos_l + 1 +$ +\includegraphics[width=0.75\linewidth]{corr/corr33.png}\\ + +\end{columns} + +\end{frame} +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +\begin{frame}\frametitle{Corr4 functions} +\begin{columns} +\column{2in} +\includegraphics[width=0.85\linewidth]{corr/corr41.png}\\ +\includegraphics[width=0.85\linewidth]{corr/corr42.png}\\ +\column{2.5in} +$ +corr3(\cos_l, \cos_k,\phi)= 0.01 \cos_k \cos_l \phi + 1 +$ +\includegraphics[width=0.75\linewidth]{corr/corr43.png}\\ + +\end{columns} + +\end{frame} + + + + +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% + + +\begin{frame}\frametitle{Corr1- MM} + + +\begin{tiny} + +\begin{center} + \begin{tabular}{ l l l l l l l l l } + \hline + \multicolumn{8}{c}{Mean of the pull} \\ \hline +$q^2$ & $S_3$ & $S_4$ & $S_5$ & $S_{6s}$ & $S_{6c}$ & $S_7$ & $S_8$ \\ \hline \hline + +0 & \scalebox{0.5}{$0.0085 \pm 0.026(0.3)$} & \scalebox{0.5}{$0.13 \pm 0.027(4.6)$} & \scalebox{0.5}{$-0.025 \pm 0.027(-0.92)$} & \scalebox{0.5}{$0.46 \pm 0.027(17)$} & \scalebox{0.5}{$-0.13 \pm 0.028(-4.7)$} & \scalebox{0.5}{$0.029 \pm 0.028(1)$} & \scalebox{0.5}{$-0.66 \pm 0.027(-25)$} \\ \hline +1 & \scalebox{0.5}{$0.0094 \pm 0.028(0.33)$} & \scalebox{0.5}{$0.078 \pm 0.028(2.8)$} & \scalebox{0.5}{$-0.02 \pm 0.028(-0.73)$} & \scalebox{0.5}{$0.24 \pm 0.028(8.5)$} & \scalebox{0.5}{$-0.075 \pm 0.028(-2.7)$} & \scalebox{0.5}{$-0.016 \pm 0.026(-0.63)$} & \scalebox{0.5}{$-0.39 \pm 0.028(-14)$} \\ \hline +2 & \scalebox{0.5}{$-0.02 \pm 0.027(-0.72)$} & \scalebox{0.5}{$0.027 \pm 0.026(1)$} & \scalebox{0.5}{$-0.024 \pm 0.027(-0.91)$} & \scalebox{0.5}{$0.18 \pm 0.027(6.8)$} & \scalebox{0.5}{$-0.024 \pm 0.027(-0.89)$} & \scalebox{0.5}{$-0.067 \pm 0.027(-2.5)$} & \scalebox{0.5}{$-0.39 \pm 0.028(-14)$} \\ \hline +3 & \scalebox{0.5}{$0.013 \pm 0.028(0.46)$} & \scalebox{0.5}{$-0.0089 \pm 0.027(-0.32)$} & \scalebox{0.5}{$0.055 \pm 0.026(2.1)$} & \scalebox{0.5}{$0.12 \pm 0.027(4.7)$} & \scalebox{0.5}{$0.11 \pm 0.027(3.9)$} & \scalebox{0.5}{$-0.018 \pm 0.028(-0.63)$} & \scalebox{0.5}{$-0.43 \pm 0.027(-16)$} \\ \hline +4 & \scalebox{0.5}{$-0.0054 \pm 0.029(-0.18)$} & \scalebox{0.5}{$-0.066 \pm 0.027(-2.4)$} & \scalebox{0.5}{$0.037 \pm 0.028(1.3)$} & \scalebox{0.5}{$0.22 \pm 0.027(8.1)$} & \scalebox{0.5}{$0.099 \pm 0.027(3.7)$} & \scalebox{0.5}{$-0.1 \pm 0.026(-3.8)$} & \scalebox{0.5}{$-0.41 \pm 0.026(-15)$} \\ \hline +5 & \scalebox{0.5}{$0.06 \pm 0.027(2.2)$} & \scalebox{0.5}{$-0.069 \pm 0.026(-2.6)$} & \scalebox{0.5}{$-0.013 \pm 0.028(-0.49)$} & \scalebox{0.5}{$0.21 \pm 0.027(7.8)$} & \scalebox{0.5}{$0.093 \pm 0.027(3.5)$} & \scalebox{0.5}{$-0.083 \pm 0.028(-3)$} & \scalebox{0.5}{$-0.41 \pm 0.028(-15)$} \\ \hline +6 & \scalebox{0.5}{$0.0064 \pm 0.026(0.25)$} & \scalebox{0.5}{$-0.051 \pm 0.027(-1.9)$} & \scalebox{0.5}{$-0.029 \pm 0.028(-1)$} & \scalebox{0.5}{$0.26 \pm 0.028(9.2)$} & \scalebox{0.5}{$0.14 \pm 0.027(5.1)$} & \scalebox{0.5}{$-0.081 \pm 0.027(-3)$} & \scalebox{0.5}{$-0.45 \pm 0.028(-16)$} \\ \hline +%7 & \scalebox{0.5}{$0.22 \pm 0.027(8)$} & \scalebox{0.5}{$-0.34 \pm 0.028(-12)$} & \scalebox{0.5}{$-0.43 \pm 0.026(-16)$} & \scalebox{0.5}{$2.4 \pm 0.029(82)$} & \scalebox{0.5}{$0.66 \pm 0.027(24)$} & \scalebox{0.5}{$-0.24 \pm 0.028(-8.6)$} & \scalebox{0.5}{$-0.51 \pm 0.027(-19)$} & +8 & \scalebox{0.5}{$0.023 \pm 0.027(0.85)$} & \scalebox{0.5}{$-0.031 \pm 0.028(-1.1)$} & \scalebox{0.5}{$0.0042 \pm 0.028(0.15)$} & \scalebox{0.5}{$0.21 \pm 0.026(7.8)$} & \scalebox{0.5}{$0.12 \pm 0.028(4.2)$} & \scalebox{0.5}{$-0.13 \pm 0.027(-4.8)$} & \scalebox{0.5}{$-0.48 \pm 0.026(-18)$} \\ \hline +9 & \scalebox{0.5}{$-0.017 \pm 0.027(-0.63)$} & \scalebox{0.5}{$-0.015 \pm 0.026(-0.56)$} & \scalebox{0.5}{$-0.0052 \pm 0.026(-0.2)$} & \scalebox{0.5}{$0.27 \pm 0.027(10)$} & \scalebox{0.5}{$0.046 \pm 0.026(1.7)$} & \scalebox{0.5}{$-0.12 \pm 0.026(-4.4)$} & \scalebox{0.5}{$-0.5 \pm 0.026(-19)$} \\ \hline +10 & \scalebox{0.5}{$-0.054 \pm 0.027(-2)$} & \scalebox{0.5}{$-0.056 \pm 0.026(-2.2)$} & \scalebox{0.5}{$0.036 \pm 0.026(1.4)$} & \scalebox{0.5}{$0.16 \pm 0.028(5.7)$} & \scalebox{0.5}{$0.077 \pm 0.028(2.8)$} & \scalebox{0.5}{$-0.034 \pm 0.027(-1.3)$} & \scalebox{0.5}{$-0.39 \pm 0.028(-14)$} \\ \hline +11 & \scalebox{0.5}{$0.023 \pm 0.027(0.88)$} & \scalebox{0.5}{$0.021 \pm 0.027(0.8)$} & \scalebox{0.5}{$-0.011 \pm 0.027(-0.41)$} & \scalebox{0.5}{$0.14 \pm 0.027(5)$} & \scalebox{0.5}{$0.042 \pm 0.027(1.6)$} & \scalebox{0.5}{$-0.098 \pm 0.028(-3.5)$} & \scalebox{0.5}{$-0.3 \pm 0.027(-11)$} \\ \hline + + + \hline + + + \end{tabular} + +\end{center} + + +\end{tiny} +\end{frame} + +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% + + +\begin{frame}\frametitle{Corr2- MM} + + +\begin{tiny} + +\begin{center} + \begin{tabular}{ l l l l l l l l l } + \hline + \multicolumn{8}{c}{Mean of the pull} \\ \hline +$q^2$ & $S_3$ & $S_4$ & $S_5$ & $S_{6s}$ & $S_{6c}$ & $S_7$ & $S_8$ \\ \hline \hline + +0 & \scalebox{0.5}{$-0.21 \pm 0.026(-8.1)$} & \scalebox{0.5}{$0.061 \pm 0.026(2.3)$} & \scalebox{0.5}{$-0.016 \pm 0.026(-0.63)$} & \scalebox{0.5}{$0.048 \pm 0.026(1.8)$} & \scalebox{0.5}{$-0.0062 \pm 0.027(-0.23)$} & \scalebox{0.5}{$-0.012 \pm 0.028(-0.44)$} & \scalebox{0.5}{$0.0091 \pm 0.026(0.36)$} \\ \hline +1 & \scalebox{0.5}{$-0.12 \pm 0.028(-4.5)$} & \scalebox{0.5}{$0.032 \pm 0.027(1.2)$} & \scalebox{0.5}{$-0.0071 \pm 0.026(-0.27)$} & \scalebox{0.5}{$0.02 \pm 0.027(0.75)$} & \scalebox{0.5}{$-0.086 \pm 0.027(-3.2)$} & \scalebox{0.5}{$-0.03 \pm 0.025(-1.2)$} & \scalebox{0.5}{$0.021 \pm 0.027(0.79)$} \\ \hline +2 & \scalebox{0.5}{$-0.15 \pm 0.027(-5.8)$} & \scalebox{0.5}{$-0.013 \pm 0.026(-0.49)$} & \scalebox{0.5}{$0.011 \pm 0.026(0.44)$} & \scalebox{0.5}{$-0.039 \pm 0.026(-1.5)$} & \scalebox{0.5}{$-0.032 \pm 0.027(-1.2)$} & \scalebox{0.5}{$-0.066 \pm 0.027(-2.5)$} & \scalebox{0.5}{$0.018 \pm 0.028(0.64)$} \\ \hline +3 & \scalebox{0.5}{$-0.15 \pm 0.027(-5.6)$} & \scalebox{0.5}{$0.025 \pm 0.026(0.96)$} & \scalebox{0.5}{$0.016 \pm 0.027(0.58)$} & \scalebox{0.5}{$-0.062 \pm 0.027(-2.3)$} & \scalebox{0.5}{$0.037 \pm 0.026(1.4)$} & \scalebox{0.5}{$0.026 \pm 0.027(0.96)$} & \scalebox{0.5}{$-0.016 \pm 0.027(-0.6)$} \\ \hline +4 & \scalebox{0.5}{$-0.12 \pm 0.028(-4.5)$} & \scalebox{0.5}{$-0.024 \pm 0.026(-0.92)$} & \scalebox{0.5}{$0.045 \pm 0.027(1.6)$} & \scalebox{0.5}{$0.0075 \pm 0.026(0.29)$} & \scalebox{0.5}{$0.015 \pm 0.027(0.53)$} & \scalebox{0.5}{$-0.036 \pm 0.026(-1.4)$} & \scalebox{0.5}{$0.037 \pm 0.026(1.4)$} \\ \hline +5 & \scalebox{0.5}{$-0.095 \pm 0.027(-3.6)$} & \scalebox{0.5}{$-0.032 \pm 0.026(-1.2)$} & \scalebox{0.5}{$0.014 \pm 0.026(0.52)$} & \scalebox{0.5}{$-0.013 \pm 0.026(-0.48)$} & \scalebox{0.5}{$-0.0093 \pm 0.027(-0.35)$} & \scalebox{0.5}{$-0.013 \pm 0.026(-0.51)$} & \scalebox{0.5}{$0.042 \pm 0.027(1.6)$} \\ \hline +6 & \scalebox{0.5}{$-0.17 \pm 0.025(-6.5)$} & \scalebox{0.5}{$0.008 \pm 0.027(0.3)$} & \scalebox{0.5}{$0.012 \pm 0.027(0.45)$} & \scalebox{0.5}{$0.029 \pm 0.027(1.1)$} & \scalebox{0.5}{$0.0072 \pm 0.027(0.27)$} & \scalebox{0.5}{$-0.0012 \pm 0.026(-0.046)$} & \scalebox{0.5}{$0.011 \pm 0.027(0.42)$} \\ \hline +%7 & \scalebox{0.5}{$0.078 \pm 0.026(3)$} & \scalebox{0.5}{$-0.3 \pm 0.026(-11)$} & \scalebox{0.5}{$-0.34 \pm 0.026(-13)$} & \scalebox{0.5}{$2.1 \pm 0.028(73)$} & \scalebox{0.5}{$0.47 \pm 0.026(18)$} & \scalebox{0.5}{$-0.17 \pm 0.027(-6.1)$} & \scalebox{0.5}{$0.0051 \pm 0.027(0.19)$} \\ \hline +8 & \scalebox{0.5}{$-0.13 \pm 0.026(-5.1)$} & \scalebox{0.5}{$-0.0077 \pm 0.027(-0.28)$} & \scalebox{0.5}{$0.05 \pm 0.027(1.9)$} & \scalebox{0.5}{$-0.03 \pm 0.026(-1.2)$} & \scalebox{0.5}{$-0.012 \pm 0.028(-0.44)$} & \scalebox{0.5}{$-0.046 \pm 0.026(-1.7)$} & \scalebox{0.5}{$0.031 \pm 0.026(1.2)$} \\ \hline +9 & \scalebox{0.5}{$-0.15 \pm 0.026(-5.7)$} & \scalebox{0.5}{$-0.0083 \pm 0.026(-0.32)$} & \scalebox{0.5}{$0.03 \pm 0.026(1.2)$} & \scalebox{0.5}{$0.044 \pm 0.027(1.6)$} & \scalebox{0.5}{$-0.07 \pm 0.026(-2.7)$} & \scalebox{0.5}{$-0.022 \pm 0.026(-0.84)$} & \scalebox{0.5}{$-0.045 \pm 0.026(-1.7)$} \\ \hline +10 & \scalebox{0.5}{$-0.15 \pm 0.025(-5.8)$} & \scalebox{0.5}{$-0.032 \pm 0.025(-1.3)$} & \scalebox{0.5}{$0.059 \pm 0.026(2.2)$} & \scalebox{0.5}{$-0.072 \pm 0.028(-2.6)$} & \scalebox{0.5}{$-0.029 \pm 0.027(-1.1)$} & \scalebox{0.5}{$0.064 \pm 0.027(2.4)$} & \scalebox{0.5}{$0.014 \pm 0.027(0.51)$} \\ \hline +11 & \scalebox{0.5}{$-0.067 \pm 0.026(-2.6)$} & \scalebox{0.5}{$0.017 \pm 0.026(0.65)$} & \scalebox{0.5}{$-0.015 \pm 0.026(-0.56)$} & \scalebox{0.5}{$-0.051 \pm 0.026(-1.9)$} & \scalebox{0.5}{$-0.0086 \pm 0.026(-0.33)$} & \scalebox{0.5}{$-0.018 \pm 0.028(-0.67)$} & \scalebox{0.5}{$0.017 \pm 0.027(0.62)$} \\ \hline + + + + + + +\hline + + + \end{tabular} + +\end{center} + + +\end{tiny} +\end{frame} + + +\begin{frame}\frametitle{Corr3- MM} + + +\begin{tiny} + +\begin{center} + \begin{tabular}{ l l l l l l l l l } + \hline + \multicolumn{8}{c}{Mean of the pull} \\ \hline +$q^2$ & $S_3$ & $S_4$ & $S_5$ & $S_{6s}$ & $S_{6c}$ & $S_7$ & $S_8$ \\ \hline \hline + +0 & \scalebox{0.5}{$-0.021 \pm 0.026(-0.81)$} & \scalebox{0.5}{$0.041 \pm 0.026(1.5)$} & \scalebox{0.5}{$0.009 \pm 0.027(0.34)$} & \scalebox{0.5}{$0.043 \pm 0.026(1.6)$} & \scalebox{0.5}{$0.13 \pm 0.028(4.8)$} & \scalebox{0.5}{$-0.0072 \pm 0.028(-0.26)$} & \scalebox{0.5}{$0.044 \pm 0.026(1.7)$} \\ \hline +1 & \scalebox{0.5}{$-0.014 \pm 0.028(-0.51)$} & \scalebox{0.5}{$0.03 \pm 0.027(1.1)$} & \scalebox{0.5}{$0.022 \pm 0.027(0.82)$} & \scalebox{0.5}{$0.015 \pm 0.028(0.53)$} & \scalebox{0.5}{$0.078 \pm 0.028(2.8)$} & \scalebox{0.5}{$-0.037 \pm 0.025(-1.4)$} & \scalebox{0.5}{$0.057 \pm 0.027(2.1)$} \\ \hline +2 & \scalebox{0.5}{$-0.037 \pm 0.027(-1.4)$} & \scalebox{0.5}{$-0.0013 \pm 0.027(-0.048)$} & \scalebox{0.5}{$-0.015 \pm 0.027(-0.54)$} & \scalebox{0.5}{$-0.052 \pm 0.026(-2)$} & \scalebox{0.5}{$0.1 \pm 0.027(3.8)$} & \scalebox{0.5}{$-0.051 \pm 0.026(-1.9)$} & \scalebox{0.5}{$0.022 \pm 0.028(0.78)$} \\ \hline +3 & \scalebox{0.5}{$-0.015 \pm 0.027(-0.55)$} & \scalebox{0.5}{$0.036 \pm 0.028(1.3)$} & \scalebox{0.5}{$-0.039 \pm 0.027(-1.4)$} & \scalebox{0.5}{$-0.072 \pm 0.027(-2.7)$} & \scalebox{0.5}{$0.17 \pm 0.027(6.2)$} & \scalebox{0.5}{$-0.0044 \pm 0.028(-0.15)$} & \scalebox{0.5}{$-0.024 \pm 0.027(-0.9)$} \\ \hline +4 & \scalebox{0.5}{$-0.00047 \pm 0.029(-0.017)$} & \scalebox{0.5}{$-0.012 \pm 0.027(-0.43)$} & \scalebox{0.5}{$0.0099 \pm 0.028(0.35)$} & \scalebox{0.5}{$-0.002 \pm 0.026(-0.076)$} & \scalebox{0.5}{$0.17 \pm 0.028(6.2)$} & \scalebox{0.5}{$-0.062 \pm 0.027(-2.3)$} & \scalebox{0.5}{$0.0086 \pm 0.027(0.32)$} \\ \hline + +5 & \scalebox{0.5}{$0.046 \pm 0.027(1.7)$} & \scalebox{0.5}{$-0.02 \pm 0.026(-0.76)$} & \scalebox{0.5}{$-0.04 \pm 0.027(-1.5)$} & \scalebox{0.5}{$-0.012 \pm 0.027(-0.44)$} & \scalebox{0.5}{$0.13 \pm 0.027(4.8)$} & \scalebox{0.5}{$-0.04 \pm 0.027(-1.5)$} & \scalebox{0.5}{$-0.0056 \pm 0.027(-0.21)$} \\ \hline +6 & \scalebox{0.5}{$-0.013 \pm 0.026(-0.52)$} & \scalebox{0.5}{$0.041 \pm 0.027(1.5)$} & \scalebox{0.5}{$-0.033 \pm 0.028(-1.2)$} & \scalebox{0.5}{$-0.0019 \pm 0.027(-0.068)$} & \scalebox{0.5}{$0.15 \pm 0.027(5.4)$} & \scalebox{0.5}{$-0.034 \pm 0.027(-1.3)$} & \scalebox{0.5}{$-0.021 \pm 0.028(-0.75)$} \\ \hline +%7 & \scalebox{0.5}{$0.25 \pm 0.027(9.1)$} & \scalebox{0.5}{$-0.27 \pm 0.027(-10)$} & \scalebox{0.5}{$-0.41 \pm 0.027(-16)$} & \scalebox{0.5}{$2.1 \pm 0.029(73)$} & \scalebox{0.5}{$0.65 \pm 0.027(24)$} & \scalebox{0.5}{$-0.19 \pm 0.028(-7)$} & \scalebox{0.5}{$-0.053 \pm 0.028(-1.9)$} \\ \hline +8 & \scalebox{0.5}{$0.039 \pm 0.026(1.5)$} & \scalebox{0.5}{$0.01 \pm 0.028(0.36)$} & \scalebox{0.5}{$-0.027 \pm 0.028(-0.96)$} & \scalebox{0.5}{$-0.024 \pm 0.026(-0.9)$} & \scalebox{0.5}{$0.12 \pm 0.027(4.3)$} & \scalebox{0.5}{$-0.092 \pm 0.026(-3.5)$} & \scalebox{0.5}{$-0.036 \pm 0.027(-1.3)$} \\ \hline +9 & \scalebox{0.5}{$-0.01 \pm 0.027(-0.38)$} & \scalebox{0.5}{$0.0024 \pm 0.027(0.09)$} & \scalebox{0.5}{$-0.018 \pm 0.026(-0.68)$} & \scalebox{0.5}{$0.022 \pm 0.028(0.79)$} & \scalebox{0.5}{$0.068 \pm 0.027(2.6)$} & \scalebox{0.5}{$-0.069 \pm 0.026(-2.6)$} & \scalebox{0.5}{$-0.078 \pm 0.026(-3)$} \\ \hline +10 & \scalebox{0.5}{$-0.017 \pm 0.027(-0.62)$} & \scalebox{0.5}{$-0.015 \pm 0.026(-0.57)$} & \scalebox{0.5}{$0.012 \pm 0.027(0.46)$} & \scalebox{0.5}{$-0.074 \pm 0.028(-2.6)$} & \scalebox{0.5}{$0.1 \pm 0.027(3.8)$} & \scalebox{0.5}{$-0.003 \pm 0.027(-0.11)$} & \scalebox{0.5}{$-0.043 \pm 0.029(-1.5)$} \\ \hline +11 & \scalebox{0.5}{$0.032 \pm 0.026(1.2)$} & \scalebox{0.5}{$0.024 \pm 0.026(0.91)$} & \scalebox{0.5}{$-0.04 \pm 0.026(-1.5)$} & \scalebox{0.5}{$-0.066 \pm 0.027(-2.5)$} & \scalebox{0.5}{$0.098 \pm 0.027(3.7)$} & \scalebox{0.5}{$-0.043 \pm 0.028(-1.6)$} & \scalebox{0.5}{$-0.0018 \pm 0.028(-0.064)$} \\ \hline + + + +\hline + + + \end{tabular} + +\end{center} + + +\end{tiny} +\end{frame} + +\begin{frame}\frametitle{Corr4- MM} + + +\begin{tiny} + +\begin{center} + \begin{tabular}{ l l l l l l l l l } + \hline + \multicolumn{8}{c}{Mean of the pull} \\ \hline +$q^2$ & $S_3$ & $S_4$ & $S_5$ & $S_{6s}$ & $S_{6c}$ & $S_7$ & $S_8$ \\ \hline \hline + + +0 & \scalebox{0.5}{$-0.019 \pm 0.026(-0.71)$} & \scalebox{0.5}{$0.048 \pm 0.027(1.8)$} & \scalebox{0.5}{$0.018 \pm 0.027(0.67)$} & \scalebox{0.5}{$0.059 \pm 0.027(2.2)$} & \scalebox{0.5}{$-0.015 \pm 0.028(-0.55)$} & \scalebox{0.5}{$0.061 \pm 0.027(2.2)$} & \scalebox{0.5}{$0.012 \pm 0.027(0.44)$} \\ \hline +1 & \scalebox{0.5}{$-0.014 \pm 0.028(-0.51)$} & \scalebox{0.5}{$0.043 \pm 0.027(1.6)$} & \scalebox{0.5}{$0.013 \pm 0.027(0.49)$} & \scalebox{0.5}{$0.024 \pm 0.028(0.86)$} & \scalebox{0.5}{$-0.038 \pm 0.028(-1.4)$} & \scalebox{0.5}{$0.024 \pm 0.026(0.94)$} & \scalebox{0.5}{$0.037 \pm 0.027(1.3)$} \\ \hline +2 & \scalebox{0.5}{$-0.03 \pm 0.027(-1.1)$} & \scalebox{0.5}{$-0.0021 \pm 0.027(-0.076)$} & \scalebox{0.5}{$-0.01 \pm 0.027(-0.39)$} & \scalebox{0.5}{$-0.017 \pm 0.027(-0.61)$} & \scalebox{0.5}{$-0.016 \pm 0.027(-0.58)$} & \scalebox{0.5}{$0.013 \pm 0.027(0.49)$} & \scalebox{0.5}{$0.027 \pm 0.028(0.98)$} \\ \hline +3 & \scalebox{0.5}{$-0.007 \pm 0.027(-0.26)$} & \scalebox{0.5}{$0.03 \pm 0.028(1.1)$} & \scalebox{0.5}{$-0.036 \pm 0.027(-1.3)$} & \scalebox{0.5}{$-0.074 \pm 0.027(-2.8)$} & \scalebox{0.5}{$0.041 \pm 0.027(1.5)$} & \scalebox{0.5}{$0.08 \pm 0.028(2.9)$} & \scalebox{0.5}{$-0.0083 \pm 0.027(-0.31)$} \\ \hline +4 & \scalebox{0.5}{$0.00089 \pm 0.029(0.031)$} & \scalebox{0.5}{$-0.021 \pm 0.027(-0.77)$} & \scalebox{0.5}{$0.0032 \pm 0.028(0.11)$} & \scalebox{0.5}{$0.0031 \pm 0.026(0.12)$} & \scalebox{0.5}{$0.012 \pm 0.027(0.44)$} & \scalebox{0.5}{$0.019 \pm 0.026(0.71)$} & \scalebox{0.5}{$0.034 \pm 0.027(1.3)$} \\ \hline +5 & \scalebox{0.5}{$0.044 \pm 0.028(1.6)$} & \scalebox{0.5}{$-0.022 \pm 0.026(-0.82)$} & \scalebox{0.5}{$-0.041 \pm 0.027(-1.5)$} & \scalebox{0.5}{$-0.014 \pm 0.027(-0.53)$} & \scalebox{0.5}{$-0.029 \pm 0.027(-1.1)$} & \scalebox{0.5}{$0.041 \pm 0.027(1.5)$} & \scalebox{0.5}{$0.042 \pm 0.028(1.5)$} \\ \hline +6 & \scalebox{0.5}{$-0.011 \pm 0.026(-0.42)$} & \scalebox{0.5}{$0.041 \pm 0.027(1.5)$} & \scalebox{0.5}{$-0.045 \pm 0.028(-1.6)$} & \scalebox{0.5}{$0.011 \pm 0.027(0.41)$} & \scalebox{0.5}{$-0.0089 \pm 0.027(-0.33)$} & \scalebox{0.5}{$0.067 \pm 0.027(2.5)$} & \scalebox{0.5}{$0.036 \pm 0.027(1.3)$} \\ \hline +%7 & \scalebox{0.5}{$0.25 \pm 0.027(9.1)$} & \scalebox{0.5}{$-0.26 \pm 0.027(-9.9)$} & \scalebox{0.5}{$-0.42 \pm 0.027(-16)$} & \scalebox{0.5}{$2.1 \pm 0.029(73)$} & \scalebox{0.5}{$0.47 \pm 0.027(18)$} & \scalebox{0.5}{$-0.077 \pm 0.028(-2.8)$} & \scalebox{0.5}{$0.029 \pm 0.028(1)$} \\ \hline +8 & \scalebox{0.5}{$0.05 \pm 0.026(1.9)$} & \scalebox{0.5}{$0.0021 \pm 0.028(0.074)$} & \scalebox{0.5}{$-0.025 \pm 0.028(-0.91)$} & \scalebox{0.5}{$-0.023 \pm 0.026(-0.87)$} & \scalebox{0.5}{$-0.024 \pm 0.028(-0.85)$} & \scalebox{0.5}{$0.022 \pm 0.026(0.82)$} & \scalebox{0.5}{$0.026 \pm 0.026(0.98)$} \\ \hline +9 & \scalebox{0.5}{$-0.0064 \pm 0.027(-0.23)$} & \scalebox{0.5}{$0.012 \pm 0.027(0.44)$} & \scalebox{0.5}{$-0.0075 \pm 0.026(-0.28)$} & \scalebox{0.5}{$0.029 \pm 0.027(1.1)$} & \scalebox{0.5}{$-0.087 \pm 0.027(-3.2)$} & \scalebox{0.5}{$0.036 \pm 0.027(1.3)$} & \scalebox{0.5}{$-0.02 \pm 0.026(-0.76)$} \\ \hline +10 & \scalebox{0.5}{$-0.019 \pm 0.027(-0.71)$} & \scalebox{0.5}{$-0.0051 \pm 0.025(-0.2)$} & \scalebox{0.5}{$0.0081 \pm 0.026(0.31)$} & \scalebox{0.5}{$-0.077 \pm 0.028(-2.7)$} & \scalebox{0.5}{$-0.03 \pm 0.027(-1.1)$} & \scalebox{0.5}{$0.11 \pm 0.027(4.1)$} & \scalebox{0.5}{$0.013 \pm 0.028(0.46)$} \\ \hline +11 & \scalebox{0.5}{$0.027 \pm 0.026(1)$} & \scalebox{0.5}{$0.032 \pm 0.027(1.2)$} & \scalebox{0.5}{$-0.038 \pm 0.027(-1.4)$} & \scalebox{0.5}{$-0.048 \pm 0.026(-1.8)$} & \scalebox{0.5}{$-0.021 \pm 0.027(-0.77)$} & \scalebox{0.5}{$0.019 \pm 0.028(0.69)$} & \scalebox{0.5}{$0.035 \pm 0.027(1.3)$} \\ \hline + + + +\hline + + \end{tabular} + +\end{center} + +\end{tiny} +\end{frame} + + + + +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +\section{Reverse Engineering Unfolding} + +\begin{frame}\frametitle{Reverse Engineering- Corr1} +\begin{itemize} +\item Let's try to understand if we can understand why this happens: +\item Let's calculate what should I expect with the unfolding +\item This is up to normalization! +\begin{itemize} +\item $M_5=0.4 S_5 \to M_5=0.00512 S_3 + 0.4 S_5 - 0.002 S_7$ +\item $M_8=0.32 S_8 \to M_8=0.0016 S_4 + 0.00512 S_7 + 0.32 S_8$ +\item $M_7=0.4 S_7 \to M_7=0.002 S_5 + 0.4 S_7 + 0.00512 S_8$ +\item $M_3=0.32 S_3 \to M_3=0.32 S_3 - 0.0008 S_9$ +\end{itemize} +\item The way you can look at this is that i just shown you how our unfolding matrix works like. +\end{itemize} + + + +\end{frame} + +\begin{frame}\frametitle{Reverse Engineering- Corr2} +\begin{itemize} +\item Let's try to understand if we can understand why this happens: +\item Let's calculate what should I expect with the unfolding +\item This is up to normalization! +\begin{itemize} +\item $M_5=0.4 S_5 \to M_5= 0.4 S_5$ +\item $M_8=0.32 S_8 \to M_8=0.32 S_5$ +\item $M_7=0.4 S_7 \to M_7=0.4 S_7$ +\item $M_3=0.32 S_3 \to M_3=-0.0036 + 0.0012 Fl + 0.32 S_3$ +\end{itemize} +\item The way you can look at this is that i just shown you how our unfolding matrix works like. +\end{itemize} + + + +\end{frame} + + + + +\begin{frame}\frametitle{Summary} +\begin{itemize} +\item Developed a systematic way how to get Unfolding matrix +\item Moments are resistant against variety of unfolding discrepancies. +\item This might lead to reduced systematics in the future. +\end{itemize} + + + + +\end{frame} + + + +\end{document} diff --git a/Zurich_group/14_07_2014/MMatrix.toc b/Zurich_group/14_07_2014/MMatrix.toc new file mode 100644 index 0000000..1e71ea5 --- /dev/null +++ b/Zurich_group/14_07_2014/MMatrix.toc @@ -0,0 +1,3 @@ +\beamer@endinputifotherversion {3.10pt} +\select@language {english} +\beamer@sectionintoc {1}{Introduction}{2}{0}{1} diff --git a/Zurich_group/14_07_2014/P5.png b/Zurich_group/14_07_2014/P5.png new file mode 100644 index 0000000..7819eef --- /dev/null +++ b/Zurich_group/14_07_2014/P5.png Binary files differ diff --git a/Zurich_group/14_07_2014/Q2_4_S8.png b/Zurich_group/14_07_2014/Q2_4_S8.png new file mode 100644 index 0000000..9176de4 --- /dev/null +++ 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closepath } def +/h { closepath } def +% path painting operators +/S { sCol stroke } def +/Sf { fCol stroke } def +/f { fCol fill } def +/f* { fCol eofill } def +% clipping operators +/W { clip newpath } def +/W* { eoclip newpath } def +% text state operators +/Tc { /pdfCharSpacing exch def } def +/Tf { dup /pdfFontSize exch def + dup pdfHorizScaling mul exch matrix scale + pdfTextMat matrix concatmatrix dup 4 0 put dup 5 0 put + exch findfont exch makefont setfont } def +/Tr { /pdfTextRender exch def } def +/Ts { /pdfTextRise exch def } def +/Tw { /pdfWordSpacing exch def } def +/Tz { /pdfHorizScaling exch def } def +% text positioning operators +/Td { pdfTextMat transform moveto } def +/Tm { /pdfTextMat exch def } def +% text string operators +/cshow where { + pop + /cshow2 { + dup { + pop pop + 1 string dup 0 3 index put 3 index exec + } exch cshow + pop pop + } def +}{ + /cshow2 { + currentfont /FontType get 0 eq { + 0 2 2 index length 1 sub { + 2 copy get exch 1 add 2 index exch get + 2 copy exch 256 mul add + 2 string dup 0 6 5 roll put dup 1 5 4 roll put + 3 index exec + } for + } { + dup { + 1 string dup 0 3 index put 3 index exec + } forall + } ifelse + pop pop + } def +} ifelse +/awcp { + exch { + false charpath + 5 index 5 index rmoveto + 6 index eq { 7 index 7 index rmoveto } if + } exch cshow2 + 6 {pop} repeat +} def +/Tj { + fCol + 1 index stringwidth pdfTextMat idtransform pop + sub 1 index length dup 0 ne { div } { pop pop 0 } ifelse + pdfWordSpacing pdfHorizScaling mul 0 pdfTextMat dtransform 32 + 4 3 roll pdfCharSpacing pdfHorizScaling mul add 0 + pdfTextMat dtransform + 6 5 roll Tj1 +} def +/Tj16 { + fCol + 2 index stringwidth pdfTextMat idtransform pop + sub exch div + pdfWordSpacing pdfHorizScaling mul 0 pdfTextMat dtransform 32 + 4 3 roll pdfCharSpacing pdfHorizScaling mul add 0 + pdfTextMat dtransform + 6 5 roll Tj1 +} def +/Tj16V { + fCol + 2 index stringwidth pdfTextMat idtransform exch pop + sub exch div + 0 pdfWordSpacing pdfTextMat 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+/pdfImBuf 100 string def +/pdfIm { + image + { currentfile pdfImBuf readline + not { pop exit } if + (%-EOD-) eq { exit } if } loop +} def +/pdfImM { + fCol imagemask + { currentfile pdfImBuf readline + not { pop exit } if + (%-EOD-) eq { exit } if } loop +} def +/pdfImClip { + gsave + 0 2 4 index length 1 sub { + dup 4 index exch 2 copy + get 5 index div put + 1 add 3 index exch 2 copy + get 3 index div put + } for + pop pop rectclip +} def +/pdfImClipEnd { grestore } def +% shading operators +/colordelta { + false 0 1 3 index length 1 sub { + dup 4 index exch get 3 index 3 2 roll get sub abs 0.004 gt { + pop true + } if + } for + exch pop exch pop +} def +/funcCol { func n array astore } def +/funcSH { + dup 0 eq { + true + } { + dup 6 eq { + false + } { + 4 index 4 index funcCol dup + 6 index 4 index funcCol dup + 3 1 roll colordelta 3 1 roll + 5 index 5 index funcCol dup + 3 1 roll colordelta 3 1 roll + 6 index 8 index funcCol dup + 3 1 roll colordelta 3 1 roll + colordelta or or or + } ifelse + } ifelse + { + 1 add + 4 index 3 index add 0.5 mul exch 4 index 3 index add 0.5 mul exch + 6 index 6 index 4 index 4 index 4 index funcSH + 2 index 6 index 6 index 4 index 4 index funcSH + 6 index 2 index 4 index 6 index 4 index funcSH + 5 3 roll 3 2 roll funcSH pop pop + } { + pop 3 index 2 index add 0.5 mul 3 index 2 index add 0.5 mul + funcCol sc + dup 4 index exch mat transform m + 3 index 3 index mat transform l + 1 index 3 index mat transform l + mat transform l pop pop h f* + } ifelse +} def +/axialCol { + dup 0 lt { + pop t0 + } { + dup 1 gt { + pop t1 + } { + dt mul t0 add + } ifelse + } ifelse + func n array astore +} def +/axialSH { + dup 0 eq { + true + } { + dup 8 eq { + false + } { + 2 index axialCol 2 index axialCol colordelta + } ifelse + } ifelse + { + 1 add 3 1 roll 2 copy add 0.5 mul + dup 4 3 roll exch 4 index axialSH + exch 3 2 roll axialSH + } { + pop 2 copy add 0.5 mul axialCol sc + exch dup dx mul x0 add exch dy mul y0 add + 3 2 roll dup dx mul x0 add exch dy mul y0 add + dx abs dy abs ge { + 2 copy yMin sub dy mul dx div add yMin m + yMax sub dy mul dx div add yMax l + 2 copy yMax sub dy mul dx div add yMax l + yMin sub dy mul dx div add yMin l + h f* + } { + exch 2 copy xMin sub dx mul dy div add xMin exch m + xMax sub dx mul dy div add xMax exch l + exch 2 copy xMax sub dx mul dy div add xMax exch l + xMin sub dx mul dy div add xMin exch l + h f* + } ifelse + } ifelse +} def +/radialCol { + dup t0 lt { + pop t0 + } { + dup t1 gt { + pop t1 + } if + } ifelse + func n array astore +} def +/radialSH { + dup 0 eq { + true + } { + dup 8 eq { + false + } { + 2 index dt mul t0 add radialCol + 2 index dt mul t0 add radialCol colordelta + } ifelse + } ifelse + { + 1 add 3 1 roll 2 copy add 0.5 mul + dup 4 3 roll exch 4 index radialSH + exch 3 2 roll radialSH + } { + pop 2 copy add 0.5 mul dt mul t0 add axialCol sc + exch dup dx mul x0 add exch dup dy mul y0 add exch dr mul r0 add + 0 360 arc h + dup dx mul x0 add exch dup dy mul y0 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3 roll pdfCharSpacing pdfHorizScaling mul add 0 + pdfTextMat dtransform + 6 5 roll Tj1 +} def +/Tj16 { + fCol + 2 index stringwidth pdfTextMat idtransform pop + sub exch div + pdfWordSpacing pdfHorizScaling mul 0 pdfTextMat dtransform 32 + 4 3 roll pdfCharSpacing pdfHorizScaling mul add 0 + pdfTextMat dtransform + 6 5 roll Tj1 +} def +/Tj16V { + fCol + 2 index stringwidth pdfTextMat idtransform exch pop + sub exch div + 0 pdfWordSpacing pdfTextMat dtransform 32 + 4 3 roll pdfCharSpacing add 0 exch + pdfTextMat dtransform + 6 5 roll Tj1 +} def +/Tj1 { + 0 pdfTextRise pdfTextMat dtransform rmoveto + currentpoint 8 2 roll + pdfTextRender 1 and 0 eq { + 6 copy awidthshow + } if + pdfTextRender 3 and dup 1 eq exch 2 eq or { + 7 index 7 index moveto + 6 copy + currentfont /FontType get 3 eq { fCol } { sCol } ifelse + false awcp currentpoint stroke moveto + } if + pdfTextRender 4 and 0 ne { + 8 6 roll moveto + false awcp + /pdfTextClipPath [ pdfTextClipPath aload pop + {/moveto cvx} + {/lineto cvx} + {/curveto cvx} + {/closepath cvx} + pathforall ] def + currentpoint newpath moveto + } { + 8 {pop} repeat + } ifelse + 0 pdfTextRise neg pdfTextMat dtransform rmoveto +} def +/TJm { pdfFontSize 0.001 mul mul neg 0 + pdfTextMat dtransform rmoveto } def +/TJmV { pdfFontSize 0.001 mul mul neg 0 exch + pdfTextMat dtransform rmoveto } def +/Tclip { pdfTextClipPath cvx exec clip newpath + /pdfTextClipPath [] def } def +% Level 2 image operators +/pdfImBuf 100 string def +/pdfIm { + image + { currentfile pdfImBuf readline + not { pop exit } if + (%-EOD-) eq { exit } if } loop +} def +/pdfImM { + fCol imagemask + { currentfile pdfImBuf readline + not { pop exit } if + (%-EOD-) eq { exit } if } loop +} def +/pdfImClip { + gsave + 0 2 4 index length 1 sub { + dup 4 index exch 2 copy + get 5 index div put + 1 add 3 index exch 2 copy + get 3 index div put + } for + pop pop rectclip +} def +/pdfImClipEnd { grestore } def +% shading operators +/colordelta { + false 0 1 3 index length 1 sub { + dup 4 index exch get 3 index 3 2 roll get sub abs 0.004 gt { + pop true + } if + } for + exch pop exch pop +} def +/funcCol { func n array astore } def +/funcSH { + dup 0 eq { + true + } { + dup 6 eq { + false + } { + 4 index 4 index funcCol dup + 6 index 4 index funcCol dup + 3 1 roll colordelta 3 1 roll + 5 index 5 index funcCol dup + 3 1 roll colordelta 3 1 roll + 6 index 8 index funcCol dup + 3 1 roll colordelta 3 1 roll + colordelta or or or + } ifelse + } ifelse + { + 1 add + 4 index 3 index add 0.5 mul exch 4 index 3 index add 0.5 mul exch + 6 index 6 index 4 index 4 index 4 index funcSH + 2 index 6 index 6 index 4 index 4 index funcSH + 6 index 2 index 4 index 6 index 4 index funcSH + 5 3 roll 3 2 roll funcSH pop pop + } { + pop 3 index 2 index add 0.5 mul 3 index 2 index add 0.5 mul + funcCol sc + dup 4 index exch mat transform m + 3 index 3 index mat transform l + 1 index 3 index mat transform l + mat transform l pop pop h f* + } ifelse +} def +/axialCol { + dup 0 lt { + pop t0 + } { + dup 1 gt { + pop t1 + } { + dt mul t0 add + } ifelse + } ifelse + func n array astore +} def +/axialSH { + dup 0 eq { + true + } { + dup 8 eq { + false + } { + 2 index axialCol 2 index axialCol colordelta + } ifelse + } ifelse + { + 1 add 3 1 roll 2 copy add 0.5 mul + dup 4 3 roll exch 4 index axialSH + exch 3 2 roll axialSH + } { + pop 2 copy add 0.5 mul axialCol sc + exch dup dx mul x0 add exch dy mul y0 add + 3 2 roll dup dx mul x0 add exch dy mul y0 add + dx abs dy abs ge { + 2 copy yMin sub dy mul dx div add yMin m + yMax sub dy mul dx div add yMax l + 2 copy yMax sub dy mul dx div add yMax l + yMin sub dy mul dx div add yMin l + h f* + } { + exch 2 copy xMin sub dx mul dy div add xMin exch m + xMax sub dx mul dy div add xMax exch l + exch 2 copy xMax sub dx mul dy div add xMax exch l + xMin sub dx mul dy div add xMin exch l + h f* + } ifelse + } ifelse +} def +/radialCol { + dup t0 lt { + pop t0 + } { + dup t1 gt { + pop t1 + } if + } ifelse + func n array astore +} def +/radialSH { + dup 0 eq { + true + } { + dup 8 eq { + false + } { + 2 index dt mul t0 add radialCol + 2 index dt mul t0 add radialCol colordelta + } ifelse + } ifelse + { + 1 add 3 1 roll 2 copy add 0.5 mul + dup 4 3 roll exch 4 index radialSH + exch 3 2 roll radialSH + } { + pop 2 copy add 0.5 mul dt mul t0 add axialCol sc + exch dup dx mul x0 add exch dup dy mul y0 add exch dr mul r0 add + 0 360 arc h + dup dx mul x0 add exch dup dy mul y0 add exch dr mul r0 add + 0 360 arc h f* + } ifelse +} def +end +%%EndResource +%%EndProlog +%%BeginSetup +xpdf begin +%%BeginResource: font CMR12 +%!FontType1-1.0: CMR12 +12 dict begin +/FontInfo 10 dict dup begin +/Notice (Copyright (C) 1997 American Mathematical Society. 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dict begin + { 1 index /FID ne { def } { pop pop } ifelse } forall + /WMode exch def + currentdict + end + definefont pop +} def +% graphics state operators +/q { gsave pdfDictSize dict begin } def +/Q { + end grestore + /pdfLastFill where { + pop + pdfLastFill { + pdfFillOP setoverprint + } { + pdfStrokeOP setoverprint + } ifelse + } if +} def +/cm { concat } def +/d { setdash } def +/i { setflat } def +/j { setlinejoin } def +/J { setlinecap } def +/M { setmiterlimit } def +/w { setlinewidth } def +% path segment operators +/m { moveto } def +/l { lineto } def +/c { curveto } def +/re { 4 2 roll moveto 1 index 0 rlineto 0 exch rlineto + neg 0 rlineto closepath } def +/h { closepath } def +% path painting operators +/S { sCol stroke } def +/Sf { fCol stroke } def +/f { fCol fill } def +/f* { fCol eofill } def +% clipping operators +/W { clip newpath } def +/W* { eoclip newpath } def +% text state operators +/Tc { /pdfCharSpacing exch def } def +/Tf { dup /pdfFontSize exch def + dup 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repeat +} def +/Tj { + fCol + 1 index stringwidth pdfTextMat idtransform pop + sub 1 index length dup 0 ne { div } { pop pop 0 } ifelse + pdfWordSpacing pdfHorizScaling mul 0 pdfTextMat dtransform 32 + 4 3 roll pdfCharSpacing pdfHorizScaling mul add 0 + pdfTextMat dtransform + 6 5 roll Tj1 +} def +/Tj16 { + fCol + 2 index stringwidth pdfTextMat idtransform pop + sub exch div + pdfWordSpacing pdfHorizScaling mul 0 pdfTextMat dtransform 32 + 4 3 roll pdfCharSpacing pdfHorizScaling mul add 0 + pdfTextMat dtransform + 6 5 roll Tj1 +} def +/Tj16V { + fCol + 2 index stringwidth pdfTextMat idtransform exch pop + sub exch div + 0 pdfWordSpacing pdfTextMat dtransform 32 + 4 3 roll pdfCharSpacing add 0 exch + pdfTextMat dtransform + 6 5 roll Tj1 +} def +/Tj1 { + 0 pdfTextRise pdfTextMat dtransform rmoveto + currentpoint 8 2 roll + pdfTextRender 1 and 0 eq { + 6 copy awidthshow + } if + pdfTextRender 3 and dup 1 eq exch 2 eq or { + 7 index 7 index moveto + 6 copy + currentfont /FontType get 3 eq { fCol } { sCol } ifelse + false awcp currentpoint stroke moveto + } if + pdfTextRender 4 and 0 ne { + 8 6 roll moveto + false awcp + /pdfTextClipPath [ pdfTextClipPath aload pop + {/moveto cvx} + {/lineto cvx} + {/curveto cvx} + {/closepath cvx} + pathforall ] def + currentpoint newpath moveto + } { + 8 {pop} repeat + } ifelse + 0 pdfTextRise neg pdfTextMat dtransform rmoveto +} def +/TJm { pdfFontSize 0.001 mul mul neg 0 + pdfTextMat dtransform rmoveto } def +/TJmV { pdfFontSize 0.001 mul mul neg 0 exch + pdfTextMat dtransform rmoveto } def +/Tclip { pdfTextClipPath cvx exec clip newpath + /pdfTextClipPath [] def } def +% Level 2 image operators +/pdfImBuf 100 string def +/pdfIm { + image + { currentfile pdfImBuf readline + not { pop exit } if + (%-EOD-) eq { exit } if } loop +} def +/pdfImM { + fCol imagemask + { currentfile pdfImBuf readline + not { pop exit } if + (%-EOD-) eq { exit } if } loop +} def +/pdfImClip { + gsave + 0 2 4 index length 1 sub { + dup 4 index exch 2 copy + get 5 index div put + 1 add 3 index exch 2 copy + get 3 index div put + } for + pop pop rectclip +} def +/pdfImClipEnd { grestore } def +% shading operators +/colordelta { + false 0 1 3 index length 1 sub { + dup 4 index exch get 3 index 3 2 roll get sub abs 0.004 gt { + pop true + } if + } for + exch pop exch pop +} def +/funcCol { func n array astore } def +/funcSH { + dup 0 eq { + true + } { + dup 6 eq { + false + } { + 4 index 4 index funcCol dup + 6 index 4 index funcCol dup + 3 1 roll colordelta 3 1 roll + 5 index 5 index funcCol dup + 3 1 roll colordelta 3 1 roll + 6 index 8 index funcCol dup + 3 1 roll colordelta 3 1 roll + colordelta or or or + } ifelse + } ifelse + { + 1 add + 4 index 3 index add 0.5 mul exch 4 index 3 index add 0.5 mul exch + 6 index 6 index 4 index 4 index 4 index funcSH + 2 index 6 index 6 index 4 index 4 index funcSH + 6 index 2 index 4 index 6 index 4 index funcSH + 5 3 roll 3 2 roll funcSH pop pop + } { + pop 3 index 2 index add 0.5 mul 3 index 2 index add 0.5 mul + funcCol sc + dup 4 index exch mat transform m + 3 index 3 index mat transform l + 1 index 3 index mat transform l + mat transform l pop pop h f* + } ifelse +} def +/axialCol { + dup 0 lt { + pop t0 + } { + dup 1 gt { + pop t1 + } { + dt mul t0 add + } ifelse + } ifelse + func n array astore +} def +/axialSH { + dup 0 eq { + true + } { + dup 8 eq { + false + } { + 2 index axialCol 2 index axialCol colordelta + } ifelse + } ifelse + { + 1 add 3 1 roll 2 copy add 0.5 mul + dup 4 3 roll exch 4 index axialSH + exch 3 2 roll axialSH + } { + pop 2 copy add 0.5 mul axialCol sc + exch dup dx mul x0 add exch dy mul y0 add + 3 2 roll dup dx mul x0 add exch dy mul y0 add + dx abs dy abs ge { + 2 copy yMin sub dy mul dx div add yMin m + yMax sub dy mul dx div add yMax l + 2 copy yMax sub dy mul dx div add yMax l + yMin sub dy mul dx div add yMin l + h f* + } { + exch 2 copy xMin sub dx mul dy div add xMin exch m + xMax sub dx mul dy div add xMax exch l + exch 2 copy xMax sub dx mul dy div add xMax exch l + xMin sub dx mul dy div add xMin exch l + h f* + } ifelse + } ifelse +} def +/radialCol { + dup t0 lt { + pop t0 + } { + dup t1 gt { + pop t1 + } if + } ifelse + func n array astore +} def +/radialSH { + dup 0 eq { + true + } { + dup 8 eq { + false + } { + 2 index dt mul t0 add radialCol + 2 index dt mul t0 add radialCol colordelta + } ifelse + } ifelse + { + 1 add 3 1 roll 2 copy add 0.5 mul + dup 4 3 roll exch 4 index radialSH + exch 3 2 roll radialSH + } { + pop 2 copy add 0.5 mul dt mul t0 add axialCol sc + exch dup dx mul x0 add exch dup dy mul y0 add exch dr mul r0 add + 0 360 arc h + dup dx mul x0 add exch dup dy mul y0 add exch dr mul r0 add + 0 360 arc h f* + } ifelse +} def +end +%%EndResource +%%EndProlog +%%BeginSetup +xpdf begin +%%BeginResource: font CMR12 +%!FontType1-1.0: CMR12 +12 dict begin +/FontInfo 10 dict dup begin +/Notice (Copyright (C) 1997 American Mathematical Society. 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gsave pdfDictSize dict begin } def +/Q { + end grestore + /pdfLastFill where { + pop + pdfLastFill { + pdfFillOP setoverprint + } { + pdfStrokeOP setoverprint + } ifelse + } if +} def +/cm { concat } def +/d { setdash } def +/i { setflat } def +/j { setlinejoin } def +/J { setlinecap } def +/M { setmiterlimit } def +/w { setlinewidth } def +% path segment operators +/m { moveto } def +/l { lineto } def +/c { curveto } def +/re { 4 2 roll moveto 1 index 0 rlineto 0 exch rlineto + neg 0 rlineto closepath } def +/h { closepath } def +% path painting operators +/S { sCol stroke } def +/Sf { fCol stroke } def +/f { fCol fill } def +/f* { fCol eofill } def +% clipping operators +/W { clip newpath } def +/W* { eoclip newpath } def +% text state operators +/Tc { /pdfCharSpacing exch def } def +/Tf { dup /pdfFontSize exch def + dup pdfHorizScaling mul exch matrix scale + pdfTextMat matrix concatmatrix dup 4 0 put dup 5 0 put + exch findfont exch makefont setfont } def +/Tr { /pdfTextRender exch 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pdfHorizScaling mul 0 pdfTextMat dtransform 32 + 4 3 roll pdfCharSpacing pdfHorizScaling mul add 0 + pdfTextMat dtransform + 6 5 roll Tj1 +} def +/Tj16 { + fCol + 2 index stringwidth pdfTextMat idtransform pop + sub exch div + pdfWordSpacing pdfHorizScaling mul 0 pdfTextMat dtransform 32 + 4 3 roll pdfCharSpacing pdfHorizScaling mul add 0 + pdfTextMat dtransform + 6 5 roll Tj1 +} def +/Tj16V { + fCol + 2 index stringwidth pdfTextMat idtransform exch pop + sub exch div + 0 pdfWordSpacing pdfTextMat dtransform 32 + 4 3 roll pdfCharSpacing add 0 exch + pdfTextMat dtransform + 6 5 roll Tj1 +} def +/Tj1 { + 0 pdfTextRise pdfTextMat dtransform rmoveto + currentpoint 8 2 roll + pdfTextRender 1 and 0 eq { + 6 copy awidthshow + } if + pdfTextRender 3 and dup 1 eq exch 2 eq or { + 7 index 7 index moveto + 6 copy + currentfont /FontType get 3 eq { fCol } { sCol } ifelse + false awcp currentpoint stroke moveto + } if + pdfTextRender 4 and 0 ne { + 8 6 roll moveto + false awcp + /pdfTextClipPath [ pdfTextClipPath aload pop + {/moveto cvx} + {/lineto cvx} + {/curveto cvx} + {/closepath cvx} + pathforall ] def + currentpoint newpath moveto + } { + 8 {pop} repeat + } ifelse + 0 pdfTextRise neg pdfTextMat dtransform rmoveto +} def +/TJm { pdfFontSize 0.001 mul mul neg 0 + pdfTextMat dtransform rmoveto } def +/TJmV { pdfFontSize 0.001 mul mul neg 0 exch + pdfTextMat dtransform rmoveto } def +/Tclip { pdfTextClipPath cvx exec clip newpath + /pdfTextClipPath [] def } def +% Level 2 image operators +/pdfImBuf 100 string def +/pdfIm { + image + { currentfile pdfImBuf readline + not { pop exit } if + (%-EOD-) eq { exit } if } loop +} def +/pdfImM { + fCol imagemask + { currentfile pdfImBuf readline + not { pop exit } if + (%-EOD-) eq { exit } if } loop +} def +/pdfImClip { + gsave + 0 2 4 index length 1 sub { + dup 4 index exch 2 copy + get 5 index div put + 1 add 3 index exch 2 copy + get 3 index div put + } for + pop pop rectclip +} def +/pdfImClipEnd { grestore } def +% shading operators +/colordelta { + false 0 1 3 index length 1 sub { + dup 4 index exch get 3 index 3 2 roll get sub abs 0.004 gt { + pop true + } if + } for + exch pop exch pop +} def +/funcCol { func n array astore } def +/funcSH { + dup 0 eq { + true + } { + dup 6 eq { + false + } { + 4 index 4 index funcCol dup + 6 index 4 index funcCol dup + 3 1 roll colordelta 3 1 roll + 5 index 5 index funcCol dup + 3 1 roll colordelta 3 1 roll + 6 index 8 index funcCol dup + 3 1 roll colordelta 3 1 roll + colordelta or or or + } ifelse + } ifelse + { + 1 add + 4 index 3 index add 0.5 mul exch 4 index 3 index add 0.5 mul exch + 6 index 6 index 4 index 4 index 4 index funcSH + 2 index 6 index 6 index 4 index 4 index funcSH + 6 index 2 index 4 index 6 index 4 index funcSH + 5 3 roll 3 2 roll funcSH pop pop + } { + pop 3 index 2 index add 0.5 mul 3 index 2 index add 0.5 mul + funcCol sc + dup 4 index exch mat transform m + 3 index 3 index mat transform l + 1 index 3 index mat transform l + mat transform l pop pop h f* + } ifelse +} def +/axialCol { + dup 0 lt { + pop t0 + } { + dup 1 gt { + pop t1 + } { + dt mul t0 add + } ifelse + } ifelse + func n array astore +} def +/axialSH { + dup 0 eq { + true + } { + dup 8 eq { + false + } { + 2 index axialCol 2 index axialCol colordelta + } ifelse + } ifelse + { + 1 add 3 1 roll 2 copy add 0.5 mul + dup 4 3 roll exch 4 index axialSH + exch 3 2 roll axialSH + } { + pop 2 copy add 0.5 mul axialCol sc + exch dup dx mul x0 add exch dy mul y0 add + 3 2 roll dup dx mul x0 add exch dy mul y0 add + dx abs dy abs ge { + 2 copy yMin sub dy mul dx div add yMin m + yMax sub dy mul dx div add yMax l + 2 copy yMax sub dy mul dx div add yMax l + yMin sub dy mul dx div add yMin l + h f* + } { + exch 2 copy xMin sub dx mul dy div add xMin exch m + xMax sub dx mul dy div add xMax exch l + exch 2 copy xMax sub dx mul dy div add xMax exch l + xMin sub dx mul dy div add xMin exch l + h f* + } ifelse + } ifelse +} def +/radialCol { + dup t0 lt { + pop t0 + } { + dup t1 gt { + pop t1 + } if + } ifelse + func n array astore +} def +/radialSH { + dup 0 eq { + true + } { + dup 8 eq { + false + } { + 2 index dt mul t0 add radialCol + 2 index dt mul t0 add radialCol colordelta + } ifelse + } ifelse + { + 1 add 3 1 roll 2 copy add 0.5 mul + dup 4 3 roll exch 4 index radialSH + exch 3 2 roll radialSH + } { + pop 2 copy add 0.5 mul dt mul t0 add axialCol sc + exch dup dx mul x0 add exch dup dy mul y0 add exch dr mul r0 add + 0 360 arc h + dup dx mul x0 add exch dup dy mul y0 add exch dr mul r0 add + 0 360 arc h f* + } ifelse +} def +end +%%EndResource +%%EndProlog +%%BeginSetup +xpdf begin +%%BeginResource: font CMR12 +%!FontType1-1.0: CMR12 +12 dict begin +/FontInfo 10 dict dup begin +/Notice (Copyright (C) 1997 American Mathematical Society. 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copy yMin sub dy mul dx div add yMin m + yMax sub dy mul dx div add yMax l + 2 copy yMax sub dy mul dx div add yMax l + yMin sub dy mul dx div add yMin l + h f* + } { + exch 2 copy xMin sub dx mul dy div add xMin exch m + xMax sub dx mul dy div add xMax exch l + exch 2 copy xMax sub dx mul dy div add xMax exch l + xMin sub dx mul dy div add xMin exch l + h f* + } ifelse + } ifelse +} def +/radialCol { + dup t0 lt { + pop t0 + } { + dup t1 gt { + pop t1 + } if + } ifelse + func n array astore +} def +/radialSH { + dup 0 eq { + true + } { + dup 8 eq { + false + } { + 2 index dt mul t0 add radialCol + 2 index dt mul t0 add radialCol colordelta + } ifelse + } ifelse + { + 1 add 3 1 roll 2 copy add 0.5 mul + dup 4 3 roll exch 4 index radialSH + exch 3 2 roll radialSH + } { + pop 2 copy add 0.5 mul dt mul t0 add axialCol sc + exch dup dx mul x0 add exch dup dy mul y0 add exch dr mul r0 add + 0 360 arc h + dup dx mul x0 add exch dup dy mul y0 add exch dr mul r0 add + 0 360 arc h f* + } ifelse 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findfont + dup length dict begin + { 1 index /FID ne { def } { pop pop } ifelse } forall + /WMode exch def + currentdict + end + definefont pop +} def +% graphics state operators +/q { gsave pdfDictSize dict begin } def +/Q { + end grestore + /pdfLastFill where { + pop + pdfLastFill { + pdfFillOP setoverprint + } { + pdfStrokeOP setoverprint + } ifelse + } if +} def +/cm { concat } def +/d { setdash } def +/i { setflat } def +/j { setlinejoin } def +/J { setlinecap } def +/M { setmiterlimit } def +/w { setlinewidth } def +% path segment operators +/m { moveto } def +/l { lineto } def +/c { curveto } def +/re { 4 2 roll moveto 1 index 0 rlineto 0 exch rlineto + neg 0 rlineto closepath } def +/h { closepath } def +% path painting operators +/S { sCol stroke } def +/Sf { fCol stroke } def +/f { fCol fill } def +/f* { fCol eofill } def +% clipping operators +/W { clip newpath } def +/W* { eoclip newpath } def +% text state operators +/Tc { /pdfCharSpacing exch def } def +/Tf { dup 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if + } exch cshow2 + 6 {pop} repeat +} def +/Tj { + fCol + 1 index stringwidth pdfTextMat idtransform pop + sub 1 index length dup 0 ne { div } { pop pop 0 } ifelse + pdfWordSpacing pdfHorizScaling mul 0 pdfTextMat dtransform 32 + 4 3 roll pdfCharSpacing pdfHorizScaling mul add 0 + pdfTextMat dtransform + 6 5 roll Tj1 +} def +/Tj16 { + fCol + 2 index stringwidth pdfTextMat idtransform pop + sub exch div + pdfWordSpacing pdfHorizScaling mul 0 pdfTextMat dtransform 32 + 4 3 roll pdfCharSpacing pdfHorizScaling mul add 0 + pdfTextMat dtransform + 6 5 roll Tj1 +} def +/Tj16V { + fCol + 2 index stringwidth pdfTextMat idtransform exch pop + sub exch div + 0 pdfWordSpacing pdfTextMat dtransform 32 + 4 3 roll pdfCharSpacing add 0 exch + pdfTextMat dtransform + 6 5 roll Tj1 +} def +/Tj1 { + 0 pdfTextRise pdfTextMat dtransform rmoveto + currentpoint 8 2 roll + pdfTextRender 1 and 0 eq { + 6 copy awidthshow + } if + pdfTextRender 3 and dup 1 eq exch 2 eq or { + 7 index 7 index moveto + 6 copy + currentfont /FontType get 3 eq { fCol } { sCol } ifelse + false awcp currentpoint stroke moveto + } if + pdfTextRender 4 and 0 ne { + 8 6 roll moveto + false awcp + /pdfTextClipPath [ pdfTextClipPath aload pop + {/moveto cvx} + {/lineto cvx} + {/curveto cvx} + {/closepath cvx} + pathforall ] def + currentpoint newpath moveto + } { + 8 {pop} repeat + } ifelse + 0 pdfTextRise neg pdfTextMat dtransform rmoveto +} def +/TJm { pdfFontSize 0.001 mul mul neg 0 + pdfTextMat dtransform rmoveto } def +/TJmV { pdfFontSize 0.001 mul mul neg 0 exch + pdfTextMat dtransform rmoveto } def +/Tclip { pdfTextClipPath cvx exec clip newpath + /pdfTextClipPath [] def } def +% Level 2 image operators +/pdfImBuf 100 string def +/pdfIm { + image + { currentfile pdfImBuf readline + not { pop exit } if + (%-EOD-) eq { exit } if } loop +} def +/pdfImM { + fCol imagemask + { currentfile pdfImBuf readline + not { pop exit } if + (%-EOD-) eq { exit } if } loop +} def +/pdfImClip { + gsave + 0 2 4 index length 1 sub { + dup 4 index exch 2 copy + get 5 index div put + 1 add 3 index exch 2 copy + get 3 index div put + } for + pop pop rectclip +} def +/pdfImClipEnd { grestore } def +% shading operators +/colordelta { + false 0 1 3 index length 1 sub { + dup 4 index exch get 3 index 3 2 roll get sub abs 0.004 gt { + pop true + } if + } for + exch pop exch pop +} def +/funcCol { func n array astore } def +/funcSH { + dup 0 eq { + true + } { + dup 6 eq { + false + } { + 4 index 4 index funcCol dup + 6 index 4 index funcCol dup + 3 1 roll colordelta 3 1 roll + 5 index 5 index funcCol dup + 3 1 roll colordelta 3 1 roll + 6 index 8 index funcCol dup + 3 1 roll colordelta 3 1 roll + colordelta or or or + } ifelse + } ifelse + { + 1 add + 4 index 3 index add 0.5 mul exch 4 index 3 index add 0.5 mul exch + 6 index 6 index 4 index 4 index 4 index funcSH + 2 index 6 index 6 index 4 index 4 index funcSH + 6 index 2 index 4 index 6 index 4 index funcSH + 5 3 roll 3 2 roll funcSH pop pop + } { + pop 3 index 2 index add 0.5 mul 3 index 2 index add 0.5 mul + funcCol sc + dup 4 index exch mat transform m + 3 index 3 index mat transform l + 1 index 3 index mat transform l + mat transform l pop pop h f* + } ifelse +} def +/axialCol { + dup 0 lt { + pop t0 + } { + dup 1 gt { + pop t1 + } { + dt mul t0 add + } ifelse + } ifelse + func n array astore +} def +/axialSH { + dup 0 eq { + true + } { + dup 8 eq { + false + } { + 2 index axialCol 2 index axialCol colordelta + } ifelse + } ifelse + { + 1 add 3 1 roll 2 copy add 0.5 mul + dup 4 3 roll exch 4 index axialSH + exch 3 2 roll axialSH + } { + pop 2 copy add 0.5 mul axialCol sc + exch dup dx mul x0 add exch dy mul y0 add + 3 2 roll dup dx mul x0 add exch dy mul y0 add + dx abs dy abs ge { + 2 copy yMin sub dy mul dx div add yMin m + yMax sub dy mul dx div add yMax l + 2 copy yMax sub dy mul dx div add yMax l + yMin sub dy mul dx div add yMin l + h f* + } { + exch 2 copy xMin sub dx mul dy div add xMin exch m + xMax sub dx mul dy div add xMax exch l + exch 2 copy xMax sub dx mul dy div add xMax exch l + xMin sub dx mul dy div add xMin exch l + h f* + } ifelse + } ifelse +} def +/radialCol { + dup t0 lt { + pop t0 + } { + dup t1 gt { + pop t1 + } if + } ifelse + func n array astore +} def +/radialSH { + dup 0 eq { + true + } { + dup 8 eq { + false + } { + 2 index dt mul t0 add radialCol + 2 index dt mul t0 add radialCol colordelta + } ifelse + } ifelse + { + 1 add 3 1 roll 2 copy add 0.5 mul + dup 4 3 roll exch 4 index radialSH + exch 3 2 roll radialSH + } { + pop 2 copy add 0.5 mul dt mul t0 add axialCol sc + exch dup dx mul x0 add exch dup dy mul y0 add exch dr mul r0 add + 0 360 arc h + dup dx mul x0 add exch dup dy mul y0 add exch dr mul r0 add + 0 360 arc h f* + } ifelse +} def +end +%%EndResource +%%EndProlog +%%BeginSetup +xpdf begin +%%BeginResource: font CMR12 +%!FontType1-1.0: CMR12 +12 dict begin +/FontInfo 10 dict dup begin +/Notice (Copyright (C) 1997 American Mathematical Society. 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operators +/q { gsave pdfDictSize dict begin } def +/Q { + end grestore + /pdfLastFill where { + pop + pdfLastFill { + pdfFillOP setoverprint + } { + pdfStrokeOP setoverprint + } ifelse + } if +} def +/cm { concat } def +/d { setdash } def +/i { setflat } def +/j { setlinejoin } def +/J { setlinecap } def +/M { setmiterlimit } def +/w { setlinewidth } def +% path segment operators +/m { moveto } def +/l { lineto } def +/c { curveto } def +/re { 4 2 roll moveto 1 index 0 rlineto 0 exch rlineto + neg 0 rlineto closepath } def +/h { closepath } def +% path painting operators +/S { sCol stroke } def +/Sf { fCol stroke } def +/f { fCol fill } def +/f* { fCol eofill } def +% clipping operators +/W { clip newpath } def +/W* { eoclip newpath } def +% text state operators +/Tc { /pdfCharSpacing exch def } def +/Tf { dup /pdfFontSize exch def + dup pdfHorizScaling mul exch matrix scale + pdfTextMat matrix concatmatrix dup 4 0 put dup 5 0 put + exch findfont exch makefont setfont } def +/Tr { 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pdfWordSpacing pdfHorizScaling mul 0 pdfTextMat dtransform 32 + 4 3 roll pdfCharSpacing pdfHorizScaling mul add 0 + pdfTextMat dtransform + 6 5 roll Tj1 +} def +/Tj16 { + fCol + 2 index stringwidth pdfTextMat idtransform pop + sub exch div + pdfWordSpacing pdfHorizScaling mul 0 pdfTextMat dtransform 32 + 4 3 roll pdfCharSpacing pdfHorizScaling mul add 0 + pdfTextMat dtransform + 6 5 roll Tj1 +} def +/Tj16V { + fCol + 2 index stringwidth pdfTextMat idtransform exch pop + sub exch div + 0 pdfWordSpacing pdfTextMat dtransform 32 + 4 3 roll pdfCharSpacing add 0 exch + pdfTextMat dtransform + 6 5 roll Tj1 +} def +/Tj1 { + 0 pdfTextRise pdfTextMat dtransform rmoveto + currentpoint 8 2 roll + pdfTextRender 1 and 0 eq { + 6 copy awidthshow + } if + pdfTextRender 3 and dup 1 eq exch 2 eq or { + 7 index 7 index moveto + 6 copy + currentfont /FontType get 3 eq { fCol } { sCol } ifelse + false awcp currentpoint stroke moveto + } if + pdfTextRender 4 and 0 ne { + 8 6 roll moveto + false awcp + 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+% shading operators +/colordelta { + false 0 1 3 index length 1 sub { + dup 4 index exch get 3 index 3 2 roll get sub abs 0.004 gt { + pop true + } if + } for + exch pop exch pop +} def +/funcCol { func n array astore } def +/funcSH { + dup 0 eq { + true + } { + dup 6 eq { + false + } { + 4 index 4 index funcCol dup + 6 index 4 index funcCol dup + 3 1 roll colordelta 3 1 roll + 5 index 5 index funcCol dup + 3 1 roll colordelta 3 1 roll + 6 index 8 index funcCol dup + 3 1 roll colordelta 3 1 roll + colordelta or or or + } ifelse + } ifelse + { + 1 add + 4 index 3 index add 0.5 mul exch 4 index 3 index add 0.5 mul exch + 6 index 6 index 4 index 4 index 4 index funcSH + 2 index 6 index 6 index 4 index 4 index funcSH + 6 index 2 index 4 index 6 index 4 index funcSH + 5 3 roll 3 2 roll funcSH pop pop + } { + pop 3 index 2 index add 0.5 mul 3 index 2 index add 0.5 mul + funcCol sc + dup 4 index exch mat transform m + 3 index 3 index mat transform l + 1 index 3 index mat transform l + mat transform l pop pop h f* + } ifelse +} def +/axialCol { + dup 0 lt { + pop t0 + } { + dup 1 gt { + pop t1 + } { + dt mul t0 add + } ifelse + } ifelse + func n array astore +} def +/axialSH { + dup 0 eq { + true + } { + dup 8 eq { + false + } { + 2 index axialCol 2 index axialCol colordelta + } ifelse + } ifelse + { + 1 add 3 1 roll 2 copy add 0.5 mul + dup 4 3 roll exch 4 index axialSH + exch 3 2 roll axialSH + } { + pop 2 copy add 0.5 mul axialCol sc + exch dup dx mul x0 add exch dy mul y0 add + 3 2 roll dup dx mul x0 add exch dy mul y0 add + dx abs dy abs ge { + 2 copy yMin sub dy mul dx div add yMin m + yMax sub dy mul dx div add yMax l + 2 copy yMax sub dy mul dx div add yMax l + yMin sub dy mul dx div add yMin l + h f* + } { + exch 2 copy xMin sub dx mul dy div add xMin exch m + xMax sub dx mul dy div add xMax exch l + exch 2 copy xMax sub dx mul dy div add xMax exch l + xMin sub dx mul dy div add xMin exch l + h f* + } ifelse + } ifelse +} def +/radialCol { + dup t0 lt { + pop t0 + } { + dup t1 gt { + pop t1 + } if + } ifelse + func n array astore +} def +/radialSH { + dup 0 eq { + true + } { + dup 8 eq { + false + } { + 2 index dt mul t0 add radialCol + 2 index dt mul t0 add radialCol colordelta + } ifelse + } ifelse + { + 1 add 3 1 roll 2 copy add 0.5 mul + dup 4 3 roll exch 4 index radialSH + exch 3 2 roll radialSH + } { + pop 2 copy add 0.5 mul dt mul t0 add axialCol sc + exch dup dx mul x0 add exch dup dy mul y0 add exch dr mul r0 add + 0 360 arc h + dup dx mul x0 add exch dup dy mul y0 add exch dr mul r0 add + 0 360 arc h f* + } ifelse +} def +end +%%EndResource +%%EndProlog +%%BeginSetup +xpdf begin +%%BeginResource: font CMR12 +%!FontType1-1.0: CMR12 +12 dict begin +/FontInfo 10 dict dup begin +/Notice (Copyright (C) 1997 American Mathematical Society. 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b/Zurich_group/14_07_2014_2/plots_tauola/mc-testerRAD_emumu.root new file mode 100644 index 0000000..3fff091 --- /dev/null +++ b/Zurich_group/14_07_2014_2/plots_tauola/mc-testerRAD_emumu.root Binary files differ diff --git a/Zurich_group/14_07_2014_2/plots_tauola/mumue_dalitz.pdf b/Zurich_group/14_07_2014_2/plots_tauola/mumue_dalitz.pdf new file mode 100644 index 0000000..2b48150 --- /dev/null +++ b/Zurich_group/14_07_2014_2/plots_tauola/mumue_dalitz.pdf Binary files differ diff --git a/Zurich_group/14_07_2014_2/plots_tauola/plotThreeMuUserAnalysis.C b/Zurich_group/14_07_2014_2/plots_tauola/plotThreeMuUserAnalysis.C new file mode 100644 index 0000000..870834a --- /dev/null +++ b/Zurich_group/14_07_2014_2/plots_tauola/plotThreeMuUserAnalysis.C @@ -0,0 +1,40 @@ +void plotThreeMuUserAnalysis(TString ss="LLLL") +{ + + + + TPaveText *pave = new TPaveText(1.8,1.8,2.7,2.7); + pave->SetFillColor(0); + pave->SetBorderSize(0); + pave->AddText("TAUOLA V Chrzaszcz"); + pave->AddText("#tau^{-} -> #mu^{-} #mu^{-} #mu^{+}"); + // pave->AddText("#tau^{-} -> e^{-} #mu^{-} #mu^{+}"); + + pave->AddText("#Gamma_{"+ss+"} Mode"); + + gStyle->SetOptStat(0); + TCanvas *c = new TCanvas("c","c",800,800); + TFile *f = new TFile("mc-tester"+ss+".root"); + TH2D *hist= f->Get("USER_HISTOGRAMS/m12_m23"); + hist->Scale(1./hist->Integral()); + hist->SetTitle(""); + hist->GetXaxis()->SetTitle("m_{--}^{2} GeV^{2}"); + hist->GetYaxis()->SetTitle("m_{+-}^{2} GeV^{2}"); + hist->GetZaxis()->SetLabelOffset(0.06); + hist->GetZaxis()->SetTitleOffset(20); + gStyle->SetPalette(1); + hist->Draw("COLZD"); + pave->Draw(); + gPad->Update(); + + TPaletteAxis *palette = (TPaletteAxis*)hist->GetListOfFunctions()->FindObject("palette"); + palette->SetX2NDC(0.85); + + gPad->Modified(); + gPad->Update(); + c->Update(); + c->SaveAs(ss+".pdf"); + + + +} diff --git a/Zurich_group/14_07_2014_2/slides.aux b/Zurich_group/14_07_2014_2/slides.aux new file mode 100644 index 0000000..23eaf1f --- /dev/null +++ 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a/Zurich_group/14_07_2014_2/slides.tex b/Zurich_group/14_07_2014_2/slides.tex new file mode 100644 index 0000000..da98534 --- /dev/null +++ b/Zurich_group/14_07_2014_2/slides.tex @@ -0,0 +1,142 @@ +\documentclass[xcolor=svgnames]{beamer} +\usepackage[utf8]{inputenc} +\usepackage[english]{babel} +\usepackage{polski} +%\usepackage{amssymb,amsmath} +%\usepackage[latin1]{inputenc} +%\usepackage{amsmath} +%\newcommand\abs[1]{\left|#1\right|} +\usepackage{amsmath} +\newcommand\abs[1]{\left|#1\right|} +\usepackage{hepnicenames} +\usepackage{hepunits} +\usepackage{color} + +\setbeamertemplate{footline}{\insertframenumber/\inserttotalframenumber} +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%5 +\definecolor{mygreen}{cmyk}{0.82,0.11,1,0.25} + + +\usetheme{Sybila} + +\title[Combining limits in LFV]{Tauola development} +\author{Marcin Chrz\k{a}szcz$^{1,2}$} +\institute{$^1$~University of Zurich,\\ $^2$~Institute of Nuclear Physics, Krakow} +\date{\today} +\begin{document} +% --------------------------- SLIDE -------------------------------------------- +\frame[plain]{\titlepage} +\author{Marcin Chrz\k{a}szcz} +% ------------------------------------------------------------------------------ +% --------------------------- SLIDE -------------------------------------------- + +\institute{~(UZH, IFJ)} + +\section{Introduction} + + +\begin{frame}\frametitle{Where are we?} +\begin{figure} +\includegraphics[width=0.8\textwidth]{TauLFV_UL_2013001.pdf} +\end{figure} + + + + +\end{frame} + +\section{Start from simple frequentist } + + +\begin{frame}\frametitle{Where are we?} +\begin{itemize} +\item I started from simple FD +\item Ultimate goal is to combine it with Bayesian. +\item There are fiew tools on the market: RooStats, CLs(tom Junk), BAT, and more. +\item One worse then the other.... +\item Decided: write own toy and check with RooStats(worse decision in my life). +\end{itemize} +Assumtions: +\begin{itemize} +\item Don't combine limits if there is an order of magnitude difference. +\item Don't take LHCb yet into account. +\end{itemize} + + + +\end{frame} + + +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% + +\begin{frame}\frametitle{Results from FD} +\begin{figure} +\includegraphics[width=0.8\textwidth]{TauLFV_UL_2013001_MY.pdf} +\end{figure} + +\end{frame} + + +\begin{frame}\frametitle{Results from FD} +\begin{itemize} +\item Don't trust fully this results. +\item With to many toys, RooStats is starting to get crazy. +\item Also with to large range for scanning the $Br$. +\item After 4 days of banning my head what this idiot does, I scheduled a meeting with an CMS expert. +\item With medium range and medium toys I am getting similar results to my toy model. +\item Also have feeling RooStats is not doing systematics correct... +\end{itemize} + +\end{frame} + + + +\begin{frame}\frametitle{TOY model} +\begin{itemize} +\item For given Br, for each experiment(Babar and Belle) in toy loop: +\begin{itemize} +\item Choose efficiency from Gaussian PDF: $\epsilon, \delta \epsilon$. +\item Choose Background accordingly to Gaussian PDF: $n_{bkg}, \delta n_{bkg}$. +\item Now we have $n_{bkg}$, and $n_{sig}$. The can now calculate the probability of two experiments(babar and belle) and multiply it in both cases fixing $n_{obs}$. +\item After the toys we can calculate the mean probability is taken. +\item Stop procedure when $mean<0.1$. +\end{itemize} +\item Resonable $0.1\times 10^{-8}$ agreement between this and FD in RooStats. +\item Bayesian calculator in RooStats gives correct results only assuming no background scenario... +\item Lots of understanding on the table. +\end{itemize} + +\end{frame} + + + +\begin{frame}\frametitle{Tauola follow up $\tau^{-} \to \mu^{-} \mu^{-} e^{+}$ } +\begin{itemize} +\item In theory paper they presented explicite new models for $\tau \to 3\mu$ and $\tau \to \mu^{-} \mu^{+} e^{-}$. +\item After sleeping with this I thought it would be bad idea not to have them for remaining 4: $\tau \to \mu^{-} \mu^{-} e^{+}$, $\tau \to 3e$, $\tau \to e^{-} e^{+} \mu^{-}$, $\tau \to e^{-} e^{-} \mu^{+}$ +\item For $\tau \to 3e$ it's extremely easy to derive the operator from $\tau \to 3\mu$ . +\item The same for: $\tau \to e^{-} e^{+} \mu^{-}$ from $\tau \to \mu^{-} \mu^{+} e^{-}$. +\item For the $\tau \mu^{-} \mu^{-} e^{+}$ and $\tau \to e^{-} e^{-} \mu^{+}$ required more dancing and talking to theorists. +\item In the and there are only two operators(radiative ones don't exist for this decays). +\end{itemize} + +\end{frame} + +\begin{frame}\frametitle{Tauola follow up} + +\begin{figure} +\includegraphics[width=0.4\textwidth]{plots_tauola/LLLL_emumuSS.pdf}{~}{~} +\includegraphics[width=0.4\textwidth]{plots_tauola/LLRR_emumuSS.pdf}\\ +\end{figure} +\begin{itemize} +\item Have all the modes :) +\item Can rest in peace from coding in FORTRAN. +\end{itemize} + +\end{frame} + + + + + +\end{document} diff --git a/Zurich_group/14_07_2014_2/slides.toc b/Zurich_group/14_07_2014_2/slides.toc new file mode 100644 index 0000000..ad11b0c --- /dev/null +++ b/Zurich_group/14_07_2014_2/slides.toc @@ -0,0 +1,4 @@ +\beamer@endinputifotherversion {3.10pt} 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b/Zurich_group/14_07_2014_2/tables/tables.synctex.gz Binary files differ diff --git a/Zurich_group/14_07_2014_2/tables/tables.tex b/Zurich_group/14_07_2014_2/tables/tables.tex new file mode 100644 index 0000000..3c0c6d8 --- /dev/null +++ b/Zurich_group/14_07_2014_2/tables/tables.tex @@ -0,0 +1,27 @@ +\documentclass[smaller]{beamer} +\usepackage[T1]{fontenc} +\usepackage{fix-cm} + +\setlength{\tabcolsep}{2pt} + +\begin{document} + \begin{frame} + \tiny{ + \begin{tabular}{|*{9}{c|}} + 0 & \scalebox{0.5}{$-0.431 \pm 0.0184(-23.4)$} & \scalebox{0.5}{$0.00218 \pm 0.0186(0.118)$} & \scalebox{0.5}{$0.0389 \pm 0.0183(2.13)$} & \scalebox{0.5}{$0.0104 \pm 0.0183(0.564)$} & \scalebox{0.5}{$0.0357 \pm 0.0183(1.96)$} & \scalebox{0.5}{$-0.0179 \pm 0.018(-0.997)$} & \scalebox{0.5}{$-0.0311 \pm 0.0187(-1.66)$} & \scalebox{0.5}{$0.0274 \pm 0.0184(1.49)$} \\ \hline +1 & \scalebox{0.5}{$-0.029 \pm 0.0188(-1.56)$} & \scalebox{0.5}{$0.0247 \pm 0.0187(1.32)$} & \scalebox{0.5}{$0.016 \pm 0.0184(0.872)$} & \scalebox{0.5}{$-0.0125 \pm 0.0191(-0.657)$} & \scalebox{0.5}{$-0.00833 \pm 0.0186(-0.449)$} & \scalebox{0.5}{$-0.0221 \pm 0.0183(-1.21)$} & \scalebox{0.5}{$-0.0592 \pm 0.0185(-3.2)$} & \scalebox{0.5}{$0.0151 \pm 0.0181(0.836)$} \\ \hline +2 & \scalebox{0.5}{$0.0090 \pm 0.0181(0.501)$} & \scalebox{0.5}{$-0.0226 \pm 0.0186(-1.21)$} & \scalebox{0.5}{$-0.00623 \pm 0.018(-0.347)$} & \scalebox{0.5}{$-0.0235 \pm 0.018(-1.3)$} & \scalebox{0.5}{$-0.0201 \pm 0.0183(-1.1)$} & \scalebox{0.5}{$-0.00449 \pm 0.0185(-0.243)$} & \scalebox{0.5}{$-0.00996 \pm 0.0188(-0.529)$} & \scalebox{0.5}{$0.00609 \pm 0.0186(0.328)$} \\ \hline +3 & \scalebox{0.5}{$-0.046 \pm 0.0183(-2.56)$} & \scalebox{0.5}{$-0.00942 \pm 0.0183(-0.515)$} & \scalebox{0.5}{$-0.00109 \pm 0.0188(-0.0579)$} & \scalebox{0.5}{$0.0108 \pm 0.0188(0.577)$} & \scalebox{0.5}{$-0.0519 \pm 0.0184(-2.83)$} & \scalebox{0.5}{$0.0274 \pm 0.0177(1.55)$} & \scalebox{0.5}{$-0.00217 \pm 0.0186(-0.117)$} & \scalebox{0.5}{$-0.00915 \pm 0.0187(-0.49)$} \\ \hline +4 & \scalebox{0.5}{$-0.031 \pm 0.0183(-1.71)$} & \scalebox{0.5}{$0.0268 \pm 0.0181(1.48)$} & \scalebox{0.5}{$-0.00687 \pm 0.0182(-0.378)$} & \scalebox{0.5}{$-0.00106 \pm 0.0187(-0.0568)$} & \scalebox{0.5}{$0.00908 \pm 0.0189(0.481)$} & \scalebox{0.5}{$0.0156 \pm 0.0181(0.861)$} & \scalebox{0.5}{$-0.0141 \pm 0.0186(-0.759)$} & \scalebox{0.5}{$0.00498 \pm 0.0178(0.279)$} \\ \hline +5 & \scalebox{0.5}{$-0.034 \pm 0.0178(-1.96)$} & \scalebox{0.5}{$0.0231 \pm 0.0189(1.22)$} & \scalebox{0.5}{$-0.0169 \pm 0.0183(-0.92)$} & \scalebox{0.5}{$-0.0138 \pm 0.0183(-0.75)$} & \scalebox{0.5}{$9.56e-05 \pm 0.0184(0.00521)$} & \scalebox{0.5}{$0.0158 \pm 0.0186(0.848)$} & \scalebox{0.5}{$0.00727 \pm 0.0191(0.381)$} & \scalebox{0.5}{$0.029 \pm 0.0185(1.57)$} \\ \hline +6 & \scalebox{0.5}{$-0.031 \pm 0.0186(-1.69)$} & \scalebox{0.5}{$0.0184 \pm 0.0183(1)$} & \scalebox{0.5}{$-0.000709 \pm 0.0182(-0.039)$} & \scalebox{0.5}{$-0.00728 \pm 0.0189(-0.386)$} & \scalebox{0.5}{$0.0223 \pm 0.0182(1.22)$} & \scalebox{0.5}{$-0.00232 \pm 0.0186(-0.125)$} & \scalebox{0.5}{$0.00974 \pm 0.0177(0.551)$} & \scalebox{0.5}{$-0.00613 \pm 0.018(-0.341)$}\\ \hline +7 & \scalebox{0.5}{$0.0042 \pm 0.0188(0.22)$} & \scalebox{0.5}{$0.022 \pm 0.0181(1.22)$} & \scalebox{0.5}{$-0.00412 \pm 0.0188(-0.22)$} & \scalebox{0.5}{$0.0044 \pm 0.0187(0.236)$} & \scalebox{0.5}{$0.0291 \pm 0.0188(1.55)$} & \scalebox{0.5}{$-0.00853 \pm 0.0184(-0.463)$} & \scalebox{0.5}{$-0.00649 \pm 0.0182(-0.356)$} & \scalebox{0.5}{$0.00402 \pm 0.0183(0.22)$} \\ \hline +8 & \scalebox{0.5}{$0.0061 \pm 0.018(0.34)$} & \scalebox{0.5}{$0.0118 \pm 0.0184(0.643)$} & \scalebox{0.5}{$-0.0169 \pm 0.0185(-0.915)$} & \scalebox{0.5}{$0.0244 \pm 0.0182(1.34)$} & \scalebox{0.5}{$0.00532 \pm 0.0188(0.283)$} & \scalebox{0.5}{$-0.0137 \pm 0.0185(-0.739)$} & \scalebox{0.5}{$-0.0167 \pm 0.0185(-0.903)$} & \scalebox{0.5}{$-0.0278 \pm 0.0183(-1.52)$} \\ \hline +9 & \scalebox{0.5}{$0.0056 \pm 0.0184(0.30)$} & \scalebox{0.5}{$-0.00938 \pm 0.0182(-0.514)$} & \scalebox{0.5}{$-0.0405 \pm 0.0182(-2.22)$} & \scalebox{0.5}{$0.00885 \pm 0.0182(0.487)$} & \scalebox{0.5}{$0.0361 \pm 0.0185(1.96)$} & \scalebox{0.5}{$-0.0229 \pm 0.019(-1.2)$} & \scalebox{0.5}{$-0.0506 \pm 0.0183(-2.77)$} & \scalebox{0.5}{$-0.0269 \pm 0.0183(-1.46)$} \\ \hline +10 & \scalebox{0.5}{$-0.0156 \pm 0.0185(-0.84)$} & \scalebox{0.5}{$-0.00611 \pm 0.018(-0.34)$} & \scalebox{0.5}{$-0.0241 \pm 0.0184(-1.31)$} & \scalebox{0.5}{$0.0204 \pm 0.0186(1.09)$} & \scalebox{0.5}{$-0.00378 \pm 0.0189(-0.201)$} & \scalebox{0.5}{$-0.0155 \pm 0.0185(-0.84)$} & \scalebox{0.5}{$0.0276 \pm 0.0184(1.5)$} & \scalebox{0.5}{$0.0137 \pm 0.0185(0.742)$} \\ \hline +11 & \scalebox{0.5}{$-0.0079 \pm 0.018(-0.44)$} & \scalebox{0.5}{$0.0539 \pm 0.0182(2.96)$} & \scalebox{0.5}{$-0.0063 \pm 0.0189(-0.334)$} & \scalebox{0.5}{$-0.0297 \pm 0.019(-1.57)$} & \scalebox{0.5}{$-0.00305 \pm 0.0183(-0.166)$} & \scalebox{0.5}{$-0.0503 \pm 0.0183(-2.75)$} & \scalebox{0.5}{$-0.0137 \pm 0.0181(-0.758)$} & \scalebox{0.5}{$0.0169 \pm 0.0187(0.902)$} \\ \hline + + \end{tabular} + } + \end{frame} +\end{document} \ No newline at end of file diff --git a/Zurich_group/14_07_2014_2/tables/tables.toc b/Zurich_group/14_07_2014_2/tables/tables.toc new file mode 100644 index 0000000..e06b51d --- /dev/null +++ b/Zurich_group/14_07_2014_2/tables/tables.toc @@ -0,0 +1 @@ +\beamer@endinputifotherversion {3.10pt} diff --git a/Zurich_group/14_07_2014_2/tauola_LFV_sim_results/LLLL.pdf b/Zurich_group/14_07_2014_2/tauola_LFV_sim_results/LLLL.pdf new file mode 100644 index 0000000..d86c166 --- /dev/null +++ b/Zurich_group/14_07_2014_2/tauola_LFV_sim_results/LLLL.pdf Binary files differ diff --git a/Zurich_group/14_07_2014_2/tauola_LFV_sim_results/LLLLRAD.pdf b/Zurich_group/14_07_2014_2/tauola_LFV_sim_results/LLLLRAD.pdf new file mode 100644 index 0000000..de023ea --- /dev/null +++ b/Zurich_group/14_07_2014_2/tauola_LFV_sim_results/LLLLRAD.pdf Binary files differ diff --git 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b/Zurich_group/14_07_2014_2/tauola_LFV_sim_results/mc-testerLLRR_emumuSS.root new file mode 100644 index 0000000..65fbdc7 --- /dev/null +++ b/Zurich_group/14_07_2014_2/tauola_LFV_sim_results/mc-testerLLRR_emumuSS.root Binary files differ diff --git a/Zurich_group/14_07_2014_2/tauola_LFV_sim_results/mc-testerLLRR_emumu_GE.root b/Zurich_group/14_07_2014_2/tauola_LFV_sim_results/mc-testerLLRR_emumu_GE.root new file mode 100644 index 0000000..1c98b36 --- /dev/null +++ b/Zurich_group/14_07_2014_2/tauola_LFV_sim_results/mc-testerLLRR_emumu_GE.root Binary files differ diff --git a/Zurich_group/14_07_2014_2/tauola_LFV_sim_results/mc-testerLLRR_emumu_GMU.root b/Zurich_group/14_07_2014_2/tauola_LFV_sim_results/mc-testerLLRR_emumu_GMU.root new file mode 100644 index 0000000..64b09f3 --- /dev/null +++ b/Zurich_group/14_07_2014_2/tauola_LFV_sim_results/mc-testerLLRR_emumu_GMU.root Binary files differ diff --git a/Zurich_group/14_07_2014_2/tauola_LFV_sim_results/mc-testerRAD.root b/Zurich_group/14_07_2014_2/tauola_LFV_sim_results/mc-testerRAD.root new file mode 100644 index 0000000..3b70c8a --- /dev/null +++ b/Zurich_group/14_07_2014_2/tauola_LFV_sim_results/mc-testerRAD.root Binary files differ diff --git a/Zurich_group/14_07_2014_2/tauola_LFV_sim_results/mc-testerRAD_emumu.root b/Zurich_group/14_07_2014_2/tauola_LFV_sim_results/mc-testerRAD_emumu.root new file mode 100644 index 0000000..3fff091 --- /dev/null +++ b/Zurich_group/14_07_2014_2/tauola_LFV_sim_results/mc-testerRAD_emumu.root Binary files differ diff --git a/Zurich_group/14_07_2014_2/tauola_LFV_sim_results/plotThreeMuUserAnalysis.C b/Zurich_group/14_07_2014_2/tauola_LFV_sim_results/plotThreeMuUserAnalysis.C new file mode 100644 index 0000000..870834a --- /dev/null +++ b/Zurich_group/14_07_2014_2/tauola_LFV_sim_results/plotThreeMuUserAnalysis.C @@ -0,0 +1,40 @@ +void plotThreeMuUserAnalysis(TString ss="LLLL") +{ + + + + TPaveText *pave = new TPaveText(1.8,1.8,2.7,2.7); + pave->SetFillColor(0); + pave->SetBorderSize(0); + pave->AddText("TAUOLA V Chrzaszcz"); + pave->AddText("#tau^{-} -> #mu^{-} #mu^{-} #mu^{+}"); + // pave->AddText("#tau^{-} -> e^{-} #mu^{-} #mu^{+}"); + + pave->AddText("#Gamma_{"+ss+"} Mode"); + + gStyle->SetOptStat(0); + TCanvas *c = new TCanvas("c","c",800,800); + TFile *f = new TFile("mc-tester"+ss+".root"); + TH2D *hist= f->Get("USER_HISTOGRAMS/m12_m23"); + hist->Scale(1./hist->Integral()); + hist->SetTitle(""); + hist->GetXaxis()->SetTitle("m_{--}^{2} GeV^{2}"); + hist->GetYaxis()->SetTitle("m_{+-}^{2} GeV^{2}"); + hist->GetZaxis()->SetLabelOffset(0.06); + hist->GetZaxis()->SetTitleOffset(20); + gStyle->SetPalette(1); + hist->Draw("COLZD"); + pave->Draw(); + gPad->Update(); + + TPaletteAxis *palette = (TPaletteAxis*)hist->GetListOfFunctions()->FindObject("palette"); + palette->SetX2NDC(0.85); + + gPad->Modified(); + gPad->Update(); + c->Update(); + c->SaveAs(ss+".pdf"); + + + +} diff --git a/Zurich_group/14_07_2014_2/tauola_LFV_sim_results/plotThreeMuUserAnalysis.C~ b/Zurich_group/14_07_2014_2/tauola_LFV_sim_results/plotThreeMuUserAnalysis.C~ new file mode 100644 index 0000000..95804c5 --- /dev/null +++ b/Zurich_group/14_07_2014_2/tauola_LFV_sim_results/plotThreeMuUserAnalysis.C~ @@ -0,0 +1,38 @@ +void plotThreeMuUserAnalysis(TString ss="LLLL") +{ + + + + TPaveText *pave = new TPaveText(1.8,1.8,2.7,2.7); + pave->SetFillColor(0); + pave->SetBorderSize(0); + pave->AddText("TAUOLA V XYZ"); + pave->AddText("#tau -> #mu^{-} #mu^{-} #mu^{+}"); + pave->AddText(ss+" Mode"); + + gStyle->SetOptStat(0); + TCanvas *c = new TCanvas("c","c",800,800); + TFile *f = new TFile("mc-tester"+ss+".root"); + TH2D *hist= f->Get("USER_HISTOGRAMS/m12_m23"); + hist->Scale(1./hist->Integral()); + hist->SetTitle(""); + hist->GetXaxis()->SetTitle("m_{--}^{2} GeV^{2}"); + hist->GetYaxis()->SetTitle("m_{+-}^{2} GeV^{2}"); + hist->GetZaxis()->SetLabelOffset(0.06); + hist->GetZaxis()->SetTitleOffset(20); + gStyle->SetPalette(1); + hist->Draw("COLZD"); + pave->Draw(); + gPad->Update(); + + TPaletteAxis *palette = (TPaletteAxis*)hist->GetListOfFunctions()->FindObject("palette"); + palette->SetX2NDC(0.85); + + gPad->Modified(); + gPad->Update(); + c->Update(); + c->SaveAs(ss+".pdf"); + + + +} diff --git a/Zurich_group/14_07_2014_2/texput.log b/Zurich_group/14_07_2014_2/texput.log new file mode 100644 index 0000000..f84449f --- /dev/null +++ b/Zurich_group/14_07_2014_2/texput.log @@ -0,0 +1,20 @@ +This is pdfTeX, Version 3.1415926-1.40.10 (TeX Live 2009/Debian) (format=pdflatex 2014.3.24) 24 JUN 2014 18:23 +entering extended mode + %&-line parsing enabled. +**beamerthemeSybila.tex + +! 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{\usebeamerfont{subtitle}\usebeamercolor[fg]{subtitle}\insertsubtitle\par}% + \fi% + \end{beamercolorbox}% + + \vskip1em + + \begin{beamercolorbox}[sep=8pt,center,#1]{author} + \usebeamerfont{author}\insertauthor + \end{beamercolorbox} + + \vskip1em + + {\usebeamercolor[fg]{titlegraphic}\inserttitlegraphic\par} + \begin{beamercolorbox}[sep=8pt,center,#1]{institute} + \usebeamerfont{date}\insertinstitute + \end{beamercolorbox} + + \vskip1em + + \begin{beamercolorbox}[sep=8pt,center,#1]{date} + \usebeamerfont{date}\insertdate + \end{beamercolorbox} + \end{centering} + \vfill +} + +%------------------------------------------------------------------------------- +% Logo +%------------------------------------------------------------------------------- + +\logo{\hspace*{0.6\textwidth}\includegraphics[width=1.2cm]{sybila-logo-paper-shaded}\hspace*{0.3cm}} + +%------------------------------------------------------------------------------- +% Colors +%------------------------------------------------------------------------------- + +\setbeamercovered{dynamic} + +\setbeamercolor{math text}{fg=green!45!black} +\setbeamercolor{title}{bg=white!30!black} +\setbeamercolor{frametitle}{bg=white!45!black} +\setbeamercolor{footline}{bg=black,fg=white} +\setbeamercolor{author in head/foot}{bg=black,fg=white} +\setbeamercolor{title in head/foot}{bg=white!45!black} +\setbeamercolor{block title}{bg=white!45!black} +\setbeamercolor{block title example}{bg=white!45!black} +\setbeamercolor{block title alerted}{bg=white!15!black} + +\colorlet{redshaded}{red!25!bg} +\colorlet{shaded}{black!25!bg} +\colorlet{shadedshaded}{black!10!bg} +\colorlet{blackshaded}{black!40!bg} + +\usecolortheme{whale} +\usecolortheme{orchid} + +%------------------------------------------------------------------------------- +% Fonts +%------------------------------------------------------------------------------- + +\setbeamerfont{block title}{size={}} +\setbeamerfont{date}{size=\small} + +%------------------------------------------------------------------------------- +% Other +%------------------------------------------------------------------------------- + +\titlegraphic{\includegraphics[width=3.0cm]{sybila-logo-slide-title-shaded.pdf}} + +\mode + diff --git a/Zurich_group/14_07_2014_2/tmp/example.tex b/Zurich_group/14_07_2014_2/tmp/example.tex new file mode 100644 index 0000000..ce0641b --- /dev/null +++ b/Zurich_group/14_07_2014_2/tmp/example.tex @@ -0,0 +1,21 @@ +\documentclass[xcolor=svgnames]{beamer} +\usepackage[utf8]{inputenc} +\usepackage[english]{babel} + +\usetheme{Sybila} + +\title[Parallelization of Methods for Dynamic System Analysis]{Parallelization of Methods for Dynamic System Analysis Using CUDA} +\author{Jan Papou\v{s}ek} +\institute{Masaryk University Brno} +\date{\today} + +\begin{document} +% --------------------------- SLIDE -------------------------------------------- +\frame[plain]{\titlepage} +% ------------------------------------------------------------------------------ +% --------------------------- SLIDE -------------------------------------------- +\begin{frame} + \frametitle{Introduction} +\end{frame} +% ------------------------------------------------------------------------------ +\end{document} diff --git a/Zurich_group/14_07_2014_2/tmp/example/beamerthemeSybila.sty b/Zurich_group/14_07_2014_2/tmp/example/beamerthemeSybila.sty new file mode 100644 index 0000000..5639601 --- /dev/null +++ b/Zurich_group/14_07_2014_2/tmp/example/beamerthemeSybila.sty @@ -0,0 +1,104 @@ +\mode + +%------------------------------------------------------------------------------- +% Themes +%------------------------------------------------------------------------------- + +\useoutertheme{split} +\useinnertheme{rounded} +\usefonttheme{structurebold} +%\useoutertheme{shadow} + +%------------------------------------------------------------------------------- +% Templates +%------------------------------------------------------------------------------- + +\beamertemplatenavigationsymbolsempty +\beamertemplateheadempty +\beamertemplateshadowblocks + +%------------------------------------------------------------------------------- +% Own templates +%------------------------------------------------------------------------------- + +% Normal title page. +\defbeamertemplate*{title page}{simple}[1][] +{ + \vfill + \begin{centering} + \begin{beamercolorbox}[center, rounded=true]{title} + \usebeamerfont{title}\inserttitle\par% + \ifx\insertsubtitle\@empty% + \else% + \vskip0.25em% + {\usebeamerfont{subtitle}\usebeamercolor[fg]{subtitle}\insertsubtitle\par}% + \fi% + \end{beamercolorbox}% + + \vskip1em + + \begin{beamercolorbox}[sep=8pt,center,#1]{author} + \usebeamerfont{author}\insertauthor + \end{beamercolorbox} + + \vskip1em + + {\usebeamercolor[fg]{titlegraphic}\inserttitlegraphic\par} + \begin{beamercolorbox}[sep=8pt,center,#1]{institute} + \usebeamerfont{date}\insertinstitute + \end{beamercolorbox} + + \vskip1em + + \begin{beamercolorbox}[sep=8pt,center,#1]{date} + \usebeamerfont{date}\insertdate + \end{beamercolorbox} + \end{centering} + \vfill +} + +%------------------------------------------------------------------------------- +% Logo +%------------------------------------------------------------------------------- + +\logo{\hspace*{0.6\textwidth}\includegraphics[width=1.2cm]{sybila-logo-paper-shaded}\hspace*{0.3cm}} + +%------------------------------------------------------------------------------- +% Colors +%------------------------------------------------------------------------------- + +\setbeamercovered{dynamic} + +\setbeamercolor{math text}{fg=green!45!black} +\setbeamercolor{title}{bg=white!30!black} +\setbeamercolor{frametitle}{bg=white!45!black} +\setbeamercolor{footline}{bg=black,fg=white} +\setbeamercolor{author in head/foot}{bg=black,fg=white} +\setbeamercolor{title in head/foot}{bg=white!45!black} +\setbeamercolor{block title}{bg=white!45!black} +\setbeamercolor{block title example}{bg=white!45!black} +\setbeamercolor{block title alerted}{bg=white!15!black} + +\colorlet{redshaded}{red!25!bg} +\colorlet{shaded}{black!25!bg} +\colorlet{shadedshaded}{black!10!bg} +\colorlet{blackshaded}{black!40!bg} + +\usecolortheme{whale} +\usecolortheme{orchid} + +%------------------------------------------------------------------------------- +% Fonts +%------------------------------------------------------------------------------- + +\setbeamerfont{block title}{size={}} +\setbeamerfont{date}{size=\small} + +%------------------------------------------------------------------------------- +% Other +%------------------------------------------------------------------------------- + +\titlegraphic{\includegraphics[width=3.0cm]{sybila-logo-slide-title-shaded.pdf}} + +\mode + diff --git a/Zurich_group/14_07_2014_2/tmp/example/example.aux b/Zurich_group/14_07_2014_2/tmp/example/example.aux new file mode 100644 index 0000000..3c3451e --- /dev/null +++ b/Zurich_group/14_07_2014_2/tmp/example/example.aux @@ -0,0 +1,28 @@ +\relax +\ifx\hyper@anchor\@undefined +\global \let \oldcontentsline\contentsline +\gdef \contentsline#1#2#3#4{\oldcontentsline{#1}{#2}{#3}} +\global \let \oldnewlabel\newlabel +\gdef \newlabel#1#2{\newlabelxx{#1}#2} +\gdef \newlabelxx#1#2#3#4#5#6{\oldnewlabel{#1}{{#2}{#3}}} +\AtEndDocument{\let \contentsline\oldcontentsline +\let \newlabel\oldnewlabel} +\else +\global \let \hyper@last\relax +\fi + +\@writefile{toc}{\beamer@endinputifotherversion {3.10pt}} +\@writefile{nav}{\beamer@endinputifotherversion {3.10pt}} +\select@language{english} +\@writefile{toc}{\select@language{english}} +\@writefile{lof}{\select@language{english}} +\@writefile{lot}{\select@language{english}} +\@writefile{nav}{\headcommand {\slideentry {0}{0}{1}{1/1}{}{0}}} +\@writefile{nav}{\headcommand {\beamer@framepages {1}{1}}} +\@writefile{nav}{\headcommand {\slideentry {0}{0}{2}{2/2}{}{0}}} 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/dev/null +++ b/Zurich_group/14_07_2014_2/tmp/example/example.snm diff --git a/Zurich_group/14_07_2014_2/tmp/example/example.synctex.gz b/Zurich_group/14_07_2014_2/tmp/example/example.synctex.gz new file mode 100644 index 0000000..5bccdb3 --- /dev/null +++ b/Zurich_group/14_07_2014_2/tmp/example/example.synctex.gz Binary files differ diff --git a/Zurich_group/14_07_2014_2/tmp/example/example.tex b/Zurich_group/14_07_2014_2/tmp/example/example.tex new file mode 100644 index 0000000..ce0641b --- /dev/null +++ b/Zurich_group/14_07_2014_2/tmp/example/example.tex @@ -0,0 +1,21 @@ +\documentclass[xcolor=svgnames]{beamer} +\usepackage[utf8]{inputenc} +\usepackage[english]{babel} + +\usetheme{Sybila} + +\title[Parallelization of Methods for Dynamic System Analysis]{Parallelization of Methods for Dynamic System Analysis Using CUDA} +\author{Jan Papou\v{s}ek} +\institute{Masaryk University Brno} +\date{\today} + +\begin{document} +% --------------------------- SLIDE -------------------------------------------- +\frame[plain]{\titlepage} +% ------------------------------------------------------------------------------ +% --------------------------- SLIDE -------------------------------------------- +\begin{frame} + \frametitle{Introduction} +\end{frame} +% ------------------------------------------------------------------------------ +\end{document} diff --git a/Zurich_group/14_07_2014_2/tmp/example/example.toc b/Zurich_group/14_07_2014_2/tmp/example/example.toc new file mode 100644 index 0000000..495658f --- /dev/null +++ b/Zurich_group/14_07_2014_2/tmp/example/example.toc @@ -0,0 +1,2 @@ +\beamer@endinputifotherversion {3.10pt} +\select@language {english} diff --git a/Zurich_group/14_07_2014_2/tmp/example/sybila-logo-paper-shaded.png b/Zurich_group/14_07_2014_2/tmp/example/sybila-logo-paper-shaded.png new file mode 100644 index 0000000..f2a2c4e --- /dev/null +++ b/Zurich_group/14_07_2014_2/tmp/example/sybila-logo-paper-shaded.png Binary files 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+%\usepackage{amssymb,amsmath} +\usepackage[latin1]{inputenc} +\usepackage{amsmath} +\newcommand\abs[1]{\left|#1\right|} +\usepackage{iwona} +\usepackage{hepparticles} +\usepackage{hepnicenames} +\usepackage{hepunits} +\progressbaroptions{imagename=images/lhcb} +%\usetheme{Boadilla}f + +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%5 +\definecolor{mygreen}{cmyk}{0.82,0.11,1,0.25} +\setbeamertemplate{blocks}[rounded][shadow=false] +\addtobeamertemplate{block begin}{\pgfsetfillopacity{0.8}}{\pgfsetfillopacity{1}} +\setbeamercolor{structure}{fg=mygreen} +\setbeamercolor*{block title example}{fg=mygreen!50, +bg= blue!10} +\setbeamercolor*{block body example}{fg= blue, +bg= blue!5} + + + + + +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%\beamersetuncovermixins{\opaqueness<1>{25}}{\opaqueness<2->{15}} +\title{Method of moments for $\PB \to \PKstar \mu \mu$} +\author{\underline{Marcin Chrzaszcz}$^{1,2}$} +\date{\today} + +\begin{document} + +{ +\institute{$^1$ University of Zurich, $^2$ Institute of Nuclear Physics} +\setbeamertemplate{footline}{} +\begin{frame} +\logo{ +\vspace{2 mm} +\includegraphics[height=1cm,keepaspectratio]{images/uzh.jpg}~ +\includegraphics[width=1cm,keepaspectratio]{images/ifj.png}} + + \titlepage +\end{frame} +} +\institute{UZH,IFJ} + +\section[Outline]{} +\begin{frame} +\tableofcontents +\end{frame} + +\section{Introduction} +\begin{frame}\frametitle{Plan} +Why method of moments: +\begin{enumerate} +\item Complementary approach in performing the fit. +\item Allows to extract info measuring quantities in event basis depending on the angular distribution. +\item Used in $\PB \to \rho \Plepton \nu$(SLAC-386 UC-414),\\ $\PJpsi \to \PK \PK \gamma$(PRD 71, 032005 (2005) ), etc. +\end{enumerate} + + +\end{frame} +\section{Method of Moments - Theory} +\begin{frame}\frametitle{Method of moments} +{~} +Let's assume we have our pdf with $k$ unknown parameters :$PDF(x_i, \alpha)$, $dim(\alpha)=k$. One can calculate $k$ moments, which are the functions of $\alpha_i$: +\begin{equation} +\mu_i=f(\alpha_1,..., \alpha_k) = E[W_i] +\end{equation} +If we have $n$ events in our $q^2$ bin, we can estimate: +\begin{equation} +\widehat{\mu}_i=\dfrac{1}{n}\sum_{j=0}^{j=n-1} w_j +\end{equation} +, where $w_j=g(x_i)$ + +\end{frame} + +\begin{frame}\frametitle{Trivial example} +{~} +Lets see how this works in practice: +\begin{equation} +f(x)=\dfrac{x^{a-1}e^{-x/b}} {b^a \Gamma(a)} +\end{equation} +we measure the moments:\\ +\begin{center} $m_1=\dfrac{X_1+X_2+...+X_n}{n}$,\\ $m_2=\dfrac{X_1^2+X_2^2+...+X_n^2}{n}$.\\\end{center} +and calculate them analytically: +\begin{center} $m_1=ab$, $m_2=b^2a(a+1)$\end{center} +So one just needs to solve this and get the answer: +\center $a=\dfrac{m_1^2}{m_2-m_1^2}$, $b=\dfrac{m_2-m_1^2}{m_1}$ +\end{frame} + +\section{Moments of Ss} + + +\begin{frame}\frametitle{Our PDF} +{~} +The angular terms: +\begin{multline} +\dfrac{d^4\Gamma}{dq^2 dcos\theta_k dcos\theta_l d\phi}=\dfrac{9}{32\pi}( \dfrac{3}{4}(1-F_l)\sin^2 \theta_k + F_l \cos^2 \theta_k + (\dfrac{1}{4}(1-F_l)\sin^2 \theta_k \\ -F_l\cos^2) \cos 2\theta_l + J_3 \sin^2 \theta_k \sin^2 \theta_l cos2\phi + J_4 \sin2 \theta_k \sin \theta_l \cos\phi +\\ J_5 \sin 2 \theta_k \sin \theta_l \cos \phi + (J_{6s} \sin^2 \theta_k + J_{6c} \cos^2 \theta_k) \cos \theta_l + \\ J_7 \sin 2\theta_k \sin \theta_l \sin \phi + J_8 \sin 2 \theta_k \sin 2 \theta_l \sin \phi + J_9 \sin^2 \theta_k \sin^2 \theta_l \sin 2 \phi) +\end{multline} +Since we are fitting a PDF we need to ensure it is normalized: +\begin{equation} +\int_{-\pi}^{\pi} d\phi \int_{-1}^{1} d cos\theta_l \int_{-1}^{1} d cos\theta_k \dfrac{d^4\Gamma}{dq^2 dcos\theta_k dcos\theta_l d\phi}=1 +\end{equation} + + +\end{frame} +\begin{frame}\frametitle{Measuring Js} +{~} +From equation 2 we have the following: + +\begin{equation} +\dfrac{1}{4}(3 J_{1c} + 6 J_{1s} - J_{2c} - 2 J_{2s}) =1 +\end{equation} +For now we will consider the following PDF: +\begin{equation} + \dfrac{d^3\Gamma}{\Gamma dcos\theta_k dcos\theta_l d\phi }(cos\theta_k , cos\theta_l, \phi) +\end{equation} + +Becouse our PDF is not normalized and we are measuring $\Gamma+\overline{\Gamma} +$ we are effectively fitting the $S_i$ (aka $J_i \to S_i$) +\end{frame} + + +\begin{frame}\frametitle{Moments for $\PB \to \PKstar \mu \mu$} +{~} +Let's calculate the moments for Ss: +\begin{equation} + \dfrac{d^3\Gamma}{\Gamma dcos\theta_k dcos\theta_l d\phi }sin^2 \theta_k sin^2 \theta_l cos 2 \phi= \dfrac{8 S_3 }{25} +\end{equation} +\begin{equation} + \dfrac{d^3\Gamma}{\Gamma dcos\theta_k dcos\theta_l d\phi } sin 2 \theta_k sin 2 \theta_k cos\phi= \dfrac{8 S_4 }{25} +\end{equation} +\begin{equation} + \dfrac{d^3\Gamma}{\Gamma dcos\theta_k dcos\theta_l d\phi }sin2\theta_k sin\theta_l cos\phi = \dfrac{2 S_5 }{5} +\end{equation} +\begin{equation} + \dfrac{d^3\Gamma}{\Gamma dcos\theta_k dcos\theta_l d\phi} sin 2 \theta_k sin \theta_l sin \phi = \dfrac{2 S_7 }{5} +\end{equation} +\begin{equation} + \dfrac{d^3\Gamma}{\Gamma dcos\theta_k dcos\theta_l d\phi} sin 2 \theta_k sin2 \theta_l sin \phi = \dfrac{8 S_8 }{25} +\end{equation} + + + +\end{frame} +\begin{frame}\frametitle{Moments for $\PB \to \PKstar \mu \mu$} +{~} +\begin{itemize} +\item The simplest solution one could imagine. +\item We are abusing the fact that the basis is orthogonal. +\item Each of the J doesn't know about other. +\item Only $S_{1s}$, $S_{2s}$, $S_{1c}$, $S_{2c}$ and $S_{6s}$, $S_{6c}$ are not orthogonal, but to get the answer you just need to solve a linear equation system so it's not a tragedy. +\end{itemize} +\begin{equation} + \dfrac{d^3\Gamma}{\Gamma dcos\theta_k dcos\theta_l d\phi} sin^2 \theta_k cos \theta_l = 0.1(S_6c+4S_6s) +\end{equation} +\begin{equation} + \dfrac{d^3\Gamma}{\Gamma dcos\theta_k dcos\theta_l d\phi} cos \theta_l = 0.25(S_{6}c+2S_{6s}) +\end{equation} + +solution: $S_{6c}=2 (4 M_{S_{6c}} - 5 M_{S_{6s}})$, $S_{6s}= -2 M_{S_{6c}} + 5 M_{S_{6s}}$ + + + +\end{frame} + + + +\section{Toy MC study} + +\begin{frame}\frametitle{Moments for $\PB \to \PKstar \mu \mu$} +{~} +Lets see if this method actually works. Let's take some random parameters for the PDF and make a toy. +\begin{columns} +\column{2.5in} +\includegraphics[scale=0.25]{images/J5.png} + + + +\column{2.5in} +\includegraphics[scale=0.25]{images/J7.png} + + +\end{columns} +\begin{itemize} +\item let's take 300 signal events as a working case. +\end{itemize} + +\end{frame} + + + + +\begin{frame}\frametitle{Moments for $\PB \to \PKstar \mu \mu$} +{~} +\small Lets see if this method actually works. Let's take some random parameters for the PDF and make a toy. +\begin{columns} +\column{2.5in} +\includegraphics[scale=0.25]{images/J3.png} + + + +\column{2.5in} +\includegraphics[scale=0.25]{images/J4.png} + + +\end{columns} + + +\begin{itemize} +\item let's take 300 signal events as a working case... we might still change the binning +\end{itemize} + +\end{frame} + + + +\begin{frame}\frametitle{Moments for $\PB \to \PKstar \mu \mu$} +{~} +Lets see if this method actually works. Let's take some random parameters for the PDF and make a toy. +\begin{columns} +\column{2.5in} +\includegraphics[scale=0.25]{images/J8.png} + + + +\column{2.5in} +\includegraphics[scale=0.25]{images/J9.png} + + +\end{columns} + +\begin{itemize} +\item let's take 300 signal events as a working case... we might still change the binning +\end{itemize} + +\end{frame} + +\begin{frame}\frametitle{Error Estimation} +{~} +\begin{itemize} +\item Since moment is the mean of a given distribution the error can be estimated as $mean/RMS$ +\item use TOY MC to check this assumption +\end{itemize} + +\includegraphics[scale=0.3]{plots/conw.png}\\ + + +\end{frame} +%%%%%%%%%%%%%%%%%%%%%%%%5 +\begin{frame}\frametitle{Correlation check} +{~} +\begin{itemize} +\item In theory $S_i$ shouldn't be correlated to $S_j$ in the moment calculation. +\item Lets put this to a test. +\end{itemize} + +\begin{columns} +\column{2.5in} +\includegraphics[scale=0.2]{plots/J9J4.png}\\ + + +\column{2.5in} +\includegraphics[scale=0.2]{plots/J8J5.png}\\ + + +\end{columns} + + +\end{frame} + + +%%%%%%%%%%%%%%%%%%%%%%%%5 +\begin{frame}\frametitle{Correlation check 2} +{~} +\begin{itemize} +\item Let's now FIX $J_x$ and simulate different $J_y$ +\item Again theory would suggest that one J shouldn't know about the other, so $J_x$ shouldn't change with scanning $J_y$ parameter +\end{itemize} + +\begin{columns} +\column{2.5in} +\includegraphics[scale=0.24]{plots/J5_vs_J9_300.png}\\ + + +\column{2.5in} +\includegraphics[scale=0.24]{plots/J3_vs_J9_300.png}\\ + + +\end{columns} + + +\end{frame} + + + +\section{2 am discovery} +\begin{frame}\frametitle{What will happen to our problem with an S-wave?} +{~} +Reminder: +\begin{multline} +\dfrac{d^4\Gamma}{dq^2 dcos\theta_k dcos\theta_l d\phi}=\dfrac{9}{32\pi}( J_{1s}sin^2 \theta_k + J_{1c}cos^2 \theta_k + (J_{2s}sin^2 \theta_k + \\ J_{2c}cos^2) cos 2\theta_l + J_3 sin^2 \theta_k sin^2 \theta_l cos2\phi + J_4 sin2 \theta_k sin \theta_l cos\phi +\\ J_5 sin2 \theta_k sin \theta_l cos \phi + (J_{6s} sin^2 \theta_k + J_{6c} cos^2 \theta_k) cos \theta_l + \\ J_7 sin 2\theta_k sin \theta_l sin \phi + J_8 sin 2 \theta_k sin 2 \theta_l sin phi + J_9 sin^2 \theta_k sin^2 \theta_l sin 2 \phi) +\end{multline} +Let's add a very discussing things that keeps us awake at night: +\begin{multline} +W_s =\dfrac{2}{3} F_s \sin^2 \theta_l + \frac{4}{3} A_s \sin^2 \theta_l \cos \theta_k + I_4 sin \theta_k sin 2 \theta_lcos \phi \\+ I_5 sin \theta_k sin \theta_l cos \phi + I_7 sin \theta_k sin \theta_l + sin \phi + I_8 sin \theta_k sin 2\theta_l sin\phi) +\end{multline} + + +\end{frame} + +\begin{frame}\frametitle{What will happen to our problem with an S-wave?} +{~} +So now our PDF is sum of eq. 15 and 16. Of coz we need to require normalization: +\begin{equation} +\dfrac{1}{12}(32 I_{1a} + 9 J_{1c} + 18 J_{1s} - 3 J_{2c} - 6 J_{2s}) =1 +\end{equation} +No surprises here. If we have a S-wave it has to enter in $\Gamma$. +To build up the preasure, what will happen to our Ss? + + + +\end{frame} + + +\begin{frame}\frametitle{NOTHING!!!!!!!!} +{~} +We are completely insensitive to S-wave: +\begin{equation} + \dfrac{d^3\Gamma}{\Gamma dcos\theta_k dcos\theta_l d\phi }sin^2 \theta_k sin^2 \theta_l cos 2 \phi= \dfrac{8 S_3 }{25} +\end{equation} +\begin{equation} + \dfrac{d^3\Gamma}{\Gamma dcos\theta_k dcos\theta_l d\phi } sin 2 \theta_k sin 2 \theta_k cos\phi= \dfrac{8 S_4 }{25} +\end{equation} +\begin{equation} + \dfrac{d^3\Gamma}{\Gamma dcos\theta_k dcos\theta_l d\phi }sin2\theta_k sin\theta_l cos\phi = \dfrac{2 S_5 }{5} +\end{equation} +\begin{equation} + \dfrac{d^3\Gamma}{\Gamma dcos\theta_k dcos\theta_l d\phi} sin 2 \theta_k sin \theta_l sin \phi = \dfrac{2 S_7 }{5} +\end{equation} +\begin{equation} + \dfrac{d^3\Gamma}{\Gamma dcos\theta_k dcos\theta_l d\phi} sin 2 \theta_k sin2 \theta_l sin \phi = \dfrac{8 S_8 }{25} +\end{equation} + + + +\end{frame} + +\begin{frame}\frametitle{Thins get better :)} +{~} +We can even measure directly the S-wave: +\begin{equation} + \dfrac{d^3\Gamma}{\Gamma dcos\theta_k dcos\theta_l d\phi }sin^2 \theta_l cos \theta_k = \dfrac{32 I_{1b} }{45} +\end{equation} +\begin{equation} + \dfrac{d^3\Gamma}{\Gamma dcos\theta_k dcos\theta_l d\phi } sin \theta_k sin 2 \theta_l cos \phi = \dfrac{16 I_4 }{45} +\end{equation} +\begin{equation} + \dfrac{d^3\Gamma}{\Gamma dcos\theta_k dcos\theta_l d\phi } sin\theta_k sin\theta_l cos\phi = \dfrac{4 I_5 }{9} +\end{equation} +\begin{equation} + \dfrac{d^3\Gamma}{\Gamma dcos\theta_k dcos\theta_l d\phi} sin \theta_k sin 2 \theta_l sin \phi = \dfrac{4 I_7 }{9} +\end{equation} +\begin{equation} + \dfrac{d^3\Gamma}{\Gamma dcos\theta_k dcos\theta_l d\phi} sin \theta_k sin2 \theta_l sin \phi = \dfrac{16 S_8 }{45} +\end{equation} + + + +\end{frame} + + +\begin{frame}\frametitle{Conclusions on S-wave} +{~} +\begin{itemize} +\item S-wave components are transparent to method of moments. +\item If they are orthogonal to others all they toy studies holds for them as well(will reapat for robustness but can bet my house that there is nothing going on there). +\item +\end{itemize} + +\end{frame} + + + +\begin{frame}\frametitle{Conclusions} +{~} +\begin{itemize} +\item Implemented moments method for the K*mm and start testing with toy MC +\item The method converge fast and works for the "simple case", i.e. signal only. +\item Method completely insensitive to S-wave component, thanks to orthogonality. +\item Complementary one can measure in-depended S-wave component. +\end{itemize} +TO DO: +\begin{itemize} +\item add realism: backgrounds +\item Do the unfolding +\item Study binning +\end{itemize} + +\end{frame} +%%%%%%%%%%%%%%%%%%%%%%%%%55 +\begin{frame}\frametitle{~} +{~} +\center \Huge BACKUPS + +\end{frame} + +\begin{frame} +{~} + +\begin{columns} +\column{2.5in} +\includegraphics[scale=0.17]{plots/pool_plots/J1c_50.png}\\ +\includegraphics[scale=0.17]{plots/pool_plots/J1c_75.png}\\ + + +\column{2.5in} +\includegraphics[scale=0.17]{plots/pool_plots/J1c_50E.png}\\ +\includegraphics[scale=0.17]{plots/pool_plots/J1c_75E.png} + + +\end{columns} +\end{frame} + +\begin{frame} +{~} + +\begin{columns} +\column{2.5in} +\includegraphics[scale=0.17]{plots/pool_plots/J1c_125.png}\\ +\includegraphics[scale=0.17]{plots/pool_plots/J1c_175.png}\\ + + +\column{2.5in} +\includegraphics[scale=0.17]{plots/pool_plots/J1c_125E.png}\\ +\includegraphics[scale=0.17]{plots/pool_plots/J1c_175E.png} + + +\end{columns} +\end{frame} + +\begin{frame} +{~} + +\begin{columns} +\column{2.5in} +\includegraphics[scale=0.17]{plots/pool_plots/J1c_225.png}\\ +\includegraphics[scale=0.17]{plots/pool_plots/J1c_300.png}\\ + + +\column{2.5in} +\includegraphics[scale=0.17]{plots/pool_plots/J1c_225E.png}\\ +\includegraphics[scale=0.17]{plots/pool_plots/J1c_300E.png} + + +\end{columns} +\end{frame} + + +\begin{frame} +{~} + +\begin{columns} +\column{2.5in} +\includegraphics[scale=0.17]{plots/pool_plots/J1c_400.png}\\ + + + +\column{2.5in} +\includegraphics[scale=0.17]{plots/pool_plots/J1c_400E.png}\\ + + + +\end{columns} +\end{frame} + +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%55 +\begin{frame} +{~} + +\begin{columns} +\column{2.5in} +\includegraphics[scale=0.17]{plots/pool_plots/J1s_50.png}\\ +\includegraphics[scale=0.17]{plots/pool_plots/J1s_75.png}\\ + + +\column{2.5in} +\includegraphics[scale=0.17]{plots/pool_plots/J1s_50E.png}\\ +\includegraphics[scale=0.17]{plots/pool_plots/J1s_75E.png} + + +\end{columns} +\end{frame} + +\begin{frame} +{~} + +\begin{columns} +\column{2.5in} +\includegraphics[scale=0.17]{plots/pool_plots/J1s_125.png}\\ +\includegraphics[scale=0.17]{plots/pool_plots/J1s_175.png}\\ + + +\column{2.5in} +\includegraphics[scale=0.17]{plots/pool_plots/J1s_125E.png}\\ +\includegraphics[scale=0.17]{plots/pool_plots/J1s_175E.png} + + +\end{columns} +\end{frame} + +\begin{frame} +{~} + +\begin{columns} +\column{2.5in} +\includegraphics[scale=0.17]{plots/pool_plots/J1s_225.png}\\ +\includegraphics[scale=0.17]{plots/pool_plots/J1s_300.png}\\ + + +\column{2.5in} +\includegraphics[scale=0.17]{plots/pool_plots/J1s_225E.png}\\ +\includegraphics[scale=0.17]{plots/pool_plots/J1s_300E.png} + + +\end{columns} +\end{frame} + + +\begin{frame} +{~} + +\begin{columns} +\column{2.5in} +\includegraphics[scale=0.17]{plots/pool_plots/J1s_400.png}\\ + + + +\column{2.5in} +\includegraphics[scale=0.17]{plots/pool_plots/J1s_400E.png}\\ + + + +\end{columns} +\end{frame} + +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +\begin{frame} +{~} + +\begin{columns} +\column{2.5in} +\includegraphics[scale=0.17]{plots/pool_plots/J2c_50.png}\\ +\includegraphics[scale=0.17]{plots/pool_plots/J2c_75.png}\\ + + +\column{2.5in} +\includegraphics[scale=0.17]{plots/pool_plots/J2c_50E.png}\\ +\includegraphics[scale=0.17]{plots/pool_plots/J2c_75E.png} + + +\end{columns} +\end{frame} + +\begin{frame} +{~} + +\begin{columns} +\column{2.5in} +\includegraphics[scale=0.17]{plots/pool_plots/J2c_125.png}\\ +\includegraphics[scale=0.17]{plots/pool_plots/J2c_175.png}\\ + + +\column{2.5in} +\includegraphics[scale=0.17]{plots/pool_plots/J2c_125E.png}\\ +\includegraphics[scale=0.17]{plots/pool_plots/J2c_175E.png} + + +\end{columns} +\end{frame} + +\begin{frame} +{~} + +\begin{columns} +\column{2.5in} +\includegraphics[scale=0.17]{plots/pool_plots/J2c_225.png}\\ +\includegraphics[scale=0.17]{plots/pool_plots/J2c_300.png}\\ + + +\column{2.5in} +\includegraphics[scale=0.17]{plots/pool_plots/J2c_225E.png}\\ +\includegraphics[scale=0.17]{plots/pool_plots/J2c_300E.png} + + +\end{columns} +\end{frame} + + +\begin{frame} +{~} + +\begin{columns} +\column{2.5in} +\includegraphics[scale=0.17]{plots/pool_plots/J2c_400.png}\\ +\includegraphics[scale=0.17]{plots/pool_plots/J2c_500.png}\\ + + +\column{2.5in} +\includegraphics[scale=0.17]{plots/pool_plots/J2c_400E.png}\\ +\includegraphics[scale=0.17]{plots/pool_plots/J2c_500E.png}\\ + + +\end{columns} +\end{frame} + + +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +\begin{frame} +{~} + +\begin{columns} +\column{2.5in} +\includegraphics[scale=0.17]{plots/pool_plots/J3_50.png}\\ +\includegraphics[scale=0.17]{plots/pool_plots/J3_75.png}\\ + + +\column{2.5in} +\includegraphics[scale=0.17]{plots/pool_plots/J3_50E.png}\\ +\includegraphics[scale=0.17]{plots/pool_plots/J3_75E.png} + + +\end{columns} +\end{frame} + +\begin{frame} +{~} + +\begin{columns} +\column{2.5in} +\includegraphics[scale=0.17]{plots/pool_plots/J3_125.png}\\ +\includegraphics[scale=0.17]{plots/pool_plots/J3_175.png}\\ + + +\column{2.5in} +\includegraphics[scale=0.17]{plots/pool_plots/J3_125E.png}\\ +\includegraphics[scale=0.17]{plots/pool_plots/J3_175E.png} + + +\end{columns} +\end{frame} + +\begin{frame} +{~} + +\begin{columns} +\column{2.5in} +\includegraphics[scale=0.17]{plots/pool_plots/J3_225.png}\\ +\includegraphics[scale=0.17]{plots/pool_plots/J3_300.png}\\ + + +\column{2.5in} +\includegraphics[scale=0.17]{plots/pool_plots/J3_225E.png}\\ +\includegraphics[scale=0.17]{plots/pool_plots/J3_300E.png} + + +\end{columns} +\end{frame} + + +\begin{frame} +{~} + +\begin{columns} +\column{2.5in} +\includegraphics[scale=0.17]{plots/pool_plots/J3_400.png}\\ +\includegraphics[scale=0.17]{plots/pool_plots/J3_500.png}\\ + + +\column{2.5in} +\includegraphics[scale=0.17]{plots/pool_plots/J3_400E.png}\\ +\includegraphics[scale=0.17]{plots/pool_plots/J3_500E.png}\\ + + +\end{columns} +\end{frame} + + + +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +\begin{frame} +{~} + +\begin{columns} +\column{2.5in} +\includegraphics[scale=0.17]{plots/pool_plots/J4_50.png}\\ +\includegraphics[scale=0.17]{plots/pool_plots/J4_75.png}\\ + + +\column{2.5in} +\includegraphics[scale=0.17]{plots/pool_plots/J4_50E.png}\\ +\includegraphics[scale=0.17]{plots/pool_plots/J4_75E.png} + + +\end{columns} +\end{frame} + +\begin{frame} +{~} + +\begin{columns} +\column{2.5in} +\includegraphics[scale=0.17]{plots/pool_plots/J4_125.png}\\ +\includegraphics[scale=0.17]{plots/pool_plots/J4_175.png}\\ + + +\column{2.5in} +\includegraphics[scale=0.17]{plots/pool_plots/J4_125E.png}\\ +\includegraphics[scale=0.17]{plots/pool_plots/J4_175E.png} + + +\end{columns} +\end{frame} + +\begin{frame} +{~} + +\begin{columns} +\column{2.5in} +\includegraphics[scale=0.17]{plots/pool_plots/J4_225.png}\\ +\includegraphics[scale=0.17]{plots/pool_plots/J4_300.png}\\ + + +\column{2.5in} +\includegraphics[scale=0.17]{plots/pool_plots/J4_225E.png}\\ +\includegraphics[scale=0.17]{plots/pool_plots/J4_300E.png} + + +\end{columns} +\end{frame} + + +\begin{frame} +{~} + +\begin{columns} +\column{2.5in} +\includegraphics[scale=0.17]{plots/pool_plots/J4_400.png}\\ +\includegraphics[scale=0.17]{plots/pool_plots/J4_500.png}\\ + + +\column{2.5in} +\includegraphics[scale=0.17]{plots/pool_plots/J4_400E.png}\\ 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+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%5 +\definecolor{mygreen}{cmyk}{0.82,0.11,1,0.25} + + +\usetheme{Sybila} + +\title[Unfolding for counting experiments]{Unfolding for counting experiments} +\author{Marcin Chrz\k{a}szcz$^{1,2}$, Nicola Serra$^{1}$} +\institute{$^1$~University of Zurich,\\ $^2$~Institute of Nuclear Physics, Krakow} +\date{\today} +\begin{document} +% --------------------------- SLIDE -------------------------------------------- +\frame[plain]{\titlepage} +\author{Marcin Chrz\k{a}szcz} +% ------------------------------------------------------------------------------ +% --------------------------- SLIDE -------------------------------------------- + +\institute{~(UZH, IFJ)} + +\section{Introduction} + + +\begin{frame}\frametitle{Reminder 1 - Constructing Matrix unfolding} +\begin{itemize} +\item We don't know explicate +\item I have proven some time ago that the matrix exist +\end{itemize} +\small{ +\begin{equation} +\epsilon(\cos \theta_k, \cos \theta_l,\phi) +\end{equation} +} +\begin{itemize} +\item I have proven some time ago that the matrix exist +\item Now a systemic way to produce it. +\item Let's use PHSP MC. +\item Moments for PHSP MC are:\\ +$v^{T}_{gen}=(2/3 ,0,0,0,0,0,0,0)$ +\item After reconstruction we get(full $q^2$ range): +$v^{T}_{rec}=( 0.7069,0.0077,-0.00236466,0.0005,0.0007,0.0011,0.0011,-0.0012)$ +\end{itemize} + + + +\end{frame} + +\begin{frame}\frametitle{Reminder 2 - Constructing Matrix unfolding} +\begin{itemize} +\item We got first column of the unfolding matrix $(\dfrac{3}{2} v_{gen})$. +\end{itemize} +\small{ +$ \begin{pmatrix} + 1.06 & \cdots & a_{1,8} \\ + 0.01157 & \cdots & a_{2,8} \\ + -0.003547 & \ddots & \vdots \\ + 0.0007841 & \ddots & \vdots \\ + 0.001126 & \ddots & \vdots \\ + 0.001766 & \ddots & \vdots \\ + 0.001664 & \ddots & \vdots \\ + -0.001937 & \cdots & a_{8,8} + \end{pmatrix}$ + + +} +\begin{itemize} +\item How about the others? +\item We can reweight accordingly to $f_x$. +\end{itemize} + +\end{frame} + + + +\begin{frame}\frametitle{Reminder 3 - Constructing Matrix unfolding} +\begin{itemize} +\item To get $S_3$ each event $i^{th}$ has has weight $f_{S_3}(\cos \theta_{k_i},\cos \theta_{l_i},\phi_i) $ +\item One can calculate on MC the reweighed moments in PHPS: +\end{itemize} +\begin{equation} +\int PDF*f_{S_3}=\dfrac{32}{225} +\end{equation} +\begin{itemize} +\item Our base vector now is:$v^{T}_{gen}=(0 ,\frac{32}{225},0,0,0,0,0,0)$ +\item So lets see what do we get as reconstructed vector(after multiplying by $\frac{225}{32}$. +\small{$v^{T}_{rec}=( 0.042, 1.105,-0.005,0.003,-0.0023,-0.005,-0.005,-0.006)$ } +\item Please notice that weights are negative, but this is not a problem for the mean. +\item Also we are avoiding the negative PDF problem :) +\end{itemize} + +\end{frame} + + + +\begin{frame}\frametitle{Reminder 4 - Constructing Matrix unfolding} +\begin{itemize} +\item Now the matrix looks like: +\end{itemize} +\small{ +$ \begin{pmatrix} + 1.06 & 0.042 & \cdots & a_{1,8} \\ + 0.01157 & 1.105 & \cdots & a_{2,8} \\ + -0.003547 & -0.005 & \ddots & \vdots \\ + 0.0007841 &-0.005 & \ddots & \vdots \\ + 0.001126 & 0.003 &\ddots & \vdots \\ + 0.001766 & -0.0023 &\ddots & \vdots \\ + 0.001664 & -0.005 &\ddots & \vdots \\ + -0.001937 & -0.006 &\cdots & a_{8,8} + \end{pmatrix}$ + + +} +\begin{itemize} +\item The others go in the same way. +\item Repenting this exercise from $1^{st}$ year algebra we can get the full matrix +\end{itemize} + + +\end{frame} + + + +\begin{frame}\frametitle{Reminder 5} +For now: +\begin{itemize} +\item We have proven that there has to exists unfolding matrix. +\item Shown how to construct transformation matrix: $Gen \to Reco$. +\item Inverting it we can have transformation matrix of $Reco \to Gen$. +\item For details: \href{https://indico.cern.ch/event/316905/session/1/contribution/18/material/slides/0.pdf}{LINK} + +\end{itemize} + +What is missing? +\begin{columns} +\column{1in} +\begin{enumerate} +\item ERROR! +\end{enumerate} +\column{4in} +\includegraphics[width=0.8\textwidth]{err.jpg}\\ +\end{columns} + +\end{frame} + + + + + + +\begin{frame}\frametitle{How to?} +\begin{itemize} +\item So lets say that transformation matrix:$Gen \to Reco$ is $\epsilon_{i,j}$. +\item Each element has an error:$\delta \epsilon_{i,j}$. +\item Then we can calculate the matrix: $\epsilon_{i,j}^{-1}$(assuming it exists). +\item The million dollar question is what is the error on inverted matrix? +\end{itemize} + +\end{frame} + + + +\begin{frame}\frametitle{Answer to 1M dolar quesion} +\only<1>{ +\begin{itemize} +\item One can toy it. +\item But toying is good for kids and Frequentist. +\end{itemize} + +} +\only<2>{ + +\begin{itemize} +\item One can toy it. +\item But toying is good for kids and Frequentist. +\end{itemize} + +\begin{itemize} +\item Solution comes from $\tau$ physics :) \href{http://arxiv.org/abs/hep-ex/9909031}{hep-ex/9909031} +\end{itemize} +\begin{itemize} +\item One can derive(prove in the paper) the general equation: +\end{itemize} +\begin{equation} +\delta \epsilon^{-1}_{\alpha ~ \beta}= [\epsilon^{-1}]^2_{\alpha i}[\delta \epsilon ]^2_{ij} [\epsilon^{-1}]^2_{j \beta} +\end{equation} +} + + +\end{frame} + + + +\begin{frame}\frametitle{Matrix, $1.1-2~GeV$} +\tiny{ +$ A_{reco\rightarrow gen}=\begin{pmatrix} + 0.9519 & -0.02665 & -0.01432 & 0.002356 & 0.02539 & 0.009878 & -0.01551 & -0.01874 \\ +-0.006272 & 0.8122 & -0.00351 & -0.00719 & 0.003585 & 6.784e-05 & 0.02445 & 0.008515 \\ +-0.005315 & -0.003716 & 1.048 & 0.01242 & 0.01209 & -0.01478 & -0.001956 & 0.01429 \\ +0.003237 & -0.007177 & 0.01533 & 0.9184 & -0.007548 & -0.0009818 & -0.01874 & 0.009407 \\ +0.01002 & 0.004084 & 0.01391 & -0.006509 & 1.194 & -0.006516 & 0.001536 & -0.02882 \\ +0.002695 & -0.001042 & -0.01721 & -0.001842 & -0.005643 & 0.9264 & 0.02106 & 0.006755 \\ +-0.004736 & 0.02346 & -0.002335 & -0.01446 & 0.001169 & 0.01697 & 1.072 & -0.003191 \\ +-0.004157 & 0.007576 & 0.01377 & 0.008058 & -0.02219 & 0.005354 & -0.0008608 & 0.8304 + + + \end{pmatrix}$ +} +{~}\\{~}\\{~}\\ +\tiny{ +$ \delta A_{reco\rightarrow gen}=\begin{pmatrix} +0.005202 & 0.01911 & 0.03258 & 0.02103 & 0.02252 & 0.02145 & 0.03366 & 0.01948 \\ +0.006648 & 0.04654 & 0.03227 & 0.02451 & 0.03602 & 0.02464 & 0.03298 & 0.03397 \\ +0.007557 & 0.03197 & 0.07845 & 0.04272 & 0.04744 & 0.03057 & 0.05698 & 0.03287 \\ +0.007902 & 0.03885 & 0.0678 & 0.04839 & 0.0384 & 0.03464 & 0.04925 & 0.03989 \\ +0.009015 & 0.04122 & 0.06374 & 0.03254 & 0.07349 & 0.03269 & 0.0649 & 0.04202 \\ +0.007939 & 0.0389 & 0.04793 & 0.03433 & 0.03828 & 0.04937 & 0.06985 & 0.04023 \\ +0.007651 & 0.03234 & 0.05611 & 0.03062 & 0.04776 & 0.04388 & 0.08157 & 0.03342 \\ +0.006719 & 0.03345 & 0.03868 & 0.02953 & 0.03633 & 0.03002 & 0.03989 & 0.04827 + + + + \end{pmatrix}$ +} + +\end{frame} +\begin{frame}\frametitle{What did go wrong?} +\begin{itemize} +\item The errors are $2-3\%$, which is very worrying. +\item WG got very worried what is going on with the errors :( +\item Started debugging. +\item After sleeping with the problem found a stupid: +\end{itemize} +\textbf{ for(int i=0;i $<$ entries/10;++i) } +\begin{itemize} +\item Ok, I am an idiot, and used $10\%$ of statistics. +\end{itemize} +\end{frame} + +\begin{frame}\frametitle{What did go wrong 2 ?} +\begin{itemize} +\item The errors are tricky. When you re-weight you have negative weights. +\item So I change the normal error +\end{itemize} +\begin{equation} +\Hat\sigma^2 = \dfrac{\sum w_i}{(\sum w_i)^2 - \sum w_i^2} + \sum w_i (x_i - \Hat\mu)^2 +\end{equation} +\begin{itemize} +\item to: +\end{itemize} +\begin{equation} +\Hat\sigma^2 = \dfrac{\sum |w_i| }{(\sum |w_i|)^2 - \sum w_i^2} + \sum |w_i| (x_i - \Hat\mu)^2 +\end{equation} +\begin{itemize} +\item And this I am not $100\%$ sure if I is ok =( +\end{itemize} + +\end{frame} +\begin{frame}\frametitle{What did go wrong 3 ?} +\begin{itemize} +\item There is a hack of this method: +\item "You can cheat on your gf, you can cheat on tax, but you can't cheat on $\sqrt{n}$ "\footnote{All rights reserved! }. +\end{itemize} +\begin{center} +\includegraphics[width=0.5\textwidth]{Q2_5_6_S5.png}\\ +\end{center} +\begin{itemize} +\item We can use this: +\item Divide the MC in 10. Then calculate the variance of each matrix element. And divide/multiply by $\sqrt{10}$ and see if the errors are ok. +\end{itemize} + + +\end{frame} + +\begin{frame}\frametitle{What did go wrong 3 ?} +\tiny{ OLD (can be wrong): \\ +$ \delta A_{gen\rightarrow reco}=\begin{pmatrix} + 0.005477 & 0.02348 & 0.03125 & 0.02305 & 0.01871 & 0.02307 & 0.03124 & 0.02339 \\ + 0.008142 & 0.06734 & 0.03621 & 0.03126 & 0.0352 & 0.03131 & 0.03624 & 0.04767 \\ + 0.007168 & 0.0359 & 0.06856 & 0.0423 & 0.03619 & 0.02995 & 0.04856 & 0.03585 \\ + 0.008573 & 0.04966 & 0.06736 & 0.05471 & 0.03332 & 0.03886 & 0.04784 & 0.04973 \\ + 0.007599 & 0.04063 & 0.04926 & 0.02847 & 0.04998 & 0.02841 & 0.04923 & 0.04059 \\ + 0.008582 & 0.04977 & 0.04768 & 0.03878 & 0.03323 & 0.05499 & 0.0676 & 0.04974 \\ + 0.007136 & 0.03571 & 0.04833 & 0.02987 & 0.036 & 0.04225 & 0.06843 & 0.0358 \\ + 0.008162 & 0.04782 & 0.04294 & 0.03731 & 0.03527 & 0.03738 & 0.04306 & 0.06736 + + + \end{pmatrix}$ +} + +\tiny{ New: \\ +$ \delta A_{gen\rightarrow reco}=\begin{pmatrix} + 0.006659 & 0.0299 & 0.02207 & 0.01802 & 0.02657 & 0.02196 & 0.02851 & 0.02507 \\ + 0.00708 & 0.02046 & 0.007998 & 0.0133 & 0.008828 & 0.01236 & 0.01505 & 0.0149\\ + 0.008469 & 0.00845 & 0.01806 & 0.01442 & 0.009856 & 0.008895 & 0.01389 & 0.01155\\ + 0.008938 & 0.01569 & 0.01798 & 0.01801 & 0.009195 & 0.01097 & 0.01108 & 0.02068\\ + 0.007867 & 0.0109 & 0.01248 & 0.0088 & 0.01104 & 0.0114 & 0.01256 & 0.01097\\ + 0.008078 & 0.01582 & 0.01117 & 0.01093 & 0.01135 & 0.01215 & 0.02122 & 0.01774 \\ + 0.008368 & 0.01521 & 0.01391 & 0.008972 & 0.009797 & 0.01702 & 0.0147 & 0.01086\\ + 0.005745 & 0.01561 & 0.0114 & 0.01649 & 0.008631 & 0.01373 & 0.01051 & 0.01792 + + \end{pmatrix}$ +} + + + + +\end{frame} + + + + + +\begin{frame}\frametitle{Summary} +\begin{itemize} +\item I really fu.. this thing ... +\item No coding after 3 am form now! +\end{itemize} + +\includegraphics[width=0.5\textwidth]{code.png}\\ + +\end{frame} + + + + + + + + +\end{document} diff --git a/Zurich_group/30_06_2014/MMatrix.tex~ b/Zurich_group/30_06_2014/MMatrix.tex~ new file mode 100644 index 0000000..2fc0e58 --- /dev/null +++ b/Zurich_group/30_06_2014/MMatrix.tex~ @@ -0,0 +1,556 @@ +\documentclass[xcolor=svgnames]{beamer} +\usepackage[utf8]{inputenc} +\usepackage[english]{babel} +\usepackage{polski} +%\usepackage{amssymb,amsmath} +%\usepackage[latin1]{inputenc} +%\usepackage{amsmath} +%\newcommand\abs[1]{\left|#1\right|} +\usepackage{amsmath} +\newcommand\abs[1]{\left|#1\right|} +\usepackage{hepnicenames} +\usepackage{hepunits} +\usepackage{color} + + + +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%5 +\definecolor{mygreen}{cmyk}{0.82,0.11,1,0.25} + + +\usetheme{Sybila} + +\title[Unfolding for counting experiments]{Unfolding for counting experiments} +\author{Marcin Chrz\k{a}szcz$^{1,2}$, Nicola Serra$^{1}$} +\institute{$^1$~University of Zurich,\\ $^2$~Institute of Nuclear Physics, Krakow} +\date{\today} + +\begin{document} +% --------------------------- SLIDE -------------------------------------------- +\frame[plain]{\titlepage} +\author{Marcin Chrz\k{a}szcz} +% ------------------------------------------------------------------------------ +% --------------------------- SLIDE -------------------------------------------- + +\begin{frame}\frametitle{Quo vadis $\PBzero \to \PKstar \mu \mu$?} + +\center \includegraphics[width=0.8\paperwidth]{diagram.png}\\ + +\end{frame} +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +\begin{frame}\frametitle{Quo vadis $\PBzero \to \PKstar \mu \mu$?} + +\center \includegraphics[width=0.8\paperwidth]{matrix.png}\\ + +\end{frame} + + +\section{Introduction} + +\begin{frame}\frametitle{Reminder} +For now: +\begin{itemize} +\item We have proven that there has to exists unfolding matrix. +\item Shown how to construct transformation matrix: $Gen \to Reco$. +\item Inverting it we can have transformation matrix of $Reco \to Gen$. +\item For details: \href{https://indico.cern.ch/event/316905/session/1/contribution/18/material/slides/0.pdf}{LINK} + +\end{itemize} + +What is missing? +\begin{columns} +\column{1in} +\begin{enumerate} +\item ERROR! +\end{enumerate} +\column{4in} +\includegraphics[width=0.8\textwidth]{err.jpg}\\ +\end{columns} + +\end{frame} + + + +\begin{frame}\frametitle{How to?} +\begin{itemize} +\item So lets say that transformation matrix:$Gen \to Reco$ is $\epsilon_{i,j}$. +\item Of coz it's easy to write the covariance matrix(error matrix): +\end{itemize} +\begin{equation} +cov(\epsilon_{\alpha, \beta},\epsilon_{a,b}) +\end{equation} +\begin{itemize} +\item Then we can calculate the matrix: $\epsilon_{i,j}^{-1}$(assuming it exists). +\item and the 1M dollar question is: $cov(\epsilon_{\alpha, \beta}^{-1},\epsilon_{a,b}^{-1}) =?$ +\end{itemize} + +\end{frame} + +\begin{frame}\frametitle{Answer to 1M dolar quesion} +\begin{itemize} +\item Solution comes from $\tau$ physics :) +\end{itemize} +\begin{equation} +cov(\epsilon_{\alpha, \beta}^{-1},\epsilon_{a,b}^{-1}) = \epsilon^{-1}_{\alpha,i} \epsilon^{-1}_{j,\beta} \epsilon^{-1}_{a,k} \epsilon^{-1}_{l,b} cov( \epsilon_{ij} \epsilon_{kl}) +\end{equation} +\begin{itemize} +\item It's way to late to latex the prove. For prove see: \href{http://arxiv.org/abs/hep-ex/9909031}{arXiv:hep-ex/9909031} +\item Thanks to orthonormal basis lifes gets simpler: +\end{itemize} +\begin{equation} +cov(\epsilon_{ij},\epsilon_{kl} ) = \sigma_{\epsilon,ij} \delta_{ik} \delta_{jl} ( no correlations) +\end{equation} + +\end{frame} + + +\begin{frame}\frametitle{Total error} +\begin{itemize} +\item So let's say: $B=\epsilon^{-1} f$ +\item Then: +\end{itemize} +\begin{equation} +cov(B_i,B_j) = f_a f_b cov(\epsilon_{i \alpha }^{-1} , \epsilon_{j \beta}^{-1} )+ \epsilon^{-1}_{ ik} \epsilon^{-1}_{jl} cov(f_k,f_l) +\end{equation} +\begin{itemize} +\item Looks easy just need to implement! +\end{itemize} + +\end{frame} + + +\begin{frame}\frametitle{Matrix, $0.1-0.98~GeV$} +\tiny{ +$ A_{reco\rightarrow gen}=\begin{pmatrix} + 0.9495 0.008518 0.01522 -0.007362 0.01496 -0.04544 -0.02468 0.002078 + 0.0002651 0.8261 0.00978 -0.001042 0.004382 0.03191 0.01247 0.01886 + -0.0003391 0.009773 1.03 0.008433 -0.002028 0.003 0.02086 0.001549 + -0.00403 -0.001336 0.01047 0.9215 0.006898 -0.0006023 0.003041 -0.004465 + 0.006557 0.005531 -0.002423 0.00691 1.171 -0.01082 -0.0158 -0.003231 + -0.01931 0.03973 0.00342 -0.0006455 -0.01081 0.9452 0.02232 -0.005304 + .008421 0.0124 0.02071 0.002415 -0.01264 0.01785 1.06 0.001084 + 0.000347 0.01886 0.001555 -0.003568 -0.002591 -0.004226 0.001093 0.8204 + + + + + \end{pmatrix}$ +} + + + + + +\end{frame} + +\begin{frame}\frametitle{Constructing Matrix unfolding} +\begin{itemize} +\item We got first column of the unfolding matrix. +\end{itemize} +\small{ +$ \begin{pmatrix} + 1.06 & \cdots & a_{1,8} \\ + 0.01157 & \cdots & a_{2,8} \\ + -0.003547 & \ddots & \vdots \\ + 0.0007841 & \ddots & \vdots \\ + 0.001126 & \ddots & \vdots \\ + 0.001766 & \ddots & \vdots \\ + 0.001664 & \ddots & \vdots \\ + -0.001937 & \cdots & a_{8,8} + \end{pmatrix}$ + + +} +\begin{itemize} +\item How about the others? +\item We can reweight accordingly to $f_x$. +\end{itemize} + +\end{frame} + +\begin{frame}\frametitle{Constructing Matrix unfolding} +\begin{itemize} +\item To get $S_3$ each event $i^{th}$ has has weight $f_{S_3}(\cos \theta_{k_i},\cos \theta_{l_i},\phi_i) $ +\item One can calculate on MC the reweighed moments in PHPS: +\end{itemize} +\begin{equation} +\int PDF*f_{S_3}=\dfrac{32}{225} +\end{equation} +\begin{itemize} +\item Our base vector now is:$v^{T}_{gen}=(0 ,\frac{32}{225},0,0,0,0,0,0)$ +\item So lets see what do we get as reconstructed vector(after multiplying by $\frac{225}{32}$. +\small{$v^{T}_{rec}=( 0.042, 1.105,-0.005,0.003,-0.0023,-0.005,-0.005,-0.006)$ } +\end{itemize} + +\end{frame} + + +\begin{frame}\frametitle{Constructing Matrix unfolding} +\begin{itemize} +\item Now the matrix looks like: +\end{itemize} +\small{ +$ \begin{pmatrix} + 1.06 & 0.042 & \cdots & a_{1,8} \\ + 0.01157 & 1.105 & \cdots & a_{2,8} \\ + -0.003547 & -0.005 & \ddots & \vdots \\ + 0.0007841 &-0.005 & \ddots & \vdots \\ + 0.001126 & 0.003 &\ddots & \vdots \\ + 0.001766 & -0.0023 &\ddots & \vdots \\ + 0.001664 & -0.005 &\ddots & \vdots \\ + -0.001937 & -0.006 &\cdots & a_{8,8} + \end{pmatrix}$ + + +} +\begin{itemize} +\item The others go in the same way. +\item Repenting this exercise from $1^{st}$ year algebra we can get the full matrix +\end{itemize} + + +\end{frame} +\begin{frame}\frametitle{Constructing Matrix unfolding} +\begin{itemize} +\item The full transformation matrix from generator space to reconstructed space: +\end{itemize} +\tiny{ +$ A_{gen\rightarrow reco}=\begin{pmatrix} + 1.06 & 0.0423 & -0.0081 & 0.0022 & 0.0049 & 0.0037 & 0.0028 & -0.0065 \\ + + 0.0115 & 1.105 & -0.0050 & 0.0027 & -0.0018 & -0.0040 &-0.0054 & -0.0065 \\ + -0.0035 & -0.0050 & 0.981 & 0.0005 & -0.0025 & 0.0002 & -0.0037 & -0.0048\\ + 0.00078 & 0.0034 & 0.0006 & 1.002 & -0.0032 & -0.0040 & 0.0003 & 0.0018\\ + 0.001126 & -0.0023 & -0.0032 & -0.0032 & 1.055 & 0.001& -0.004 & 0.0023\\ + 0.00176 & -0.0050 & 0.00036 & -0.0040 & 0.0011 & 0.96 & -0.0057 & 0.0009 \\ + 0.0016 & -0.005 & -0.003 & 0.00029& -0.003 &-0.004 & 0.9543 & 0.0000\\ + -0.0019 & -0.0065 & -0.004 & 0.001 & 0.0018 & 0.0007 & 0.000 & 1.098 \\ + + + + + + \end{pmatrix}$ + + +} +\begin{itemize} +\item Inverting the matrix is simple, and doable +\end{itemize} +\tiny{ +$ A_{reco\rightarrow gen}=\begin{pmatrix} + 0.9434 & -0.036 & 0.007& -0.0020 & -0.0044& -0.0038 & -0.0030 & 0.0054\\ + -0.009 & 0.90 & 0.0045 & -0.0024& 0.0016 & 0.003873 & 0.00527& 0.005 \\ + 0.003 & 0.00454& 1.019 & -0.00058 & 0.0025& -0.000291 & 0.004 & 0.004 \\ +-0.00071 & -0.0030 & -0.0007 & 0.9977 & 0.0030 & 0.004206 &-0.0003 & -0.0017 \\ + -0.001 & 0.0020 & 0.0031& 0.0030 & 0.9483 & -0.0010 & 0.004626 & -0.0019 \\ + -0.001 & 0.004 & -0.0003 & 0.0042 & -0.001087 & 1.037 & 0.0063 & -0.0009\\ + -0.0017 & 0.0053 & 0.0042 & -0.0002 & 0.00370& 0.0050 & 1.048 & 0.0000 \\ + 0.0016& 0.0053& 0.00452 & -0.001 & -0.001582 & -0.0007213 &0.000 & 0.9105 \\ + + + + + \end{pmatrix}$ +} + +\end{frame} + + + +\begin{frame}\frametitle{Sensitivity to unknowns} +\begin{itemize} +\item We are unfolding based on MC. +\item There are MC/Data differences, which can have impact on the unfolding. +\end{itemize} +Let's put small modification: +\begin{equation} +w_j \to \overline{w_j}= \dfrac{1}{eff(\cos \theta_{l~j}, \cos \theta_{k~j}, \phi_{j})} \times corr(\cos \theta_{l~j}, \cos \theta_{k~j}, \phi_{j}) +\end{equation} +Unfortunately God didn't allowed me sneak peak into his cards so I don't know $corr(\cos \theta_{l}, \cos \theta_{k}, \phi)$, but let's try out some functions and see what happens :) + + +\end{frame} + +\begin{frame}\frametitle{Corr1 functions} +\begin{columns} +\column{2in} +\includegraphics[width=\linewidth]{corr/Corr1_cosk.png}\\ +\includegraphics[width=\linewidth]{corr/Corr1_cosl.png}\\ +\column{2.5in} +$ +corr1(\cos_l, \cos_k,\phi)= 1+ 0.032 \cos_l - 0.032 \cos_k + 0.01 \phi +$ +\includegraphics[width=0.8\linewidth]{corr/Corr1_phi.png}\\ + +\end{columns} + +\end{frame} +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +\begin{frame}\frametitle{Corr2 functions} +\begin{columns} +\column{2in} +\includegraphics[width=0.85\linewidth]{corr/corr21.png}\\ +\includegraphics[width=0.85\linewidth]{corr/corr22.png}\\ +\column{2.5in} +$ +corr2(\cos_l, \cos_k,\phi)= -0.02 \cos_l^2 + 0.02 \cos_k^2 - + 0.015 \phi^2+ 1 +$ +\includegraphics[width=0.75\linewidth]{corr/corr23.png}\\ + +\end{columns} + +\end{frame} + +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +\begin{frame}\frametitle{Corr3 functions} +\begin{columns} +\column{2in} +\includegraphics[width=0.85\linewidth]{corr/corr31.png}\\ +\includegraphics[width=0.85\linewidth]{corr/corr32.png}\\ +\column{2.5in} +$ +corr3(\cos_l, \cos_k,\phi)= 0.02 \cos_l \cos_k + 0.01 \cos_k \phi - 0.01 \phi \cos_l + 1 +$ +\includegraphics[width=0.75\linewidth]{corr/corr33.png}\\ + +\end{columns} + +\end{frame} +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +\begin{frame}\frametitle{Corr4 functions} +\begin{columns} +\column{2in} +\includegraphics[width=0.85\linewidth]{corr/corr41.png}\\ +\includegraphics[width=0.85\linewidth]{corr/corr42.png}\\ +\column{2.5in} +$ +corr3(\cos_l, \cos_k,\phi)= 0.01 \cos_k \cos_l \phi + 1 +$ +\includegraphics[width=0.75\linewidth]{corr/corr43.png}\\ + +\end{columns} + +\end{frame} + + + + +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% + + +\begin{frame}\frametitle{Corr1- MM} + + +\begin{tiny} + +\begin{center} + \begin{tabular}{ l l l l l l l l l } + \hline + \multicolumn{8}{c}{Mean of the pull} \\ \hline +$q^2$ & $S_3$ & $S_4$ & $S_5$ & $S_{6s}$ & $S_{6c}$ & $S_7$ & $S_8$ \\ \hline \hline + +0 & \scalebox{0.5}{$0.0085 \pm 0.026(0.3)$} & \scalebox{0.5}{$0.13 \pm 0.027(4.6)$} & \scalebox{0.5}{$-0.025 \pm 0.027(-0.92)$} & \scalebox{0.5}{$0.46 \pm 0.027(17)$} & \scalebox{0.5}{$-0.13 \pm 0.028(-4.7)$} & \scalebox{0.5}{$0.029 \pm 0.028(1)$} & \scalebox{0.5}{$-0.66 \pm 0.027(-25)$} \\ \hline +1 & \scalebox{0.5}{$0.0094 \pm 0.028(0.33)$} & \scalebox{0.5}{$0.078 \pm 0.028(2.8)$} & \scalebox{0.5}{$-0.02 \pm 0.028(-0.73)$} & \scalebox{0.5}{$0.24 \pm 0.028(8.5)$} & \scalebox{0.5}{$-0.075 \pm 0.028(-2.7)$} & \scalebox{0.5}{$-0.016 \pm 0.026(-0.63)$} & \scalebox{0.5}{$-0.39 \pm 0.028(-14)$} \\ \hline +2 & \scalebox{0.5}{$-0.02 \pm 0.027(-0.72)$} & \scalebox{0.5}{$0.027 \pm 0.026(1)$} & \scalebox{0.5}{$-0.024 \pm 0.027(-0.91)$} & \scalebox{0.5}{$0.18 \pm 0.027(6.8)$} & \scalebox{0.5}{$-0.024 \pm 0.027(-0.89)$} & \scalebox{0.5}{$-0.067 \pm 0.027(-2.5)$} & \scalebox{0.5}{$-0.39 \pm 0.028(-14)$} \\ \hline +3 & \scalebox{0.5}{$0.013 \pm 0.028(0.46)$} & \scalebox{0.5}{$-0.0089 \pm 0.027(-0.32)$} & \scalebox{0.5}{$0.055 \pm 0.026(2.1)$} & \scalebox{0.5}{$0.12 \pm 0.027(4.7)$} & \scalebox{0.5}{$0.11 \pm 0.027(3.9)$} & \scalebox{0.5}{$-0.018 \pm 0.028(-0.63)$} & \scalebox{0.5}{$-0.43 \pm 0.027(-16)$} \\ \hline +4 & \scalebox{0.5}{$-0.0054 \pm 0.029(-0.18)$} & \scalebox{0.5}{$-0.066 \pm 0.027(-2.4)$} & \scalebox{0.5}{$0.037 \pm 0.028(1.3)$} & \scalebox{0.5}{$0.22 \pm 0.027(8.1)$} & \scalebox{0.5}{$0.099 \pm 0.027(3.7)$} & \scalebox{0.5}{$-0.1 \pm 0.026(-3.8)$} & \scalebox{0.5}{$-0.41 \pm 0.026(-15)$} \\ \hline +5 & \scalebox{0.5}{$0.06 \pm 0.027(2.2)$} & \scalebox{0.5}{$-0.069 \pm 0.026(-2.6)$} & \scalebox{0.5}{$-0.013 \pm 0.028(-0.49)$} & \scalebox{0.5}{$0.21 \pm 0.027(7.8)$} & \scalebox{0.5}{$0.093 \pm 0.027(3.5)$} & \scalebox{0.5}{$-0.083 \pm 0.028(-3)$} & \scalebox{0.5}{$-0.41 \pm 0.028(-15)$} \\ \hline +6 & \scalebox{0.5}{$0.0064 \pm 0.026(0.25)$} & \scalebox{0.5}{$-0.051 \pm 0.027(-1.9)$} & \scalebox{0.5}{$-0.029 \pm 0.028(-1)$} & \scalebox{0.5}{$0.26 \pm 0.028(9.2)$} & \scalebox{0.5}{$0.14 \pm 0.027(5.1)$} & \scalebox{0.5}{$-0.081 \pm 0.027(-3)$} & \scalebox{0.5}{$-0.45 \pm 0.028(-16)$} \\ \hline +%7 & \scalebox{0.5}{$0.22 \pm 0.027(8)$} & \scalebox{0.5}{$-0.34 \pm 0.028(-12)$} & \scalebox{0.5}{$-0.43 \pm 0.026(-16)$} & \scalebox{0.5}{$2.4 \pm 0.029(82)$} & \scalebox{0.5}{$0.66 \pm 0.027(24)$} & \scalebox{0.5}{$-0.24 \pm 0.028(-8.6)$} & \scalebox{0.5}{$-0.51 \pm 0.027(-19)$} & +8 & \scalebox{0.5}{$0.023 \pm 0.027(0.85)$} & \scalebox{0.5}{$-0.031 \pm 0.028(-1.1)$} & \scalebox{0.5}{$0.0042 \pm 0.028(0.15)$} & \scalebox{0.5}{$0.21 \pm 0.026(7.8)$} & \scalebox{0.5}{$0.12 \pm 0.028(4.2)$} & \scalebox{0.5}{$-0.13 \pm 0.027(-4.8)$} & \scalebox{0.5}{$-0.48 \pm 0.026(-18)$} \\ \hline +9 & \scalebox{0.5}{$-0.017 \pm 0.027(-0.63)$} & \scalebox{0.5}{$-0.015 \pm 0.026(-0.56)$} & \scalebox{0.5}{$-0.0052 \pm 0.026(-0.2)$} & \scalebox{0.5}{$0.27 \pm 0.027(10)$} & \scalebox{0.5}{$0.046 \pm 0.026(1.7)$} & \scalebox{0.5}{$-0.12 \pm 0.026(-4.4)$} & \scalebox{0.5}{$-0.5 \pm 0.026(-19)$} \\ \hline +10 & \scalebox{0.5}{$-0.054 \pm 0.027(-2)$} & \scalebox{0.5}{$-0.056 \pm 0.026(-2.2)$} & \scalebox{0.5}{$0.036 \pm 0.026(1.4)$} & \scalebox{0.5}{$0.16 \pm 0.028(5.7)$} & \scalebox{0.5}{$0.077 \pm 0.028(2.8)$} & \scalebox{0.5}{$-0.034 \pm 0.027(-1.3)$} & \scalebox{0.5}{$-0.39 \pm 0.028(-14)$} \\ \hline +11 & \scalebox{0.5}{$0.023 \pm 0.027(0.88)$} & \scalebox{0.5}{$0.021 \pm 0.027(0.8)$} & \scalebox{0.5}{$-0.011 \pm 0.027(-0.41)$} & \scalebox{0.5}{$0.14 \pm 0.027(5)$} & \scalebox{0.5}{$0.042 \pm 0.027(1.6)$} & \scalebox{0.5}{$-0.098 \pm 0.028(-3.5)$} & \scalebox{0.5}{$-0.3 \pm 0.027(-11)$} \\ \hline + + + \hline + + + \end{tabular} + +\end{center} + + +\end{tiny} +\end{frame} + +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% + + +\begin{frame}\frametitle{Corr2- MM} + + +\begin{tiny} + +\begin{center} + \begin{tabular}{ l l l l l l l l l } + \hline + \multicolumn{8}{c}{Mean of the pull} \\ \hline +$q^2$ & $S_3$ & $S_4$ & $S_5$ & $S_{6s}$ & $S_{6c}$ & $S_7$ & $S_8$ \\ \hline \hline + +0 & \scalebox{0.5}{$-0.21 \pm 0.026(-8.1)$} & \scalebox{0.5}{$0.061 \pm 0.026(2.3)$} & \scalebox{0.5}{$-0.016 \pm 0.026(-0.63)$} & \scalebox{0.5}{$0.048 \pm 0.026(1.8)$} & \scalebox{0.5}{$-0.0062 \pm 0.027(-0.23)$} & \scalebox{0.5}{$-0.012 \pm 0.028(-0.44)$} & \scalebox{0.5}{$0.0091 \pm 0.026(0.36)$} \\ \hline +1 & \scalebox{0.5}{$-0.12 \pm 0.028(-4.5)$} & \scalebox{0.5}{$0.032 \pm 0.027(1.2)$} & \scalebox{0.5}{$-0.0071 \pm 0.026(-0.27)$} & \scalebox{0.5}{$0.02 \pm 0.027(0.75)$} & \scalebox{0.5}{$-0.086 \pm 0.027(-3.2)$} & \scalebox{0.5}{$-0.03 \pm 0.025(-1.2)$} & \scalebox{0.5}{$0.021 \pm 0.027(0.79)$} \\ \hline +2 & \scalebox{0.5}{$-0.15 \pm 0.027(-5.8)$} & \scalebox{0.5}{$-0.013 \pm 0.026(-0.49)$} & \scalebox{0.5}{$0.011 \pm 0.026(0.44)$} & \scalebox{0.5}{$-0.039 \pm 0.026(-1.5)$} & \scalebox{0.5}{$-0.032 \pm 0.027(-1.2)$} & \scalebox{0.5}{$-0.066 \pm 0.027(-2.5)$} & \scalebox{0.5}{$0.018 \pm 0.028(0.64)$} \\ \hline +3 & \scalebox{0.5}{$-0.15 \pm 0.027(-5.6)$} & \scalebox{0.5}{$0.025 \pm 0.026(0.96)$} & \scalebox{0.5}{$0.016 \pm 0.027(0.58)$} & \scalebox{0.5}{$-0.062 \pm 0.027(-2.3)$} & \scalebox{0.5}{$0.037 \pm 0.026(1.4)$} & \scalebox{0.5}{$0.026 \pm 0.027(0.96)$} & \scalebox{0.5}{$-0.016 \pm 0.027(-0.6)$} \\ \hline +4 & \scalebox{0.5}{$-0.12 \pm 0.028(-4.5)$} & \scalebox{0.5}{$-0.024 \pm 0.026(-0.92)$} & \scalebox{0.5}{$0.045 \pm 0.027(1.6)$} & \scalebox{0.5}{$0.0075 \pm 0.026(0.29)$} & \scalebox{0.5}{$0.015 \pm 0.027(0.53)$} & \scalebox{0.5}{$-0.036 \pm 0.026(-1.4)$} & \scalebox{0.5}{$0.037 \pm 0.026(1.4)$} \\ \hline +5 & \scalebox{0.5}{$-0.095 \pm 0.027(-3.6)$} & \scalebox{0.5}{$-0.032 \pm 0.026(-1.2)$} & \scalebox{0.5}{$0.014 \pm 0.026(0.52)$} & \scalebox{0.5}{$-0.013 \pm 0.026(-0.48)$} & \scalebox{0.5}{$-0.0093 \pm 0.027(-0.35)$} & \scalebox{0.5}{$-0.013 \pm 0.026(-0.51)$} & \scalebox{0.5}{$0.042 \pm 0.027(1.6)$} \\ \hline +6 & \scalebox{0.5}{$-0.17 \pm 0.025(-6.5)$} & \scalebox{0.5}{$0.008 \pm 0.027(0.3)$} & \scalebox{0.5}{$0.012 \pm 0.027(0.45)$} & \scalebox{0.5}{$0.029 \pm 0.027(1.1)$} & \scalebox{0.5}{$0.0072 \pm 0.027(0.27)$} & \scalebox{0.5}{$-0.0012 \pm 0.026(-0.046)$} & \scalebox{0.5}{$0.011 \pm 0.027(0.42)$} \\ \hline +%7 & \scalebox{0.5}{$0.078 \pm 0.026(3)$} & \scalebox{0.5}{$-0.3 \pm 0.026(-11)$} & \scalebox{0.5}{$-0.34 \pm 0.026(-13)$} & \scalebox{0.5}{$2.1 \pm 0.028(73)$} & \scalebox{0.5}{$0.47 \pm 0.026(18)$} & \scalebox{0.5}{$-0.17 \pm 0.027(-6.1)$} & \scalebox{0.5}{$0.0051 \pm 0.027(0.19)$} \\ \hline +8 & \scalebox{0.5}{$-0.13 \pm 0.026(-5.1)$} & \scalebox{0.5}{$-0.0077 \pm 0.027(-0.28)$} & \scalebox{0.5}{$0.05 \pm 0.027(1.9)$} & \scalebox{0.5}{$-0.03 \pm 0.026(-1.2)$} & \scalebox{0.5}{$-0.012 \pm 0.028(-0.44)$} & \scalebox{0.5}{$-0.046 \pm 0.026(-1.7)$} & \scalebox{0.5}{$0.031 \pm 0.026(1.2)$} \\ \hline +9 & \scalebox{0.5}{$-0.15 \pm 0.026(-5.7)$} & \scalebox{0.5}{$-0.0083 \pm 0.026(-0.32)$} & \scalebox{0.5}{$0.03 \pm 0.026(1.2)$} & \scalebox{0.5}{$0.044 \pm 0.027(1.6)$} & \scalebox{0.5}{$-0.07 \pm 0.026(-2.7)$} & \scalebox{0.5}{$-0.022 \pm 0.026(-0.84)$} & \scalebox{0.5}{$-0.045 \pm 0.026(-1.7)$} \\ \hline +10 & \scalebox{0.5}{$-0.15 \pm 0.025(-5.8)$} & \scalebox{0.5}{$-0.032 \pm 0.025(-1.3)$} & \scalebox{0.5}{$0.059 \pm 0.026(2.2)$} & \scalebox{0.5}{$-0.072 \pm 0.028(-2.6)$} & \scalebox{0.5}{$-0.029 \pm 0.027(-1.1)$} & \scalebox{0.5}{$0.064 \pm 0.027(2.4)$} & \scalebox{0.5}{$0.014 \pm 0.027(0.51)$} \\ \hline +11 & \scalebox{0.5}{$-0.067 \pm 0.026(-2.6)$} & \scalebox{0.5}{$0.017 \pm 0.026(0.65)$} & \scalebox{0.5}{$-0.015 \pm 0.026(-0.56)$} & \scalebox{0.5}{$-0.051 \pm 0.026(-1.9)$} & \scalebox{0.5}{$-0.0086 \pm 0.026(-0.33)$} & \scalebox{0.5}{$-0.018 \pm 0.028(-0.67)$} & \scalebox{0.5}{$0.017 \pm 0.027(0.62)$} \\ \hline + + + + + + +\hline + + + \end{tabular} + +\end{center} + + +\end{tiny} +\end{frame} + + +\begin{frame}\frametitle{Corr3- MM} + + +\begin{tiny} + +\begin{center} + \begin{tabular}{ l l l l l l l l l } + \hline + \multicolumn{8}{c}{Mean of the pull} \\ \hline +$q^2$ & $S_3$ & $S_4$ & $S_5$ & $S_{6s}$ & $S_{6c}$ & $S_7$ & $S_8$ \\ \hline \hline + +0 & \scalebox{0.5}{$-0.021 \pm 0.026(-0.81)$} & \scalebox{0.5}{$0.041 \pm 0.026(1.5)$} & \scalebox{0.5}{$0.009 \pm 0.027(0.34)$} & \scalebox{0.5}{$0.043 \pm 0.026(1.6)$} & \scalebox{0.5}{$0.13 \pm 0.028(4.8)$} & \scalebox{0.5}{$-0.0072 \pm 0.028(-0.26)$} & \scalebox{0.5}{$0.044 \pm 0.026(1.7)$} \\ \hline +1 & \scalebox{0.5}{$-0.014 \pm 0.028(-0.51)$} & \scalebox{0.5}{$0.03 \pm 0.027(1.1)$} & \scalebox{0.5}{$0.022 \pm 0.027(0.82)$} & \scalebox{0.5}{$0.015 \pm 0.028(0.53)$} & \scalebox{0.5}{$0.078 \pm 0.028(2.8)$} & \scalebox{0.5}{$-0.037 \pm 0.025(-1.4)$} & \scalebox{0.5}{$0.057 \pm 0.027(2.1)$} \\ \hline +2 & \scalebox{0.5}{$-0.037 \pm 0.027(-1.4)$} & \scalebox{0.5}{$-0.0013 \pm 0.027(-0.048)$} & \scalebox{0.5}{$-0.015 \pm 0.027(-0.54)$} & \scalebox{0.5}{$-0.052 \pm 0.026(-2)$} & \scalebox{0.5}{$0.1 \pm 0.027(3.8)$} & \scalebox{0.5}{$-0.051 \pm 0.026(-1.9)$} & \scalebox{0.5}{$0.022 \pm 0.028(0.78)$} \\ \hline +3 & \scalebox{0.5}{$-0.015 \pm 0.027(-0.55)$} & \scalebox{0.5}{$0.036 \pm 0.028(1.3)$} & \scalebox{0.5}{$-0.039 \pm 0.027(-1.4)$} & \scalebox{0.5}{$-0.072 \pm 0.027(-2.7)$} & \scalebox{0.5}{$0.17 \pm 0.027(6.2)$} & \scalebox{0.5}{$-0.0044 \pm 0.028(-0.15)$} & \scalebox{0.5}{$-0.024 \pm 0.027(-0.9)$} \\ \hline +4 & \scalebox{0.5}{$-0.00047 \pm 0.029(-0.017)$} & \scalebox{0.5}{$-0.012 \pm 0.027(-0.43)$} & \scalebox{0.5}{$0.0099 \pm 0.028(0.35)$} & \scalebox{0.5}{$-0.002 \pm 0.026(-0.076)$} & \scalebox{0.5}{$0.17 \pm 0.028(6.2)$} & \scalebox{0.5}{$-0.062 \pm 0.027(-2.3)$} & \scalebox{0.5}{$0.0086 \pm 0.027(0.32)$} \\ \hline + +5 & \scalebox{0.5}{$0.046 \pm 0.027(1.7)$} & \scalebox{0.5}{$-0.02 \pm 0.026(-0.76)$} & \scalebox{0.5}{$-0.04 \pm 0.027(-1.5)$} & \scalebox{0.5}{$-0.012 \pm 0.027(-0.44)$} & \scalebox{0.5}{$0.13 \pm 0.027(4.8)$} & \scalebox{0.5}{$-0.04 \pm 0.027(-1.5)$} & \scalebox{0.5}{$-0.0056 \pm 0.027(-0.21)$} \\ \hline +6 & \scalebox{0.5}{$-0.013 \pm 0.026(-0.52)$} & \scalebox{0.5}{$0.041 \pm 0.027(1.5)$} & \scalebox{0.5}{$-0.033 \pm 0.028(-1.2)$} & \scalebox{0.5}{$-0.0019 \pm 0.027(-0.068)$} & \scalebox{0.5}{$0.15 \pm 0.027(5.4)$} & \scalebox{0.5}{$-0.034 \pm 0.027(-1.3)$} & \scalebox{0.5}{$-0.021 \pm 0.028(-0.75)$} \\ \hline +%7 & \scalebox{0.5}{$0.25 \pm 0.027(9.1)$} & \scalebox{0.5}{$-0.27 \pm 0.027(-10)$} & \scalebox{0.5}{$-0.41 \pm 0.027(-16)$} & \scalebox{0.5}{$2.1 \pm 0.029(73)$} & \scalebox{0.5}{$0.65 \pm 0.027(24)$} & \scalebox{0.5}{$-0.19 \pm 0.028(-7)$} & \scalebox{0.5}{$-0.053 \pm 0.028(-1.9)$} \\ \hline +8 & \scalebox{0.5}{$0.039 \pm 0.026(1.5)$} & \scalebox{0.5}{$0.01 \pm 0.028(0.36)$} & \scalebox{0.5}{$-0.027 \pm 0.028(-0.96)$} & \scalebox{0.5}{$-0.024 \pm 0.026(-0.9)$} & \scalebox{0.5}{$0.12 \pm 0.027(4.3)$} & \scalebox{0.5}{$-0.092 \pm 0.026(-3.5)$} & \scalebox{0.5}{$-0.036 \pm 0.027(-1.3)$} \\ \hline +9 & \scalebox{0.5}{$-0.01 \pm 0.027(-0.38)$} & \scalebox{0.5}{$0.0024 \pm 0.027(0.09)$} & \scalebox{0.5}{$-0.018 \pm 0.026(-0.68)$} & \scalebox{0.5}{$0.022 \pm 0.028(0.79)$} & \scalebox{0.5}{$0.068 \pm 0.027(2.6)$} & \scalebox{0.5}{$-0.069 \pm 0.026(-2.6)$} & \scalebox{0.5}{$-0.078 \pm 0.026(-3)$} \\ \hline +10 & \scalebox{0.5}{$-0.017 \pm 0.027(-0.62)$} & \scalebox{0.5}{$-0.015 \pm 0.026(-0.57)$} & \scalebox{0.5}{$0.012 \pm 0.027(0.46)$} & \scalebox{0.5}{$-0.074 \pm 0.028(-2.6)$} & \scalebox{0.5}{$0.1 \pm 0.027(3.8)$} & \scalebox{0.5}{$-0.003 \pm 0.027(-0.11)$} & \scalebox{0.5}{$-0.043 \pm 0.029(-1.5)$} \\ \hline +11 & \scalebox{0.5}{$0.032 \pm 0.026(1.2)$} & \scalebox{0.5}{$0.024 \pm 0.026(0.91)$} & \scalebox{0.5}{$-0.04 \pm 0.026(-1.5)$} & \scalebox{0.5}{$-0.066 \pm 0.027(-2.5)$} & \scalebox{0.5}{$0.098 \pm 0.027(3.7)$} & \scalebox{0.5}{$-0.043 \pm 0.028(-1.6)$} & \scalebox{0.5}{$-0.0018 \pm 0.028(-0.064)$} \\ \hline + + + +\hline + + + \end{tabular} + +\end{center} + + +\end{tiny} +\end{frame} + +\begin{frame}\frametitle{Corr4- MM} + + +\begin{tiny} + +\begin{center} + \begin{tabular}{ l l l l l l l l l } + \hline + \multicolumn{8}{c}{Mean of the pull} \\ \hline +$q^2$ & $S_3$ & $S_4$ & $S_5$ & $S_{6s}$ & $S_{6c}$ & $S_7$ & $S_8$ \\ \hline \hline + + +0 & \scalebox{0.5}{$-0.019 \pm 0.026(-0.71)$} & \scalebox{0.5}{$0.048 \pm 0.027(1.8)$} & \scalebox{0.5}{$0.018 \pm 0.027(0.67)$} & \scalebox{0.5}{$0.059 \pm 0.027(2.2)$} & \scalebox{0.5}{$-0.015 \pm 0.028(-0.55)$} & \scalebox{0.5}{$0.061 \pm 0.027(2.2)$} & \scalebox{0.5}{$0.012 \pm 0.027(0.44)$} \\ \hline +1 & \scalebox{0.5}{$-0.014 \pm 0.028(-0.51)$} & \scalebox{0.5}{$0.043 \pm 0.027(1.6)$} & \scalebox{0.5}{$0.013 \pm 0.027(0.49)$} & \scalebox{0.5}{$0.024 \pm 0.028(0.86)$} & \scalebox{0.5}{$-0.038 \pm 0.028(-1.4)$} & \scalebox{0.5}{$0.024 \pm 0.026(0.94)$} & \scalebox{0.5}{$0.037 \pm 0.027(1.3)$} \\ \hline +2 & \scalebox{0.5}{$-0.03 \pm 0.027(-1.1)$} & \scalebox{0.5}{$-0.0021 \pm 0.027(-0.076)$} & \scalebox{0.5}{$-0.01 \pm 0.027(-0.39)$} & \scalebox{0.5}{$-0.017 \pm 0.027(-0.61)$} & \scalebox{0.5}{$-0.016 \pm 0.027(-0.58)$} & \scalebox{0.5}{$0.013 \pm 0.027(0.49)$} & \scalebox{0.5}{$0.027 \pm 0.028(0.98)$} \\ \hline +3 & \scalebox{0.5}{$-0.007 \pm 0.027(-0.26)$} & \scalebox{0.5}{$0.03 \pm 0.028(1.1)$} & \scalebox{0.5}{$-0.036 \pm 0.027(-1.3)$} & \scalebox{0.5}{$-0.074 \pm 0.027(-2.8)$} & \scalebox{0.5}{$0.041 \pm 0.027(1.5)$} & \scalebox{0.5}{$0.08 \pm 0.028(2.9)$} & \scalebox{0.5}{$-0.0083 \pm 0.027(-0.31)$} \\ \hline +4 & \scalebox{0.5}{$0.00089 \pm 0.029(0.031)$} & \scalebox{0.5}{$-0.021 \pm 0.027(-0.77)$} & \scalebox{0.5}{$0.0032 \pm 0.028(0.11)$} & \scalebox{0.5}{$0.0031 \pm 0.026(0.12)$} & \scalebox{0.5}{$0.012 \pm 0.027(0.44)$} & \scalebox{0.5}{$0.019 \pm 0.026(0.71)$} & \scalebox{0.5}{$0.034 \pm 0.027(1.3)$} \\ \hline +5 & \scalebox{0.5}{$0.044 \pm 0.028(1.6)$} & \scalebox{0.5}{$-0.022 \pm 0.026(-0.82)$} & \scalebox{0.5}{$-0.041 \pm 0.027(-1.5)$} & \scalebox{0.5}{$-0.014 \pm 0.027(-0.53)$} & \scalebox{0.5}{$-0.029 \pm 0.027(-1.1)$} & \scalebox{0.5}{$0.041 \pm 0.027(1.5)$} & \scalebox{0.5}{$0.042 \pm 0.028(1.5)$} \\ \hline +6 & \scalebox{0.5}{$-0.011 \pm 0.026(-0.42)$} & \scalebox{0.5}{$0.041 \pm 0.027(1.5)$} & \scalebox{0.5}{$-0.045 \pm 0.028(-1.6)$} & \scalebox{0.5}{$0.011 \pm 0.027(0.41)$} & \scalebox{0.5}{$-0.0089 \pm 0.027(-0.33)$} & \scalebox{0.5}{$0.067 \pm 0.027(2.5)$} & \scalebox{0.5}{$0.036 \pm 0.027(1.3)$} \\ \hline +%7 & \scalebox{0.5}{$0.25 \pm 0.027(9.1)$} & \scalebox{0.5}{$-0.26 \pm 0.027(-9.9)$} & \scalebox{0.5}{$-0.42 \pm 0.027(-16)$} & \scalebox{0.5}{$2.1 \pm 0.029(73)$} & \scalebox{0.5}{$0.47 \pm 0.027(18)$} & \scalebox{0.5}{$-0.077 \pm 0.028(-2.8)$} & \scalebox{0.5}{$0.029 \pm 0.028(1)$} \\ \hline +8 & \scalebox{0.5}{$0.05 \pm 0.026(1.9)$} & \scalebox{0.5}{$0.0021 \pm 0.028(0.074)$} & \scalebox{0.5}{$-0.025 \pm 0.028(-0.91)$} & \scalebox{0.5}{$-0.023 \pm 0.026(-0.87)$} & \scalebox{0.5}{$-0.024 \pm 0.028(-0.85)$} & \scalebox{0.5}{$0.022 \pm 0.026(0.82)$} & \scalebox{0.5}{$0.026 \pm 0.026(0.98)$} \\ \hline +9 & \scalebox{0.5}{$-0.0064 \pm 0.027(-0.23)$} & \scalebox{0.5}{$0.012 \pm 0.027(0.44)$} & \scalebox{0.5}{$-0.0075 \pm 0.026(-0.28)$} & \scalebox{0.5}{$0.029 \pm 0.027(1.1)$} & \scalebox{0.5}{$-0.087 \pm 0.027(-3.2)$} & \scalebox{0.5}{$0.036 \pm 0.027(1.3)$} & \scalebox{0.5}{$-0.02 \pm 0.026(-0.76)$} \\ \hline +10 & \scalebox{0.5}{$-0.019 \pm 0.027(-0.71)$} & \scalebox{0.5}{$-0.0051 \pm 0.025(-0.2)$} & \scalebox{0.5}{$0.0081 \pm 0.026(0.31)$} & \scalebox{0.5}{$-0.077 \pm 0.028(-2.7)$} & \scalebox{0.5}{$-0.03 \pm 0.027(-1.1)$} & \scalebox{0.5}{$0.11 \pm 0.027(4.1)$} & \scalebox{0.5}{$0.013 \pm 0.028(0.46)$} \\ \hline +11 & \scalebox{0.5}{$0.027 \pm 0.026(1)$} & \scalebox{0.5}{$0.032 \pm 0.027(1.2)$} & \scalebox{0.5}{$-0.038 \pm 0.027(-1.4)$} & \scalebox{0.5}{$-0.048 \pm 0.026(-1.8)$} & \scalebox{0.5}{$-0.021 \pm 0.027(-0.77)$} & \scalebox{0.5}{$0.019 \pm 0.028(0.69)$} & \scalebox{0.5}{$0.035 \pm 0.027(1.3)$} \\ \hline + + + +\hline + + \end{tabular} + +\end{center} + +\end{tiny} +\end{frame} + + + + +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +\section{Reverse Engineering Unfolding} + +\begin{frame}\frametitle{Reverse Engineering- Corr1} +\begin{itemize} +\item Let's try to understand if we can understand why this happens: +\item Let's calculate what should I expect with the unfolding +\item This is up to normalization! +\begin{itemize} +\item $M_5=0.4 S_5 \to M_5=0.00512 S_3 + 0.4 S_5 - 0.002 S_7$ +\item $M_8=0.32 S_8 \to M_8=0.0016 S_4 + 0.00512 S_7 + 0.32 S_8$ +\item $M_7=0.4 S_7 \to M_7=0.002 S_5 + 0.4 S_7 + 0.00512 S_8$ +\item $M_3=0.32 S_3 \to M_3=0.32 S_3 - 0.0008 S_9$ +\end{itemize} +\item The way you can look at this is that i just shown you how our unfolding matrix works like. +\end{itemize} + + + +\end{frame} + +\begin{frame}\frametitle{Reverse Engineering- Corr2} +\begin{itemize} +\item Let's try to understand if we can understand why this happens: +\item Let's calculate what should I expect with the unfolding +\item This is up to normalization! +\begin{itemize} +\item $M_5=0.4 S_5 \to M_5= 0.4 S_5$ +\item $M_8=0.32 S_8 \to M_8=0.32 S_5$ +\item $M_7=0.4 S_7 \to M_7=0.4 S_7$ +\item $M_3=0.32 S_3 \to M_3=-0.0036 + 0.0012 Fl + 0.32 S_3$ +\end{itemize} +\item The way you can look at this is that i just shown you how our unfolding matrix works like. +\end{itemize} + + + +\end{frame} + + + + +\begin{frame}\frametitle{Summary} +\begin{itemize} +\item Developed a systematic way how to get Unfolding matrix +\item Moments are resistant against variety of unfolding discrepancies. +\item This might lead to reduced systematics in the future. +\end{itemize} + + + + +\end{frame} + + + +\end{document} diff --git a/Zurich_group/30_06_2014/MMatrix.toc b/Zurich_group/30_06_2014/MMatrix.toc new file mode 100644 index 0000000..1e71ea5 --- /dev/null +++ b/Zurich_group/30_06_2014/MMatrix.toc @@ -0,0 +1,3 @@ +\beamer@endinputifotherversion {3.10pt} +\select@language {english} +\beamer@sectionintoc {1}{Introduction}{2}{0}{1} diff --git a/Zurich_group/30_06_2014/P5.png b/Zurich_group/30_06_2014/P5.png new file mode 100644 index 0000000..7819eef --- /dev/null +++ b/Zurich_group/30_06_2014/P5.png Binary files differ diff --git a/Zurich_group/30_06_2014/Q2_4_S8.png b/Zurich_group/30_06_2014/Q2_4_S8.png new file mode 100644 index 0000000..9176de4 --- /dev/null +++ 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b/Zurich_group/30_06_2014/tmp/example/example.snm diff --git a/Zurich_group/30_06_2014/tmp/example/example.synctex.gz b/Zurich_group/30_06_2014/tmp/example/example.synctex.gz new file mode 100644 index 0000000..5bccdb3 --- /dev/null +++ b/Zurich_group/30_06_2014/tmp/example/example.synctex.gz Binary files differ diff --git a/Zurich_group/30_06_2014/tmp/example/example.tex b/Zurich_group/30_06_2014/tmp/example/example.tex new file mode 100644 index 0000000..ce0641b --- /dev/null +++ b/Zurich_group/30_06_2014/tmp/example/example.tex @@ -0,0 +1,21 @@ +\documentclass[xcolor=svgnames]{beamer} +\usepackage[utf8]{inputenc} +\usepackage[english]{babel} + +\usetheme{Sybila} + +\title[Parallelization of Methods for Dynamic System Analysis]{Parallelization of Methods for Dynamic System Analysis Using CUDA} +\author{Jan Papou\v{s}ek} +\institute{Masaryk University Brno} +\date{\today} + +\begin{document} +% --------------------------- SLIDE -------------------------------------------- +\frame[plain]{\titlepage} +% ------------------------------------------------------------------------------ +% --------------------------- SLIDE -------------------------------------------- +\begin{frame} + \frametitle{Introduction} +\end{frame} +% ------------------------------------------------------------------------------ +\end{document} diff --git a/Zurich_group/30_06_2014/tmp/example/example.toc b/Zurich_group/30_06_2014/tmp/example/example.toc new file mode 100644 index 0000000..495658f --- /dev/null +++ b/Zurich_group/30_06_2014/tmp/example/example.toc @@ -0,0 +1,2 @@ +\beamer@endinputifotherversion {3.10pt} +\select@language {english} diff --git a/Zurich_group/30_06_2014/tmp/example/sybila-logo-paper-shaded.png b/Zurich_group/30_06_2014/tmp/example/sybila-logo-paper-shaded.png new file mode 100644 index 0000000..f2a2c4e --- /dev/null +++ b/Zurich_group/30_06_2014/tmp/example/sybila-logo-paper-shaded.png Binary files differ diff --git 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100644 index 0000000..5639601 --- /dev/null +++ b/Zurich_group/30_06_2014/tmp/theme/beamerthemeSybila.sty @@ -0,0 +1,104 @@ +\mode + +%------------------------------------------------------------------------------- +% Themes +%------------------------------------------------------------------------------- + +\useoutertheme{split} +\useinnertheme{rounded} +\usefonttheme{structurebold} +%\useoutertheme{shadow} + +%------------------------------------------------------------------------------- +% Templates +%------------------------------------------------------------------------------- + +\beamertemplatenavigationsymbolsempty +\beamertemplateheadempty +\beamertemplateshadowblocks + +%------------------------------------------------------------------------------- +% Own templates +%------------------------------------------------------------------------------- + +% Normal title page. +\defbeamertemplate*{title page}{simple}[1][] +{ + \vfill + \begin{centering} + \begin{beamercolorbox}[center, rounded=true]{title} + \usebeamerfont{title}\inserttitle\par% + \ifx\insertsubtitle\@empty% + \else% + \vskip0.25em% + {\usebeamerfont{subtitle}\usebeamercolor[fg]{subtitle}\insertsubtitle\par}% + \fi% + \end{beamercolorbox}% + + \vskip1em + + \begin{beamercolorbox}[sep=8pt,center,#1]{author} + \usebeamerfont{author}\insertauthor + \end{beamercolorbox} + + \vskip1em + + {\usebeamercolor[fg]{titlegraphic}\inserttitlegraphic\par} + \begin{beamercolorbox}[sep=8pt,center,#1]{institute} + \usebeamerfont{date}\insertinstitute + \end{beamercolorbox} + + \vskip1em + + \begin{beamercolorbox}[sep=8pt,center,#1]{date} + \usebeamerfont{date}\insertdate + \end{beamercolorbox} + \end{centering} + \vfill +} + +%------------------------------------------------------------------------------- +% Logo +%------------------------------------------------------------------------------- + +\logo{\hspace*{0.6\textwidth}\includegraphics[width=1.2cm]{sybila-logo-paper-shaded}\hspace*{0.3cm}} + +%------------------------------------------------------------------------------- +% Colors +%------------------------------------------------------------------------------- + +\setbeamercovered{dynamic} + +\setbeamercolor{math text}{fg=green!45!black} +\setbeamercolor{title}{bg=white!30!black} +\setbeamercolor{frametitle}{bg=white!45!black} +\setbeamercolor{footline}{bg=black,fg=white} +\setbeamercolor{author in head/foot}{bg=black,fg=white} +\setbeamercolor{title in head/foot}{bg=white!45!black} +\setbeamercolor{block title}{bg=white!45!black} +\setbeamercolor{block title example}{bg=white!45!black} +\setbeamercolor{block title alerted}{bg=white!15!black} + +\colorlet{redshaded}{red!25!bg} +\colorlet{shaded}{black!25!bg} +\colorlet{shadedshaded}{black!10!bg} +\colorlet{blackshaded}{black!40!bg} + +\usecolortheme{whale} +\usecolortheme{orchid} + +%------------------------------------------------------------------------------- +% Fonts +%------------------------------------------------------------------------------- + +\setbeamerfont{block title}{size={}} +\setbeamerfont{date}{size=\small} + +%------------------------------------------------------------------------------- +% Other +%------------------------------------------------------------------------------- + +\titlegraphic{\includegraphics[width=3.0cm]{sybila-logo-slide-title-shaded.pdf}} + +\mode + diff --git a/Zurich_group/30_06_2014/tmp/theme/sybila-logo-paper-shaded.png b/Zurich_group/30_06_2014/tmp/theme/sybila-logo-paper-shaded.png new file mode 100644 index 0000000..f2a2c4e --- /dev/null +++ b/Zurich_group/30_06_2014/tmp/theme/sybila-logo-paper-shaded.png Binary files differ diff --git a/Zurich_group/30_06_2014/tmp/theme/sybila-logo-slide-title-shaded.pdf b/Zurich_group/30_06_2014/tmp/theme/sybila-logo-slide-title-shaded.pdf new file mode 100644 index 0000000..670c6a6 --- /dev/null +++ b/Zurich_group/30_06_2014/tmp/theme/sybila-logo-slide-title-shaded.pdf Binary files differ diff --git a/tau23mu_lhcb/25_11_2013/group_meeting.tex b/tau23mu_lhcb/25_11_2013/group_meeting.tex index 3b82abd..cbf25cc 100644 --- a/tau23mu_lhcb/25_11_2013/group_meeting.tex +++ b/tau23mu_lhcb/25_11_2013/group_meeting.tex @@ -148,7 +148,7 @@ \title{Trigger impact on MVA} %\subtitle{a bias report} \author{ Marcin Chrz\k{a}szcz$^{1,2}$} -\institute[UTH, IFJ] +\institute[UZH, IFJ] { %\begin{tiny} $ ^1$ University of Zurich , $ ^2$ Institute of Nuclear Physics, Krakow, diff --git a/tau23mu_lhcb/6_01_2014/group_meeting.log b/tau23mu_lhcb/6_01_2014/group_meeting.log index a5f9db0..1168284 100644 --- a/tau23mu_lhcb/6_01_2014/group_meeting.log +++ b/tau23mu_lhcb/6_01_2014/group_meeting.log @@ -1,4 +1,4 @@ -This is pdfTeX, Version 3.1415926-1.40.10 (TeX Live 2009/Debian) (format=pdflatex 2013.10.11) 6 JAN 2014 10:27 +This is pdfTeX, Version 3.1415926-1.40.10 (TeX Live 2009/Debian) (format=pdflatex 2014.3.24) 23 JUN 2014 13:32 entering extended mode %&-line parsing enabled. **group_meeting.tex @@ -11,7 +11,7 @@ skrit, italian, latin, latvian, lithuanian, mongolian2a, mongolian, bokmal, nyn orsk, romanian, irish, coptic, serbian, turkish, welsh, esperanto, uppersorbian , estonian, indonesian, interlingua, icelandic, kurmanji, slovenian, polish, po -rtuguese, spanish, galician, catalan, swedish, ukenglish, loaded. +rtuguese, spanish, galician, catalan, swedish, ukenglish, pinyin, loaded. (/usr/share/texmf/tex/latex/beamer/base/beamer.cls (/usr/share/texmf/tex/latex/beamer/base/beamerbasercs.sty Package: beamerbasercs 2010/06/12 (rcs-revision c3821710bb40) @@ -770,7 +770,7 @@ Option `thickqspace' provided! Option `textstyle' provided! Option `squaren' provided! -)) (/usr/share/texmf-texlive/tex/generic/babel/babel.sty +)) (/var/lib/texmf/tex/generic/babel/babel.sty Package: babel 2008/07/06 v3.8l The Babel package (/usr/share/texmf-texlive/tex/generic/babel/english.ldf @@ -1224,7 +1224,7 @@ File: pic/ifj.png Graphic file (type png) -Overfull \vbox (249.64534pt too high) detected at line 192 +Overfull \vbox (248.96103pt too high) detected at line 192 [] @@ -1267,10 +1267,26 @@ [3 <./slide_bg.png (PNG copy)>] - -File: final2/ROC_2012.png Graphic file (type png) - +LaTeX Warning: File `final2/ROC_2012.png' not found on input line 259. + + +! Package pdftex.def Error: File `final2/ROC_2012.png' not found. + +See the pdftex.def package documentation for explanation. +Type H for immediate help. + ... + +l.259 \end{frame} + +Using draft setting for this image. +Try typing to proceed. +If that doesn't work, type X to quit. + +LaTeX Font Info: Try loading font information for T1+pcr on input line 259. +(/usr/share/texmf-texlive/tex/latex/psnfss/t1pcr.fd +File: t1pcr.fd 2001/06/04 font definitions for T1/pcr. +) File: slide_bg.png Graphic file (type png) Overfull \hbox (3.63992pt too wide) has occurred while \output is active @@ -1279,41 +1295,104 @@ [4 - <./final2/ROC_2012.png>] -File: final2/ROC_2012.png Graphic file (type png) - +] + +LaTeX Warning: File `final2/ROC_2012.png' not found on input line 278. + + +! Package pdftex.def Error: File `final2/ROC_2012.png' not found. + +See the pdftex.def package documentation for explanation. +Type H for immediate help. + ... + +l.278 \end{frame} + +Using draft setting for this image. +Try typing to proceed. +If that doesn't work, type X to quit. + File: slide_bg.png Graphic file (type png) - + Overfull \hbox (3.63992pt too wide) has occurred while \output is active [][] [] [5 -] -File: final2/ROC_2011.png Graphic file (type png) +] - +LaTeX Warning: File `final2/ROC_2011.png' not found on input line 296. + + +! Package pdftex.def Error: File `final2/ROC_2011.png' not found. + +See the pdftex.def package documentation for explanation. +Type H for immediate help. + ... + +l.296 \end{frame} + +Using draft setting for this image. +Try typing to proceed. +If that doesn't work, type X to quit. + File: slide_bg.png Graphic file (type png) - + Overfull \hbox (3.63992pt too wide) has occurred while \output is active [][] [] [6 - <./final2/ROC_2011.png>] -File: final2/bckmn.png Graphic file (type png) +] - -File: final2/MN.png Graphic file (type png) +LaTeX Warning: File `final2/bckmn.png' not found on input line 314. - -File: final2/MN_FLAT.png Graphic file (type png) - -Overfull \vbox (4.08972pt too high) detected at line 314 - [] +! Package pdftex.def Error: File `final2/bckmn.png' not found. + +See the pdftex.def package documentation for explanation. +Type H for immediate help. + ... + +l.314 \end{frame} + +Using draft setting for this image. +Try typing to proceed. +If that doesn't work, type X to quit. + + +LaTeX Warning: File `final2/MN.png' not found on input line 314. + + +! Package pdftex.def Error: File `final2/MN.png' not found. + +See the pdftex.def package documentation for explanation. +Type H for immediate help. + ... + +l.314 \end{frame} + +Using draft setting for this image. +Try typing to proceed. +If that doesn't work, type X to quit. + + +LaTeX Warning: File `final2/MN_FLAT.png' not found on input line 314. + + +! Package pdftex.def Error: File `final2/MN_FLAT.png' not found. + +See the pdftex.def package documentation for explanation. +Type H for immediate help. + ... + +l.314 \end{frame} + +Using draft setting for this image. +Try typing to proceed. +If that doesn't work, type X to quit. File: slide_bg.png Graphic file (type png) @@ -1323,33 +1402,57 @@ [7 - <./final2/bckmn.png (PNG copy)> <./final2/MN.png (PNG copy)> <./final2/MN_FLAT -.png (PNG copy)>] -File: final2/corr_BLend.png Graphic file (type png) +] - +LaTeX Warning: File `final2/corr_BLend.png' not found on input line 339. + + +! Package pdftex.def Error: File `final2/corr_BLend.png' not found. + +See the pdftex.def package documentation for explanation. +Type H for immediate help. + ... + +l.339 \end{frame} + +Using draft setting for this image. +Try typing to proceed. +If that doesn't work, type X to quit. + File: slide_bg.png Graphic file (type png) - + Overfull \hbox (3.63992pt too wide) has occurred while \output is active [][] [] [8 - <./final2/corr_BLend.png>] - -File: final2/corr_Geo.png Graphic file (type png) +] - +LaTeX Warning: File `final2/corr_Geo.png' not found on input line 360. + + +! Package pdftex.def Error: File `final2/corr_Geo.png' not found. + +See the pdftex.def package documentation for explanation. +Type H for immediate help. + ... + +l.360 \end{frame} + +Using draft setting for this image. +Try typing to proceed. +If that doesn't work, type X to quit. + File: slide_bg.png Graphic file (type png) - + Overfull \hbox (3.63992pt too wide) has occurred while \output is active [][] [] [9 - <./final2/corr_Geo.png (PNG copy)>] +] File: slide_bg.png Graphic file (type png) Overfull \hbox (3.63992pt too wide) has occurred while \output is active @@ -1358,11 +1461,22 @@ [10 -] -File: final2/cl1.png Graphic file (type png) - -Overfull \vbox (7.05582pt too high) detected at line 394 - [] +] + +LaTeX Warning: File `final2/cl1.png' not found on input line 394. + + +! 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pop +} def +% +%gsave abs CLW add /a ED a 0 dtransform round exch round exch +%2 copy idtransform exch Atan rotate idtransform pop /a ED .25 .25 +%% DG/SR modification begin - Dec. 12, 1997 - Patch 2 +%%itransform translate pathbbox /y2 ED a Div ceiling cvi /x2 ED /y1 ED a +%itransform pathbbox /y2 ED a Div ceiling cvi /x2 ED /y1 ED a +%% DG/SR modification end +%Div cvi /x1 ED /y2 y2 y1 sub def clip newpath 2 setlinecap systemdict +%/setstrokeadjust known { true setstrokeadjust } if x2 x1 sub 1 add { x1 +%% DG/SR modification begin - Jun. 1, 1998 - Patch 3 (from Michael Vulis) +%% a mul y1 moveto 0 y2 rlineto stroke /x1 x1 1 add def } repeat grestore } +%% def +%a mul y1 moveto 0 y2 rlineto stroke /x1 x1 1 add def } repeat grestore +%pop pop } def +%% DG/SR modification end +% +/BeginArrow { + ADict begin % hold it local, for end see EndArrow + /@mtrx CM def + gsave + 2 copy T + 2 index sub neg exch + 3 index sub exch Atan + rotate newpath +} def +% +/EndArrow { @mtrx setmatrix CP grestore end } def % end the ADict +% +/Arrow { + CLW mul add dup + 2 div /w ED + mul dup /h ED + mul /a ED + { 0 h T 1 -1 scale } if + w neg h moveto + 0 0 L w h L w neg a neg rlineto + gsave fill grestore +} def +% +/ArrowD { % the sides are drawn as curves (hv 20071211) + CLW mul add dup + 2 div /w ED + mul dup /h ED + mul /Inset ED + { 0 h T 1 -1 scale } if % changes the direction +% we use y=w/h^2 * x^2 as equation for the control points +% for the coordinates the arrow is seen from top to bottom +% the bottom (tip) is (0;0) + w neg h moveto % lower left of > + w 9 div 4 mul neg h 3 div 2 mul + w 9 div neg h 3 div + 0 0 curveto % tip of > + w 9 div h 3 div + w 9 div 4 mul h 3 div 2 mul + w h curveto % upper left of > + w neg Inset neg rlineto % move to x=0 and inset + gsave fill grestore +} def +% +/Tbar { + CLW mul add /z ED + z -2 div CLW 2 div moveto + z 0 rlineto stroke + 0 CLW moveto +} def +% +/Bracket { + CLW mul add dup CLW sub 2 div + /x ED mul CLW add /y ED /z CLW 2 div def + x neg y moveto + x neg CLW 2 div L x CLW 2 div L x y L stroke + 0 CLW moveto +} def +% +/RoundBracket { + CLW mul add dup 2 div + /x ED mul /y ED /mtrx CM def + 0 CLW 2 div T x y mul 0 ne { x y scale } if + 1 1 moveto + .85 .5 .35 0 0 0 curveto + -.35 0 -.85 .5 -1 1 curveto + mtrx setmatrix stroke 0 CLW moveto +} def +% +/SD { 0 360 arc fill } def +% +/EndDot { % DS is the dot size + { /z DS def } { /z 0 def } ifelse + /b ED 0 z DS SD b { 0 z DS CLW sub SD } if + 0 DS z add CLW 4 div sub moveto } def +% +/Shadow { [ { /moveto load } { /lineto load } { /curveto load } { + /closepath load } /pathforall load stopped { pop pop pop pop CP /moveto + load } if ] cvx newpath 3 1 roll T exec } def +% +%/NArray { +% aload length 2 div dup dup cvi eq not { exch pop } if /n exch +% cvi def +%} def +% +/NArray { % holds the coordinates and on top of stack the showpoints boolean + /showpoints ED + counttomark 2 div dup cvi /n ED + n eq not { exch pop } if + showpoints { ] aload /Points ED } { n 2 mul 1 add -1 roll pop } ifelse +} def +% +/Line { + NArray n 0 eq not + { n 1 eq { 0 0 /n 2 def } if ArrowA /n n 2 sub def + n { Lineto } repeat + CP 4 2 roll ArrowB L pop pop + } if +} def +% +/Arcto { + /a [ 6 -2 roll ] cvx def + a r + /arcto load stopped { 5 } { 4 } ifelse { pop } repeat + a +} def +% +/CheckClosed { dup n 2 mul 1 sub index eq 2 index n 2 mul 1 add index eq + and { pop pop /n n 1 sub def } if } def +/Polygon { NArray n 2 eq { 0 0 /n 3 def } if n 3 lt { n { pop pop } + repeat } { n 3 gt { CheckClosed } if n 2 mul -2 roll /y0 ED /x0 ED /y1 + ED /x1 ED x1 y1 /x1 x0 x1 add 2 div def /y1 y0 y1 add 2 div def x1 y1 + moveto /n n 2 sub def n { Lineto } repeat x1 y1 x0 y0 6 4 roll Lineto + Lineto pop pop closepath } ifelse } def +/Diamond { + /mtrx CM def + T rotate + /h ED + /w ED + dup 0 eq { pop } { CLW mul neg + /d ED + /a w h Atan def + /h d a sin Div h add def + /w d a cos Div w add def } ifelse + mark w 2 div h 2 div w 0 0 h neg w neg 0 0 h w 2 div h 2 div + /ArrowA { moveto } def + /ArrowB { } def + false Line + closepath mtrx setmatrix } def +% DG modification begin - Jan. 15, 1997 +%/Triangle { /mtrx CM def translate rotate /h ED 2 div /w ED dup 0 eq { +%pop } { CLW mul /d ED /h h d w h Atan sin Div sub def /w w d h w Atan 2 +%div dup cos exch sin Div mul sub def } ifelse mark 0 d w neg d 0 h w d 0 +%d /ArrowA { moveto } def /ArrowB { } def false Line closepath mtrx +%setmatrix } def +% +/Triangle { + /mtrx CM def + translate + rotate /h ED 2 div /w ED + dup CLW mul /d ED + /h h d w h Atan sin Div sub def + /w w d h w Atan 2 div dup cos exch sin Div mul sub def + mark + 0 d w neg d 0 h w d 0 d + /ArrowA { moveto } def + /ArrowB { } def + false + Line + closepath + mtrx +% DG/SR modification begin - Jun. 1, 1998 - Patch 3 (from Michael Vulis) +% setmatrix } def + setmatrix pop +} def +% DG/SR modification end +% +/CCA { + /y ED /x ED + 2 copy y sub /dy1 ED + x sub /dx1 ED + /l1 dx1 dy1 Pyth def +} def +% +/CC { + /l0 l1 def + /x1 x dx sub def + /y1 y dy sub def + /dx0 dx1 def + /dy0 dy1 def + CCA + /dx dx0 l1 c exp mul dx1 l0 c exp mul add def + /dy dy0 l1 c exp mul dy1 l0 c exp mul add def + /m dx0 dy0 Atan dx1 dy1 Atan sub 2 div cos abs b exp a mul dx dy Pyth Div 2 div def + /x2 x l0 dx mul m mul sub def + /y2 y l0 dy mul m mul sub def + /dx l1 dx mul m mul neg def + /dy l1 dy mul m mul neg def +} def +% +/IC { + /c c 1 add def + c 0 lt { /c 0 def } { c 3 gt { /c 3 def } if } ifelse + /a a 2 mul 3 div 45 cos b exp div def + CCA + /dx 0 def + /dy 0 def +} def +% +/BOC { IC CC x2 y2 x1 y1 ArrowA CP 4 2 roll x y curveto } def +/NC { CC x1 y1 x2 y2 x y curveto } def +/EOC { x dx sub y dy sub 4 2 roll ArrowB 2 copy curveto } def +/BAC { IC CC x y moveto CC x1 y1 CP ArrowA } def +/NAC { x2 y2 x y curveto CC x1 y1 } def +/EAC { x2 y2 x y ArrowB curveto pop pop } def +% +/OpenCurve { + NArray n 3 lt + { n { pop pop } repeat } + { BOC /n n 3 sub def n { NC } repeat EOC } ifelse +} def +% +/AltCurve { + { false NArray n 2 mul 2 roll + [ n 2 mul 3 sub 1 roll ] aload + /Points ED + n 2 mul -2 roll } + { false NArray } ifelse + n 4 lt { n { pop pop } repeat } { BAC /n n 4 sub def n { NAC } repeat EAC } ifelse +} def +% +/ClosedCurve { + NArray n 3 lt + { n { pop pop } repeat } + { n 3 gt { CheckClosed } if + 6 copy n 2 mul 6 add 6 roll + IC CC x y moveto n { NC } repeat + closepath pop pop + } ifelse +} def +% +/SQ { /r ED r r moveto r r neg L r neg r neg L r neg r L fill } def +/ST { /y ED /x ED x y moveto x neg y L 0 x L fill } def +/SP { /r ED gsave 0 r moveto 4 { 72 rotate 0 r L } repeat fill grestore } def +% +/FontDot { + DS 2 mul dup + matrix scale matrix concatmatrix exch matrix + rotate matrix concatmatrix exch + findfont exch makefont setfont +} def +% +/Rect { + x1 y1 y2 add 2 div moveto + x1 y2 lineto + x2 y2 lineto + x2 y1 lineto + x1 y1 lineto + closepath +} def +% +/OvalFrame { + x1 x2 eq y1 y2 eq or + { pop pop x1 y1 moveto x2 y2 L } + { y1 y2 sub abs x1 x2 sub abs 2 copy gt + { exch pop } { pop } ifelse + 2 div exch { dup 3 1 roll mul exch } if + 2 copy lt { pop } { exch pop } ifelse + /b ED + x1 y1 y2 add 2 div moveto + x1 y2 x2 y2 b arcto + x2 y2 x2 y1 b arcto + x2 y1 x1 y1 b arcto + x1 y1 x1 y2 b arcto + 16 { pop } repeat + closepath + } ifelse +} def +% +/Frame { + CLW mul /a ED + 3 -1 roll + 2 copy gt { exch } if + a sub /y2 ED + a add /y1 ED + 2 copy gt { exch } if + a sub /x2 ED + a add /x1 ED + 1 index 0 eq { pop pop Rect } { OvalFrame } ifelse +} def +% +/BezierNArray { + /f ED + counttomark 2 div dup cvi /n ED + n eq not { exch pop } if + n 1 sub neg 3 mod 3 add 3 mod { 0 0 /n n 1 add def } repeat + f { ] aload /Points ED } { n 2 mul 1 add -1 roll pop } ifelse +} def +% +/OpenBezier { + BezierNArray + n 1 eq + { pop pop } + { ArrowA n 4 sub 3 idiv + { 6 2 roll 4 2 roll curveto } repeat + 6 2 roll 4 2 roll ArrowB curveto } ifelse +} def +% +/ClosedBezier { + BezierNArray + n 1 eq + { pop pop } + { moveto n 1 sub 3 idiv + { 6 2 roll 4 2 roll curveto } repeat + closepath } ifelse +} def +% +/BezierShowPoints { + gsave + Points aload length 2 div cvi /n ED + moveto + n 1 sub { lineto } repeat + CLW 2 div SLW [ 4 4 ] 0 setdash stroke + grestore +} def +% +/Parab { + /y0 ED /x0 ED /y1 ED /x1 ED + /dx x0 x1 sub 3 div def + /dy y0 y1 sub 3 div def + x0 dx sub y0 dy add x1 y1 ArrowA + x0 dx add y0 dy add x0 2 mul x1 sub y1 ArrowB + curveto + /Points [ x1 y1 x0 y0 x0 2 mul x1 sub y1 ] def +} def +% +/Grid { + newpath + /a 4 string def + /b ED /c ED /n ED + cvi dup 1 lt { pop 1 } if + /s ED + s div dup 0 eq { pop 1 } if + /dy ED s div dup 0 eq { pop 1 } if + /dx ED dy div round dy mul + /y0 ED dx div round dx mul + /x0 ED dy div round cvi + /y2 ED dx div round cvi + /x2 ED dy div round cvi + /y1 ED dx div round cvi + /x1 ED + /h y2 y1 sub 0 gt { 1 } { -1 } ifelse def + /w x2 x1 sub 0 gt { 1 } { -1 } ifelse def + b 0 gt { + /z1 b 4 div CLW 2 div add def +% /Helvetica findfont b scalefont setfont + /b b .95 mul CLW 2 div add def } if + systemdict /setstrokeadjust known + { true setstrokeadjust /t { } def } + { /t { transform 0.25 sub round 0.25 add exch 0.25 sub round 0.25 add + exch itransform } bind def } ifelse + gsave n 0 gt { 1 setlinecap [ 0 dy n div ] dy n div 2 div setdash } { 2 setlinecap } ifelse + /i x1 def + /f y1 dy mul n 0 gt { dy n div 2 div h mul sub } if def + /g y2 dy mul n 0 gt { dy n div 2 div h mul add } if def + x2 x1 sub w mul 1 add dup 1000 gt { pop 1000 } if + { i dx mul dup y0 moveto + b 0 gt + { gsave c i a cvs dup stringwidth pop + /z2 ED w 0 gt {z1} {z1 z2 add neg} ifelse + h 0 gt {b neg}{z1} ifelse + rmoveto show grestore } if + dup t f moveto + g t L stroke + /i i w add def + } repeat + grestore + gsave + n 0 gt + % DG/SR modification begin - Nov. 7, 1997 - Patch 1 + %{ 1 setlinecap [ 0 dx n div ] dy n div 2 div setdash } + { 1 setlinecap [ 0 dx n div ] dx n div 2 div setdash } + % DG/SR modification end + { 2 setlinecap } ifelse + /i y1 def + /f x1 dx mul n 0 gt { dx n div 2 div w mul sub } if def + /g x2 dx mul n 0 gt { dx n div 2 div w mul add } if def + y2 y1 sub h mul 1 add dup 1000 gt { pop 1000 } if + { newpath i dy mul dup x0 exch moveto + b 0 gt { gsave c i a cvs dup stringwidth pop + /z2 ED + w 0 gt {z1 z2 add neg} {z1} ifelse + h 0 gt {z1} {b neg} ifelse + rmoveto show grestore } if + dup f exch t moveto + g exch t L stroke + /i i h add def + } repeat + grestore +} def +% +/ArcArrow { + /d ED /b ED /a ED + gsave + newpath 0 -1000 moveto clip + newpath + 0 1 0 0 b + grestore + c mul + /e ED + pop pop pop r a e d PtoC y add exch x add + exch r a PtoC y add exch x add exch b pop pop pop pop a e d CLW 8 div c + mul neg d +} def +% +/Ellipse { /mtrx CM def T scale 0 0 1 5 3 roll arc mtrx setmatrix } def +% +/ArcAdjust { %%%% Vincent Guirardel +% given a target length (targetLength) and an initial angle (angle0) [in the stack], +% let M(angle0)=(rx*cos(angle0),ry*sin(angle0))=(x0,y0). +% This computes an angle t such that (x0,y0) is at distance +% targetLength from the point M(t)=(rx*cos(t),ry*sin(t)). +% NOTE: this an absolute angle, it does not have to be added or substracted to angle0 +% contrary to TvZ's code. +% To achieve, this, one iterates the following process: start with some angle t, +% compute the point M' at distance targetLength of (x0,y0) on the semi-line [(x0,y0) M(t)]. +% Now take t' (= new angle) so that (0,0) M(t') and M' are aligned. +% +% Another difference with TvZ's code is that we need d (=add/sub) to be defined. +% the value of d = add/sub is used to know on which side we have to move. +% It is only used in the initialisation of the angle before the iteration. +% +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +% Input stack: 1: target length 2: initial angle +% variables used : rx, ry, d (=add/sub) +% + /targetLength ED /angle0 ED + /x0 rx angle0 cos mul def + /y0 ry angle0 sin mul def +% we are looking for an angle t such that (x0,y0) is at distance targetLength +% from the point M(t)=(rx*cos(t),ry*sin(t))) +%initialisation of angle (using 1st order approx = TvZ's code) + targetLength 57.2958 mul + angle0 sin rx mul dup mul + angle0 cos ry mul dup mul + add sqrt div +% if initialisation angle is two large (more than 90 degrees) set it to 90 degrees +% (if the ellipse is very curved at the point where we draw the arrow, % +% the value can be much more than 360 degrees !) +% this should avoid going on the wrong side (more than 180 degrees) or go near +% a bad attractive point (at 180 degrees) + dup 90 ge { pop 90 } if + angle0 exch d % add or sub +% maximum number of times to iterate the iterative procedure: +% iterative procedure: takes an angle t on top of stack, computes a +% better angle (and put it on top of stack) + 30 { dup +% compute distance D between (x0,y0) and M(t) + dup cos rx mul x0 sub dup mul exch sin ry mul y0 sub dup mul add sqrt +% if D almost equals targetLength, we stop + dup targetLength sub abs 1e-5 le { pop exit } if +% stack now contains D t +% compute the point M(t') at distance targetLength of (x0,y0) on the semi-line [(x0,y0) M(t)]: +% M(t')= ( (x(t)-x0)*targetLength/d+x0 , (y(t)-y0)*targetLength/d+y0 ) + exch dup cos rx mul x0 sub exch sin ry mul y0 sub +% stack contains: y(t)-y0, x(t)-x0, d + 2 index Div targetLength mul y0 add ry Div exch + 2 index Div targetLength mul x0 add rx Div +% stack contains x(t')/rx , y(t')/ry , d +% now compute t', and remove D from stack + atan exch pop + } repeat +% we don't look at what happened... in particular, if targetLength is greater +% than the diameter of the ellipse... +% the final angle will be around /angle0 + 180. maybe we should treat this pathological case... +% after iteration, stack contains an angle t such that M(t) is the tail of the arrow +% to give back the result as a an angle relative to angle0 we could add the following line: +% angle0 sub 0 exch d +% +% begin bug fix 2006-01-11 +% we want to adjust the new angle t' by a multiple of 360 so that | t'-angle0 | <= 180 +%(we don't want to make the ellipse turn more or less than it should)... +dup angle0 sub dup abs 180 gt { 180 add 360 div floor 360 mul sub } { pop } ifelse +% end bug fix +} def +% +/EllipticArcArrow { + /d ED % is add or sub + /b ED % arrow procedure + /a1 ED % angle + gsave + newpath + 0 -1000 moveto + clip % Set clippath far from arrow. + newpath + 0 1 0 0 b % Draw arrow to determine length. + grestore +% Length of arrow is on top of stack. Next 3 numbers are junk. +% + a1 exch ArcAdjust % Angular position of base of arrow. + /a2 ED + pop pop pop + a2 cos rx mul xOrig add % hv 2007-08-29 x->xOrig + a2 sin ry mul yOrig add % hv 2007-08-29 y->yOrig + a1 cos rx mul xOrig add % + a1 sin ry mul yOrig add % +% Now arrow tip coor and base coor are on stack. + b pop pop pop pop % Draw arrow, and discard coordinates. + a2 CLW 8 div +% change value of d (test it by looking if `` 1 1 d '' gives 2 or not ) + 1 1 d 2 eq { /d { sub } def } { /d { add } def } ifelse + ArcAdjust +% resets original value of d + 1 1 d 2 eq { /d { sub } def } { /d { add } def } ifelse % Adjust angle to give overlap. +} def +%%------------------ tvz/DG/hv (2004-05-10) end -------------------%% +% +/Rot { CP CP translate 3 -1 roll neg rotate NET } def +% +/RotBegin { + tx@Dict /TMatrix known not { /TMatrix { } def /RAngle { 0 } def } if + /TMatrix [ TMatrix CM ] cvx def + /a ED + a Rot /RAngle [ RAngle dup a add ] cvx def +} def +% +/RotEnd { + /TMatrix [ TMatrix setmatrix ] cvx def + /RAngle [ RAngle pop ] cvx def +} def +% +/PutCoor { gsave CP T CM STV exch exec moveto setmatrix CP grestore } def +/PutBegin { /TMatrix [ TMatrix CM ] cvx def CP 4 2 roll T moveto } def +/PutEnd { CP /TMatrix [ TMatrix setmatrix ] cvx def moveto } def +% +/Uput { + /a ED + add 2 div /h ED 2 + div /w ED + /s a sin def + /c a cos def + /b s abs c abs 2 copy gt dup + /q ED + { pop } { exch pop } ifelse def + /w1 c b div w mul def + /h1 s b div h mul def + q { w1 abs w sub dup c mul abs }{ h1 abs h sub dup s mul abs } ifelse +} def +% +/UUput { + /z ED + abs /y ED + /x ED + q { x s div c mul abs y gt }{ x c div s mul abs y gt } ifelse + { x x mul y y mul sub z z mul add sqrt z add } + { q { x s div } { x c div } ifelse abs + } ifelse + a PtoC + h1 add exch + w1 add exch +} def +% +/BeginOL { + dup (all) eq exch TheOL eq or + { IfVisible not { Visible /IfVisible true def } if } + { IfVisible { Invisible /IfVisible false def } if } ifelse +} def +% +/InitOL { + /OLUnit [ 3000 3000 matrix defaultmatrix dtransform ] cvx def + /Visible { CP OLUnit idtransform T moveto } def + /Invisible { CP OLUnit neg exch neg exch idtransform T moveto } def + /BOL { BeginOL } def + /IfVisible true def +} def +% +end +%-----------------------------------------------------------------------------% +% +% END pstricks.pro + +%%EndProcSet +%%BeginProcSet: pst-algparser.pro 0 0 +% $Id: pst-algparser.pro 26 2008-06-14 11:50:02Z herbert $ +%% +%% PostScript prologue for PSTricks algorithm parser +%% Version 0.01, 2008/01/01 +%% +%% This program can be redistributed and/or modified under the terms +%% of the LaTeX Project Public License Distributed from CTAN archives +%% in directory macros/latex/base/lppl.txt. +%% +%%-----------------------------------------------------------------------------% +% +/AlgParser { tx@AlgToPs begin AlgToPs end } def % Dominique Rodriguez +% +/tx@CoreAnalyzerDict 100 dict def tx@CoreAnalyzerDict begin +% +% PS ANALYZER FOR ALGEBRAIC EXPRESSION V1.12 +% E->T|E+T +% T->FS|T*FS +% FS -> F | +FS | -FS +% F->P|F^SF +% P->(E)|literal +% literal->number|var|var[E]|func(params) +% params->E|E,param +% number->TOBEFINISHED +% +%% E expression, T term, SF signed factor, F factor, P power +% +%% parser +% +%% str +% +%% C->EE +%% STR index -> STR index+lenExpr +/AnalyzeCond { AnalyzeExpr ReadCondOp AnalyzeExpr EvalCondOp } def +% +%% analyze Expression List (separator , or | ) +%% STR index -> STR index+lenExpr +%% /AnalyzeListOfE { +%% { NextNonBlankChar pop AnalyzeExpr%%dup Strlen eq { exit } if NextNonBlankChar +%% NextNonBlankChar dup 0 eq { pop exit } if +%% dup 44 ne 1 index 124 ne and { dup 41 ne { PROBLEMCONTACTBILLOU } { pop exit } ifelse } if +%% pop NextNonBlankChar dup 0 eq { exit } if 124 ne { PROBLEMCONTACTBILLOU } if 1 add NextNonBlankChar 0 eq {toto} if } loop +%% AnalyzeListOfEPostHook +%% } def +/AnalyzeListOfE { + /NotFirst false def + { NextNonBlankChar pop AnalyzeExpr + NotFirst { EvalListOfExpr } { /NotFirst true def } ifelse + dup Strlen eq { exit } if NextNonBlankChar + dup 44 ne 1 index 124 ne and + { dup 41 ne { PROBLEMCONTACTBILLOU } { pop exit } ifelse } + if pop 1 add } loop + AnalyzeListOfEPostHook +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% E->T|E+T +%% STR index -> STR index+lenExpr +/AnalyzeExpr { + AnalyzePreHook AnalyzeTerm IsEndingExpr + { dup 0 ne { 32 eq { NextNonBlankChar } if } { pop } ifelse } + { { RollOp 1 add NextNonBlankChar pop AnalyzeTerm PreEvalHook EvalAddSub IsEndingExpr { pop exit } if } loop } + ifelse + AnalyzePostHook +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% T->FS|T*FS +%% STR index +/AnalyzeTerm { + AnalyzePreHook AnalyzeSignedFactor IsEndingTerm + { dup 0 ne { 32 eq { NextNonBlankChar } if } { pop } ifelse } + { { RollOp 1 add NextNonBlankChar pop AnalyzeSignedFactor PreEvalHook EvalMulDiv IsEndingTerm { pop exit } if} loop } + ifelse + AnalyzePostHook +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% FS -> F | +FS | -FS +%% STR index +/AnalyzeSignedFactor { + AnalyzePreHook 2 copy get dup IsUnaryOp + { RollOp 1 add NextNonBlankChar pop AnalyzeSignedFactor EvalUnaryOp } + { pop AnalyzeFactor } + ifelse AnalyzePostHook +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% F->P|F^P +%% STR index +/AnalyzeFactor { + AnalyzePreHook AnalyzePower IsEndingFactor + { dup 0 ne { 32 eq { NextNonBlankChar } if } { pop } ifelse } + { { RollOp 1 add NextNonBlankChar pop AnalyzePower PreEvalHook EvalPower IsEndingFactor { pop exit } if} loop } + ifelse AnalyzePostHook +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% P->(E)|literal +%% STR index +/AnalyzePower { + %% depending of first char either a number, or a literal + 2 copy get dup 40 eq%%an open par + { pop 1 add NextNonBlankChar pop AnalyzeExpr 1 add NextNonBlankChar pop } + { AnalyzeLiteral } + ifelse +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% STR index STR[index] -> STR index +%/AnalyzeLiteral { IsNumber { EvalNumber } { EvalLiteral } ifelse } def +/AnalyzeLiteral { dup IsUnaryOp exch IsNumber or { EvalNumber } { EvalLiteral } ifelse } def%%dr 09102006 +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% recognize + or - +%% chr -> T/F +/IsUnaryOp { dup 43 eq exch 45 eq or } bind def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% a number can contain only : 0123456789. +%% chr -> T/F +/IsNumber { dup 48 ge exch dup 57 le 3 -1 roll and exch 46 eq or } bind def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% STR index -> STR index number +%% a number can be of the form [0-9]*.[0-9]*\([eE][+-]?[0-9]+\)? +%% STR index -> STR index' number +/ReadNumber { + exch dup 3 -1 roll dup 3 1 roll + %%read mantissa + { 1 add 2 copy dup Strlen eq { pop pop 0 exit } if get dup IsNumber not { exit } if pop } loop + dup 101 eq exch 69 eq or + %%% there is a "e" or "E" -> read exponant + { 1 add 2 copy get dup IsUnaryOp + { pop 1 add 2 copy get } if + { IsNumber not { exit } if 1 add 2 copy get } loop } + if + dup 4 1 roll + 3 -1 roll exch 1 index sub getinterval +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% a number can contain only : 0123456789. +%% chr -> T/F +/IsCondOp { dup 30 eq exch dup 60 ge exch 62 le and or } bind def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% STR index -> STR index number +%% a number can be of the form [0-9]*.[0-9]*\([eE][+-]?[0-9]+\)? +%% STR index -> STR index' number +/ReadCondOp { + NextNonBlankChar 1 index 4 1 roll + { IsCondOp not { exit } if 1 add 2 copy get } loop + 2 copy 5 -1 roll + exch 1 index sub getinterval 3 1 roll +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% a literal can contain only : 0123456789. +%% chr -> T/F +/IsLiteral {% + dup 48 ge exch dup 57 le 3 -1 roll and exch + dup 65 ge exch dup 90 le 3 -1 roll and 3 -1 roll or exch + dup 97 ge exch 122 le and or } bind def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% a literal can be of the form [a-zA-Z][a-zA-Z0-9]*\(\((Expression)\)|\(\[Expression\]\)\)? +%% STR index -> literal STR index' nextchr +/ReadLiteral { + exch dup 3 -1 roll dup 3 1 roll + %%read literal core + { 2 copy dup Strlen eq { pop pop 0 exit } if get dup IsLiteral not { exit } if pop 1 add } loop + 4 1 roll dup 5 1 roll 3 -1 roll exch 1 index sub getinterval 4 1 roll +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% expr is ended by end of str or a clpar +%% STR index -> STR index STR[index] T/F +/IsEndingExpr {% + 2 copy dup Strlen eq + %% if end of str is reached -> end ! + { pop pop 0 true } + %% ending chr -> clpar, comma, |, <, >, =, !, + {get dup dup 41 eq + exch dup 124 eq + exch dup 93 eq + exch dup 44 eq + exch dup 30 eq + exch dup 60 ge exch 62 le and or or or or or} + ifelse } def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% expr is ended by end of str or a +- +%% STR index -> STR index STR[index] T/F +/IsEndingTerm { IsEndingExpr { true } { dup dup 43 eq exch 45 eq or } ifelse } def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% expr is ended by end of str or */ +%% STR index -> STR index STR[index] T/F +/IsEndingFactor { IsEndingTerm { true } { dup dup 42 eq exch 47 eq or } ifelse } def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% expr is ended by end of str or ^ +%% STR index -> STR index STR[index] T/F +/IsEndingPower { IsEndingFactor { true } { dup 94 eq } ifelse } def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% STR index -> STR index STR[index] +/NextNonBlankChar { { dup Strlen eq { 0 exit } if 2 copy get dup neBlkChar { exit } if pop 1 add } loop } bind def +/neBlkChar { dup 32 ne exch dup 10 ne exch 9 ne and and } bind def +%%%%%%%%%%%%%%%%%%%%%%%% +%% DEBUG +/BRK {false} def +/BRKtrue {/BRK true def} def +/BRKStop {BRK {BRKtoto} if } def +/BRKEvalStop {BRK exch if } def +/BRKBRK2true {BRK {BRK2true} if } def +/BRK2 {false} def +/BRK2true {/BRK2 true def} def +/BRK2Stop {BRK2 {BRK2toto} if } def/BRK {false} def +end +% +%-------------------------------------------------------------------------------% +% +/tx@AlgToPs 12 dict def tx@AlgToPs begin +% +%% algExpr -> PSVector +/AlgToPs { tx@CoreAnalyzerDict begin InitParser AnalyzeListOfE pop pop EndingSequence end } def +/EndingSequence { ExpressionVector aload length /end cvx exch 1 add array astore } def +/InitParser { /ExpressionVector [ /tx@AddMathFunc cvx /begin cvx ] def dup length /Strlen exch def 0 } def +/Strlen 0 def +/EvalListOfExpr {} def% +/EvalNumber {% + ReadNumber cvr /ExpressionVector ExpressionVector aload length dup 3 add -1 roll cvx + exch 1 add array astore def NextNonBlankChar pop } def +/EvalAddSub {% + /ExpressionVector ExpressionVector aload length dup 5 add -1 roll + 43 eq { /add } { /sub } ifelse cvx exch 1 add array astore def +} def +/EvalMulDiv {% + /ExpressionVector ExpressionVector aload length dup 5 add -1 roll + 42 eq { /mul } { /div } ifelse cvx exch 1 add array astore def +} def +/EvalPower {% + /ExpressionVector ExpressionVector aload length dup 5 add -1 roll + pop /exp cvx exch 1 add array astore def +} def +/EvalLiteral {% + ReadLiteral + dup 40 eq%%% there is an open par -> function call + { pop 2 index + dup (Sum) eq { EvalSum } + { dup (IfTE) eq { EvalCond } + { dup (Derive) eq { pop EvalDerive } + { pop 1 add NextNonBlankChar pop AnalyzeListOfE 2 index TrigoFunc + /ExpressionVector ExpressionVector aload length dup 5 add -1 roll cvn cvx + exch 1 add array astore def 1 add NextNonBlankChar pop } ifelse } ifelse} ifelse } + { /ExpressionVector ExpressionVector aload length dup 6 add -1 roll cvn cvx exch 1 add array astore def + dup 91 eq%%% there is an open bracket -> vector element + { pop 1 add NextNonBlankChar pop AnalyzeExpr + /ExpressionVector ExpressionVector aload length /cvi cvx exch /get cvx exch 2 add array astore def 1 add } + { pop NextNonBlankChar pop } + ifelse} + ifelse +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% the derive function : Derive(n,f(x)) +%% firstparindex lastparindex -> +/EvalDerive { + %% manage the function descripiton + 1 add ReadNumber 3 1 roll NextNonBlankChar + 44 ne { ANALYZER_ERROR_missing_second_comma_in_Sum } if + 1 add NextNonBlankChar pop + 3 -1 roll cvi + dup 0 eq + { pop AnalyzeExpr 3 -1 roll pop 1 add } + { 1 sub 3 1 roll (x) exch tx@Derive begin DeriveIndexed end 4 -1 roll + { (x) tx@Derive begin Derive end } repeat + ExpressionVector exch /ExpressionVector [] def + AlgToPs aload length + /ExpressionVector 1 index 3 add -1 roll aload length dup 3 add -1 roll /l2 exch def /l1 exch def + l1 l2 add 1 add l2 neg roll l1 l2 add array astore def 3 -1 roll pop 1 add + 1 index length /Strlen exch def } ifelse +} def +/EvalSum {% + pop 1 add NextNonBlankChar pop + %% read the variable name + ReadLiteral pop NextNonBlankChar + 44 ne { ANALYZER_ERROR_missing_first_comma_in_Sum } if + %% read the initial value + 1 add NextNonBlankChar pop ReadNumber cvi 3 1 roll + 2 copy get 44 ne { ANALYZER_ERROR_missing_second_comma_in_Sum } if + %% read the increment value + 1 add NextNonBlankChar pop ReadNumber cvi 3 1 roll + 2 copy get 44 ne { ANALYZER_ERROR_missing_second_comma_in_Sum } if + %% read the limit value + 1 add NextNonBlankChar pop ReadNumber cvi 3 1 roll + 2 copy get 44 ne { ANALYZER_ERROR_missing_second_comma_in_Sum } if + /ExpressionVector ExpressionVector aload length dup 7 add -3 roll 0 4 1 roll + 5 -1 roll 4 add array astore def + %% keep ExpressionVector for later and create a new one for internal Sum computation + ExpressionVector 3 1 roll /ExpressionVector [ 6 -1 roll cvn /exch cvx /def cvx ] def + 1 add NextNonBlankChar pop AnalyzeExpr + %% add each term + /ExpressionVector ExpressionVector aload length 1 add /add cvx exch array astore def + /ExpressionVector 4 -1 roll aload length ExpressionVector cvx /for cvx 3 -1 roll 2 add + array astore def 3 -1 roll pop 1 add +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% Convert to radians if trigo function call +%% (name) -> +/TrigoFunc { + dup (cos) eq 1 index (sin) eq or exch (tan) eq or + { /ExpressionVector ExpressionVector aload length Pi /div cvx 180 /mul cvx 5 -1 roll 4 add + array astore def + } if +} def +/EvalCond {% + pop 1 add AnalyzeCond NextNonBlankChar + 44 ne { ANALYZER_ERROR_missing_first_comma_in_IfTE } if + ExpressionVector 3 1 roll /ExpressionVector [] def + 1 add AnalyzeExpr ExpressionVector 3 1 roll /ExpressionVector [] def + NextNonBlankChar 44 ne { ANALYZER_ERROR_missing_second_comma_in_IfTE } if + 1 add AnalyzeExpr + NextNonBlankChar 41 ne { ANALYZER_ERROR_missing_ending parenthesis_in_IfTE } if + ExpressionVector + /ExpressionVector 6 -1 roll aload length dup + 6 add -1 roll cvx exch dup 4 add -1 roll cvx /ifelse cvx 3 -1 roll 3 add array astore def + 1 add 3 -1 roll pop +} def +%% CondOp STR index +/EvalCondOp {% + 3 -1 roll + dup (=) eq { /eq } {% + dup (<) eq { /lt } {% + dup (>) eq { /gt } {% + dup (>=) eq { /ge } {% + dup (<=) eq { /ge } {% + dup (!=) eq { /ne } { ERROR_non_valid_conditional_operator } + ifelse } ifelse } ifelse } ifelse } ifelse } ifelse + cvx exch pop + /ExpressionVector ExpressionVector aload length dup 3 add -1 roll exch 1 add array astore def } def +/EvalUnaryOp { + 3 -1 roll 45 eq { /ExpressionVector ExpressionVector aload length /neg cvx exch 1 add array astore def } if +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% H O O K S +/AnalyzePreHook {} bind def +/PreEvalHook {} bind def +/AnalyzeListOfEPostHook {} bind def +/AnalyzePostHook {} def +/RollOp { 3 1 roll } bind def +end %tx@CoreAnalyzerDict +% +%--------------------------------------------------------------------% +% +/tx@Derive 41 dict def tx@Derive begin +%%increase ^^ for each function added +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% algExpr variable -> PSVector +/Derive {% + 10240 string 3 1 roll 0 3 1 roll + /Variable exch def + tx@CoreAnalyzerDict begin InitParser AnalyzeListOfE end +} def +/Strlen 0 def +/InitParser { dup length /Strlen exch def 0 } def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% algExpr variable index -> PSVector +/DeriveIndexed {% + 3 1 roll 10240 string 3 1 roll 0 3 1 roll + /Variable exch def + tx@CoreAnalyzerDict begin InitParser pop 4 -1 roll AnalyzeExpr 4 -2 roll pop pop 4 -2 roll exch pop end +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% (u,v)'=-(u',v') +/EvalListOfExpr {% + 4 2 roll 2 copy 9 -1 roll dup length 4 1 roll putinterval add AddPipe + 2 copy 7 -1 roll dup length 4 1 roll putinterval add + 6 -2 roll pop pop + 2 copy pop 0 6 2 roll GetIntervalNewStr 5 1 roll 2 copy 0 exch getinterval 6 1 roll } def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% (-u)'=-(u') +/EvalUnaryOp { + 4 -2 roll 4 index (0) eq + { (0) StrConcat 7 -1 roll pop } + { 7 -1 roll 45 eq + { AddSub AddOpPar true } { false } ifelse + 3 1 roll 5 index StrConcat 3 -1 roll { AddClPar } if } ifelse + 2 copy pop 0 6 2 roll GetIntervalNewStr + 7 -2 roll pop pop 2 index 6 index dup 4 index exch sub getinterval exch 6 2 roll +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% (number)'=0 +/EvalNumber { ReadNumber (0) 6 2 roll } def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% (u+v)'=u'+v' +/EvalAddSub {% + 7 index dup (0) eq + { pop true }%% du=0 nothing added + { dup length exch 5 index 5 index 3 -1 roll putinterval 4 -1 roll add 3 1 roll false } + ifelse + 5 index dup (0) eq + { pop { (0) } { 4 -2 roll 2 copy pop 0 6 2 roll GetIntervalNewStr } ifelse }%%dv=0 + { exch + { 5 -2 roll 7 index 45 eq { AddSub } if false } %%nothing yet added + { 5 -2 roll 7 index 43 eq%%something yet added + { AddAdd false } { AddSub AddOpPar true } ifelse } + ifelse 11 1 roll + 3 -1 roll StrConcat 10 -1 roll { AddClPar } if + 2 copy pop 0 6 2 roll GetIntervalNewStr } + ifelse + mark 11 -5 roll cleartomark 2 index 6 index dup 4 index exch sub getinterval exch 6 2 roll +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% (u*v)' or (u/v)' +/EvalMulDiv { 6 index 42 eq {EvalMul} {EvalDiv} ifelse } def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% (u*v)'=u'*v+u*v' +/EvalMul {% + 4 -2 roll 7 index dup (0) eq + { pop false }%%du=0 + { (1) eq%%du=1 + { false } + { AddOpPar 7 index StrConcat AddClPar AddMul AddOpPar true } ifelse + 3 1 roll 6 index StrConcat 3 -1 roll { AddClPar } if + true }%%du!=0 + ifelse + 5 1 roll 5 index (0) eq + { 5 -1 roll not { (0) StrConcat } if }%%dv=0 + { 5 -1 roll { AddAdd } if + 4 index (1) eq + { 8 index StrConcat } + { AddOpPar 8 index StrConcat AddClPar AddMul AddOpPar 4 index StrConcat AddClPar } + ifelse + }%%dv!=0 + ifelse + 2 copy pop 0 6 2 roll GetIntervalNewStr + mark 11 -5 roll cleartomark 2 index 6 index dup 4 index exch sub getinterval exch 6 2 roll +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% (u/v)'=(u'*v-u*v')/v^2 +/EvalDiv {% + 4 -2 roll + 4 index (0) eq%%dv=0 -> u'/v + { 7 index (0) eq { (0) StrConcat } { AddOpPar 7 index StrConcat AddClPar AddDiv 5 index StrConcat } ifelse } + { 7 index dup (0) eq + { pop }%%du=0 + { (1) eq%%du=1 + { false } + { AddOpPar 7 index StrConcat AddClPar AddMul AddOpPar true } ifelse + 3 1 roll 6 index StrConcat 3 -1 roll { AddClPar } if}%%du!=0 + ifelse + AddSub + 4 index (1) eq + { 8 index StrConcat } + { AddOpPar 8 index StrConcat AddClPar AddMul AddOpPar 4 index StrConcat AddClPar } + ifelse + %}%%dv!=0 + 2 copy GetIntervalNewStr 3 1 roll pop 0 AddOpPar 3 -1 roll StrConcat AddClPar + AddDiv AddOpPar 5 index StrConcat AddClPar 2 copy (^2) putinterval 2 add } + ifelse + 2 copy pop 0 6 2 roll GetIntervalNewStr + mark 11 -5 roll cleartomark 2 index 6 index dup 4 index exch sub getinterval exch 6 2 roll +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% str1 index str2 -> str1 index +/StrConcat { dup length 4 2 roll 2 copy 6 -1 roll putinterval 3 -1 roll add } bind def +/GetIntervalNewStr { 0 exch getinterval dup length string copy } bind def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% (u^v)'=(u^v)'=u'vu^(v-1)+v'u^(v)ln(u) +/EvalPower {% + 4 -2 roll 7 index (0) eq + {%%if du=0 then (u^v)'=v'ln(u)u^v + 4 index (0) eq + { (0) StrConcat }%%if dv=0 then (u^v)'=0 + { 4 index (1) ne { AddOpPar 4 index StrConcat (\)*) StrConcat } if + 8 index (e) ne { (ln\() StrConcat 8 index StrConcat (\)*) StrConcat } if + AddOpPar 8 index StrConcat (\)^\() StrConcat 5 index StrConcat AddClPar } ifelse + } + {%%du!=0 + 4 index (0) eq + {%%if dv=0 then (u^v)'=vu'u^(v-1) + 5 index dup IsStrNumber + { dup (0) eq + { StrConcat } + { dup dup (1) eq exch (1.0) eq or + { StrConcat } + { StrConcat + 7 index dup (1) ne exch (1.0) ne and%%%dr 09102006 insert du if <> 1 + { (*\() StrConcat 7 index StrConcat (\)) StrConcat } if%%%dr 09102006 + (*\() StrConcat 8 index StrConcat (\)) StrConcat + 5 index dup dup (2) eq exch (2.0) eq or + { pop } { cvr 1 sub 20 string cvs 3 1 roll (^) StrConcat 3 -1 roll StrConcat } ifelse } ifelse } ifelse } + { pop AddOpPar 5 index StrConcat (\)*\() StrConcat 8 index StrConcat (\)^\() StrConcat + 5 index StrConcat (-1\)) StrConcat } ifelse + } + {%%if dv!=0 and du!=0 then (u^v)'=u'vu^(v-1)+v'u^(v)ln(u) + 7 index (1) ne { AddOpPar 7 index StrConcat (\)*) StrConcat } if + AddOpPar 5 index StrConcat (\)*\() StrConcat + 8 index StrConcat (\)^\() StrConcat + 5 index StrConcat (-1\)+\() StrConcat + 4 index (1) ne { 4 index StrConcat (\)*\() StrConcat } if + 8 index StrConcat (\)^\() StrConcat + 5 index StrConcat (\)*ln\() StrConcat + 8 index StrConcat AddClPar + } ifelse + } ifelse + 2 copy pop 0 6 2 roll GetIntervalNewStr + mark 11 -5 roll cleartomark 2 index 6 index dup 4 index exch sub getinterval exch 6 2 roll +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% str -> true/false +/IsStrNumber {% + true exch + { dup 48 lt exch dup 57 gt 3 -1 roll or + exch dup 46 ne%%. + exch dup 43 ne%%+ + exch 45 ne%%- + and and and { pop false } if } forall +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% literal switch -> func call, vector, variables +/EvalLiteral {% + ReadLiteral dup 40 eq%%% there is an open par -> function call + { pop (EvalFunc_ ) 9 4 index StrConcat 0 exch getinterval cvn cvx exec } + { dup 91 eq%%% there is an open bracket -> vector element + { ERROR_vector_not_yet_implemented } + { pop EvalVariable } + ifelse } + ifelse +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% first last parpos Expr[first:parpos-1] -> +/EvalVariable { 2 index Variable eq { (1) } { (0) } ifelse 4 -1 roll exch 6 2 roll } def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% (f(u))'=u'f'(u) +/EvalFunc { + 4 2 roll 4 index (1) ne + { AddOpPar 4 index StrConcat (\)*) StrConcat } if + (Eval ) 4 8 index StrConcat 0 exch getinterval cvn cvx exec + 2 copy pop 0 6 2 roll GetIntervalNewStr + mark 9 -3 roll cleartomark 2 index 6 index dup 4 index exch sub getinterval exch 6 2 roll +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% Func derivative -> Eval +/EvalFunc_sin {% + PreCommonFunc + { (cos\() StrConcat 5 index StrConcat AddClPar } if + PostCommonFunc } def +/EvalFunc_cos {% + PreCommonFunc + { (\(-sin\() StrConcat 5 index StrConcat (\)\)) StrConcat } if + PostCommonFunc } def +/EvalFunc_tan {% + PreCommonFunc + { dup 0 eq { (1) StrConcat } { 1 sub } ifelse (/cos\() StrConcat 5 index StrConcat (\)^2) StrConcat } if + PostCommonFunc } def +/EvalFunc_asin {% + PreCommonFunc + { (1/sqrt\(1-\() StrConcat 5 index StrConcat (\)^2\)\)) StrConcat } if + PostCommonFunc } def +/EvalFunc_acos {% + PreCommonFunc + { (-1/sqrt\(1-\() StrConcat 5 index StrConcat (\)^2\)\)) StrConcat } if + PostCommonFunc } def +/EvalFunc_atg {% + PreCommonFunc + { (1/\(1+\() StrConcat 5 index StrConcat (\)^2\)\)) StrConcat } if + PostCommonFunc } def +/EvalFunc_ln {% + PreCommonFunc + { dup 0 eq { (1) StrConcat } { 1 sub } ifelse (/\() StrConcat 5 index StrConcat AddClPar } if + PostCommonFunc } def +/EvalFunc_exp {% + PreCommonFunc + { (exp\() StrConcat 5 index StrConcat AddClPar } if + PostCommonFunc } def +/EvalFunc_sqrt {% + PreCommonFunc + { dup 0 eq { (1) StrConcat } { 1 sub } ifelse (/\(2*sqrt\() StrConcat 5 index StrConcat (\)\)) StrConcat } if + PostCommonFunc } def +/EvalFunc_Fact {% + PreCommonFunc { ERROR_no_variable_expression_in_Fact } if + PostCommonFunc } def +/EvalFunc_sh {% + PreCommonFunc + { (ch\() StrConcat 5 index StrConcat AddClPar } if + PostCommonFunc } def +/EvalFunc_ch {% + PreCommonFunc + { (sh\() StrConcat 5 index StrConcat AddClPar } if + PostCommonFunc } def +/EvalFunc_th {% + PreCommonFunc + { dup 0 eq { (1) StrConcat } { 1 sub } ifelse (/ch\() StrConcat 5 index StrConcat (\)^2) StrConcat } if + PostCommonFunc } def +/EvalFunc_Argsh {% + PreCommonFunc + { (1/sqrt\(1+\() StrConcat 5 index StrConcat (\)^2\)\)) StrConcat } if + PostCommonFunc } def +/EvalFunc_Argch {% + PreCommonFunc + { (1/sqrt\(\() StrConcat 5 index StrConcat (\)^2-1\)\)) StrConcat } if + PostCommonFunc } def +/EvalFunc_Argth {% + PreCommonFunc + { (1/\(1-\() StrConcat 5 index StrConcat (\)^2\)\)) StrConcat } if + PostCommonFunc } def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +/PreCommonFunc { + 1 add NextNonBlankChar pop 3 -1 roll 5 1 roll AnalyzeExpr 1 add NextNonBlankChar pop + 4 2 roll 4 index (0) eq + { (0) StrConcat false } + { 4 index (1) ne { AddOpPar 4 index StrConcat (\)*) StrConcat } if true } ifelse +} def +/PostCommonFunc { + 2 copy pop 0 6 2 roll GetIntervalNewStr + mark 9 -3 roll cleartomark 2 index 6 index dup 4 index exch sub getinterval exch 6 2 roll +} def +/EvalFunc_Derive {% + 1 add ReadNumber cvi 1 add dup cvr log 1 add cvi string cvs + 4 -1 roll pop 5 1 roll 1 add NextNonBlankChar pop AnalyzeExpr 1 add + 4 -2 roll (Derive\() StrConcat 7 -1 roll StrConcat (,) StrConcat 6 -1 roll StrConcat AddClPar + 2 copy pop 0 6 2 roll GetIntervalNewStr 6 -1 roll pop 2 index 6 index dup 4 index exch sub getinterval + exch 6 2 roll } def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% literal switch -> func call, vector, variables +/EvalFunc_Sum {% + 1 add NextNonBlankChar pop + %% read the variable name + ReadLiteral pop 3 -1 roll pop NextNonBlankChar + 44 ne { ANALYZER_ERROR_missing_first_comma_in_Sum } if + %% read the initial value + 1 add NextNonBlankChar pop ReadNumber pop + 2 copy get 44 ne { ANALYZER_ERROR_missing_second_comma_in_Sum } if + %% read the increment value + 1 add NextNonBlankChar pop ReadNumber pop + 2 copy get 44 ne { ANALYZER_ERROR_missing_third_comma_in_Sum } if + %% read the limit value + 1 add NextNonBlankChar pop ReadNumber pop + 2 copy get 44 ne { ANALYZER_ERROR_missing_fourth_comma_in_Sum } if + 1 add NextNonBlankChar pop dup 6 1 roll 3 -1 roll pop AnalyzeExpr 1 add NextNonBlankChar pop + 4 -2 roll 3 index 8 index dup 9 index exch sub getinterval StrConcat + 4 index StrConcat AddClPar + 2 copy pop 0 6 2 roll GetIntervalNewStr + mark 9 -3 roll cleartomark 2 index 6 index dup 4 index exch sub getinterval exch 6 2 roll +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% literal switch -> func call, vector, variables +/EvalFunc_IfTE {% + 3 -1 roll pop 1 add NextNonBlankChar pop SkipCond + NextNonBlankChar + 44 ne { ANALYZER_ERROR_missing_first_comma_in_IfTE } if + 1 add NextNonBlankChar pop dup 5 1 roll + AnalyzeExpr NextNonBlankChar + 44 ne { ANALYZER_ERROR_missing_second_comma_in_IfTE } if + 1 add NextNonBlankChar pop + AnalyzeExpr 1 add NextNonBlankChar pop + 4 -2 roll 3 index 10 index dup 11 index exch sub getinterval StrConcat + 6 index StrConcat (,) StrConcat 4 index StrConcat AddClPar + 2 copy pop 0 6 2 roll GetIntervalNewStr + mark 11 -5 roll cleartomark 2 index 6 index dup 4 index exch sub getinterval exch 6 2 roll +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% advance in str until a comma is found (no error detection!) +%% str index -> str index' +/SkipCond { { 1 add 2 copy get 44 eq {exit } if } loop } bind def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% Convert to radians if trigo function call +%% (name) -> +/TrigoFunc { + dup (cos) eq 1 index (sin) eq or exch (tan) eq or + { /ExpressionVector ExpressionVector aload length Pi /div cvx 180 /mul cvx 5 -1 roll 4 add + array astore def + } if +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% No derivative for condition.... +/EvalCondOp { 3 -1 roll pop } bind def +/PutIntervalOneAdd {putinterval 1 add} bind def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% Add open parenthesis in string at the given index +%% str index -> str index+1 +/AddOpPar {2 copy (\() PutIntervalOneAdd} bind def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% Add close parenthesis in string at the given index +%% str index -> str index+1 +/AddClPar {2 copy (\)) PutIntervalOneAdd} bind def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% Add 0 in string at the given index +%% str index -> str index+1 +/AddZero {2 copy (0) PutIntervalOneAdd} bind def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% Add open parenthesis in string at the given index +%% str index -> str index+1 +/AddMul {2 copy (*) PutIntervalOneAdd} bind def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% Add open parenthesis in string at the given index +%% str index -> str index+1 +/AddDiv {2 copy (/) PutIntervalOneAdd} bind def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% Add a plus sign in string at the given index +%% str index -> str index+1 +/AddAdd {2 copy (+) PutIntervalOneAdd} bind def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% Add a minus sign in string at the given index +%% str index -> str index+1 +/AddSub {2 copy (-) PutIntervalOneAdd} bind def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% Add a pipe sign in string at the given index +%% str index -> str index+1 +/AddPipe {2 copy (|) PutIntervalOneAdd} bind def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% H O O K S +/AnalyzePreHook { dup 5 1 roll } bind def +/PreEvalHook {} def +/AnalyzePostHook { 7 -1 roll pop } bind def +/AnalyzeListOfEPostHook { 6 -1 roll mark 6 1 roll cleartomark } bind def +/RollOp { 5 1 roll } bind def +end%%%tx@CoreAnalyzerDict +/tx@AddMathFunc 12 dict def tx@AddMathFunc begin +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% NEW FUNC +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% function arcsine in radians asin(x)=atan(x/sqrt(1-x^2)) +%% x -> theta +/asin {% + dup abs 1 gt { EQDFasinrangeerror } if + dup dup dup mul 1 exch sub sqrt atan exch 0 lt { 360 sub } if DegtoRad +} def +%% function arccosine in radians acos(x)=atan(sqrt(1-x^2)/x) +%% x -> theta +/acos {% + dup abs 1 gt { EQDFacosrangeerror } if + dup dup mul 1 exch sub sqrt exch atan DegtoRad +} def +%% function arctangent in radians +%% x -> theta +/atg { 1 atan dup 90 gt { 360 sub } if DegtoRad } bind def +%% HYPERBOLIC FUNCTIONS +/sh { dup Ex exch neg Ex sub 2 div } def +/ch { dup Ex exch neg Ex add 2 div } def +/th { dup sh exch ch div } def +/Argsh { dup dup mul 1 add sqrt add ln } def +/Argch { dup dup mul 1 sub sqrt add ln } def +/Argth { dup 1 add exch 1 exch sub div ln 2 div } def +%% modified exponential funtion for 0 +%% x n -> x^n +/Exp { dup 0 eq { pop pop 1 } { exp } ifelse } bind def +%% modified exponential funtion for 0 +%% x -> e^x +/Ex { Euler exch exp } bind def +%% +%% factorial function +%% n -> n! +/Fact { 1 exch 2 exch 1 exch { mul } for } bind def +/fact { Fact } bind def +end + +% END pstricks.pro + +%%EndProcSet +%%BeginProcSet: pst-dots.pro 0 0 +% $Id: pst-dots.pro 26 2008-06-14 11:50:02Z herbert $ +% +%% PostScript prologue for pstricks.tex. +%% Version 2.02, 2008/04/18 +%% +%% For distribution, see pstricks.tex. +%% +%% Timothy Van Zandt +%% +%% This program can be redistributed and/or modified under the terms +%% of the LaTeX Project Public License Distributed from CTAN archives +%% in directory macros/latex/base/lppl.txt. +%% +%% Modified by Etienne Riga - Dec. 16, 1999 +%% Modified by Etienne Riga - 2005/01/01 (er) +%% to add /Diamond, /SolidDiamond and /BoldDiamond +%% Modified by Herbert Voss (hv) - 2008/04/17 +% +10 dict dup begin % hold local + /FontType 3 def + /FontMatrix [.001 0 0 .001 0 0] def + /FontBBox [-571.5 -742.5 571.5 742.5] def +% /FontBBox [-1000 -1000 1000 1000] def % See end of file in /BuildGlyph + /Encoding 256 array def + 0 1 255 {Encoding exch /.notdef put} for % fill the array with /.notdef + Encoding % replace with given dot names + dup (b) 0 get /Bullet put % get the numerical position of b in ASCII +% % and save /Bullet at this place in Encoding + dup (c) 0 get /Circle put + dup (C) 0 get /BoldCircle put % 67 + dup (u) 0 get /SolidTriangle put + dup (t) 0 get /Triangle put + dup (T) 0 get /BoldTriangle put + dup (r) 0 get /SolidSquare put + dup (s) 0 get /Square put + dup (S) 0 get /BoldSquare put + dup (q) 0 get /SolidPentagon put + dup (p) 0 get /Pentagon put + dup (P) 0 get 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index 0000000..c3bce27 --- /dev/null +++ b/tau23mu_lhcb/APROVAL/mchrzasz.synctex.gz Binary files differ diff --git a/tau23mu_lhcb/APROVAL/mchrzasz.tex b/tau23mu_lhcb/APROVAL/mchrzasz.tex new file mode 100644 index 0000000..5d815d6 --- /dev/null +++ b/tau23mu_lhcb/APROVAL/mchrzasz.tex @@ -0,0 +1,745 @@ +\documentclass[xcolor=svgnames]{beamer} +\usepackage[utf8]{inputenc} +\usepackage[english]{babel} +\usepackage{polski} +%\usepackage{amssymb,amsmath} +%\usepackage[latin1]{inputenc} +%\usepackage{amsmath} +%\newcommand\abs[1]{\left|#1\right|} +\usepackage{amsmath} +\newcommand\abs[1]{\left|#1\right|} +\usepackage{hepnicenames} +\usepackage{hepunits} +\usepackage{color} +\usepackage{feynmp} +\usepackage{pst-pdf} +\usepackage{hyperref} + + + +\setbeamertemplate{footline}{\insertframenumber/\inserttotalframenumber} +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%5 +\definecolor{mygreen}{cmyk}{0.82,0.11,1,0.25} + + +\usetheme{Sybila} +\title[$\Ptau \to \Pmu \Pmu \Pmu$ approval presentation ]{$\Ptau \to \Pmu \Pmu \Pmu$ approval presentation} + + \author[Paul Seyfert]{ + Johannes Albrecht\inst{1}, Marta Calvi\inst{2}, \underline{Marcin Chrzaszcz\inst{3,4}}, \\Laura Gavardi\inst{1}, Jon Harrison\inst{5}, Basem Khanji\inst{2}, George Lafferty\inst{5}, Tatiana Likhomanenko\inst{6}, Eduardo Rodrigues\inst{5}, \\Nicola Serra\inst{3}, Paul Seyfert\inst{7}\\{~}\\ +\textbf{Referees}:\\ Benoit Viaud (Chair) , Matteo Rama, Frederic Machefert (EB) } + \institute[Uni Heidelberg]{ + \inst{1}Dortmund, + \inst{2}Milano Bicocca, + \inst{3}Zurich, \inst{4}IFJ Cracow, \inst{5}Manchester, \inst{6}Yandex, \inst{7}Uni. Heidelberg + } +\date{\today} +\begin{document} +% --------------------------- SLIDE -------------------------------------------- +\frame[plain]{\titlepage} +\author{Marcin Chrz\k{a}szcz} +% ------------------------------------------------------------------------------ +% --------------------------- SLIDE -------------------------------------------- + +\institute{~(UZH, IFJ)} + + + % \begin{frame}\frametitle{Outline} + % \begin{enumerate} + % \item introduction\vspace{.5em} + % \item multivariate technique\vspace{.5em} + % \item normalisation\vspace{.5em} + % % \item backgrounds\vspace{.5em} + % \item expected sensitivity\vspace{.5em} + % \item model dependence\vspace{.5em} data from Reco14Stripping20(r1) + % \end{enumerate} + % Major news wrt.\ the $1~fb^{-1}$ analysis are highlighted in \textcolor{mygreen}{green} + % \end{frame} + + \begin{frame}\frametitle{Outline} + \tableofcontents + \end{frame} + + + + + \begin{frame} + \frametitle{Yellow pages} + \begin{itemize} + \item TWiki: \href{https://twiki.cern.ch/twiki/bin/viewauth/LHCbPhysics/Tau_LFV_3fb}{\url{https://twiki.cern.ch/twiki/bin/viewauth/LHCbPhysics/Tau_LFV_3fb}} + \item ANA note: \href{https://twiki.cern.ch/twiki/pub/LHCbPhysics/Tau_LFV_3fb/v8.pdf}{LHCb-ANA-2014-005} + \item Paper draft: \href{https://twiki.cern.ch/twiki/pub/LHCbPhysics/Tau_LFV_3fb/paper_v1.pdf}{LHCb-PAPER-2014-X} + \item Target journal: JHEP + \item Conference: Tau 2014 + \end{itemize} + + \end{frame} + + + + +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% + \section{Introduction} + + \begin{frame} + \frametitle{Status of $\Ptau\to\Pmu\Pmu\Pmu$} + \begin{columns} + \begin{column}{.62\textwidth} + + \includegraphics[width=.95\textwidth]{feymn.png} + + {{ + \begin{itemize} + \item Charged Lepton Flavour Violation process + \item Possible as penguin with neutrino oscillation + \item SM prediction is beyond experimental reach~$O(10^{-40})$ + + \end{itemize} + }} + \end{column} + \begin{column}{.45\textwidth} + \begin{alertblock}{current limits ($ 90\,\%$ CL)} + + \begin{description} + \item[BaBar] $3.3\times 10^{-8}$ + \item[Belle] $2.1\times 10^{-8}$ + \item[LHCb] $8.0\times 10^{-8}$ + \end{description} + \end{alertblock} + \begin{alertblock}{BSM predictions} + \begin{description} + \item[var.\ SUSY] $10^{-10}$ + \item[non universal $\PZprime$] $10^{-8}$ + \item[mSUGRA+seesaw] $10^{-9}$ + \item[and many more...] + \end{description} + \end{alertblock} + \end{column} + \end{columns} + \end{frame} +%%%%%%%%%%%%%%%%% + \begin{frame} + \frametitle{Strategy} + \begin{itemize} + \item Following same approach as other RD searches. + \item Loose stripping selection + \item Multivariate classification in: mass, PID, ``geometry/topology'' + \item Binning optimisation. + \item Relative normalisation ($\PDs\to\Pphi(\Pmu\Pmu)\Ppi$) + \item Invariant mass fit for expected background in each likelihood bin: fit in $\left| m-m_{\Ptau} \right| >\unit{30}{\MeV}$ + \item ``middle sidebands'' for classifier evaluation and tests.($\unit{20}{\MeV}<\left| m-m_{\Ptau}\right| <\unit{30}{\MeV}$). + \item CLs for limit calculation + \end{itemize} + + \end{frame} + +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% + \begin{frame} + \frametitle{$\Ptau$ production} + \begin{itemize} + \item Consider five production channels (fractions at $\unit{8}{\TeV}$):\begin{itemize} + \item Prompt $\PDs\to\Ptau$ ($72.4\pm2.7\,\%$) + \item Prompt $\PDplus\to\Ptau$ ($4.2\pm0.7\,\%$) + \item Non-prompt $\PDs\to\Ptau$ ($8.5\pm1.7\,\%$) + \item Non-prompt $\PDplus\to\Ptau$ ($0.17\pm0.04\,\%$) + \item $X_{\Pbottom}\to\Ptau$ (meson or baryon) ($14.7\pm2.3\,\%$) + \end{itemize} + \item Use $\sigma(\Pbottom\APbottom)$ at $\unit{8}{\TeV}$ from LHCb + \item Use Pythia scaling for $\sigma(\Pcharm\APcharm)$ at $\unit{8}{\TeV}$ + \end{itemize} + + \begin{columns} + \column{0.8\textwidth} + \begin{exampleblock}{$\mathcal{B}(\PDplus\to\Ptau)$} + \begin{itemize} + \item There is no measurement of $\mathcal{B}(\PDplus\to\Ptau)$ + \item One can calculate it form: $\mathcal{B}(\PDplus\to\Pmu\Pnum)$ + helicity suppression + phase space + \item \texttt{hep-ex:0604043} + \item $\mathcal{B}(\PDplus\to\Ptau\Pnut)=1.0\times10^{-3}$ + \end{itemize} + \end{exampleblock} + \column{0.2\textwidth} + {~} + \end{columns} + + \end{frame} + \begin{frame} + \frametitle{Datasets} + \begin{itemize} + \item Data from Reco14Stripping20(r1) + \item Much MC\begin{itemize} + \item 24M Inclusive background events ($\Pbottom\APbottom$ and $\Pcharm\APcharm$) + \item 10M Exclusive background events ($\PDs\to\Peta(\Pmu\Pmu\Pphoton)\Pmu\Pnum$) + \item 2M Signal events (split over 5 production channels) + \item 12M $\PD \to \PK \Ppi \Ppi$ (missID studies) + \item 10M $\PDstar \to \PD(\PK \Pmu \Pnum) \Ppi$ (missID studies) + + \end{itemize} + \item[$\Rightarrow$] Generator level cuts for improved use of computing resources + \begin{itemize} + \item $\sim 14$ times more signal statistics after stripping + \item $\sim 2$ times more background statistics + \end{itemize} + \item Mix $\Ptau$ production on ntuple level instead of reweighting. + \newline$\Rightarrow$ Ease up ntuple usage (no forgotten weighting, no double weighting, \dots) + \end{itemize} + \end{frame} + \section{Selection} + \begin{frame} + \frametitle{Stripping and selection} +{\footnotesize{ +\begin{tabular}{|c|cc|} +\hline + &$\Ptau\to\Pmu\Pmu\Pmu$&$\PDs\to\Pphi\Ppi$\\ +\hline +$\mu^\pm$ , $ \pi^\pm$ &\multicolumn{2}{c|}{} \\ +$p_T$ &\multicolumn{2}{c|}{$>300\MeV$} \\ +Track $\chi^2$/ndf &\multicolumn{2}{c|}{$<3 $} \\ +IP $\chi^2$/ndf &\multicolumn{2}{c|}{$>9 $} \\ +track ghost probability &\multicolumn{2}{c|}{$<0.3 $} \\ +\hline +$\mu$ pairs &\multicolumn{2}{c|}{} \\ +$m_{\mu^+\mu^-} - m_{\phi}$ & $>20\MeV$ & $<20\MeV$\\ +$m_{\mu^+\mu^-}$ & $> 450\MeV$ & - \\ +$m_{\mu^+\mu^+}$ & $> 250\MeV$ & - \\ +\hline +$\tau^\pm$ and \PDs &\multicolumn{2}{c|}{} \\ +$\Delta m$ & $<400\MeV$ & $<50\MeV$\\ +Vertex $\chi^2$ &\multicolumn{2}{c|}{$<15$} \\ +IP $\chi^2$ &\multicolumn{2}{c|}{$<225 $} \\ +$\cos\alpha$ &\multicolumn{2}{c|}{$>0.99$} \\ +$c\tau$ (stripping) &\multicolumn{2}{c|}{$>\unit{100}{\mu m}$} \\ + &\multicolumn{2}{c|}{no PV refitting}\\ +decay time (offline) &\multicolumn{2}{c|}{$> -0.01$ ns \& $< 0.025$ ns}\\ + &\multicolumn{2}{c|}{PV refitting}\\ +\hline +\end{tabular} +}} + + \end{frame} + + %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% + + + \begin{frame} + \frametitle{Triggers} + {\footnotesize{ + \begin{tabular}{l|c|c} + & signal & normalisation \\\hline\hline + L0$^1$ & \multicolumn{2}{c}{L0Muon TOS}\\\hline + Hlt1$^1$ & \multicolumn{2}{c}{Hlt1TrackMuon TOS}\\\hline + Hlt2 2011 & Hlt2CharmSemilepD2HMuMu TOS & Hlt2DiMuonDetached$^2$ TOS \\ + & $||$ Hlt2TriMuonTau TOS & \\\hline + Hlt2 2012 & Hlt2TriMuonTau$^1$ TOS & Hlt2DiMuonDetached$^2$ TOS\\\hline + \end{tabular} + } + } + \only<1>{ + \begin{block}{$^1$ triggers in 2012} + \begin{itemize} + \item Cuts changed through 2012 + \item[$\rightarrow$]emulated two different TCKs for 2012 + \item[$\rightarrow$] Found negligible differences + \item Choice of triggers were optimised based on $\dfrac{s}{\sqrt{b}}$ FOM. + \end{itemize} + \end{block}} + % \only<2>{ + % \begin{block}{$^2$ word on Hlt2DiMuonDetached} + % \begin{itemize} + % \item keep it simple here + % \item line unchanged in 2012 + % \item[$\rightarrow$] choice keeps Hlt2 trigger efficiency stable + % \item $\PDs\to\Pphi\Ppi$ anyhow doesn't behave like $\Ptau\to\Pmu\Pmu\Pmu$ in the TriMuon trigger (requires misidentification) + % \end{itemize} + % \end{block}} + + \end{frame} + +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% + \section{Multivariate technique} + + \begin{frame} + \frametitle{Geometric likelihood} +Much work has been put in improving our geometric and kinematic classifier: + \begin{itemize} + \item Classify the displaced 3-body decay properties of a signal candidate + \item Revisit variable choice + \item Revisit classification technique + \item More toolkits tried: MatrixNet, NeuroBayes, TMVA + \item Retune input variables\newline($\PBs\to\Pmu\Pmu$ isolation $\rightarrow$ BDT isolation: CERN-THESIS-2013-259) + \item Blending technique. + \end{itemize} + + \end{frame} + + \begin{frame} + \frametitle{Basic Setup - Step I} + \begin{itemize} + \item Train $1/3$ signal MC against $1/2$ background MC + \item variables \begin{itemize} + \item DOCA + \item Vertex $\chi^2$ + \item $\tau$ decay time + \item $\tau$ IP$\chi^2$ + \item min.\ $\mu$ IP$\chi^2$ + \item $\Ptau$ pointing angle + \item $\tau$ $p_T$ + \item max.\ track $\chi^2$ + \item $\PBs\to\Pmu\Pmu$ track isolation + \item Cone isolation + \item BDT isolation + \end{itemize} + \item Using these variables, train several classifiers (''Base'') \\for each of the $\Ptau$ source + \end{itemize} + \end{frame} + + + \begin{frame} + \frametitle{Step II} +\begin{itemize} +\item Train using second $1/3$ signal MC against second $1/2$ background MC. +\item Introduce Blending technique +\end{itemize} + \begin{exampleblock}{Blending technique} + \begin{itemize} + \item For each signal channel we train: one BDT, three Fisher classifier, four MLPs, one FDA, one LD classifier and MatrixNet classifier. + \item One final MatrixNet classifier using the 13 base variables and the base classifiers as input + + \end{itemize} + \end{exampleblock} + \begin{itemize} +\item All evaluation is done on $3rd$ $1/3$ signal sample and middle side-bands. +\item Splitting into independent samples makes the procedure insensitive to +overtraining. +\end{itemize} + + + \end{frame} + + + + \begin{frame} + \frametitle{Performance of Blend classifier} + \begin{itemize} + \item Classifier prefers $\Ptau$ from prompt $\PDs$ + \end{itemize} + \begin{columns} + \begin{column}{.48\textwidth} + \begin{exampleblock}{MC response for different\newline $\Ptau$ production channels} + \includegraphics[width=.95\textwidth]{./mn_sig.png} + \end{exampleblock} + \end{column} + \begin{column}{.48\textwidth} + \begin{exampleblock}{response for $\PDs\to\Pphi\Ppi$\newline data and MC} + \includegraphics[width=.95\textwidth]{./MN_BLEND_FLAT.png} + \end{exampleblock} + \end{column} + \end{columns} + \end{frame} + + \begin{frame} + \frametitle{Calibration} + \begin{itemize} + \item Assume all differences between $\Ptau\to\Pmu\Pmu\Pmu$ and $\PDs\to\Pphi\Ppi$ come from kinematics (mass, resonance, decay time) + \item Get correction $\PDs\leadsto\Ptau$ from MC + \item Apply corrections to $\PDs\to\Pphi\Ppi$ on data + \end{itemize} + \begin{block}{validation} + \begin{itemize} + \item done for 2011 analysis, treating smeared MC as data + \end{itemize} + \end{block} + \begin{columns} + \begin{column}{.45\textwidth} + \begin{itemize} + \item $\PDs\to\Pphi\Ppi$ well modelled in MC + % \item[$\rightarrow$] i.e.\ also badly pointing non-prompt $\PDs$ + \end{itemize} + \end{column} + \begin{column}{.45\textwidth} + \includegraphics[width=.95\textwidth]{MN_BLEND_FLAT.png} + \end{column} + \end{columns} + \end{frame} + + \begin{frame} + \frametitle{PID} + \begin{itemize} + \item We used ProbNNmu already in the previous round of the analysis + \item Now use MC12TuneV2 (latest) + \item Two-fold reason:\begin{itemize} + \item Expect better performance than CombDLL variables + \item ``one variable for everything'':\newline with CombDLL we needed both CombDLL($\mu-\pi$) and CombDLL($\mu-K$) + \end{itemize} + \end{itemize} + \end{frame} + + \begin{frame} + \frametitle{PID calibration } + \begin{itemize} + \item Since PIDCalib tool didn't work for us, we choose a phenomenological approach. + \item Many thanks to Barbara Sciascia for help understanding this problem. + \end{itemize} + \begin{exampleblock}{phenomenologic treatment} + \begin{itemize} + \item correlations are small in $\PDs\to\Pphi\Ppi$ data and MC + \newline $\varepsilon(\text{cut on one muon})^2 = \varepsilon(\text{cut on two muons})$ + \item[$\Rightarrow$] use $c^3=(\varepsilon(\text{cut and fit})/\varepsilon(\text{PIDCalib}))^3$ as correction to PIDCalib for $\Ptau\to\Pmu\Pmu\Pmu$ + \item assign error of $0.02$ for $c$ + \end{itemize} + \end{exampleblock} +\begin{itemize} +\item Many x-checks done. +\item Everything works fine. +\end{itemize} + + \end{frame} + + + + \begin{frame} + \frametitle{Binning optimisation} + \begin{itemize} + \item How to optimise the binning in two classifiers? + \item $\unit{1}{\reciprocal\femtobarn}$ CONF note: two one-dimensional optimisations as in $\PBs\to\Pmu\Pmu$ + \item $\unit{1}{\reciprocal\femtobarn}$ PAPER: iterative loop of one-dimensional optimisations\newline optimising one classifier on the sensitive range of the other classifier + \item Now: optimise two-dimensions (optimise bin boundaries in both dimensions at the same time) + \item Unchanged: don't use lowest likelihood bins\newline(reflection backgrounds, no sensitivity gain) + \end{itemize} + \end{frame} + \begin{frame} + \frametitle{Impact of new binning optimisation} + \begin{itemize} + \item Removal of tiny bins which contribute negligible sensitivity + \item Colour: limit obtained, using only this particular bin + \item Number: rank of that bin (1=best sensitivity bin) + \end{itemize} + + ~ + + \begin{columns} + \begin{column}{.5\textwidth} + old analysis + + ~ + + \includegraphics[width=.95\textwidth]{./90CLonebinlimit.pdf} + \end{column} + \begin{column}{.5\textwidth} + new analysis + + (2011 data) + \includegraphics[width=.95\textwidth]{./rank.pdf} + \end{column} + \end{columns} + \end{frame} + + \begin{frame} + \frametitle{Mass shape} + \begin{itemize} + \item Double-Gaussian with fixed fraction ($70\,\%$ inner Gaussian) + \item Fix fraction to ease calibration:\newline + $\sigma_{data}^{\Ptau} = \frac{\sigma_{MC}^{\Ptau}}{\sigma_{MC}^{\PDs}}\times\sigma_{data}^{\PDs}$ + \end{itemize} + \includegraphics[width=.44\textwidth]{./Ds_data_2011.pdf} + \includegraphics[width=.44\textwidth]{./Ds_data_2012.pdf} + + {\footnotesize{ + \begin{tabular}{|c|c|c|} + \hline + Calibrated $\Ptau$ Mass shape & 7~TeV & 8~TeV\\ + \hline + Mean ($\MeV$) & $1779.1 \pm 0.1$ & $1779.0 \pm 0.1$\\ + \hline + $\sigma_1$ ($\MeV$) & $7.7 \pm 0.1$ & $7.6 \pm 0.1$\\ + \hline + $\sigma_2$ ($\MeV$) & $12.0 \pm 0.8$ & $11.5 \pm 0.5$\\ + \hline + \end{tabular} + } + } + \end{frame} + + + + \section{Normalisation} + + \begin{frame} + \frametitle{Relative normalisation} + $\mathcal{B}(\Ptau\to\Pmu\Pmu\Pmu) = \frac{\mathcal{B}(\PDs\to\Pphi\Ppi)}{\mathcal{B}(\PDs\to\Ptau\Pnut)} \times f_{\PDs}^{\Ptau} \times \frac{\varepsilon_\text{norm} }{\varepsilon_\text{sig} } \times \frac{N_\text{sig}}{N_\text{norm}} = \alpha\times N_\text{sig}$ + \begin{itemize} + \item where $\varepsilon$ stands for trigger, reconstruction, selection + \item $\text{norm}$ = normalisation channel $\PDs\to\Pphi\Ppi$ + \item $f_{\PDs}^{\Ptau}$ is the fraction of $\Ptau$ coming from $\PDs$ + \newline i.e.\ $(83\pm3)\,\%$ for 2012 + \end{itemize} + \includegraphics[width=.47\textwidth]{./Ds_data_2011.pdf} + \includegraphics[width=.47\textwidth]{./Ds_data_2012.pdf} + \end{frame} + + \begin{frame}[allowframebreaks] + \frametitle{Normalisation in numbers} + {\footnotesize{ +$\begin{array}{c|c|c} +& \rm{7~TeV} & \rm{8~TeV}\\ +\hline +\rm{\epsilon\mathstrut_{sig}}^{GEN} (\%) & 8.989 \pm 0.40 & 9.21 \pm 0.35\\ +\hline +\rm{\epsilon_{cal}}^{GEN} (\%) & 11.19 \pm 0.34 & 11.53 \pm 0.32\\ +\hline +\rm{\epsilon_{sig}}^{REC,isMuon,SEL} (\%) & 9.927 \pm 0.028 & 9.261 \pm 0.023 \\ +\hline +\rm{\epsilon_{cal}}^{REC,isMuon,SEL} (\%) & 7.187 \pm 0.022 & 6.690 \pm 0.022 \\ +\hline +\frac{\rm{c_{cal}}^{track}}{\rm{c_{sig}}^{track}} & 0.997 \pm 0.009 \pm 0.026 & 0.996 \pm 0.009 \pm 0.026 \\ +\hline +\frac{\rm{c_{cal}}^{\mu ID}}{\rm{c_{sig}}^{\mu ID}} & 0.9731 \pm 0.0031 \pm 0.0264 & 1.0071 \pm 0.0022 \pm 0.0204 \\ +\hline +\rm{c}^{\phi} & \multicolumn{2}{c}{0.98 \pm 0.01} \\ +\hline +\rm{c}^{\tau} & 1.032 \pm 0.006 & 1.026 \pm 0.006\\ +\hline +\rm{c}^{trash} & 1.89 \pm 0.12 & 1.96 \pm 0.12\\ +\hline +\rm{\epsilon\mathstrut_{sig}}^{TRIG} (\%) & 35.52 \pm 0.14 \pm 0.14 & 39.3 \pm 1.7 \pm 2.0 \\ +\hline +\rm{\epsilon\mathstrut_{cal}}^{TRIG} (\%) & 23.42 \pm 0.14 \pm 0.09 & 20.62 \pm 0.76 \pm 1.07 \\ +\end{array}$ + }} + +\framebreak + + {\footnotesize{ +$\begin{array}{c|c|c} +& \rm{7~TeV} & \rm{8~TeV}\\ +\hline +\mathcal{B}(PDs \to \Pphi \Ppi) & \multicolumn{2}{c}{(1.317 \pm 0.099) \times 10^{-5}}\\ +\hline +f^{\tau}_{D_{s}} & 0.78 \pm 0.04 & 0.80 \pm 0.03 \\ +\hline +\mathcal{B} (\PDs \to \Ptau \Pnut) & \multicolumn{2}{c}{0.0561 \pm 0.0024}\\ +\hline +\rm{\epsilon\mathstrut_{cal}}^{REC\&SEL}/ +\rm{\epsilon\mathstrut_{sig}}^{REC\&SEL} +& 0.898 \pm 0.060 & 0.912 \pm 0.054 \\ +\hline +\rm{\epsilon\mathstrut_{cal}}^{TRIG}/ +\rm{\epsilon\mathstrut_{sig}}^{TRIG} +& 0.6593 \pm 0.0058 & 0.525 \pm 0.040\\ +\hline +N_{cal} & 28,207 \pm 440 & 52,131 \pm 695\\ +\hline & \\[-0.8em]\hline +\alpha & (3.81 \pm 0.46) \times 10^{-9} & (1.72 \pm 0.23) \times 10^{-9}\\ +\alpha^{trash} & (7.20 \pm 0.98) \times 10^{-9} & (3.37 \pm 0.50) \times 10^{-9}\\ +\end{array}$ +}} + \end{frame} + + + \section{Backgrounds} + + \begin{frame} + \frametitle{Misidentification} + \begin{itemize} + \item Most dominant: $\PDplus\to\PK\Ppi\Ppi$ + \item Experience from last round: cut away low ProbNNmu range + \item Check remaining data under $\PK\Ppi\Ppi$ hypothesis for $\PDplus$ peak + \item[$\Rightarrow$] misid safely contained in ``trash'' bin + \item $\PDplus\to\Ppi\Ppi\Ppi$ and $\PDs\to\Ppi\Ppi\Ppi$ start to become visible in 2012 + \end{itemize} + \includegraphics[width=.45\textwidth]{./Dp2Kpipi_all_2012_senseBins.pdf} + \includegraphics[width=.45\textwidth]{./FittoD23pi_2012.pdf} + \end{frame} + + \begin{frame} + \frametitle{Evil backgrounds} + \begin{itemize} + \item $\Pphi\to\Pmu\Pmu + X$: narrow veto on dimuon mass + \item $\PDs\to\Peta(\Pmu\Pmu\Pphoton)\Pmu\Pnum$: not so easy + \begin{itemize} + \item Modelled in CONF note + \item Optimised veto in PAPER + \item Right now: both versions in the ANA note + \end{itemize} + \item Baseline: veto $m_{\APmuon\Pmuon} < \unit{450}{\MeV}$ + \begin{itemize} + \item Fits better understood + \item Sensitivity unchanged when removing veto + \item Smaller uncertainty on expected background + \end{itemize} + \end{itemize} + \end{frame} + + \begin{frame} + \frametitle{Remaining backgrounds} + \begin{itemize} + \item Fit exponential to invariant mass spectrum in each likelihood bin + \item Don't use $\pm \unit{30}{\MeV}$ in the fit + \item[$\rightarrow$] Compatible results blinding only $\pm \unit{20}{\MeV}$\footnote{partially used in classifier developement} + \end{itemize} + {\begin{center} + Example of most sensitive regions in 2011 and 2012 + \includegraphics[width=0.9\textwidth]{./fits.png} + + \end{center}} + \end{frame} + + \section{Expected limit} + + \begin{frame} + \frametitle{expected limit} + \begin{itemize} + \item Consider nuisance parameters from background fit, signal pdf calibration, normalisation + \item Nuisance parameters due to $\Ptau$ production, normalization. + \item Limit for combined 2011+2012 analysis + \end{itemize} + \end{frame} + + \begin{frame} + \frametitle{Sensitivity} + $\mathcal{B}(\Ptau\to\Pmu\Pmu\Pmu)<5.0 \times 10^{-8}$ at 90\% CL + + \includegraphics[width=.8\textwidth]{./banana.png} + \end{frame} + + + + \section{Model dependence} + + \begin{frame} + \frametitle{Model dependence} + \begin{itemize} + \item $\Peta$ veto $\Rightarrow$ our limit not applicable to New Physics with small $m_{\APmuon\Pmuon}$ + \item Model description in \texttt{arXiv:0707.0988} + \item 5 relevant Dalitz distributions: 2 four-point operators, 1 radiative operator, 2 interference terms + \end{itemize} + \only<2->{ + \begin{itemize} + \item With radiative distribution limit gets worse by $51\,\%$ (dominantly from the $\Peta$ veto) + \item The other four Dalitz distributions behave nicely (within $7\,\%$) + \end{itemize} + } + \only<1>{ + \includegraphics[width=.331\textwidth]{./gammallll.pdf} + \includegraphics[width=.331\textwidth]{./gammallrr.pdf} + \includegraphics[width=.331\textwidth]{./gammarad.pdf} + + \includegraphics[width=.331\textwidth]{./gammarad-llll.pdf} + \includegraphics[width=.331\textwidth]{./gammarad-llrr.pdf} +} + + \end{frame} + + + % \begin{frame} + % \frametitle{Conclusion} + % \begin{columns} + % \begin{column}{.55\textwidth} + % \begin{itemize} + % \item finally all pieces put together + % \item model (in)dependence of $\Peta$ veto investigated + % \item expected sensitivity computed\newline $5.6\times 10^{-8}$ + % \end{itemize} + % \end{column} + % \begin{column}{.45\textwidth} + % \includegraphics[width=\textwidth]{party-music-hd-wallpaper-1920x1200-3850.jpg} + % \end{column} + % \end{columns} + + % \end{frame} + + + \section{Unblinded results} + + \begin{frame} + \frametitle{Unblinding 1} +\begin{columns} +\column{1in}{~} +\column{3in} +'' +THERE came a day at summer’s full \\ +Entirely for us \\ +I thought that such were for the saints, \\ +Where revelations be. ''\footnote{E.Dickinson} \\ + \column{1in}{~} +\end{columns} +{~}\\ +{~}\\ +\begin{Large} +On Monday $4^{th}$ of August we were given the permission to unblind. +\end{Large} + + + \end{frame} + + + + \begin{frame} + \frametitle{Unblinding 2} +\begin{itemize} +\item Unfortunately no big ''revelations'' were there: +\item 2011 numbers: +\end{itemize} + \includegraphics[width=1.\textwidth]{2011.png} + + \end{frame} + + \begin{frame} + \frametitle{Unblinding 3} +\begin{itemize} +\item Unfortunately no big ''revelations'' were also in 2012 data: + +\end{itemize} + \includegraphics[width=1.1\textwidth]{2012.png} + + \end{frame} + + + + \begin{frame} + \frametitle{Unblinding 4} + + \begin{center} + \includegraphics[width=0.7\textwidth]{banana_line.pdf} + \end{center} +\begin{columns} + +\column{0.2in}{~} +\column{2in} +Limits(PHSP):\\ +Observed(Expected)\\ +$4.6~(5.0)\times 10^{-8}$ at $90\%$ CL\\ +$5.6~(6.1)\times 10^{-8}$ at $95\%$ CL\\ + + \column{3in} + \includegraphics[width=0.5\textwidth]{model.png} +\end{columns} + \end{frame} + + \begin{frame} + \frametitle{Conclusions} + \begin{columns} + \column{2.5in} + \begin{itemize} + \item We didn't find NP (yet). + \item Limits set with full LHCb dataset. + \item Awaiting for the future data! + \end{itemize} +\column{2.5in} + + \includegraphics[width=1\textwidth]{TauLFV_UL_2013001.pdf} + + + + \end{columns} + \begin{itemize} + \item We would like to thank our referees for very friendly,thorough and fruitful review. + \item With this presentation we ask collaboration for approval. + \end{itemize} + + + \end{frame} + + + +\end{document} diff --git a/tau23mu_lhcb/APROVAL/mchrzasz.toc b/tau23mu_lhcb/APROVAL/mchrzasz.toc new file mode 100644 index 0000000..b1816fc --- /dev/null +++ b/tau23mu_lhcb/APROVAL/mchrzasz.toc @@ -0,0 +1,10 @@ +\beamer@endinputifotherversion {3.10pt} +\select@language {english} +\beamer@sectionintoc {1}{Introduction}{4}{0}{1} +\beamer@sectionintoc {2}{Selection}{8}{0}{2} 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{35}{35}} +\headcommand {\beamer@partpages {1}{35}} +\headcommand {\beamer@subsectionpages {31}{35}} +\headcommand {\beamer@sectionpages {31}{35}} +\headcommand {\beamer@documentpages {35}} +\headcommand {\def \inserttotalframenumber {34}} diff --git a/tau23mu_lhcb/APROVAL/mchrzasz2.out b/tau23mu_lhcb/APROVAL/mchrzasz2.out new file mode 100644 index 0000000..800a6dd --- /dev/null +++ b/tau23mu_lhcb/APROVAL/mchrzasz2.out @@ -0,0 +1,8 @@ +\BOOKMARK [2][]{Outline0.1}{Introduction}{} +\BOOKMARK [2][]{Outline0.2}{Selection}{} +\BOOKMARK [2][]{Outline0.3}{Multivariate technique}{} +\BOOKMARK [2][]{Outline0.4}{Normalisation}{} +\BOOKMARK [2][]{Outline0.5}{Backgrounds}{} +\BOOKMARK [2][]{Outline0.6}{Expected limit}{} +\BOOKMARK [2][]{Outline0.7}{Model dependence}{} +\BOOKMARK [2][]{Outline0.8}{Unblinded results}{} diff --git a/tau23mu_lhcb/APROVAL/mchrzasz2.pdf b/tau23mu_lhcb/APROVAL/mchrzasz2.pdf new file mode 100644 index 0000000..3ec2afe --- /dev/null +++ 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+\usepackage{hepunits} +\usepackage{color} +\usepackage{feynmp} +\usepackage{pst-pdf} +\usepackage{hyperref} +\usepackage{xcolor} + +\setbeamertemplate{footline}{\insertframenumber/\inserttotalframenumber} +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%5 +\definecolor{mygreen}{cmyk}{0.82,0.11,1,0.25} + + +\usetheme{Sybila} +\title[ $\color{white} \tau \to \mu \mu \mu$ approval presentation ]{$\color{white} \tau \to \mu \mu \mu$ approval presentation} + + \author[Marcin Chrzaszcz]{ + Johannes Albrecht\inst{1}, Marta Calvi\inst{2,3}, \underline{Marcin Chrzaszcz}\inst{4,5}, \\Laura Gavardi\inst{1}, Jon Harrison\inst{6}, Basem Khanji\inst{3},\\ George Lafferty\inst{6}, Tatiana Likhomanenko\inst{7}, Eduardo Rodrigues\inst{6}, \\Nicola Serra\inst{4}, Paul Seyfert\inst{7}\\ + \textbf{Referees}:\\ Benoit Viaud (Chair) , Matteo Rama, Frederic Machefert (EB) } + \institute[UZH, IFJ]{\begin{tiny} + +$ ^1$ Fakult\"at Physik, Technische Universit\"at Dortmund, Germany\\ +$ ^2$ The University of Milano Bicocca, Milano, Italy\\ +$ ^3$ INFN Milano Bicocca, Milano, Italy\\ +$ ^4$ Physik-Institut der Universit\"{a}t Z\"{u}rich, Switzerland\\ +$ ^5$ Henryk Niewodniczanski Institute of Nuclear Physics Polish Academy of Sciences, Cracow, Poland\\ +$ ^6$ The University of Manchester, UK\\ +$ ^7$ Yandex, Moscow, Russia \\ +$ ^8$ Physikalisches Institut Heidelberg, Germany\\ + \end{tiny} + } +\date{\today} +\begin{document} +% --------------------------- SLIDE -------------------------------------------- +\frame[plain]{\titlepage} +\author{Marcin Chrz\k{a}szcz} +% ------------------------------------------------------------------------------ +% --------------------------- SLIDE -------------------------------------------- + +\institute{~(UZH, IFJ)} + + + % \begin{frame}\frametitle{Outline} + % \begin{enumerate} + % \item introduction\vspace{.5em} + % \item multivariate technique\vspace{.5em} + % \item normalisation\vspace{.5em} + % % \item backgrounds\vspace{.5em} + % \item expected sensitivity\vspace{.5em} + % \item model dependence\vspace{.5em} data from Reco14Stripping20(r1) + % \end{enumerate} + % Major news wrt.\ the $1~fb^{-1}$ analysis are highlighted in \textcolor{mygreen}{green} + % \end{frame} + + \begin{frame}\frametitle{Outline} + \tableofcontents + \end{frame} + + + + + \begin{frame} + \frametitle{Yellow pages} + \begin{itemize} + \item TWiki: \href{https://twiki.cern.ch/twiki/bin/viewauth/LHCbPhysics/Tau_LFV_3fb}{\url{https://twiki.cern.ch/twiki/bin/viewauth/LHCbPhysics/Tau_LFV_3fb}}. + \item ANA note: \href{https://twiki.cern.ch/twiki/pub/LHCbPhysics/Tau_LFV_3fb/v8.pdf}{LHCb-ANA-2014-005}. + \item Paper draft: \href{https://twiki.cern.ch/twiki/pub/LHCbPhysics/Tau_LFV_3fb/paper_v1.pdf}{LHCb-PAPER-2014-X}. + \item Target journal: JHEP. + \item Conference: Tau 2014. + \end{itemize} + + \end{frame} + + + + +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% + \section{Introduction} + + \begin{frame} + \frametitle{Status of $\color{white} \tau \to \mu \mu \mu$} + \begin{columns} + \begin{column}{.62\textwidth} + + \includegraphics[width=.95\textwidth]{feymn.png} + + {{ + \begin{itemize} + \item Charged Lepton Flavour Violation process. + \item Possible as penguin with neutrino oscillation. + \item SM prediction is beyond experimental reach~$O(10^{-40})$. + + \end{itemize} + }} + \end{column} + \begin{column}{.45\textwidth} + \begin{alertblock}{current limits ($ \color{white} 90\,\%$ CL)} + + \begin{description} + \item[BaBar] $3.3\times 10^{-8}$ + \item[Belle] $2.1\times 10^{-8}$ + \item[LHCb] $8.0\times 10^{-8}$ + \end{description} + \end{alertblock} + \begin{alertblock}{BSM predictions} + \begin{description} + \item[var.\ SUSY] $10^{-10}$ + \item[non universal $\PZprime$] $10^{-8}$ + \item[mSUGRA+seesaw] $10^{-9}$ + \item[and many more...] + \end{description} + \end{alertblock} + \end{column} + \end{columns} + \end{frame} +%%%%%%%%%%%%%%%%% + \begin{frame} + \frametitle{Strategy} + \begin{itemize} + \item Following same approach as other RD searches. + \item Loose stripping selection. + \item Multivariate classification in: mass, PID, ``geometry/topology''. + \item Binning optimisation. + \item Relative normalisation ($\PDs\to\Pphi(\Pmu\Pmu)\Ppi$). + \item Invariant mass fit for expected background in each likelihood bin: fit in $\left| m-m_{\Ptau} \right| >\unit{30}{\MeV}$. + \item ``middle sidebands'' for classifier evaluation and tests.($\unit{20}{\MeV}<\left| m-m_{\Ptau}\right| <\unit{30}{\MeV}$). + \item CLs for limit calculation. + \end{itemize} + + \end{frame} + +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% + \begin{frame} + \frametitle{$\color{white} \tau$ production} + \begin{itemize} + \item $\Ptau$'s in LHCb come from five main sources: + \end{itemize} + \begin{center} + + +\begin{tabular}{| c | c | c | } +\hline + Mode & $7~\TeV$ & $8~\TeV$ \\ \hline + Prompt $\PDs\to\Ptau$ & $71.1\pm3.0\,\%$ & $72.4\pm2.7\,\%$ \\ + Prompt $\PDplus\to\Ptau$ & $4.1\pm0.8\,\%$ & $4.2\pm0.7\,\%$ \\ + Non-prompt $\PDs\to\Ptau$ & $9.0\pm2.0\,\%$ & $8.5\pm1.7\,\%$ \\ + Non-prompt $\PDplus\to\Ptau$ & $0.18\pm0.04\,\%$ & $0.17\pm0.04\,\%$ \\ + $X_{\Pbottom}\to\Ptau$ & $15.5\pm2.7\,\%$ & $14.7\pm2.3\,\%$ \\ \hline + +\end{tabular} + \end{center} + + + \begin{columns} + \column{0.8\textwidth} + \begin{exampleblock}{$\mathcal{B}(\PDplus\to\Ptau)$} + \begin{itemize} + \item There is no measurement of $\mathcal{B}(\PDplus\to\Ptau)$. + \item One can calculate it from: $\mathcal{B}(\PDplus\to\Pmu\Pnum)$ + helicity suppression + phase space. + \item \texttt{hep-ex:0604043}. + \item $\mathcal{B}(\PDplus\to\Ptau\Pnut)=(1.0\pm0.1) \times10^{-3}$. + \end{itemize} + \end{exampleblock} + \column{0.2\textwidth} + {~} + \end{columns} + + \end{frame} + \begin{frame} + \frametitle{Datasets} + \begin{itemize} + \item Data from Reco14Stripping20(r1). + \item Large MC samples: + \begin{itemize} + \item 24M Inclusive background events ($\Pbottom\APbottom$ and $\Pcharm\APcharm$). + \item 10M Exclusive background events ($\PDs\to\Peta(\Pmu\Pmu\Pphoton)\Pmu\Pnum$). + \item 2M Signal events (split over 5 production channels). + \item 12M $\PD \to \PK \Ppi \Ppi$ (missID studies). + \item 10M $\PDstar \to \PD(\PK \Pmu \Pnum) \Ppi$ (missID studies). + + \end{itemize} + \item[$\Rightarrow$] Generator level cuts for improved use of computing resources. + \begin{itemize} + \item $\sim 14$ times more signal statistics after stripping. + \item $\sim 2$ times more background statistics. + \end{itemize} + \item Mix $\Ptau$ production on ntuple level instead of reweighting. + \newline$\Rightarrow$ Ease up ntuple usage (no forgotten weighting, no double weighting, \dots). + \end{itemize} + \end{frame} + \section{Selection} + \begin{frame} + \frametitle{Stripping and selection} +{\footnotesize{ +\begin{tabular}{|c|cc|} +\hline + &$\Ptau\to\Pmu\Pmu\Pmu$&$\PDs\to\Pphi\Ppi$\\ +\hline +$\mu^\pm$ , $ \pi^\pm$ &\multicolumn{2}{c|}{} \\ +$p_T$ &\multicolumn{2}{c|}{$>300\MeV$} \\ +Track $\chi^2$/ndf &\multicolumn{2}{c|}{$<3 $} \\ +IP $\chi^2$/ndf &\multicolumn{2}{c|}{$>9 $} \\ +track ghost probability &\multicolumn{2}{c|}{$<0.3 $} \\ +\hline +$\mu$ pairs &\multicolumn{2}{c|}{} \\ +$m_{\mu^+\mu^-} - m_{\phi}$ & $>20\MeV$ & $<20\MeV$\\ +$m_{\mu^+\mu^-}$ & $> 450\MeV$ & - \\ +$m_{\mu^+\mu^+}$ & $> 250\MeV$ & - \\ +\hline +$\tau^\pm$ and \PDs &\multicolumn{2}{c|}{} \\ +$\Delta m$ & $<400\MeV$ & $<50\MeV$\\ +Vertex $\chi^2$ &\multicolumn{2}{c|}{$<15$} \\ +IP $\chi^2$ &\multicolumn{2}{c|}{$<225 $} \\ +$\cos\alpha$ &\multicolumn{2}{c|}{$>0.99$} \\ +$c\tau$ (stripping) &\multicolumn{2}{c|}{$>\unit{100}{\mu m}$} \\ + &\multicolumn{2}{c|}{no PV refitting}\\ +decay time (offline) &\multicolumn{2}{c|}{$> -0.01$ ns \& $< 0.025$ ns}\\ + &\multicolumn{2}{c|}{PV refitting}\\ +\hline +\end{tabular} +}} + + \end{frame} + + %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% + + + \begin{frame} + \frametitle{Triggers} + {\footnotesize{ + \begin{tabular}{l|c|c} + & signal & normalisation \\\hline\hline + L0$^1$ & \multicolumn{2}{c}{L0Muon TOS}\\\hline + Hlt1$^1$ & \multicolumn{2}{c}{Hlt1TrackMuon TOS}\\\hline + Hlt2 2011 & Hlt2CharmSemilepD2HMuMu TOS & Hlt2DiMuonDetached$^2$ TOS \\ + & $||$ Hlt2TriMuonTau TOS & \\\hline + Hlt2 2012 & Hlt2TriMuonTau$^1$ TOS & Hlt2DiMuonDetached$^2$ TOS\\\hline + \end{tabular} + } + } + \only<1>{ + \begin{block}{Triggers in 2012} + \begin{itemize} + \item Cuts changed through 2012. + \item[$\rightarrow$]emulated two different TCKs for 2012. + \item[$\rightarrow$] Found negligible differences in ratio of signal/normalisation channels. + \item Choice of triggers was optimised based on $\dfrac{s}{\sqrt{b}}$ FOM. + \end{itemize} + \end{block}} + % \only<2>{ + % \begin{block}{$^2$ word on Hlt2DiMuonDetached} + % \begin{itemize} + % \item keep it simple here + % \item line unchanged in 2012 + % \item[$\rightarrow$] choice keeps Hlt2 trigger efficiency stable + % \item $\PDs\to\Pphi\Ppi$ anyhow doesn't behave like $\Ptau\to\Pmu\Pmu\Pmu$ in the TriMuon trigger (requires misidentification) + % \end{itemize} + % \end{block}} + + \end{frame} + +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% + \section{Multivariate technique} + + \begin{frame} + \frametitle{Geometric likelihood} +Much work has been put into improving our geometric and kinematic classifier: + \begin{itemize} + \item Classify the displaced 3-body decay properties of a signal candidate. + \item Revisit variable choice. + \item Revisit classification technique. + \item More toolkits tried: MatrixNet, NeuroBayes, TMVA. + \item Retune input variables\newline($\PBs\to\Pmu\Pmu$ isolation $\rightarrow$ BDT isolation: CERN-THESIS-2013-259). + \item Apply Blending technique. + \end{itemize} + + \end{frame} + + \begin{frame} + \frametitle{Basic Setup - Step I} + \begin{itemize} + \item Train $1/3$ signal MC against $1/2$ background MC. + \item Input variables: \begin{itemize} + \item DOCA + \item Vertex $\chi^2$ + \item $\tau$ decay time + \item $\tau$ IP$\chi^2$ + \item min.\ $\mu$ IP$\chi^2$ + \item $\Ptau$ pointing angle + \item $\tau$ $p_T$ + \item max.\ track $\chi^2$ + \item $\PBs\to\Pmu\Pmu$ track isolation + \item Cone isolation + \item BDT isolation + \end{itemize} + \item Using these variables, train several classifiers (''Base'') \\for each of the $\Ptau$ source. + \end{itemize} + \end{frame} + + + \begin{frame} + \frametitle{Step II} +\begin{itemize} +\item Train using second $1/3$ signal MC against second $1/2$ background MC. +\item Introduce Blending technique. +\end{itemize} + \begin{exampleblock}{Blending technique} + \begin{itemize} + \item For each signal channel we train: one BDT, three Fisher classifier, four MLPs, one FDA, one LD classifier and MatrixNet classifier. + \item One final MatrixNet classifier using the 13 base variables and the base classifiers as input. + + \end{itemize} + \end{exampleblock} + \begin{itemize} +\item All evaluation is done on $3rd$ $1/3$ signal sample and middle side-bands. +\item Splitting into independent samples makes the procedure insensitive to +overtraining. +\end{itemize} + + + \end{frame} + + + + \begin{frame} + \frametitle{Performance of Blend classifier} + \begin{itemize} + \item Classifier prefers $\Ptau$'s from prompt $\PDs$, the dominant channel. + \end{itemize} + \begin{columns} + \begin{column}{.49\textwidth} + \begin{exampleblock}{MC response for different\newline $\color{white} \tau$ production channels} + \includegraphics[width=.98\textwidth]{./mixing.pdf} + \end{exampleblock} + \end{column} + \begin{column}{.49\textwidth} + \begin{exampleblock}{Response for $\color{white} D_s \rightarrow \phi\pi$\newline data and MC} + \includegraphics[width=.98\textwidth]{./dataMC.pdf} + \end{exampleblock} + \end{column} + \end{columns} + \end{frame} + + \begin{frame} + \frametitle{Calibration} + \begin{itemize} + \item Assume all differences between $\Ptau\to\Pmu\Pmu\Pmu$ and $\PDs\to\Pphi\Ppi$ come from kinematics (mass, resonance, decay time), which is correct in MC. + \item Get correction $\PDs\leadsto\Ptau$ from MC. + \item Apply corrections to $\PDs\to\Pphi\Ppi$ on data. + \end{itemize} + \begin{block}{validation} + \begin{itemize} + \item done for 2011 analysis, treating smeared MC as data + \end{itemize} + \end{block} + \begin{columns} + + \begin{column}{.45\textwidth} + \includegraphics[width=.95\textwidth]{m3body_2012.pdf} + \end{column} + \begin{column}{.45\textwidth} + \begin{itemize} + \item $\PDs\to\Pphi\Ppi$ well modelled in MC. + % \item[$\rightarrow$] i.e.\ also badly pointing non-prompt $\PDs$ + \end{itemize} + \end{column} + + \end{columns} + \end{frame} + + \begin{frame} + \frametitle{PID} + \begin{itemize} + \item We used ProbNNmu already in the previous round of the analysis. + \item Now use MC12TuneV2. + \item Two-fold reason:\begin{itemize} + \item Expect better performance than CombDLL variables. + \item ``one variable for everything'':\newline with CombDLL we needed both CombDLL($\mu-\pi$) and CombDLL($\mu-K$). + \end{itemize} + \end{itemize} + \begin{columns} + + \end{columns} + \begin{itemize} + \item We tested if PIDCalib samples~($\PJpsi$) are suited for us. + \item $\PDs \to \Pphi \Ppi$ better representing $\tau \to 3\mu$ than $\PJpsi \to \mu \mu$. + \item Many thanks to Barbara Sciascia for help understanding the details: \href{https://indico.cern.ch/event/250103/contribution/3/material/slides/0.pdf}{LINK} + \end{itemize} + + \end{frame} + + \begin{frame} + \frametitle{PID calibration } + + \begin{exampleblock}{Phenomenological treatment} + \begin{itemize} + \item correlations are small in $\PDs\to\Pphi\Ppi$ data and MC: + \newline $\varepsilon(\text{cut on one muon})^2 = \varepsilon(\text{cut on two muons})$ + \item[$\Rightarrow$] use $c^3=(\varepsilon(\text{cut and fit})/\varepsilon(\text{PIDCalib}))^3$ as correction to PIDCalib for $\Ptau\to\Pmu\Pmu\Pmu$ + \item assign error of $0.02$ for $c$. + \end{itemize} + \end{exampleblock} +\begin{itemize} +\item Many cross-checks done. +\item Everything works fine. +\end{itemize} + \begin{columns} + \begin{column}{.45\textwidth} + \includegraphics[width=.95\textwidth]{mPID_2012.pdf} + \end{column} + \end{columns} + \end{frame} + + + + \begin{frame} + \frametitle{Binning optimisation} + \begin{itemize} + \item How to optimise the binning in two classifiers? + \item $\unit{1}{\reciprocal\femtobarn}$ CONF note: two one-dimensional optimisations as in $\PBs\to\Pmu\Pmu$. + \item $\unit{1}{\reciprocal\femtobarn}$ PAPER: iterative loop of one-dimensional optimisations\newline optimising one classifier on the sensitive range of the other classifier. + \item Now: optimise two-dimensions (optimise bin boundaries in both dimensions simultaneously). + \item Unchanged: don't use lowest likelihood bins\newline(reflection backgrounds, no sensitivity gain). + \end{itemize} + \end{frame} + \begin{frame} + \frametitle{Impact of new binning optimisation} + \begin{itemize} + \item Removal of tiny bins which contribute negligible sensitivity. + \item Colour: limit obtained, using only this particular bin. + \item Number: rank of that bin (1=best sensitivity bin). + \end{itemize} + + + \begin{columns} + + \begin{column}{.8\textwidth} + \begin{center} + Bin sensitivity + (2011 data) +\end{center} + \includegraphics[width=.95\textwidth]{./rank.pdf} + \end{column} + \begin{column}{.2\textwidth} + {~} + \end{column} + \end{columns} + \end{frame} + + \begin{frame} + \frametitle{Mass shape} + \begin{itemize} + \item Double-Gaussian with fixed fraction ($70\,\%$ inner Gaussian). + \item Fix fraction to ease calibration. + \item Correct mass by MC:\newline + $\sigma_{data}^{\Ptau} = \frac{\sigma_{MC}^{\Ptau}}{\sigma_{MC}^{\PDs}}\times\sigma_{data}^{\PDs}$ + \end{itemize} + \includegraphics[width=.44\textwidth]{./Ds_data_2011.pdf} + \includegraphics[width=.44\textwidth]{./Ds_data_2012.pdf} + + {\footnotesize{ + \begin{tabular}{|c|c|c|} + \hline + Calibrated $\Ptau$ Mass shape & 7~TeV & 8~TeV\\ + \hline + Mean ($\MeV$) & $1779.1 \pm 0.1$ & $1779.0 \pm 0.1$\\ + \hline + $\sigma_1$ ($\MeV$) & $7.7 \pm 0.1$ & $7.6 \pm 0.1$\\ + \hline + $\sigma_2$ ($\MeV$) & $12.0 \pm 0.8$ & $11.5 \pm 0.5$\\ + \hline + \end{tabular} + } + } + \end{frame} + + + + \section{Normalisation} + + \begin{frame} + \frametitle{Relative normalisation} + $\mathcal{B}(\Ptau\to\Pmu\Pmu\Pmu) = \frac{\mathcal{B}(\PDs\to\Pphi\Ppi)}{\mathcal{B}(\PDs\to\Ptau\Pnut)} \times f_{\PDs}^{\Ptau} \times \frac{\varepsilon_\text{norm} }{\varepsilon_\text{sig} } \times \frac{N_\text{sig}}{N_\text{norm}} = \alpha\times N_\text{sig}$ + \begin{itemize} + \item where $\varepsilon$ stands for trigger, reconstruction, selection, + \item $f_{\PDs}^{\Ptau}$ is the fraction of $\Ptau$ coming from $\PDs$, + \item $\text{norm}$ = normalisation channel $\PDs\to\Pphi\Ppi$ + \newline i.e.\ $(83\pm3)\,\%$ for 2012. + \end{itemize} + \includegraphics[width=.47\textwidth]{./Ds_data_2011.pdf} + \includegraphics[width=.47\textwidth]{./Ds_data_2012.pdf} + \end{frame} + + \begin{frame}[allowframebreaks] + \frametitle{Normalisation in numbers} + {\footnotesize{ +$\begin{array}{c|c|c} +& \rm{7~TeV} & \rm{8~TeV}\\ +\hline +\rm{\epsilon\mathstrut_{sig}}^{GEN} (\%) & 8.989 \pm 0.40 & 9.21 \pm 0.35\\ +\hline +\rm{\epsilon_{cal}}^{GEN} (\%) & 11.19 \pm 0.34 & 11.53 \pm 0.32\\ +\hline +\rm{\epsilon_{sig}}^{REC,isMuon,SEL} (\%) & 9.927 \pm 0.028 & 9.261 \pm 0.023 \\ +\hline +\rm{\epsilon_{cal}}^{REC,isMuon,SEL} (\%) & 7.187 \pm 0.022 & 6.690 \pm 0.022 \\ +\hline +\frac{\rm{c_{cal}}^{track}}{\rm{c_{sig}}^{track}} & 0.997 \pm 0.009 \pm 0.026 & 0.996 \pm 0.009 \pm 0.026 \\ +\hline +\frac{\rm{c_{cal}}^{\mu ID}}{\rm{c_{sig}}^{\mu ID}} & 0.9731 \pm 0.0031 \pm 0.0264 & 1.0071 \pm 0.0022 \pm 0.0204 \\ +\hline +\rm{c}^{\phi} & \multicolumn{2}{c}{0.98 \pm 0.01} \\ +\hline +\rm{c}^{\tau} & 1.032 \pm 0.006 & 1.026 \pm 0.006\\ +\hline +\rm{c}^{trash} & 1.89 \pm 0.12 & 1.96 \pm 0.12\\ +\hline +\rm{\epsilon\mathstrut_{sig}}^{TRIG} (\%) & 35.52 \pm 0.14 \pm 0.14 & 39.3 \pm 1.7 \pm 2.0 \\ +\hline +\rm{\epsilon\mathstrut_{cal}}^{TRIG} (\%) & 23.42 \pm 0.14 \pm 0.09 & 20.62 \pm 0.76 \pm 1.07 \\ +\end{array}$ + }} + +\framebreak + + {\footnotesize{ +$\begin{array}{c|c|c} +& \rm{7~TeV} & \rm{8~TeV}\\ +\hline +\mathcal{B}(\PDs \to \Pphi \Ppi) & \multicolumn{2}{c}{(1.317 \pm 0.099) \times 10^{-5}}\\ +\hline +f^{\tau}_{D_{s}} & 0.78 \pm 0.04 & 0.80 \pm 0.03 \\ +\hline +\mathcal{B} (\PDs \to \Ptau \Pnut) & \multicolumn{2}{c}{0.0561 \pm 0.0024}\\ +\hline +\rm{\epsilon\mathstrut_{cal}}^{REC\&SEL}/ +\rm{\epsilon\mathstrut_{sig}}^{REC\&SEL} +& 0.898 \pm 0.060 & 0.912 \pm 0.054 \\ +\hline +\rm{\epsilon\mathstrut_{cal}}^{TRIG}/ +\rm{\epsilon\mathstrut_{sig}}^{TRIG} +& 0.6593 \pm 0.0058 & 0.525 \pm 0.040\\ +\hline +N_{cal} & 28,207 \pm 440 & 52,131 \pm 695\\ +\hline & \\[-0.8em]\hline +\alpha & (3.81 \pm 0.46) \times 10^{-9} & (1.72 \pm 0.23) \times 10^{-9}\\ +\alpha^{trash} & (7.20 \pm 0.98) \times 10^{-9} & (3.37 \pm 0.50) \times 10^{-9}\\ +\end{array}$ +}} + \end{frame} + + + \section{Backgrounds} + + \begin{frame} + \frametitle{Misidentification 1} + \begin{columns} + \column{3in} + \begin{itemize} + \item Most dominant: $\PDplus\to\PK\Ppi\Ppi$. + \item Also seen $\PDplus\to\Ppi\Ppi\Ppi$ and $\PDs\to\Ppi\Ppi\Ppi$. + \item Looked in all mass hypothesis combinations. + % \item Experience from last round: cut away \\low ProbNNmu range + % \item Check remaining data under \\$\PK\Ppi\Ppi$ hypothesis for $\PDplus$ peak + % \item[$\Rightarrow$] misid safely contained in ``trash'' bin + \end{itemize} + \column{2in} + \includegraphics[width=.95\textwidth]{./WMH.pdf} + \end{columns} + \includegraphics[width=.45\textwidth]{./Dp2Kpipi_all_2012_senseBins.pdf} + \includegraphics[width=.45\textwidth]{./FittoD23pi_2012.pdf} + \end{frame} + + \begin{frame} + \frametitle{Misidentification 2} +\begin{itemize} +\item Many tests were performed to be sure we are safe from $\PD_x \to 3h$. +\item Tested both on MC and data. +\item Referees also suggest looking into semileptonic decays. +\item Our background is safely contained in ''trash''\footnote{\begin{tiny} Lowest $ProbNNmu$ and $M_{blend}$ bins, not taken for limit calculation. \end{tiny}} bins. +\end{itemize} + + \includegraphics[width=.7\textwidth]{./c_2dHisto_2012.pdf} + + \end{frame} + + \begin{frame} + \frametitle{Dangerous backgrounds} + \begin{columns} + \column{3in} + \begin{itemize} + \item $\Pphi\to\Pmu\Pmu + X$: narrow veto on dimuon mass. + \item $\PDs\to\Peta(\Pmu\Pmu\Pphoton)\Pmu\Pnum$: not so easy: + \begin{itemize} + \item Modelled in CONF note. + \item Optimised veto in PAPER. + \item Both versions in the ANA note. + \end{itemize} + \item Baseline: veto $m_{\APmuon\Pmuon} < \unit{450}{\MeV}$: + \begin{itemize} + \item Fits better understood. + \item Sensitivity unchanged when removing veto. + \item Smaller uncertainty on expected background. + \end{itemize} + \end{itemize} + \column{2in} + \includegraphics[width=.95\textwidth]{./etaMass.pdf}\\ + \includegraphics[width=.95\textwidth]{./etaDalitz.pdf} + + \end{columns} + + \end{frame} + + \begin{frame} + \frametitle{Remaining backgrounds} + \begin{itemize} + \item Fit exponential to invariant mass spectrum in each likelihood bin. + \item Don't use blinded region ( $\pm \unit{30}{\MeV}$ ). + \item[$\rightarrow$] Compatible results blinding only $\pm \unit{20}{\MeV}$\footnote{partially used in classifier development} + \end{itemize} + {\begin{center} + Example of most sensitive regions in 2011 and 2012 + \includegraphics[width=0.9\textwidth]{./fits.png} + + \end{center}} + \end{frame} + + \section{Expected limit} + + \begin{frame} + \frametitle{Expected limit} + \begin{itemize} + \item Consider nuisance parameters from background fit, signal pdf calibration, normalisation. + \item Nuisance parameters due to $\Ptau$ production, normalization. + \item Limit for combined 2011+2012 analysis. + \end{itemize} + \end{frame} + + \begin{frame} + \frametitle{Sensitivity} + $\mathcal{B}(\Ptau\to\Pmu\Pmu\Pmu)<5.0 \times 10^{-8}$ at 90\% CL + + \includegraphics[width=.8\textwidth]{limit_blind.png} + \end{frame} + + + + \section{Model dependence} + + \begin{frame} + \frametitle{Model dependence} + \begin{itemize} + \item $\Peta$ veto $\Rightarrow$ our limit not constraining to New Physics with small $m_{\APmuon\Pmuon}$. + \item Model description in \texttt{arXiv:0707.0988}. + \item 5 relevant Dalitz distributions: 2 four-point operators, 1 radiative operator, 2 interference terms. + \end{itemize} + \only<2->{ + \begin{itemize} + \item With radiative distribution limit gets worse by a factor of $1.5$ (dominantly from the $\Peta$ veto). + \item The other four Dalitz distributions behave nicely (within $7\,\%$). + \end{itemize} + } + \only<1>{ + \includegraphics[width=.331\textwidth]{./gammallll.pdf} + \includegraphics[width=.331\textwidth]{./gammallrr.pdf} + \includegraphics[width=.331\textwidth]{./gammarad.pdf} + + \includegraphics[width=.331\textwidth]{./gammarad-llll.pdf} + \includegraphics[width=.331\textwidth]{./gammarad-llrr.pdf} +} + + \end{frame} + + + % \begin{frame} + % \frametitle{Conclusion} + % \begin{columns} + % \begin{column}{.55\textwidth} + % \begin{itemize} + % \item finally all pieces put together + % \item model (in)dependence of $\Peta$ veto investigated + % \item expected sensitivity computed\newline $5.6\times 10^{-8}$ + % \end{itemize} + % \end{column} + % \begin{column}{.45\textwidth} + % \includegraphics[width=\textwidth]{party-music-hd-wallpaper-1920x1200-3850.jpg} + % \end{column} + % \end{columns} + + % \end{frame} + + + \section{Unblinded results} + + \begin{frame} + \frametitle{Unblinding 1} +\begin{columns} +\column{1in}{~} +\column{3in} +'' +THERE came a day at summer’s full \\ +Entirely for us \\ +I thought that such were for the saints, \\ +Where revelations be. ''\footnote{E.Dickinson} \\ + \column{1in}{~} +\end{columns} +{~}\\ +{~}\\ +\begin{Large} +On Monday $4^{th}$ of August we were given the permission to unblind. +\end{Large} + + + \end{frame} + + + + \begin{frame} + \frametitle{Unblinding 2} +\begin{itemize} +\item Unfortunately no big ''revelations'' were there. +\item 2011 numbers: +\end{itemize} + \includegraphics[width=1.\textwidth]{2011.png} + + \end{frame} + + \begin{frame} + \frametitle{Unblinding 3} +\begin{itemize} +\item Unfortunately no big ''revelations'' were either in 2012 data: + +\end{itemize} + \includegraphics[width=1.1\textwidth]{2012.png} + + \end{frame} + + + + \begin{frame} + \frametitle{Unblinding 4} + + \begin{center} + \includegraphics[width=0.7\textwidth]{banana_line.pdf} + \end{center} +\begin{columns} + +\column{0.2in}{~} +\column{2in} +Limits(PHSP):\\ +Observed(Expected)\\ +$4.6~(5.0)\times 10^{-8}$ at $90\%$ CL\\ +$5.6~(6.1)\times 10^{-8}$ at $95\%$ CL\\ + + \column{3in} + \includegraphics[width=0.5\textwidth]{model.png} +\end{columns} + \end{frame} + + \begin{frame} + \frametitle{Conclusions} + \begin{columns} + \column{2.5in} + \begin{itemize} + \item We didn't find NP (yet). + \item Limits set with full LHCb dataset. + \item We wait for the Run 2 dataset! + \end{itemize} +\column{2.5in} + + \includegraphics[width=1\textwidth]{TauLFV_UL_2013001.pdf} + + + + \end{columns} + \begin{itemize} + \item We would like to thank our referees for very friendly,thorough and fruitful review. + \item With this presentation we ask collaboration for approval. + \end{itemize} + + + \end{frame} + + + +\end{document} diff --git a/tau23mu_lhcb/APROVAL/mchrzasz2.toc b/tau23mu_lhcb/APROVAL/mchrzasz2.toc new file mode 100644 index 0000000..d909493 --- /dev/null +++ b/tau23mu_lhcb/APROVAL/mchrzasz2.toc @@ -0,0 +1,10 @@ +\beamer@endinputifotherversion {3.10pt} +\select@language {english} +\beamer@sectionintoc {1}{Introduction}{4}{0}{1} +\beamer@sectionintoc 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Emergency stop. +<*> p + +End of file on the terminal! + + +Here is how much of TeX's memory you used: + 3 strings out of 494673 + 102 string characters out of 3173157 + 47775 words of memory out of 3000000 + 3323 multiletter control sequences out of 15000+200000 + 3640 words of font info for 14 fonts, out of 3000000 for 9000 + 243 hyphenation exceptions out of 8191 + 0i,0n,0p,1b,6s stack positions out of 5000i,500n,10000p,200000b,50000s +! ==> Fatal error occurred, no output PDF file produced! diff --git a/tau23mu_lhcb/APROVAL/tmp.tex b/tau23mu_lhcb/APROVAL/tmp.tex new file mode 100644 index 0000000..b78638c --- /dev/null +++ b/tau23mu_lhcb/APROVAL/tmp.tex @@ -0,0 +1,701 @@ +\documentclass[xcolor=dvipsnames,table]{beamer} + + + + + + \author[Paul Seyfert]{ + Johannes Albrecht\inst{1}, Marta Calvi\inst{2}, Marcin Chrz\k{a}szcz\inst{3,4}, Laura Gavardi\inst{1}, Jon Harrison\inst{5}, Basem Khanji\inst{2}, George Lafferty\inst{5}, Tatiana Likhomanenko\inst{6}, Eduardo Rodrigues\inst{5}, Nicola Serra\inst{4}, \underline{Paul Seyfert\inst{7}}} + + \institute[Uni Heidelberg]{ + \inst{1}Dortmund, + \inst{2}Milano Bicocca, + \inst{3}Cracow, \inst{4}Zurich, \inst{5}Manchester, \inst{6}Yandex, \inst{7}Heidelberg University + } + + \date{\today} + \subject{} + + + \AtBeginSection[] + { + \begin{frame}{} + \tableofcontents[currentsection,currentsubsection] + \end{frame} + } + + + \begin{document} + \begin{frame} + \titlepage + \end{frame} + + + \begin{frame} + \begin{enumerate} + \item introduction\vspace{.5em} + \item multivariate technique\vspace{.5em} + \item choice of triggers\vspace{.5em} + \item normalisation\vspace{.5em} + \item backgrounds\vspace{.5em} + \item expected sensitivity\vspace{.5em} + \item model dependence\vspace{.5em} + \end{enumerate} + Major news wrt.\ the previous analysis rounds highlighted in \textcolor{darkgreen}{green} + \end{frame} + + \section{introduction} + + \begin{frame} + \frametitle{Status $\Ptau\to\Pmu\Pmu\Pmu$} + \begin{columns} + \begin{column}{.62\textwidth} + \begin{fmffile}{sm} + \begin{fmfgraph*}(200,150) + \fmfstraight + \fmfleft{is3,is2,is1,i1,i2,i3,i4,i5,i6} + \fmfright{os3,os2,os1,o1,o2,o3,o4,o5,o6} + + + \fmf{phantom}{o1,g1} + \fmf{phantom,tension=1.5}{g1,i1} + + \fmffreeze + + \fmf{photon, tension=2.,lab.side=left, lab=$\Pphoton$}{g1,g2} + \fmf{fermion,lab.side=left,label=$\APmuon$}{o3,g2} + \fmf{fermion,lab.side=left,label=$\Pmuon$}{g2,o5} + \fmf{phantom,tension=1.5}{i6,g2} + + \fmffreeze + + + \fmf{fermion,lab.side=left,label=$\Pgtm$}{i1,w1} + \fmf{dashes,lab.side=right,label=$\PWminus$}{w1,w2} + \fmf{fermion,lab.side=left,label=$\Pmuon$}{w2,o1} + + + \fmfipath{p[]} + \fmf{plain,tension=0,right,label={$\Pgngt\to\Pgngm$},tag=1}{w1,w2} + \fmffreeze + \fmfiset{p1}{vpath1(__w1,__w2)} + \fmfiv{d.sh=cross,d.ang=0,d.size=5thick}{point length(p1)/2 of p1} + + + \end{fmfgraph*} + + \end{fmffile} + {\footnotesize{ + \begin{itemize} + \item charged Lepton Flavour Violation process + \item possible as penguin with neutrino oscillation + \item unmeasurable small + \end{itemize} + }} + \end{column} + \begin{column}{.37\textwidth} + \begin{block}{current limits ($ 90\,\%$ CL)} + + \begin{description} + \item[BaBar] $3.3\times 10^{-8}$ + \item[Belle] $2.1\times 10^{-8}$ + \item[LHCb] $8.0\times 10^{-8}$ + \end{description} + \end{block} + \begin{block}{BSM predictions} + \begin{description} + \item[var.\ SUSY] $10^{-10}$ + \item[non universal $\PZprime$] $10^{-8}$ + \item[mSUGRA+seesaw] $10^{-9}$ + \end{description} + \end{block} + \end{column} + \end{columns} + \end{frame} + + \begin{frame} + \frametitle{$\Ptau$ production} + \begin{itemize} + \item consider five production channels (fractions at $\unit{8}{\TeV}$):\begin{itemize} + \item prompt $\PDs\to\Ptau$ ($73.1\pm3.9\,\%$) + \item prompt $\PDplus\to\Ptau$ ($0.42\pm0.43\,\%$) + \item non-prompt $\PDs\to\Ptau$ ($9.7\pm2.1\,\%$) + \item non-prompt $\PDplus\to\Ptau$ ($0.02\pm0.02\,\%$) + \item $X_{\Pbottom}\to\Ptau$ (meson or baryon) ($16.8\pm3.0\,\%$) + \end{itemize} + \item \textcolor{darkgreen}{use $\sigma(\Pbottom\APbottom)$ at $\unit{8}{\TeV}$ from LHCb} + \item \textcolor{darkgreen}{use Pythia scaling for $\sigma(\Pcharm\APcharm)$ at $\unit{8}{\TeV}$} + \end{itemize} + \begin{exampleblock}{$\mathcal{B}(\PDplus\to\Ptau)$} + \begin{itemize} + \item old analysis: used upper limit + \item now: $\mathcal{B}(\PDplus\to\Pmu\Pnum)$ + helicity suppression + phase space + \item \texttt{hep-ex:0604043} + \item $\mathcal{B}(\PDplus\to\Ptau\Pnut)=1\pm1\times10^{-4}$ + \end{itemize} + \end{exampleblock} + \end{frame} + + \begin{frame} + \frametitle{Strategy} + \begin{itemize} + \item mostly as in many rare decay searches: + \item loose stripping selection + \item multivariate classification in: mass, PID, ``geometry/topology'' + \item relative normalisation ($\PDs\to\Pphi(\Pmu\Pmu)\Ppi$) + \item invariant mass fit for expected background in each likelihood bin\newline fit in $m-m_{\Ptau}>\unit{30}{\MeV}$ + \item ``middle sidebands'' for classifier evaluation ($\unit{20}{\MeV}300\MeV$} \\ +Track $\chi^2$/ndf &\multicolumn{2}{c|}{$<3 $} \\ +IP $\chi^2$/ndf &\multicolumn{2}{c|}{$>9 $} \\ +\textcolor{darkgreen}{track ghost probability} &\multicolumn{2}{c|}{\textcolor{darkgreen}{$<0.3 $}} \\ +\hline +$\mu$ pairs &\multicolumn{2}{c|}{} \\ +$m_{\mu^+\mu^-} - m_{\phi}$ & $>20\MeV$ & $<20\MeV$\\ +$m_{\mu^+\mu^-}$ & $> 450\MeV$ & - \\ +$m_{\mu^+\mu^+}$ & $> 250\MeV$ & - \\ +\hline +$\tau^\pm$ and \PDs &\multicolumn{2}{c|}{} \\ +$\Delta m$ & $<400\MeV$ & $<50\MeV$\\ +Vertex $\chi^2$ &\multicolumn{2}{c|}{$<15$} \\ +\textcolor{darkgreen}{IP $\chi^2$} &\multicolumn{2}{c|}{$<225^1 $} \\ +$\cos\alpha$ &\multicolumn{2}{c|}{$>0.99$} \\ +$c\tau$ (stripping) &\multicolumn{2}{c|}{$>\unit{100}{\mu m}$} \\ + &\multicolumn{2}{c|}{no PV refitting}\\ +decay time (offline) &\multicolumn{2}{c|}{$> -0.01$ ns \& $< 0.025$ ns}\\ + &\multicolumn{2}{c|}{PV refitting}\\ +\hline +\end{tabular} +}} + +{\footnotesize{$^1$ different LoKi functor}} + \end{frame} + + \section{multivariate technique} + + \begin{frame} + \frametitle{``geometric likelihood''} + \begin{itemize} + \item classify the displaced 3-body decay properties of a signal candidate + \item revisit variable choice + \item revisit classification technique + \item \textcolor{darkgreen}{more toolkits tried: MatrixNet, NeuroBayes}, TMVA + \item \textcolor{darkgreen}{retune input variables\newline($\PBs\to\Pmu\Pmu$ isolation $\rightarrow$ Laura's BDT isolation: CERN-THESIS-2013-259)} + \end{itemize} + + \end{frame} + \begin{frame} + \frametitle{setup} + \begin{itemize} + \item train $1/3$ signal MC against $1/2$ background MC + \item variables \begin{itemize} + \item $3\times$ DOCA + \item vertex $\chi^2$ + \item $\tau$ decay time + \item $\tau$ IP$\chi^2$ + \item min.\ $\mu$ IP$\chi^2$ + \item $\Ptau$ pointing angle + \item $\tau$ $p_T$ + \item max.\ track $\chi^2$ + \item $\PBs\to\Pmu\Pmu$ track isolation + \item cone isolation + \item \textcolor{darkgreen}{BDT isolation} + \end{itemize} + \end{itemize} + \end{frame} + \begin{frame} + \frametitle{futher tweaking} + \begin{itemize} + \item \textcolor{darkgreen}{remove fully reconstructed 3-body decays from background sample\newline (don't expect to be able to discriminate these)} + \item don't apply trigger prior to training + \end{itemize} + + \begin{exampleblock}{``blending'' technique} + \begin{itemize} + \item for each signal channel we train: one BDT, three Fisher classifier, four MLPs, one FDA, and one LD classifier + \item[$\Rightarrow$] 50 classifiers + \item one final MatrixNet classifier using the 13 base variables and the 50 classifiers as input + \newline(trained on the second $1/3$ of signal MC and the second $1/2$ of background MC) + \end{itemize} + \end{exampleblock} + \end{frame} + + \begin{frame} + \frametitle{performance} + \begin{itemize} + \item classifier prefers $\Ptau$ from prompt $\PDs$ + \end{itemize} + \begin{columns} + \begin{column}{.48\textwidth} + \begin{block}{MC response for different\newline $\Ptau$ production channels} + \includegraphics[width=.95\textwidth]{./for_paul.png} + \end{block} + \end{column} + \begin{column}{.48\textwidth} + \begin{block}{response for $\PDs\to\Pphi\Ppi$\newline data and MC} + \includegraphics[width=.95\textwidth]{./MN_BLEND_FLAT.png} + \end{block} + \end{column} + \end{columns} + \end{frame} + + \begin{frame} + \frametitle{calibration} + \begin{itemize} + \item assume all differences between $\Ptau\to\Pmu\Pmu\Pmu$ and $\PDs\to\Pphi\Ppi$ come from kinematics (mass, resonance, decay time) + \item get correction $\PDs\leadsto\Ptau$ from MC + \item apply corrections to $\PDs\to\Pphi\Ppi$ on data + \end{itemize} + \begin{block}{validation} + \begin{itemize} + \item done for 2011 analysis, treating smeared MC as data + \end{itemize} + \end{block} + \begin{columns} + \begin{column}{.45\textwidth} + \begin{itemize} + \item $\PDs\to\Pphi\Ppi$ well modelled in MC + \item until the very low likelihood end of the distribution + \item[$\rightarrow$] i.e.\ also badly pointing non-prompt $\PDs$ + \end{itemize} + \end{column} + \begin{column}{.45\textwidth} + \includegraphics[width=.95\textwidth]{MN_BLEND_FLAT.png} + \end{column} + \end{columns} + \end{frame} + + \begin{frame} + \frametitle{PID} + \begin{itemize} + \item we used ProbNNmu already in the previous round of the analysis + \item now use MC12TuneV2 (latest) + \item two-fold reason:\begin{itemize} + \item expect better performance than CombDLL variables + \item ``one variable for everything'':\newline with CombDLL we needed both CombDLL($\mu-\pi$) and CombDLL($\mu-K$) + \end{itemize} + \end{itemize} + \end{frame} + + \begin{frame} + \frametitle{PIDCalib} + \begin{itemize} + \item calibration strategy: use PIDCalib + \item confirm with $\PDs\to\Pphi\Ppi$ if everything is fine + \end{itemize} + \begin{columns} + \begin{column}{.45\textwidth} + cut\&fit: + \begin{itemize} + \item fit $\PDs\to\Pphi\Ppi$ with a TIS muon in data + \item cut on ProbNNmu of one muon + \item fit again + \item[$\rightarrow$] ratio is ``true'' cut efficiency + \end{itemize} + \begin{block}{ProbNNmu>0.4} + $\varepsilon=86.3\,\%$ + \end{block} + \end{column} + \begin{column}{.45\textwidth} + PIDCalib + \begin{itemize} + \item apply full selection (incl. trigger) to $\PDs\to\Pphi\Ppi$ MC reference sample + \item avoid IsMuon bias + \end{itemize} + \begin{block}{ProbNNmu>0.4} + $\varepsilon=89.8\,\%$ + \end{block} + \end{column} + \end{columns} + \end{frame} + + \begin{frame} + \frametitle{?} + \begin{itemize} + \item first shown at \myhref{https://indico.cern.ch/event/291727/}{charming VRD meeting} + \item also mentionned at last \myhref{https://indico.cern.ch/event/298021/}{LHCb week} + \item many emails exchanged with Barbara Sciascia + \item mistakes on user side found + \item still no agreement + \end{itemize} + \begin{exampleblock}{phenomenologic treatment} + \begin{itemize} + \item correlations are small in $\PDs\to\Pphi\Ppi$ data and MC + \newline $\varepsilon(\text{cut on one muon})^2 = \varepsilon(\text{cut on two muons})$ + \item[$\Rightarrow$] use $c^3=(\varepsilon(\text{cut and fit})/\varepsilon(\text{PIDCalib}))^3$ as correction to PIDCalib for $\Ptau\to\Pmu\Pmu\Pmu$ + \item assign error of $0.02$ for $c$ + \end{itemize} + \end{exampleblock} + \begin{itemize} + \item planned: investigate further (usage/bug/samples) + \item planned: use muons from $\PDs\to\Pphi\Ppi$ directly + \end{itemize} + \end{frame} + + \begin{frame} + \frametitle{binning optimisation} + \begin{itemize} + \item how to optimise the binning in two classifiers? + \item $\unit{1}{\reciprocal\femtobarn}$ CONF note: two one-dimensional optimisations as in $\PBs\to\Pmu\Pmu$ + \item $\unit{1}{\reciprocal\femtobarn}$ PAPER: iterative loop of one-dimensional optimisations\newline optimising one classifier on the sensitive range of the other classifier + \item \textcolor{darkgreen}{now: optimise two-dimensions (optimise bin boundaries in both dimensions at the same time)} + \item unchanged: don't use lowest likelihood bins\newline(reflection backgrounds, no sensitivity gain) + \end{itemize} + \end{frame} + \begin{frame} + \frametitle{impact of new binning optimisation} + \begin{itemize} + \item removal of tiny bins which contribute negligible sensitivity + \item colour: limit obtained, using only this particular bin + \item number: rank of that bin (1=best sensitivity bin) + \end{itemize} + + ~ + + \begin{columns} + \begin{column}{.5\textwidth} + old analysis + + ~ + + \includegraphics[width=.95\textwidth]{./90CLonebinlimit.eps} + \end{column} + \begin{column}{.5\textwidth} + new analysis + + (2011 data, not final calibration) + \includegraphics[width=.95\textwidth]{./rank.eps} + \end{column} + \end{columns} + \end{frame} + + + \begin{frame} + \frametitle{mass shape} + \begin{itemize} + \item double-Gaussian with fixed fraction ($70\,\%$ inner Gaussian) + \item fix fraction to ease calibration:\newline + $\sigma_{data}^{\Ptau} = \frac{\sigma_{MC}^{\Ptau}}{\sigma_{MC}^{\PDs}}\times\sigma_{data}^{\PDs}$ + \end{itemize} + \includegraphics[width=.44\textwidth]{./Ds_data_2011.pdf} + \includegraphics[width=.44\textwidth]{./Ds_data_2012.pdf} + + {\footnotesize{ + \begin{tabular}{|c|c|c|} + \hline + calibrated $\Ptau$ mass shape & 7~TeV & 8~TeV\\ + \hline + Mean ($\MeV$) & $1779.1 \pm 0.1$ & $1779.0 \pm 0.1$\\ + \hline + $\sigma_1$ ($\MeV$) & $7.7 \pm 0.1$ & $7.6 \pm 0.1$\\ + \hline + $\sigma_2$ ($\MeV$) & $12.0 \pm 0.8$ & $11.5 \pm 0.5$\\ + \hline + \end{tabular} + } + } + \end{frame} + +\beamertemplateshadingbackground{darkgreen!30}{PineGreen!30} + \section{choice of triggers} + \begin{frame} + \frametitle{the story} + \begin{itemize} + \item first look at $\PDs\to\Pphi\Ppi$ revealed: signal/background much worse in 2012 + \item[$\rightarrow$] charm got more bandwidth in 2012 + \item taking all events quite unsatisfactory:\begin{itemize} + \item strictly speaking: we don't know why the events ended up on tape + \item trigger efficiencies unstable (TIS/TPS/TOS efficiencies for lots of lines and TCKs) + \item signal anyhow mostly TOS in a muon trigger + \end{itemize} + \item[$\Rightarrow$] if an event was background in the trigger, then don't consider it signal afterwards. + \end{itemize} + \end{frame} + + \begin{frame} + \frametitle{strategy} + \begin{itemize} + \item back of the envelope: limit scales with $1/\varepsilon_\text{sig}$ + \item back of the envelope: limit scales with $\sqrt{\varepsilon_\text{bkg}}$ + \item[$\Rightarrow$] minimise $FOM=\frac{\sqrt{\varepsilon_\text{bkg}}}{\varepsilon_\text{sig}}$ + \item running TCKsh and some combinatorics: $\mathcal{O}(2^{256}\approx 10^{75})$ possibilities of using HLT2 line (ignoring that there are different TCKs, TIS/TOS/TPS/DEC, \dots) + \item[$\rightarrow$] be more pragmatic! + \end{itemize} + \begin{exampleblock}{trigger optimisation} + \begin{itemize} + \item sort trigger lines (Punzi FoM) + \item start with events from the best trigger line and compute $FOM$ + \item add events from the next trigger and recompute $FOM$ + \item iterate and converge to $FOM(\text{all triggers})$ + \item use all triggers until $FOM$ starts rising. + \end{itemize} + \end{exampleblock} + \end{frame} + + \begin{frame} + \frametitle{our triggers} + {\footnotesize{ + \begin{tabular}{l|c|c} + & signal & normalisation \\\hline\hline + L0$^1$ & \multicolumn{2}{c}{L0Muon TOS}\\\hline + Hlt1$^1$ & \multicolumn{2}{c}{Hlt1TrackMuon TOS}\\\hline + Hlt2 2011 & Hlt2CharmSemilepD2HMuMu TOS & Hlt2DiMuonDetached$^2$ TOS \\ + & || Hlt2TriMuonTau TOS & \\\hline + Hlt2 2012 & Hlt2TriMuonTau$^1$ TOS & Hlt2DiMuonDetached$^2$ TOS\\\hline + \end{tabular} + } + } + \only<1>{ + \begin{block}{$^1$ triggers in 2012} + \begin{itemize} + \item cuts changed through 2012 + \item[$\rightarrow$] \textcolor{darkgreen}{emulated two different TCKs for 2012} + \end{itemize} + \end{block}} + \only<2>{ + \begin{block}{$^2$ word on Hlt2DiMuonDetached} + \begin{itemize} + \item keep it simple here + \item line unchanged in 2012 + \item[$\rightarrow$] choice keeps Hlt2 trigger efficiency stable + \item $\PDs\to\Pphi\Ppi$ anyhow doesn't behave like $\Ptau\to\Pmu\Pmu\Pmu$ in the TriMuon trigger (requires misidentification) + \end{itemize} + \end{block}} + + \end{frame} + + \begin{frame} + \frametitle{cross check (not in the note)} + \begin{itemize} + \item shouldn't the multivariate classifier do better than any trigger? + \item back-of-the-envelope overestimates the improvement (expect $\sim 9\,\%$ improvement) + \item[$\rightarrow$] add events back to the ntuple, recalculate normalisation, redid fits + \item[$\Rightarrow$] \textcolor{darkgreen}{restricting the triggers gains $\sim 3\,\%$ sensitivity wrt.\ previous round} + \end{itemize} + \end{frame} +\beamertemplateshadingbackground{White}{White} + + \section{normalisation} + + \begin{frame} + \frametitle{relative normalisation} + $\mathcal{B}(\Ptau\to\Pmu\Pmu\Pmu) = \frac{\mathcal{B}(\PDs\to\Pphi\Ppi)}{\mathcal{B}(\PDs\to\Ptau\Pnut)} \times f_{\PDs}^{\Ptau} \times \frac{\varepsilon_\text{norm} }{\varepsilon_\text{sig} } \times \frac{N_\text{sig}}{N_\text{norm}} = \alpha\times N_\text{sig}$ + \begin{itemize} + \item where $\varepsilon$ stands for trigger, reconstruction, selection + \item $\text{norm}$ = normalisation channel $\PDs\to\Pphi\Ppi$ + \item $f_{\PDs}^{\Ptau}$ is the fraction of $\Ptau$ coming from $\PDs$ + \newline i.e.\ $(83\pm3)\,\%$ for 2012 + \end{itemize} + \includegraphics[width=.47\textwidth]{./Ds_data_2011.pdf} + \includegraphics[width=.47\textwidth]{./Ds_data_2012.pdf} + \end{frame} + + \begin{frame}[allowframebreaks] + \frametitle{normalisation in numbers} + {\footnotesize{ +$\begin{array}{c|c|c} +& \rm{7~TeV} & \rm{8~TeV}\\ +\hline +\rm{\epsilon\mathstrut_{sig}}^{GEN} & 8.98 \pm 0.41 & 9.20 \pm 0.36\\ +\hline +\rm{\epsilon_{cal}}^{GEN} & 11.19 \pm 0.34 & 11.53 \pm 0.32\\ +\hline +\rm{\epsilon_{sig}}^{REC,isMuon,SEL} & 9.794 \pm 0.028 & 9.134 \pm 0.023 \\ +\hline +\rm{\epsilon_{cal}}^{REC,isMuon,SEL} & 7.187 \pm 0.022 & 6.690 \pm 0.022 \\ +\hline +\frac{\rm{c_{cal}}^{track}}{\rm{c_{sig}}^{track}} & 0.997 \pm 0.009 \pm 0.026 & 0.996 \pm 0.009 \pm 0.026 \\ +\hline +\frac{\rm{c_{cal}}^{\mu ID}}{\rm{c_{sig}}^{\mu ID}} & 0.9731 \pm 0.0031 \pm 0.0264 & 1.0071 \pm 0.0022 \pm 0.0204 \\ +\hline +\rm{c}^{\Pphi} & \multicolumn{2}{c}{0.98 \pm 0.01} \\ +\hline +\rm{c}^{\Ptau} & 1.032 \pm 0.006 & 1.026 \pm 0.006\\ +\hline +\rm{c}^{trash} & 1.95 \pm 0.12 & 2.05 \pm 0.12\\ +\hline +\rm{\epsilon\mathstrut_{sig}}^{TRIG} & 35.45 \pm 0.11 \pm 0.14 & 39.1 \pm 1.7 \pm 2.0 \\ +\hline +\rm{\epsilon\mathstrut_{cal}}^{TRIG} & 23.42 \pm 0.14 \pm 0.09 & 20.62 \pm 0.76 \pm 1.07 \\ +\end{array}$ + }} + +\framebreak + + {\footnotesize{ +$\begin{array}{c|c|c} +& \rm{7~TeV} & \rm{8~TeV}\\ +\hline +\mathcal{B}(\PDs\to\Pphi\Ppi) & \multicolumn{2}{c}{(1.317 \pm 0.099) \times 10^{-5}}\\ +\hline +f^{\Ptau}_{\PDs} & 0.82 \pm 0.03 & 0.83 \pm 0.03 \\ +\hline +\mathcal{B}(\PDs\to\Ptau\Pnut) & \multicolumn{2}{c}{0.0561 \pm 0.0024}\\ +\hline +\rm{\epsilon\mathstrut_{norm}}^{REC\&SEL}/ +\rm{\epsilon\mathstrut_{sig}}^{REC\&SEL} +& 0.897 \pm 0.061 & 0.926 \pm 0.056 \\ +\hline +\rm{\epsilon\mathstrut_{norm}}^{TRIG}/ +\rm{\epsilon\mathstrut_{sig}}^{TRIG} +& 0.6606 \pm 0.0059 & 0.527 \pm 0.041\\ +\hline +N_{norm} & 28,162 \pm 434 & 51,998 \pm 684\\ +\hline & \\[-1.5em]\hline +\alpha & (4.05 \pm 0.48) \times 10^{-9} & (1.83 \pm 0.25) \times 10^{-9}\\ +\alpha^{trash} & (7.90 \pm 0.49) \times 10^{-9} & (3.75 \pm 0.27) \times 10^{-9}\\ +\end{array}$ +}} + \end{frame} + + + \section{backgrounds} + + \begin{frame} + \frametitle{misidentification} + \begin{itemize} + \item most dominant: $\PDplus\to\PK\Ppi\Ppi$ + \item experience from last round: cut away low ProbNNmu range + \item check remaining data under $\PK\Ppi\Ppi$ hypothesis for $\PDplus$ peak + \item[$\Rightarrow$] misid safely contained in ``trash'' bin + \item \textcolor{darkgreen}{$\PDplus\to\Ppi\Ppi\Ppi$ and $\PDs\to\Ppi\Ppi\Ppi$ start to become visible in 2012} + \end{itemize} + \includegraphics[width=.45\textwidth]{./Dp2Kpipi_all_2012_senseBins.pdf} + \includegraphics[width=.45\textwidth]{./FittoD23pi_2012.pdf} + \end{frame} + + \begin{frame} + \frametitle{evil backgrounds} + \begin{itemize} + \item $\Pphi\to\Pmu\Pmu + X$: narrow veto on dimuon mass + \item $\PDs\to\Peta(\Pmu\Pmu\Pphoton)\Pmu\Pnum$: not so easy + \begin{itemize} + \item modelled in CONF note + \item optimised veto in PAPER + \item right now: both versions in the ANA note + \end{itemize} + \item baseline: veto $m_{\APmuon\Pmuon} < \unit{450}{\MeV}$ + \begin{itemize} + \item fits better understood + \item sensitivity unchanged when removing veto + \item smaller uncertainty on expected background + \end{itemize} + \end{itemize} + \end{frame} + + \begin{frame} + \frametitle{remaining backgrounds} + \begin{itemize} + \item fit exponential to invariant mass spectrum in each likelihood bin + \item don't use $\pm \unit{30}{\MeV}$ in the fit + \item[$\rightarrow$] compatible results blinding only $\pm \unit{20}{\MeV}$\footnote{partially used in classifier developement} + \end{itemize} + {\begin{center} + most sensitive bins in 2011 and 2012 + \includegraphics[width=.4\textwidth]{./fit2011.png} + \includegraphics[width=.4\textwidth]{./fit2012.png} + \end{center}} + \end{frame} + + \section{results} + + \begin{frame} + \frametitle{expected limit} + \begin{itemize} + \item still blinded + \item consider nuisance parameters from background fit, signal pdf calibration, normalisation + \item nuisance parameters due to $\Ptau$ production not included in signal pdf shape, yet + \item limit for combined 2011+2012 analysis + \end{itemize} + \end{frame} + + \begin{frame} + \frametitle{sensitivity} + $\mathcal{B}(\Ptau\to\Pmu\Pmu\Pmu)<5.6 \times 10^{-8}$ at 90\% CL + + \includegraphics[width=.8\textwidth]{./banana.png} + \end{frame} + +\beamertemplateshadingbackground{PineGreen!30}{White} + \section{model dependence} + + \begin{frame} + \frametitle{model dependence} + \begin{itemize} + \item $\Peta$ veto $\Rightarrow$ our limit not applicable to New Physics with small $m_{\APmuon\Pmuon}$ + \item model independent description in \texttt{arXiv:0707.0988} + \item 5 relevant Dalitz distributions: 2 four-point operators, 1 radiative operator, 2 interference terms + \end{itemize} + \only<2->{ + \begin{itemize} + \item with radiative distribution limit gets worse by $51\,\%$ (dominantly from the $\Peta$ veto) + \item the other four Dalitz distributions behave nicely (within $7\,\%$) + \end{itemize} + } + \only<1>{ + \includegraphics[width=.331\textwidth]{./gammallll.eps} + \includegraphics[width=.331\textwidth]{./gammallrr.eps} + \includegraphics[width=.331\textwidth]{./gammarad.eps} + + \includegraphics[width=.331\textwidth]{./gammarad-llll.eps} + \includegraphics[width=.331\textwidth]{./gammarad-llrr.eps} +} + + \end{frame} + +\beamertemplateshadingbackground{White}{White} + + \begin{frame} + \frametitle{Conclusion} + \begin{columns} + \begin{column}{.55\textwidth} + \begin{itemize} + \item finally all pieces put together + \item model (in)dependence of $\Peta$ veto investigated + \item expected sensitivity computed\newline $5.6\times 10^{-8}$ + \end{itemize} + \end{column} + \begin{column}{.45\textwidth} + \includegraphics[width=\textwidth]{party-music-hd-wallpaper-1920x1200-3850.jpg} + \end{column} + \end{columns} + + \end{frame} + \end{document} diff --git a/tau23mu_lhcb/APROVAL/xwindow.png b/tau23mu_lhcb/APROVAL/xwindow.png new file mode 100644 index 0000000..f43cc7e --- /dev/null +++ b/tau23mu_lhcb/APROVAL/xwindow.png Binary files differ diff --git a/tauola/Bug1/MM.aux b/tauola/Bug1/MM.aux new file mode 100644 index 0000000..b7fa3c4 --- /dev/null +++ b/tauola/Bug1/MM.aux @@ -0,0 +1,163 @@ +\relax +\ifx\hyper@anchor\@undefined +\global \let \oldcontentsline\contentsline +\gdef 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mode 100644 index 0000000..160ac5e --- /dev/null +++ b/tauola/Bug1/MM.pdf Binary files differ diff --git a/tauola/Bug1/MM.snm b/tauola/Bug1/MM.snm new file mode 100644 index 0000000..e69de29 --- /dev/null +++ b/tauola/Bug1/MM.snm diff --git a/tauola/Bug1/MM.synctex.gz b/tauola/Bug1/MM.synctex.gz new file mode 100644 index 0000000..78b4daf --- /dev/null +++ b/tauola/Bug1/MM.synctex.gz Binary files differ diff --git a/tauola/Bug1/MM.tex b/tauola/Bug1/MM.tex new file mode 100644 index 0000000..2e9ab92 --- /dev/null +++ b/tauola/Bug1/MM.tex @@ -0,0 +1,1097 @@ +\documentclass[]{beamer} +\setbeamertemplate{navigation symbols}{} +\usepackage{beamerthemesplit} +\useoutertheme{infolines} +\usecolortheme{dolphin} +%\usetheme{Warsaw} +\usetheme{progressbar} +\usecolortheme{progressbar} + +\usefonttheme{progressbar} +\useoutertheme{progressbar} +\useinnertheme{progressbar} +\usepackage{graphicx} +%\usepackage{amssymb,amsmath} +\usepackage[latin1]{inputenc} +\usepackage{amsmath} +\newcommand\abs[1]{\left|#1\right|} +\usepackage{iwona} +\usepackage{hepparticles} +\usepackage{hepnicenames} +\usepackage{hepunits} +\progressbaroptions{imagename=images/lhcb} +%\usetheme{Boadilla}f + +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%5 +\definecolor{mygreen}{cmyk}{0.82,0.11,1,0.25} +\setbeamertemplate{blocks}[rounded][shadow=false] +\addtobeamertemplate{block begin}{\pgfsetfillopacity{0.8}}{\pgfsetfillopacity{1}} +\setbeamercolor{structure}{fg=mygreen} +\setbeamercolor*{block title example}{fg=mygreen!50, +bg= blue!10} +\setbeamercolor*{block body example}{fg= blue, +bg= blue!5} + + + + + +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%\beamersetuncovermixins{\opaqueness<1>{25}}{\opaqueness<2->{15}} +\title{Method of moments for $\PB \to \PKstar \mu \mu$} +\author{\underline{Marcin Chrzaszcz}$^{1,2}$} +\date{\today} + +\begin{document} + +{ +\institute{$^1$ University of Zurich, $^2$ Institute of Nuclear Physics} +\setbeamertemplate{footline}{} +\begin{frame} +\logo{ +\vspace{2 mm} +\includegraphics[height=1cm,keepaspectratio]{images/uzh.jpg}~ +\includegraphics[width=1cm,keepaspectratio]{images/ifj.png}} + + \titlepage +\end{frame} +} +\institute{UZH,IFJ} + +\section[Outline]{} +\begin{frame} +\tableofcontents +\end{frame} + +\section{Introduction} +\begin{frame}\frametitle{Plan} +Why method of moments: +\begin{enumerate} +\item Complementary approach in performing the fit. +\item Allows to extract info measuring quantities in event basis depending on the angular distribution. +\item Used in $\PB \to \rho \Plepton \nu$(SLAC-386 UC-414),\\ $\PJpsi \to \PK \PK \gamma$(PRD 71, 032005 (2005) ), etc. +\end{enumerate} + + +\end{frame} +\section{Method of Moments - Theory} +\begin{frame}\frametitle{Method of moments} +{~} +Let's assume we have our pdf with $k$ unknown parameters :$PDF(x_i, \alpha)$, $dim(\alpha)=k$. One can calculate $k$ moments, which are the functions of $\alpha_i$: +\begin{equation} +\mu_i=f(\alpha_1,..., \alpha_k) = E[W_i] +\end{equation} +If we have $n$ events in our $q^2$ bin, we can estimate: +\begin{equation} +\widehat{\mu}_i=\dfrac{1}{n}\sum_{j=0}^{j=n-1} w_j +\end{equation} +, where $w_j=g(x_i)$ + +\end{frame} + +\begin{frame}\frametitle{Trivial example} +{~} +Lets see how this works in practice: +\begin{equation} +f(x)=\dfrac{x^{a-1}e^{-x/b}} {b^a \Gamma(a)} +\end{equation} +we measure the moments:\\ +\begin{center} $m_1=\dfrac{X_1+X_2+...+X_n}{n}$,\\ $m_2=\dfrac{X_1^2+X_2^2+...+X_n^2}{n}$.\\\end{center} +and calculate them analytically: +\begin{center} $m_1=ab$, $m_2=b^2a(a+1)$\end{center} +So one just needs to solve this and get the answer: +\center $a=\dfrac{m_1^2}{m_2-m_1^2}$, $b=\dfrac{m_2-m_1^2}{m_1}$ +\end{frame} + +\section{Moments of Ss} + + +\begin{frame}\frametitle{Our PDF} +{~} +The angular terms: +\begin{multline} +\dfrac{d^4\Gamma}{dq^2 dcos\theta_k dcos\theta_l d\phi}=\dfrac{9}{32\pi}( \dfrac{3}{4}(1-F_l)\sin^2 \theta_k + F_l \cos^2 \theta_k + (\dfrac{1}{4}(1-F_l)\sin^2 \theta_k \\ -F_l\cos^2) \cos 2\theta_l + J_3 \sin^2 \theta_k \sin^2 \theta_l cos2\phi + J_4 \sin2 \theta_k \sin \theta_l \cos\phi +\\ J_5 \sin 2 \theta_k \sin \theta_l \cos \phi + (J_{6s} \sin^2 \theta_k + J_{6c} \cos^2 \theta_k) \cos \theta_l + \\ J_7 \sin 2\theta_k \sin \theta_l \sin \phi + J_8 \sin 2 \theta_k \sin 2 \theta_l \sin \phi + J_9 \sin^2 \theta_k \sin^2 \theta_l \sin 2 \phi) +\end{multline} +Since we are fitting a PDF we need to ensure it is normalized: +\begin{equation} +\int_{-\pi}^{\pi} d\phi \int_{-1}^{1} d cos\theta_l \int_{-1}^{1} d cos\theta_k \dfrac{d^4\Gamma}{dq^2 dcos\theta_k dcos\theta_l d\phi}=1 +\end{equation} + + +\end{frame} +\begin{frame}\frametitle{Measuring Js} +{~} +From equation 2 we have the following: + +\begin{equation} +\dfrac{1}{4}(3 J_{1c} + 6 J_{1s} - J_{2c} - 2 J_{2s}) =1 +\end{equation} +For now we will consider the following PDF: +\begin{equation} + \dfrac{d^3\Gamma}{\Gamma dcos\theta_k dcos\theta_l d\phi }(cos\theta_k , cos\theta_l, \phi) +\end{equation} + +Becouse our PDF is not normalized and we are measuring $\Gamma+\overline{\Gamma} +$ we are effectively fitting the $S_i$ (aka $J_i \to S_i$) +\end{frame} + + +\begin{frame}\frametitle{Moments for $\PB \to \PKstar \mu \mu$} +{~} +Let's calculate the moments for Ss: +\begin{equation} + \dfrac{d^3\Gamma}{\Gamma dcos\theta_k dcos\theta_l d\phi }sin^2 \theta_k sin^2 \theta_l cos 2 \phi= \dfrac{8 S_3 }{25} +\end{equation} +\begin{equation} + \dfrac{d^3\Gamma}{\Gamma dcos\theta_k dcos\theta_l d\phi } sin 2 \theta_k sin 2 \theta_k cos\phi= \dfrac{8 S_4 }{25} +\end{equation} +\begin{equation} + \dfrac{d^3\Gamma}{\Gamma dcos\theta_k dcos\theta_l d\phi }sin2\theta_k sin\theta_l cos\phi = \dfrac{2 S_5 }{5} +\end{equation} +\begin{equation} + \dfrac{d^3\Gamma}{\Gamma dcos\theta_k dcos\theta_l d\phi} sin 2 \theta_k sin \theta_l sin \phi = \dfrac{2 S_7 }{5} +\end{equation} +\begin{equation} + \dfrac{d^3\Gamma}{\Gamma dcos\theta_k dcos\theta_l d\phi} sin 2 \theta_k sin2 \theta_l sin \phi = \dfrac{8 S_8 }{25} +\end{equation} + + + +\end{frame} +\begin{frame}\frametitle{Moments for $\PB \to \PKstar \mu \mu$} +{~} +\begin{itemize} +\item The simplest solution one could imagine. +\item We are abusing the fact that the basis is orthogonal. +\item Each of the J doesn't know about other. +\item Only $S_{1s}$, $S_{2s}$, $S_{1c}$, $S_{2c}$ and $S_{6s}$, $S_{6c}$ are not orthogonal, but to get the answer you just need to solve a linear equation system so it's not a tragedy. +\end{itemize} +\begin{equation} + \dfrac{d^3\Gamma}{\Gamma dcos\theta_k dcos\theta_l d\phi} sin^2 \theta_k cos \theta_l = 0.1(S_6c+4S_6s) +\end{equation} +\begin{equation} + \dfrac{d^3\Gamma}{\Gamma dcos\theta_k dcos\theta_l d\phi} cos \theta_l = 0.25(S_{6}c+2S_{6s}) +\end{equation} + +solution: $S_{6c}=2 (4 M_{S_{6c}} - 5 M_{S_{6s}})$, $S_{6s}= -2 M_{S_{6c}} + 5 M_{S_{6s}}$ + + + +\end{frame} + + + +\section{Toy MC study} + +\begin{frame}\frametitle{Moments for $\PB \to \PKstar \mu \mu$} +{~} +Lets see if this method actually works. Let's take some random parameters for the PDF and make a toy. +\begin{columns} +\column{2.5in} +\includegraphics[scale=0.25]{images/J5.png} + + + +\column{2.5in} +\includegraphics[scale=0.25]{images/J7.png} + + +\end{columns} +\begin{itemize} +\item let's take 300 signal events as a working case. +\end{itemize} + +\end{frame} + + + + +\begin{frame}\frametitle{Moments for $\PB \to \PKstar \mu \mu$} +{~} +\small Lets see if this method actually works. Let's take some random parameters for the PDF and make a toy. +\begin{columns} +\column{2.5in} +\includegraphics[scale=0.25]{images/J3.png} + + + +\column{2.5in} +\includegraphics[scale=0.25]{images/J4.png} + + +\end{columns} + + +\begin{itemize} +\item let's take 300 signal events as a working case... we might still change the binning +\end{itemize} + +\end{frame} + + + +\begin{frame}\frametitle{Moments for $\PB \to \PKstar \mu \mu$} +{~} +Lets see if this method actually works. Let's take some random parameters for the PDF and make a toy. +\begin{columns} +\column{2.5in} +\includegraphics[scale=0.25]{images/J8.png} + + + +\column{2.5in} +\includegraphics[scale=0.25]{images/J9.png} + + +\end{columns} + +\begin{itemize} +\item let's take 300 signal events as a working case... we might still change the binning +\end{itemize} + +\end{frame} + +\begin{frame}\frametitle{Error Estimation} +{~} +\begin{itemize} +\item Since moment is the mean of a given distribution the error can be estimated as $mean/RMS$ +\item use TOY MC to check this assumption +\end{itemize} + +\includegraphics[scale=0.3]{plots/conw.png}\\ + + +\end{frame} +%%%%%%%%%%%%%%%%%%%%%%%%5 +\begin{frame}\frametitle{Correlation check} +{~} +\begin{itemize} +\item In theory $S_i$ shouldn't be correlated to $S_j$ in the moment calculation. +\item Lets put this to a test. +\end{itemize} + +\begin{columns} +\column{2.5in} +\includegraphics[scale=0.2]{plots/J9J4.png}\\ + + +\column{2.5in} +\includegraphics[scale=0.2]{plots/J8J5.png}\\ + + +\end{columns} + + +\end{frame} + + +%%%%%%%%%%%%%%%%%%%%%%%%5 +\begin{frame}\frametitle{Correlation check 2} +{~} +\begin{itemize} +\item Let's now FIX $J_x$ and simulate different $J_y$ +\item Again theory would suggest that one J shouldn't know about the other, so $J_x$ shouldn't change with scanning $J_y$ parameter +\end{itemize} + +\begin{columns} +\column{2.5in} +\includegraphics[scale=0.24]{plots/J5_vs_J9_300.png}\\ + + +\column{2.5in} +\includegraphics[scale=0.24]{plots/J3_vs_J9_300.png}\\ + + +\end{columns} + + +\end{frame} + + + +\section{2 am discovery} +\begin{frame}\frametitle{What will happen to our problem with an S-wave?} +{~} +Reminder: +\begin{multline} +\dfrac{d^4\Gamma}{dq^2 dcos\theta_k dcos\theta_l d\phi}=\dfrac{9}{32\pi}( J_{1s}sin^2 \theta_k + J_{1c}cos^2 \theta_k + (J_{2s}sin^2 \theta_k + \\ J_{2c}cos^2) cos 2\theta_l + J_3 sin^2 \theta_k sin^2 \theta_l cos2\phi + J_4 sin2 \theta_k sin \theta_l cos\phi +\\ J_5 sin2 \theta_k sin \theta_l cos \phi + (J_{6s} sin^2 \theta_k + J_{6c} cos^2 \theta_k) cos \theta_l + \\ J_7 sin 2\theta_k sin \theta_l sin \phi + J_8 sin 2 \theta_k sin 2 \theta_l sin phi + J_9 sin^2 \theta_k sin^2 \theta_l sin 2 \phi) +\end{multline} +Let's add a very discussing things that keeps us awake at night: +\begin{multline} +W_s =\dfrac{2}{3} F_s \sin^2 \theta_l + \frac{4}{3} A_s \sin^2 \theta_l \cos \theta_k + I_4 sin \theta_k sin 2 \theta_lcos \phi \\+ I_5 sin \theta_k sin \theta_l cos \phi + I_7 sin \theta_k sin \theta_l + sin \phi + I_8 sin \theta_k sin 2\theta_l sin\phi) +\end{multline} + + +\end{frame} + +\begin{frame}\frametitle{What will happen to our problem with an S-wave?} +{~} +So now our PDF is sum of eq. 15 and 16. Of coz we need to require normalization: +\begin{equation} +\dfrac{1}{12}(32 I_{1a} + 9 J_{1c} + 18 J_{1s} - 3 J_{2c} - 6 J_{2s}) =1 +\end{equation} +No surprises here. If we have a S-wave it has to enter in $\Gamma$. +To build up the preasure, what will happen to our Ss? + + + +\end{frame} + + +\begin{frame}\frametitle{NOTHING!!!!!!!!} +{~} +We are completely insensitive to S-wave: +\begin{equation} + \dfrac{d^3\Gamma}{\Gamma dcos\theta_k dcos\theta_l d\phi }sin^2 \theta_k sin^2 \theta_l cos 2 \phi= \dfrac{8 S_3 }{25} +\end{equation} +\begin{equation} + \dfrac{d^3\Gamma}{\Gamma dcos\theta_k dcos\theta_l d\phi } sin 2 \theta_k sin 2 \theta_k cos\phi= \dfrac{8 S_4 }{25} +\end{equation} +\begin{equation} + \dfrac{d^3\Gamma}{\Gamma dcos\theta_k dcos\theta_l d\phi }sin2\theta_k sin\theta_l cos\phi = \dfrac{2 S_5 }{5} +\end{equation} +\begin{equation} + \dfrac{d^3\Gamma}{\Gamma dcos\theta_k dcos\theta_l d\phi} sin 2 \theta_k sin \theta_l sin \phi = \dfrac{2 S_7 }{5} +\end{equation} +\begin{equation} + \dfrac{d^3\Gamma}{\Gamma dcos\theta_k dcos\theta_l d\phi} sin 2 \theta_k sin2 \theta_l sin \phi = \dfrac{8 S_8 }{25} +\end{equation} + + + +\end{frame} + +\begin{frame}\frametitle{Thins get better :)} +{~} +We can even measure directly the S-wave: +\begin{equation} + \dfrac{d^3\Gamma}{\Gamma dcos\theta_k dcos\theta_l d\phi }sin^2 \theta_l cos \theta_k = \dfrac{32 I_{1b} }{45} +\end{equation} +\begin{equation} + \dfrac{d^3\Gamma}{\Gamma dcos\theta_k dcos\theta_l d\phi } sin \theta_k sin 2 \theta_l cos \phi = \dfrac{16 I_4 }{45} +\end{equation} +\begin{equation} + \dfrac{d^3\Gamma}{\Gamma dcos\theta_k dcos\theta_l d\phi } sin\theta_k sin\theta_l cos\phi = \dfrac{4 I_5 }{9} +\end{equation} +\begin{equation} + \dfrac{d^3\Gamma}{\Gamma dcos\theta_k dcos\theta_l d\phi} sin \theta_k sin 2 \theta_l sin \phi = \dfrac{4 I_7 }{9} +\end{equation} +\begin{equation} + \dfrac{d^3\Gamma}{\Gamma dcos\theta_k dcos\theta_l d\phi} sin \theta_k sin2 \theta_l sin \phi = \dfrac{16 S_8 }{45} +\end{equation} + + + +\end{frame} + + +\begin{frame}\frametitle{Conclusions on S-wave} +{~} +\begin{itemize} +\item S-wave components are transparent to method of moments. +\item If they are orthogonal to others all they toy studies holds for them as well(will reapat for robustness but can bet my house that there is nothing going on there). +\item +\end{itemize} + +\end{frame} + + + +\begin{frame}\frametitle{Conclusions} +{~} +\begin{itemize} +\item Implemented moments method for the K*mm and start testing with toy MC +\item The method converge fast and works for the "simple case", i.e. signal only. +\item Method completely insensitive to S-wave component, thanks to orthogonality. +\item Complementary one can measure in-depended S-wave component. +\end{itemize} +TO DO: +\begin{itemize} +\item add realism: backgrounds +\item Do the unfolding +\item Study binning +\end{itemize} + +\end{frame} +%%%%%%%%%%%%%%%%%%%%%%%%%55 +\begin{frame}\frametitle{~} +{~} +\center \Huge BACKUPS + +\end{frame} + +\begin{frame} +{~} + +\begin{columns} +\column{2.5in} +\includegraphics[scale=0.17]{plots/pool_plots/J1c_50.png}\\ +\includegraphics[scale=0.17]{plots/pool_plots/J1c_75.png}\\ + + +\column{2.5in} +\includegraphics[scale=0.17]{plots/pool_plots/J1c_50E.png}\\ +\includegraphics[scale=0.17]{plots/pool_plots/J1c_75E.png} + + +\end{columns} +\end{frame} + +\begin{frame} +{~} + +\begin{columns} +\column{2.5in} +\includegraphics[scale=0.17]{plots/pool_plots/J1c_125.png}\\ +\includegraphics[scale=0.17]{plots/pool_plots/J1c_175.png}\\ + + +\column{2.5in} +\includegraphics[scale=0.17]{plots/pool_plots/J1c_125E.png}\\ +\includegraphics[scale=0.17]{plots/pool_plots/J1c_175E.png} + + +\end{columns} +\end{frame} + +\begin{frame} +{~} + +\begin{columns} +\column{2.5in} +\includegraphics[scale=0.17]{plots/pool_plots/J1c_225.png}\\ +\includegraphics[scale=0.17]{plots/pool_plots/J1c_300.png}\\ + + +\column{2.5in} +\includegraphics[scale=0.17]{plots/pool_plots/J1c_225E.png}\\ +\includegraphics[scale=0.17]{plots/pool_plots/J1c_300E.png} + + +\end{columns} +\end{frame} + + +\begin{frame} +{~} + +\begin{columns} +\column{2.5in} +\includegraphics[scale=0.17]{plots/pool_plots/J1c_400.png}\\ + + + +\column{2.5in} +\includegraphics[scale=0.17]{plots/pool_plots/J1c_400E.png}\\ + + + +\end{columns} +\end{frame} + +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%55 +\begin{frame} +{~} + +\begin{columns} +\column{2.5in} +\includegraphics[scale=0.17]{plots/pool_plots/J1s_50.png}\\ +\includegraphics[scale=0.17]{plots/pool_plots/J1s_75.png}\\ + + +\column{2.5in} +\includegraphics[scale=0.17]{plots/pool_plots/J1s_50E.png}\\ +\includegraphics[scale=0.17]{plots/pool_plots/J1s_75E.png} + + +\end{columns} +\end{frame} + +\begin{frame} +{~} + +\begin{columns} +\column{2.5in} +\includegraphics[scale=0.17]{plots/pool_plots/J1s_125.png}\\ +\includegraphics[scale=0.17]{plots/pool_plots/J1s_175.png}\\ + + +\column{2.5in} +\includegraphics[scale=0.17]{plots/pool_plots/J1s_125E.png}\\ +\includegraphics[scale=0.17]{plots/pool_plots/J1s_175E.png} + + +\end{columns} +\end{frame} + +\begin{frame} +{~} + +\begin{columns} +\column{2.5in} +\includegraphics[scale=0.17]{plots/pool_plots/J1s_225.png}\\ +\includegraphics[scale=0.17]{plots/pool_plots/J1s_300.png}\\ + + +\column{2.5in} +\includegraphics[scale=0.17]{plots/pool_plots/J1s_225E.png}\\ +\includegraphics[scale=0.17]{plots/pool_plots/J1s_300E.png} + + +\end{columns} +\end{frame} + + +\begin{frame} +{~} + +\begin{columns} +\column{2.5in} +\includegraphics[scale=0.17]{plots/pool_plots/J1s_400.png}\\ + + + +\column{2.5in} +\includegraphics[scale=0.17]{plots/pool_plots/J1s_400E.png}\\ + + + +\end{columns} +\end{frame} + +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +\begin{frame} +{~} + +\begin{columns} +\column{2.5in} +\includegraphics[scale=0.17]{plots/pool_plots/J2c_50.png}\\ +\includegraphics[scale=0.17]{plots/pool_plots/J2c_75.png}\\ + + +\column{2.5in} +\includegraphics[scale=0.17]{plots/pool_plots/J2c_50E.png}\\ +\includegraphics[scale=0.17]{plots/pool_plots/J2c_75E.png} + + +\end{columns} +\end{frame} + +\begin{frame} +{~} + +\begin{columns} +\column{2.5in} +\includegraphics[scale=0.17]{plots/pool_plots/J2c_125.png}\\ +\includegraphics[scale=0.17]{plots/pool_plots/J2c_175.png}\\ + + +\column{2.5in} +\includegraphics[scale=0.17]{plots/pool_plots/J2c_125E.png}\\ +\includegraphics[scale=0.17]{plots/pool_plots/J2c_175E.png} + + +\end{columns} +\end{frame} + +\begin{frame} +{~} + +\begin{columns} +\column{2.5in} +\includegraphics[scale=0.17]{plots/pool_plots/J2c_225.png}\\ +\includegraphics[scale=0.17]{plots/pool_plots/J2c_300.png}\\ + + +\column{2.5in} +\includegraphics[scale=0.17]{plots/pool_plots/J2c_225E.png}\\ +\includegraphics[scale=0.17]{plots/pool_plots/J2c_300E.png} + + +\end{columns} +\end{frame} + + +\begin{frame} +{~} + +\begin{columns} +\column{2.5in} +\includegraphics[scale=0.17]{plots/pool_plots/J2c_400.png}\\ +\includegraphics[scale=0.17]{plots/pool_plots/J2c_500.png}\\ + + +\column{2.5in} +\includegraphics[scale=0.17]{plots/pool_plots/J2c_400E.png}\\ +\includegraphics[scale=0.17]{plots/pool_plots/J2c_500E.png}\\ + + +\end{columns} +\end{frame} + + +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +\begin{frame} +{~} + +\begin{columns} +\column{2.5in} +\includegraphics[scale=0.17]{plots/pool_plots/J3_50.png}\\ +\includegraphics[scale=0.17]{plots/pool_plots/J3_75.png}\\ + + +\column{2.5in} +\includegraphics[scale=0.17]{plots/pool_plots/J3_50E.png}\\ +\includegraphics[scale=0.17]{plots/pool_plots/J3_75E.png} + + +\end{columns} +\end{frame} + +\begin{frame} +{~} + +\begin{columns} +\column{2.5in} +\includegraphics[scale=0.17]{plots/pool_plots/J3_125.png}\\ +\includegraphics[scale=0.17]{plots/pool_plots/J3_175.png}\\ + + +\column{2.5in} +\includegraphics[scale=0.17]{plots/pool_plots/J3_125E.png}\\ +\includegraphics[scale=0.17]{plots/pool_plots/J3_175E.png} + + +\end{columns} +\end{frame} + +\begin{frame} +{~} + +\begin{columns} +\column{2.5in} +\includegraphics[scale=0.17]{plots/pool_plots/J3_225.png}\\ +\includegraphics[scale=0.17]{plots/pool_plots/J3_300.png}\\ + + +\column{2.5in} +\includegraphics[scale=0.17]{plots/pool_plots/J3_225E.png}\\ +\includegraphics[scale=0.17]{plots/pool_plots/J3_300E.png} + + +\end{columns} +\end{frame} + + +\begin{frame} +{~} + +\begin{columns} +\column{2.5in} +\includegraphics[scale=0.17]{plots/pool_plots/J3_400.png}\\ +\includegraphics[scale=0.17]{plots/pool_plots/J3_500.png}\\ + + +\column{2.5in} +\includegraphics[scale=0.17]{plots/pool_plots/J3_400E.png}\\ +\includegraphics[scale=0.17]{plots/pool_plots/J3_500E.png}\\ + + +\end{columns} +\end{frame} + + + +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +\begin{frame} +{~} + +\begin{columns} +\column{2.5in} +\includegraphics[scale=0.17]{plots/pool_plots/J4_50.png}\\ +\includegraphics[scale=0.17]{plots/pool_plots/J4_75.png}\\ + + +\column{2.5in} +\includegraphics[scale=0.17]{plots/pool_plots/J4_50E.png}\\ +\includegraphics[scale=0.17]{plots/pool_plots/J4_75E.png} + + +\end{columns} +\end{frame} + +\begin{frame} +{~} + +\begin{columns} +\column{2.5in} +\includegraphics[scale=0.17]{plots/pool_plots/J4_125.png}\\ +\includegraphics[scale=0.17]{plots/pool_plots/J4_175.png}\\ + + +\column{2.5in} +\includegraphics[scale=0.17]{plots/pool_plots/J4_125E.png}\\ +\includegraphics[scale=0.17]{plots/pool_plots/J4_175E.png} + + +\end{columns} +\end{frame} + +\begin{frame} +{~} + +\begin{columns} +\column{2.5in} +\includegraphics[scale=0.17]{plots/pool_plots/J4_225.png}\\ +\includegraphics[scale=0.17]{plots/pool_plots/J4_300.png}\\ + + +\column{2.5in} +\includegraphics[scale=0.17]{plots/pool_plots/J4_225E.png}\\ +\includegraphics[scale=0.17]{plots/pool_plots/J4_300E.png} + + +\end{columns} +\end{frame} + + +\begin{frame} +{~} + +\begin{columns} +\column{2.5in} +\includegraphics[scale=0.17]{plots/pool_plots/J4_400.png}\\ +\includegraphics[scale=0.17]{plots/pool_plots/J4_500.png}\\ + + +\column{2.5in} +\includegraphics[scale=0.17]{plots/pool_plots/J4_400E.png}\\ +\includegraphics[scale=0.17]{plots/pool_plots/J4_500E.png}\\ + + +\end{columns} +\end{frame} + + + +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +\begin{frame} +{~} + +\begin{columns} +\column{2.5in} +\includegraphics[scale=0.17]{plots/pool_plots/J5_50.png}\\ +\includegraphics[scale=0.17]{plots/pool_plots/J5_75.png}\\ + + +\column{2.5in} +\includegraphics[scale=0.17]{plots/pool_plots/J5_50E.png}\\ +\includegraphics[scale=0.17]{plots/pool_plots/J5_75E.png} + + +\end{columns} +\end{frame} + +\begin{frame} +{~} + +\begin{columns} +\column{2.5in} +\includegraphics[scale=0.17]{plots/pool_plots/J5_125.png}\\ +\includegraphics[scale=0.17]{plots/pool_plots/J5_175.png}\\ + + +\column{2.5in} +\includegraphics[scale=0.17]{plots/pool_plots/J5_125E.png}\\ +\includegraphics[scale=0.17]{plots/pool_plots/J5_175E.png} + + +\end{columns} +\end{frame} + +\begin{frame} +{~} + +\begin{columns} +\column{2.5in} +\includegraphics[scale=0.17]{plots/pool_plots/J5_225.png}\\ +\includegraphics[scale=0.17]{plots/pool_plots/J5_300.png}\\ + + +\column{2.5in} +\includegraphics[scale=0.17]{plots/pool_plots/J5_225E.png}\\ +\includegraphics[scale=0.17]{plots/pool_plots/J5_300E.png} + + +\end{columns} +\end{frame} + + +\begin{frame} +{~} + +\begin{columns} +\column{2.5in} +\includegraphics[scale=0.17]{plots/pool_plots/J5_400.png}\\ +\includegraphics[scale=0.17]{plots/pool_plots/J5_500.png}\\ + + +\column{2.5in} +\includegraphics[scale=0.17]{plots/pool_plots/J5_400E.png}\\ +\includegraphics[scale=0.17]{plots/pool_plots/J5_500E.png}\\ + + +\end{columns} +\end{frame} + + +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +\begin{frame} +{~} + +\begin{columns} +\column{2.5in} +\includegraphics[scale=0.17]{plots/pool_plots/J7_50.png}\\ +\includegraphics[scale=0.17]{plots/pool_plots/J7_75.png}\\ + + +\column{2.5in} +\includegraphics[scale=0.17]{plots/pool_plots/J7_50E.png}\\ +\includegraphics[scale=0.17]{plots/pool_plots/J7_75E.png} + + +\end{columns} +\end{frame} + +\begin{frame} +{~} + +\begin{columns} +\column{2.5in} +\includegraphics[scale=0.17]{plots/pool_plots/J7_125.png}\\ +\includegraphics[scale=0.17]{plots/pool_plots/J7_175.png}\\ + + +\column{2.5in} +\includegraphics[scale=0.17]{plots/pool_plots/J7_125E.png}\\ +\includegraphics[scale=0.17]{plots/pool_plots/J7_175E.png} + + +\end{columns} +\end{frame} + +\begin{frame} +{~} + +\begin{columns} +\column{2.5in} +\includegraphics[scale=0.17]{plots/pool_plots/J7_225.png}\\ +\includegraphics[scale=0.17]{plots/pool_plots/J7_300.png}\\ + + +\column{2.5in} +\includegraphics[scale=0.17]{plots/pool_plots/J7_225E.png}\\ +\includegraphics[scale=0.17]{plots/pool_plots/J7_300E.png} + + +\end{columns} +\end{frame} + + +\begin{frame} +{~} + +\begin{columns} +\column{2.5in} +\includegraphics[scale=0.17]{plots/pool_plots/J7_400.png}\\ +\includegraphics[scale=0.17]{plots/pool_plots/J7_500.png}\\ + + +\column{2.5in} +\includegraphics[scale=0.17]{plots/pool_plots/J7_400E.png}\\ +\includegraphics[scale=0.17]{plots/pool_plots/J7_500E.png}\\ + + +\end{columns} +\end{frame} + + +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +\begin{frame} +{~} + +\begin{columns} +\column{2.5in} +\includegraphics[scale=0.17]{plots/pool_plots/J8_50.png}\\ +\includegraphics[scale=0.17]{plots/pool_plots/J8_75.png}\\ + + +\column{2.5in} +\includegraphics[scale=0.17]{plots/pool_plots/J8_50E.png}\\ +\includegraphics[scale=0.17]{plots/pool_plots/J8_75E.png} + + +\end{columns} +\end{frame} + +\begin{frame} +{~} + +\begin{columns} +\column{2.5in} +\includegraphics[scale=0.17]{plots/pool_plots/J8_125.png}\\ +\includegraphics[scale=0.17]{plots/pool_plots/J8_175.png}\\ + + +\column{2.5in} +\includegraphics[scale=0.17]{plots/pool_plots/J8_125E.png}\\ +\includegraphics[scale=0.17]{plots/pool_plots/J8_175E.png} + + +\end{columns} +\end{frame} + +\begin{frame} +{~} + +\begin{columns} +\column{2.5in} +\includegraphics[scale=0.17]{plots/pool_plots/J8_225.png}\\ 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+\end{frame} + +\begin{frame} +{~} + +\begin{columns} +\column{2.5in} +\includegraphics[scale=0.17]{plots/pool_plots/J9_125.png}\\ +\includegraphics[scale=0.17]{plots/pool_plots/J9_175.png}\\ + + +\column{2.5in} +\includegraphics[scale=0.17]{plots/pool_plots/J9_125E.png}\\ +\includegraphics[scale=0.17]{plots/pool_plots/J9_175E.png} + + +\end{columns} +\end{frame} + +\begin{frame} +{~} + +\begin{columns} +\column{2.5in} +\includegraphics[scale=0.17]{plots/pool_plots/J9_225.png}\\ +\includegraphics[scale=0.17]{plots/pool_plots/J9_300.png}\\ + + +\column{2.5in} +\includegraphics[scale=0.17]{plots/pool_plots/J9_225E.png}\\ +\includegraphics[scale=0.17]{plots/pool_plots/J9_300E.png} + + +\end{columns} +\end{frame} + + +\begin{frame} +{~} + +\begin{columns} +\column{2.5in} +\includegraphics[scale=0.17]{plots/pool_plots/J9_400.png}\\ +\includegraphics[scale=0.17]{plots/pool_plots/J9_500.png}\\ + + +\column{2.5in} +\includegraphics[scale=0.17]{plots/pool_plots/J9_400E.png}\\ +\includegraphics[scale=0.17]{plots/pool_plots/J9_500E.png}\\ + + +\end{columns} +\end{frame} + +%%%%%%%%%%%%%%%%%%%%%%% +\begin{frame} +{~} + +\begin{columns} +\column{2.5in} +\includegraphics[scale=0.2]{plots/J9J8.png}\\ +\includegraphics[scale=0.2]{plots/J9J5.png}\\ + +\column{2.5in} +\includegraphics[scale=0.2]{plots/J9J7.png}\\ +\includegraphics[scale=0.2]{plots/J9J4.png}\\ + +\end{columns} + +\end{frame} + +\begin{frame} +{~} + +\begin{columns} +\column{2.5in} +\includegraphics[scale=0.2]{plots/J9J3.png}\\ +\includegraphics[scale=0.2]{plots/J8J7.png}\\ + +\column{2.5in} +\includegraphics[scale=0.2]{plots/J8J5.png}\\ +\includegraphics[scale=0.2]{plots/J8J4.png}\\ + +\end{columns} + +\end{frame} + + + + + + +\end{document} \ No newline at end of file diff --git a/tauola/Bug1/MM.toc b/tauola/Bug1/MM.toc new file mode 100644 index 0000000..77ff2e8 --- /dev/null +++ b/tauola/Bug1/MM.toc @@ -0,0 +1,6 @@ +\beamer@endinputifotherversion {3.10pt} +\beamer@sectionintoc {2}{Introduction}{3}{0}{1} +\beamer@sectionintoc {3}{Method of Moments - Theory}{4}{0}{2} +\beamer@sectionintoc {4}{Moments of Ss}{6}{0}{3} +\beamer@sectionintoc {5}{Toy MC study}{10}{0}{4} +\beamer@sectionintoc {6}{2 am discovery}{16}{0}{5} diff --git a/tauola/Bug1/MM_v2.toc b/tauola/Bug1/MM_v2.toc new file mode 100644 index 0000000..bedbea4 --- /dev/null +++ b/tauola/Bug1/MM_v2.toc @@ -0,0 +1,7 @@ +\beamer@endinputifotherversion {3.10pt} +\select@language {english} +\beamer@sectionintoc {1}{Introduction}{4}{0}{1} +\beamer@sectionintoc {2}{Method of Moments - Theory}{5}{0}{2} +\beamer@sectionintoc {3}{Moments of Ss}{7}{0}{3} +\beamer@sectionintoc {4}{Toy MC study}{12}{0}{4} +\beamer@sectionintoc {5}{S-wave}{16}{0}{5} diff --git a/tauola/Bug1/MMatrix.aux b/tauola/Bug1/MMatrix.aux new file mode 100644 index 0000000..3a81bc2 --- /dev/null +++ b/tauola/Bug1/MMatrix.aux @@ -0,0 +1,36 @@ +\relax +\ifx\hyper@anchor\@undefined +\global \let \oldcontentsline\contentsline +\gdef 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@@ +\documentclass[xcolor=svgnames]{beamer} +\usepackage[utf8]{inputenc} +\usepackage[english]{babel} +\usepackage{polski} +%\usepackage{amssymb,amsmath} +%\usepackage[latin1]{inputenc} +%\usepackage{amsmath} +%\newcommand\abs[1]{\left|#1\right|} +\usepackage{amsmath} +\newcommand\abs[1]{\left|#1\right|} +\usepackage{hepnicenames} +\usepackage{hepunits} +\usepackage{color} + +\setbeamertemplate{footline}{\insertframenumber/\inserttotalframenumber} +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%5 +\definecolor{mygreen}{cmyk}{0.82,0.11,1,0.25} + + +\usetheme{Sybila} + +\title[Tauola LFV tests]{Tauola LFV tests} +\author{Marcin Chrz\k{a}szcz$^{1,2}$} +\institute{$^1$~University of Zurich,\\ $^2$~Institute of Nuclear Physics, Krakow} +\date{\today} +\begin{document} +% --------------------------- SLIDE -------------------------------------------- +%\frame[plain]{\titlepage} +\author{Marcin Chrz\k{a}szcz} +% ------------------------------------------------------------------------------ +% --------------------------- SLIDE -------------------------------------------- + +\institute{~(UZH, IFJ)} + + + +\begin{frame}\frametitle{Theory vs Generator $\Gamma_{LLLL}$} +For theory see: \href{http:/0707.0988.pdf}{0707.0988} +\begin{figure} +\includegraphics[width=0.45\textwidth]{plots/vllll_mmm.pdf} +\includegraphics[width=0.45\textwidth]{plots_tauola/LLLL.pdf}\\ +\end{figure} + + +\end{frame} + +\begin{frame}\frametitle{Theory vs Generator $\Gamma_{LLRR}$} +For theory see: \href{http:/0707.0988.pdf}{0707.0988} +\begin{figure} +\includegraphics[width=0.45\textwidth]{plots/vllrr_mmm.pdf} +\includegraphics[width=0.45\textwidth]{plots_tauola/LLRR.pdf}\\ +\end{figure} + + +\end{frame} + + + +\begin{frame}\frametitle{Theory vs Generator $\Gamma_{rad}$} +For theory see: \href{http:/0707.0988.pdf}{0707.0988} +\begin{figure} +\includegraphics[width=0.45\textwidth]{plots/radlr_mmm.pdf} +\includegraphics[width=0.45\textwidth]{plots_tauola/RAD.pdf}\\ +\end{figure} + + +\end{frame} + + +\begin{frame}\frametitle{Theory vs Generator $\Gamma_{rad}^{LL}$} +For theory see: \href{http:/0707.0988.pdf}{0707.0988} +\begin{figure} +\includegraphics[width=0.45\textwidth]{plots/mixlrll_mmm.pdf} +\includegraphics[width=0.45\textwidth]{plots_tauola/LLLLRAD.pdf}\\ +\end{figure} + + +\end{frame} + + +\begin{frame}\frametitle{Theory vs Generator $\Gamma_{rad}^{LR}$} +For theory see: \href{http:/0707.0988.pdf}{0707.0988} +\begin{figure} +\includegraphics[width=0.45\textwidth]{plots/mixlrrr_mmm.pdf} +\includegraphics[width=0.45\textwidth]{plots_tauola/LLRRRAD.pdf}\\ +\end{figure} + + +\end{frame} + + +\begin{frame}\frametitle{Conclusion} +\begin{itemize} +\item All modes are ok. +\end{itemize} + + +\end{frame} + + +\end{document} diff --git a/tauola/Bug1/MMatrix.toc b/tauola/Bug1/MMatrix.toc new file mode 100644 index 0000000..495658f --- /dev/null +++ b/tauola/Bug1/MMatrix.toc @@ -0,0 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false charpath + 5 index 5 index rmoveto + 6 index eq { 7 index 7 index rmoveto } if + } exch cshow2 + 6 {pop} repeat +} def +/Tj { + fCol + 1 index stringwidth pdfTextMat idtransform pop + sub 1 index length dup 0 ne { div } { pop pop 0 } ifelse + pdfWordSpacing pdfHorizScaling mul 0 pdfTextMat dtransform 32 + 4 3 roll pdfCharSpacing pdfHorizScaling mul add 0 + pdfTextMat dtransform + 6 5 roll Tj1 +} def +/Tj16 { + fCol + 2 index stringwidth pdfTextMat idtransform pop + sub exch div + pdfWordSpacing pdfHorizScaling mul 0 pdfTextMat dtransform 32 + 4 3 roll pdfCharSpacing pdfHorizScaling mul add 0 + pdfTextMat dtransform + 6 5 roll Tj1 +} def +/Tj16V { + fCol + 2 index stringwidth pdfTextMat idtransform exch pop + sub exch div + 0 pdfWordSpacing pdfTextMat dtransform 32 + 4 3 roll pdfCharSpacing add 0 exch + pdfTextMat dtransform + 6 5 roll Tj1 +} def +/Tj1 { + 0 pdfTextRise pdfTextMat dtransform rmoveto + currentpoint 8 2 roll + pdfTextRender 1 and 0 eq { + 6 copy awidthshow + } if + 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false charpath + 5 index 5 index rmoveto + 6 index eq { 7 index 7 index rmoveto } if + } exch cshow2 + 6 {pop} repeat +} def +/Tj { + fCol + 1 index stringwidth pdfTextMat idtransform pop + sub 1 index length dup 0 ne { div } { pop pop 0 } ifelse + pdfWordSpacing pdfHorizScaling mul 0 pdfTextMat dtransform 32 + 4 3 roll pdfCharSpacing pdfHorizScaling mul add 0 + pdfTextMat dtransform + 6 5 roll Tj1 +} def +/Tj16 { + fCol + 2 index stringwidth pdfTextMat idtransform pop + sub exch div + pdfWordSpacing pdfHorizScaling mul 0 pdfTextMat dtransform 32 + 4 3 roll pdfCharSpacing pdfHorizScaling mul add 0 + pdfTextMat dtransform + 6 5 roll Tj1 +} def +/Tj16V { + fCol + 2 index stringwidth pdfTextMat idtransform exch pop + sub exch div + 0 pdfWordSpacing pdfTextMat dtransform 32 + 4 3 roll pdfCharSpacing add 0 exch + pdfTextMat dtransform + 6 5 roll Tj1 +} def +/Tj1 { + 0 pdfTextRise pdfTextMat dtransform rmoveto + currentpoint 8 2 roll + pdfTextRender 1 and 0 eq { + 6 copy awidthshow + } if + 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index 6 index 4 index funcSH + 5 3 roll 3 2 roll funcSH pop pop + } { + pop 3 index 2 index add 0.5 mul 3 index 2 index add 0.5 mul + funcCol sc + dup 4 index exch mat transform m + 3 index 3 index mat transform l + 1 index 3 index mat transform l + mat transform l pop pop h f* + } ifelse +} def +/axialCol { + dup 0 lt { + pop t0 + } { + dup 1 gt { + pop t1 + } { + dt mul t0 add + } ifelse + } ifelse + func n array astore +} def +/axialSH { + dup 0 eq { + true + } { + dup 8 eq { + false + } { + 2 index axialCol 2 index axialCol colordelta + } ifelse + } ifelse + { + 1 add 3 1 roll 2 copy add 0.5 mul + dup 4 3 roll exch 4 index axialSH + exch 3 2 roll axialSH + } { + pop 2 copy add 0.5 mul axialCol sc + exch dup dx mul x0 add exch dy mul y0 add + 3 2 roll dup dx mul x0 add exch dy mul y0 add + dx abs dy abs ge { + 2 copy yMin sub dy mul dx div add yMin m + yMax sub dy mul dx div add yMax l + 2 copy yMax sub dy mul dx div add yMax l + yMin sub dy mul dx div add yMin l + h f* + } { + exch 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def +/Tj16 { + fCol + 2 index stringwidth pdfTextMat idtransform pop + sub exch div + pdfWordSpacing pdfHorizScaling mul 0 pdfTextMat dtransform 32 + 4 3 roll pdfCharSpacing pdfHorizScaling mul add 0 + pdfTextMat dtransform + 6 5 roll Tj1 +} def +/Tj16V { + fCol + 2 index stringwidth pdfTextMat idtransform exch pop + sub exch div + 0 pdfWordSpacing pdfTextMat dtransform 32 + 4 3 roll pdfCharSpacing add 0 exch + pdfTextMat dtransform + 6 5 roll Tj1 +} def +/Tj1 { + 0 pdfTextRise pdfTextMat dtransform rmoveto + currentpoint 8 2 roll + pdfTextRender 1 and 0 eq { + 6 copy awidthshow + } if + pdfTextRender 3 and dup 1 eq exch 2 eq or { + 7 index 7 index moveto + 6 copy + currentfont /FontType get 3 eq { fCol } { sCol } ifelse + false awcp currentpoint stroke moveto + } if + pdfTextRender 4 and 0 ne { + 8 6 roll moveto + false awcp + /pdfTextClipPath [ pdfTextClipPath aload pop + {/moveto cvx} + {/lineto cvx} + {/curveto cvx} + {/closepath cvx} + pathforall ] def + currentpoint newpath moveto + } { + 8 {pop} repeat + } ifelse + 0 pdfTextRise neg pdfTextMat dtransform rmoveto +} def +/TJm { pdfFontSize 0.001 mul mul neg 0 + pdfTextMat dtransform rmoveto } def +/TJmV { pdfFontSize 0.001 mul mul neg 0 exch + pdfTextMat dtransform rmoveto } def +/Tclip { pdfTextClipPath cvx exec clip newpath + /pdfTextClipPath [] def } def +% Level 2 image operators +/pdfImBuf 100 string def +/pdfIm { + image + { currentfile pdfImBuf readline + not { pop exit } if + (%-EOD-) eq { exit } if } loop +} def +/pdfImM { + fCol imagemask + { currentfile pdfImBuf readline + not { pop exit } if + (%-EOD-) eq { exit } if } loop +} def +/pdfImClip { + gsave + 0 2 4 index length 1 sub { + dup 4 index exch 2 copy + get 5 index div put + 1 add 3 index exch 2 copy + get 3 index div put + } for + pop pop rectclip +} def +/pdfImClipEnd { grestore } def +% shading operators +/colordelta { + false 0 1 3 index length 1 sub { + dup 4 index exch get 3 index 3 2 roll get sub abs 0.004 gt { + pop true + } if + } for + exch pop exch pop +} def +/funcCol { func n array astore } def +/funcSH { + dup 0 eq { + true + } { + dup 6 eq { + false + } { + 4 index 4 index funcCol dup + 6 index 4 index funcCol dup + 3 1 roll colordelta 3 1 roll + 5 index 5 index funcCol dup + 3 1 roll colordelta 3 1 roll + 6 index 8 index funcCol dup + 3 1 roll colordelta 3 1 roll + colordelta or or or + } ifelse + } ifelse + { + 1 add + 4 index 3 index add 0.5 mul exch 4 index 3 index add 0.5 mul exch + 6 index 6 index 4 index 4 index 4 index funcSH + 2 index 6 index 6 index 4 index 4 index funcSH + 6 index 2 index 4 index 6 index 4 index funcSH + 5 3 roll 3 2 roll funcSH pop pop + } { + pop 3 index 2 index add 0.5 mul 3 index 2 index add 0.5 mul + funcCol sc + dup 4 index exch mat transform m + 3 index 3 index mat transform l + 1 index 3 index mat transform l + mat transform l pop pop h f* + } ifelse +} def +/axialCol { + dup 0 lt { + pop t0 + } { + dup 1 gt { + pop t1 + } { + dt mul t0 add + } ifelse + } ifelse + func n array astore +} def +/axialSH { + dup 0 eq { + true + } { + dup 8 eq { + false + } { + 2 index axialCol 2 index axialCol colordelta + } ifelse + } ifelse + { + 1 add 3 1 roll 2 copy add 0.5 mul + dup 4 3 roll exch 4 index axialSH + exch 3 2 roll axialSH + } { + pop 2 copy add 0.5 mul axialCol sc + exch dup dx mul x0 add exch dy mul y0 add + 3 2 roll dup dx mul x0 add exch dy mul y0 add + dx abs dy abs ge { + 2 copy yMin sub dy mul dx div add yMin m + yMax sub dy mul dx div add yMax l + 2 copy yMax sub dy mul dx div add yMax l + yMin sub dy mul dx div add yMin l + h f* + } { + exch 2 copy xMin sub dx mul dy div add xMin exch m + xMax sub dx mul dy div add xMax exch l + exch 2 copy xMax sub dx mul dy div add xMax exch l + xMin sub dx mul dy div add xMin exch l + h f* + } ifelse + } ifelse +} def +/radialCol { + dup t0 lt { + pop t0 + } { + dup t1 gt { + pop t1 + } if + } ifelse + func n array astore +} def +/radialSH { + dup 0 eq { + true + } { + dup 8 eq { + false + } { + 2 index dt mul t0 add radialCol + 2 index dt mul t0 add radialCol colordelta + } ifelse + } ifelse + { + 1 add 3 1 roll 2 copy add 0.5 mul + dup 4 3 roll exch 4 index radialSH + exch 3 2 roll radialSH + } { + pop 2 copy add 0.5 mul dt mul t0 add axialCol sc + exch dup dx mul x0 add exch dup dy mul y0 add exch dr mul r0 add + 0 360 arc h + dup dx mul x0 add exch dup dy mul y0 add exch dr mul r0 add + 0 360 arc h f* + } ifelse +} def +end +%%EndResource +%%EndProlog +%%BeginSetup +xpdf begin +%%BeginResource: font CMR12 +%!FontType1-1.0: CMR12 +12 dict begin +/FontInfo 10 dict dup begin +/Notice (Copyright (C) 1997 American Mathematical Society. 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def + { /Duplex true def } if + currentdict end setpagedevice + } { + pop pop + } ifelse +} def +/pdfStartPage { + pdfDictSize dict begin + /pdfFillCS [] def + /pdfFillXform {} def + /pdfStrokeCS [] def + /pdfStrokeXform {} def + /pdfFill [0] def + /pdfStroke [0] def + /pdfFillOP false def + /pdfStrokeOP false def + /pdfLastFill false def + /pdfLastStroke false def + /pdfTextMat [1 0 0 1 0 0] def + /pdfFontSize 0 def + /pdfCharSpacing 0 def + /pdfTextRender 0 def + /pdfTextRise 0 def + /pdfWordSpacing 0 def + /pdfHorizScaling 1 def + /pdfTextClipPath [] def +} def +/pdfEndPage { end } def +% PDF color state +/cs { /pdfFillXform exch def dup /pdfFillCS exch def + setcolorspace } def +/CS { /pdfStrokeXform exch def dup /pdfStrokeCS exch def + setcolorspace } def +/sc { pdfLastFill not { pdfFillCS setcolorspace } if + dup /pdfFill exch def aload pop pdfFillXform setcolor + /pdfLastFill true def /pdfLastStroke false def } def +/SC { pdfLastStroke not { pdfStrokeCS setcolorspace } if + dup /pdfStroke exch def aload pop pdfStrokeXform setcolor + /pdfLastStroke true def /pdfLastFill false def } def +/op { /pdfFillOP exch def + pdfLastFill { pdfFillOP setoverprint } if } def +/OP { /pdfStrokeOP exch def + pdfLastStroke { pdfStrokeOP setoverprint } if } def +/fCol { + pdfLastFill not { + pdfFillCS setcolorspace + pdfFill aload pop pdfFillXform setcolor + pdfFillOP setoverprint + /pdfLastFill true def /pdfLastStroke false def + } if +} def +/sCol { + pdfLastStroke not { + pdfStrokeCS setcolorspace + pdfStroke aload pop pdfStrokeXform setcolor + pdfStrokeOP setoverprint + /pdfLastStroke true def /pdfLastFill false def + } if +} def +% build a font +/pdfMakeFont { + 4 3 roll findfont + 4 2 roll matrix scale makefont + dup length dict begin + { 1 index /FID ne { def } { pop pop } ifelse } forall + /Encoding exch def + currentdict + end + definefont pop +} def +/pdfMakeFont16 { + exch findfont + dup length dict begin + { 1 index /FID ne { def } { pop pop } ifelse } forall + /WMode exch def + currentdict + end + definefont pop +} def +% graphics state operators +/q { gsave pdfDictSize dict begin } def +/Q { + end grestore + /pdfLastFill where { + pop + pdfLastFill { + pdfFillOP setoverprint + } { + pdfStrokeOP setoverprint + } ifelse + } if +} def +/cm { concat } def +/d { setdash } def +/i { setflat } def +/j { setlinejoin } def +/J { setlinecap } def +/M { setmiterlimit } def +/w { setlinewidth } def +% path segment operators +/m { moveto } def +/l { lineto } def +/c { curveto } def +/re { 4 2 roll moveto 1 index 0 rlineto 0 exch rlineto + neg 0 rlineto closepath } def +/h { closepath } def +% path painting operators +/S { sCol stroke } def +/Sf { fCol stroke } def +/f { fCol fill } def +/f* { fCol eofill } def +% clipping operators +/W { clip newpath } def +/W* { eoclip newpath } def +% text state operators +/Tc { /pdfCharSpacing exch def } def +/Tf { dup /pdfFontSize exch def + dup pdfHorizScaling mul exch matrix scale + pdfTextMat matrix concatmatrix dup 4 0 put dup 5 0 put + exch findfont exch makefont setfont } def +/Tr { /pdfTextRender exch def } def +/Ts { /pdfTextRise exch def } def +/Tw { /pdfWordSpacing exch def } def +/Tz { /pdfHorizScaling exch def } def +% text positioning operators +/Td { pdfTextMat transform moveto } def +/Tm { /pdfTextMat exch def } def +% text string operators +/cshow where { + pop + /cshow2 { + dup { + pop pop + 1 string dup 0 3 index put 3 index exec + } exch cshow + pop pop + } def +}{ + /cshow2 { + currentfont /FontType get 0 eq { + 0 2 2 index length 1 sub { + 2 copy get exch 1 add 2 index exch get + 2 copy exch 256 mul add + 2 string dup 0 6 5 roll put dup 1 5 4 roll put + 3 index exec + } for + } { + dup { + 1 string dup 0 3 index put 3 index exec + } forall + } ifelse + pop pop + } def +} ifelse +/awcp { + exch { + false charpath + 5 index 5 index rmoveto + 6 index eq { 7 index 7 index rmoveto } if + } exch cshow2 + 6 {pop} repeat +} def +/Tj { + fCol + 1 index stringwidth pdfTextMat idtransform pop + sub 1 index length dup 0 ne { div } { pop pop 0 } ifelse + pdfWordSpacing pdfHorizScaling mul 0 pdfTextMat dtransform 32 + 4 3 roll pdfCharSpacing pdfHorizScaling mul add 0 + pdfTextMat dtransform + 6 5 roll Tj1 +} def +/Tj16 { + fCol + 2 index stringwidth pdfTextMat idtransform pop + sub exch div + pdfWordSpacing pdfHorizScaling mul 0 pdfTextMat dtransform 32 + 4 3 roll pdfCharSpacing pdfHorizScaling mul add 0 + pdfTextMat dtransform + 6 5 roll Tj1 +} def +/Tj16V { + fCol + 2 index stringwidth pdfTextMat idtransform exch pop + sub exch div + 0 pdfWordSpacing pdfTextMat dtransform 32 + 4 3 roll pdfCharSpacing add 0 exch + pdfTextMat dtransform + 6 5 roll Tj1 +} def +/Tj1 { + 0 pdfTextRise pdfTextMat dtransform rmoveto + currentpoint 8 2 roll + pdfTextRender 1 and 0 eq { + 6 copy awidthshow + } if + pdfTextRender 3 and dup 1 eq exch 2 eq or { + 7 index 7 index moveto + 6 copy + currentfont /FontType get 3 eq { fCol } { sCol } ifelse + false awcp currentpoint stroke moveto + } if + pdfTextRender 4 and 0 ne { + 8 6 roll moveto + false awcp + /pdfTextClipPath [ pdfTextClipPath aload pop + {/moveto cvx} + {/lineto cvx} + {/curveto cvx} + {/closepath cvx} + pathforall ] def + currentpoint newpath moveto + } { + 8 {pop} repeat + } ifelse + 0 pdfTextRise neg pdfTextMat dtransform rmoveto +} def +/TJm { pdfFontSize 0.001 mul mul neg 0 + pdfTextMat dtransform rmoveto } def +/TJmV { pdfFontSize 0.001 mul mul neg 0 exch + pdfTextMat dtransform rmoveto } def +/Tclip { pdfTextClipPath cvx exec clip newpath + /pdfTextClipPath [] def } def +% Level 2 image operators +/pdfImBuf 100 string def +/pdfIm { + image + { currentfile pdfImBuf readline + not { pop exit } if + (%-EOD-) eq { exit } if } loop +} def +/pdfImM { + fCol imagemask + { currentfile pdfImBuf readline + not { pop exit } if + (%-EOD-) eq { exit } if } loop +} def +/pdfImClip { + gsave + 0 2 4 index length 1 sub { + dup 4 index exch 2 copy + get 5 index div put + 1 add 3 index exch 2 copy + get 3 index div put + } for + pop pop rectclip +} def +/pdfImClipEnd { grestore } def +% shading operators +/colordelta { + false 0 1 3 index length 1 sub { + dup 4 index exch get 3 index 3 2 roll get sub abs 0.004 gt { + pop true + } if + } for + exch pop exch pop +} def +/funcCol { func n array astore } def +/funcSH { + dup 0 eq { + true + } { + dup 6 eq { + false + } { + 4 index 4 index funcCol dup + 6 index 4 index funcCol dup + 3 1 roll colordelta 3 1 roll + 5 index 5 index funcCol dup + 3 1 roll colordelta 3 1 roll + 6 index 8 index funcCol dup + 3 1 roll colordelta 3 1 roll + colordelta or or or + } ifelse + } ifelse + { + 1 add + 4 index 3 index add 0.5 mul exch 4 index 3 index add 0.5 mul exch + 6 index 6 index 4 index 4 index 4 index funcSH + 2 index 6 index 6 index 4 index 4 index funcSH + 6 index 2 index 4 index 6 index 4 index funcSH + 5 3 roll 3 2 roll funcSH pop pop + } { + pop 3 index 2 index add 0.5 mul 3 index 2 index add 0.5 mul + funcCol sc + dup 4 index exch mat transform m + 3 index 3 index mat transform l + 1 index 3 index mat transform l + mat transform l pop pop h f* + } ifelse +} def +/axialCol { + dup 0 lt { + pop t0 + } { + dup 1 gt { + pop t1 + } { + dt mul t0 add + } ifelse + } ifelse + func n array astore +} def +/axialSH { + dup 0 eq { + true + } { + dup 8 eq { + false + } { + 2 index axialCol 2 index axialCol colordelta + } ifelse + } ifelse + { + 1 add 3 1 roll 2 copy add 0.5 mul + dup 4 3 roll exch 4 index axialSH + exch 3 2 roll axialSH + } { + pop 2 copy add 0.5 mul axialCol sc + exch dup dx mul x0 add exch dy mul y0 add + 3 2 roll dup dx mul x0 add exch dy mul y0 add + dx abs dy abs ge { + 2 copy yMin sub dy mul dx div add yMin m + yMax sub dy mul dx div add yMax l + 2 copy yMax sub dy mul dx div add yMax l + yMin sub dy mul dx div add yMin l + h f* + } { + exch 2 copy xMin sub dx mul dy div add xMin exch m + xMax sub dx mul dy div add xMax exch l + exch 2 copy xMax sub dx mul dy div add xMax exch l + xMin sub dx mul dy div add xMin exch l + h f* + } ifelse + } ifelse +} def +/radialCol { + dup t0 lt { + pop t0 + } { + dup t1 gt { + pop t1 + } if + } ifelse + func n array astore +} def +/radialSH { + dup 0 eq { + true + } { + dup 8 eq { + false + } { + 2 index dt mul t0 add radialCol + 2 index dt mul t0 add radialCol colordelta + } ifelse + } ifelse + { + 1 add 3 1 roll 2 copy add 0.5 mul + dup 4 3 roll exch 4 index radialSH + exch 3 2 roll radialSH + } { + pop 2 copy add 0.5 mul dt mul t0 add axialCol sc + exch dup dx mul x0 add exch dup dy mul y0 add exch dr mul r0 add + 0 360 arc h + dup dx mul x0 add exch dup dy mul y0 add exch dr mul r0 add + 0 360 arc h f* + } ifelse +} def +end +%%EndResource +%%EndProlog +%%BeginSetup +xpdf begin +%%BeginResource: font CMR12 +%!FontType1-1.0: CMR12 +12 dict begin +/FontInfo 10 dict dup begin +/Notice (Copyright (C) 1997 American Mathematical Society. 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pdfFillOP setoverprint + } { + pdfStrokeOP setoverprint + } ifelse + } if +} def +/cm { concat } def +/d { setdash } def +/i { setflat } def +/j { setlinejoin } def +/J { setlinecap } def +/M { setmiterlimit } def +/w { setlinewidth } def +% path segment operators +/m { moveto } def +/l { lineto } def +/c { curveto } def +/re { 4 2 roll moveto 1 index 0 rlineto 0 exch rlineto + neg 0 rlineto closepath } def +/h { closepath } def +% path painting operators +/S { sCol stroke } def +/Sf { fCol stroke } def +/f { fCol fill } def +/f* { fCol eofill } def +% clipping operators +/W { clip newpath } def +/W* { eoclip newpath } def +% text state operators +/Tc { /pdfCharSpacing exch def } def +/Tf { dup /pdfFontSize exch def + dup pdfHorizScaling mul exch matrix scale + pdfTextMat matrix concatmatrix dup 4 0 put dup 5 0 put + exch findfont exch makefont setfont } def +/Tr { /pdfTextRender exch def } def +/Ts { /pdfTextRise exch def } def +/Tw { /pdfWordSpacing exch def } def +/Tz { /pdfHorizScaling exch def } def +% text positioning operators +/Td { pdfTextMat transform moveto } def +/Tm { /pdfTextMat exch def } def +% text string operators +/cshow where { + pop + /cshow2 { + dup { + pop pop + 1 string dup 0 3 index put 3 index exec + } exch cshow + pop pop + } def +}{ + /cshow2 { + currentfont /FontType get 0 eq { + 0 2 2 index length 1 sub { + 2 copy get exch 1 add 2 index exch get + 2 copy exch 256 mul add + 2 string dup 0 6 5 roll put dup 1 5 4 roll put + 3 index exec + } for + } { + dup { + 1 string dup 0 3 index put 3 index exec + } forall + } ifelse + pop pop + } def +} ifelse +/awcp { + exch { + false charpath + 5 index 5 index rmoveto + 6 index eq { 7 index 7 index rmoveto } if + } exch cshow2 + 6 {pop} repeat +} def +/Tj { + fCol + 1 index stringwidth pdfTextMat idtransform pop + sub 1 index length dup 0 ne { div } { pop pop 0 } ifelse + pdfWordSpacing pdfHorizScaling mul 0 pdfTextMat dtransform 32 + 4 3 roll pdfCharSpacing pdfHorizScaling mul add 0 + pdfTextMat dtransform + 6 5 roll Tj1 +} def +/Tj16 { + fCol + 2 index stringwidth pdfTextMat idtransform pop + sub exch div + pdfWordSpacing pdfHorizScaling mul 0 pdfTextMat dtransform 32 + 4 3 roll pdfCharSpacing pdfHorizScaling mul add 0 + pdfTextMat dtransform + 6 5 roll Tj1 +} def +/Tj16V { + fCol + 2 index stringwidth pdfTextMat idtransform exch pop + sub exch div + 0 pdfWordSpacing pdfTextMat dtransform 32 + 4 3 roll pdfCharSpacing add 0 exch + pdfTextMat dtransform + 6 5 roll Tj1 +} def +/Tj1 { + 0 pdfTextRise pdfTextMat dtransform rmoveto + currentpoint 8 2 roll + pdfTextRender 1 and 0 eq { + 6 copy awidthshow + } if + pdfTextRender 3 and dup 1 eq exch 2 eq or { + 7 index 7 index moveto + 6 copy + currentfont /FontType get 3 eq { fCol } { sCol } ifelse + false awcp currentpoint stroke moveto + } if + pdfTextRender 4 and 0 ne { + 8 6 roll moveto + false awcp + /pdfTextClipPath [ pdfTextClipPath aload pop + {/moveto cvx} + {/lineto cvx} + {/curveto cvx} + {/closepath cvx} + pathforall ] def + currentpoint newpath moveto + } { + 8 {pop} repeat + } ifelse + 0 pdfTextRise neg pdfTextMat dtransform rmoveto +} def +/TJm { pdfFontSize 0.001 mul mul neg 0 + pdfTextMat dtransform rmoveto } def +/TJmV { pdfFontSize 0.001 mul mul neg 0 exch + pdfTextMat dtransform rmoveto } def +/Tclip { pdfTextClipPath cvx exec clip newpath + /pdfTextClipPath [] def } def +% Level 2 image operators +/pdfImBuf 100 string def +/pdfIm { + image + { currentfile pdfImBuf readline + not { pop exit } if + (%-EOD-) eq { exit } if } loop +} def +/pdfImM { + fCol imagemask + { currentfile pdfImBuf readline + not { pop exit } if + (%-EOD-) eq { exit } if } loop +} def +/pdfImClip { + gsave + 0 2 4 index length 1 sub { + dup 4 index exch 2 copy + get 5 index div put + 1 add 3 index exch 2 copy + get 3 index div put + } for + pop pop rectclip +} def +/pdfImClipEnd { grestore } def +% shading operators +/colordelta { + false 0 1 3 index length 1 sub { + dup 4 index exch get 3 index 3 2 roll get sub abs 0.004 gt { + pop true + } if + } for + exch pop exch pop +} def +/funcCol { func n array astore } def +/funcSH { + dup 0 eq { + true + } { + dup 6 eq { + false + } { + 4 index 4 index funcCol dup + 6 index 4 index funcCol dup + 3 1 roll colordelta 3 1 roll + 5 index 5 index funcCol dup + 3 1 roll colordelta 3 1 roll + 6 index 8 index funcCol dup + 3 1 roll colordelta 3 1 roll + colordelta or or or + } ifelse + } ifelse + { + 1 add + 4 index 3 index add 0.5 mul exch 4 index 3 index add 0.5 mul exch + 6 index 6 index 4 index 4 index 4 index funcSH + 2 index 6 index 6 index 4 index 4 index funcSH + 6 index 2 index 4 index 6 index 4 index funcSH + 5 3 roll 3 2 roll funcSH pop pop + } { + pop 3 index 2 index add 0.5 mul 3 index 2 index add 0.5 mul + funcCol sc + dup 4 index exch mat transform m + 3 index 3 index mat transform l + 1 index 3 index mat transform l + mat transform l pop pop h f* + } ifelse +} def +/axialCol { + dup 0 lt { + pop t0 + } { + dup 1 gt { + pop t1 + } { + dt mul t0 add + } ifelse + } ifelse + func n array astore +} def +/axialSH { + dup 0 eq { + true + } { + dup 8 eq { + false + } { + 2 index axialCol 2 index axialCol colordelta + } ifelse + } ifelse + { + 1 add 3 1 roll 2 copy add 0.5 mul + dup 4 3 roll exch 4 index axialSH + exch 3 2 roll axialSH + } { + pop 2 copy add 0.5 mul axialCol sc + exch dup dx mul x0 add exch dy mul y0 add + 3 2 roll dup dx mul x0 add exch dy mul y0 add + dx abs dy abs ge { + 2 copy yMin sub dy mul dx div add yMin m + yMax sub dy mul dx div add yMax l + 2 copy yMax sub dy mul dx div add yMax l + yMin sub dy mul dx div add yMin l + h f* + } { + exch 2 copy xMin sub dx mul dy div add xMin exch m + xMax sub dx mul dy div add xMax exch l + exch 2 copy xMax sub dx mul dy div add xMax exch l + xMin sub dx mul dy div add xMin exch l + h f* + } ifelse + } ifelse +} def +/radialCol { + dup t0 lt { + pop t0 + } { + dup t1 gt { + pop t1 + } if + } ifelse + func n array astore +} def +/radialSH { + dup 0 eq { + true + } { + dup 8 eq { + false + } { + 2 index dt mul t0 add radialCol + 2 index dt mul t0 add radialCol colordelta + } ifelse + } ifelse + { + 1 add 3 1 roll 2 copy add 0.5 mul + dup 4 3 roll exch 4 index radialSH + exch 3 2 roll radialSH + } { + pop 2 copy add 0.5 mul dt mul t0 add axialCol sc + exch dup dx mul x0 add exch dup dy mul y0 add exch dr mul r0 add + 0 360 arc h + dup dx mul x0 add exch dup dy mul y0 add exch dr mul r0 add + 0 360 arc h f* + } ifelse +} def +end +%%EndResource +%%EndProlog +%%BeginSetup +xpdf begin +%%BeginResource: font CMR12 +%!FontType1-1.0: CMR12 +12 dict begin +/FontInfo 10 dict dup begin +/Notice (Copyright (C) 1997 American Mathematical Society. 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\frametitle{Introduction} +\end{frame} +% ------------------------------------------------------------------------------ +\end{document} diff --git a/tauola/Bug1/tmp/example/beamerthemeSybila.sty b/tauola/Bug1/tmp/example/beamerthemeSybila.sty new file mode 100644 index 0000000..5639601 --- /dev/null +++ b/tauola/Bug1/tmp/example/beamerthemeSybila.sty @@ -0,0 +1,104 @@ +\mode + +%------------------------------------------------------------------------------- +% Themes +%------------------------------------------------------------------------------- + +\useoutertheme{split} +\useinnertheme{rounded} +\usefonttheme{structurebold} +%\useoutertheme{shadow} + +%------------------------------------------------------------------------------- +% Templates +%------------------------------------------------------------------------------- + +\beamertemplatenavigationsymbolsempty +\beamertemplateheadempty +\beamertemplateshadowblocks + 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\end{centering} + \vfill +} + +%------------------------------------------------------------------------------- +% Logo +%------------------------------------------------------------------------------- + +\logo{\hspace*{0.6\textwidth}\includegraphics[width=1.2cm]{sybila-logo-paper-shaded}\hspace*{0.3cm}} + +%------------------------------------------------------------------------------- +% Colors +%------------------------------------------------------------------------------- + +\setbeamercovered{dynamic} + +\setbeamercolor{math text}{fg=green!45!black} +\setbeamercolor{title}{bg=white!30!black} +\setbeamercolor{frametitle}{bg=white!45!black} +\setbeamercolor{footline}{bg=black,fg=white} +\setbeamercolor{author in head/foot}{bg=black,fg=white} +\setbeamercolor{title in head/foot}{bg=white!45!black} +\setbeamercolor{block title}{bg=white!45!black} +\setbeamercolor{block title example}{bg=white!45!black} +\setbeamercolor{block title alerted}{bg=white!15!black} + 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+\definecolor{mygreen}{cmyk}{0.82,0.11,1,0.25} + + +\usetheme{Sybila} + +\title[Tauola development]{Tauola development} +\author{Marcin Chrz\k{a}szcz$^{1,2}$} +\institute{$^1$~University of Zurich,\\ $^2$~Institute of Nuclear Physics, Krakow} +\date{\today} +\begin{document} +% --------------------------- SLIDE -------------------------------------------- +\frame[plain]{\titlepage} +\author{Marcin Chrz\k{a}szcz} +% ------------------------------------------------------------------------------ +% --------------------------- SLIDE -------------------------------------------- + +\institute{~(UZH, IFJ)} + +\section{Introduction} + + +\begin{frame}\frametitle{TAUOLA - $\Ptau$ generator} +\begin{itemize} +\item TAUOLA is a specific generator for $\Ptau$ decays. +\item The only one that takes all the spin correlation into account. +\item For few months I have been working on new release. +\end{itemize} + + + +\end{frame} + +\begin{frame}\frametitle{New decays} +\begin{itemize} +\item Till now TAUOLA was focused on precise SM decays. +\item Added ALL LFV channels ever searched(now we have $\sim 200$ channels. +\item Especially for $\tau \to \Plepton \Plepton \Plepton$ added different NP models. +\item Needed to do hacking: TAUOLA wants always matrix elements... +\item From some time also available in LHCb(although not extensively used). +\end{itemize} + +\end{frame} + +\begin{frame}\frametitle{New decays: $\tau \to 3\mu$ } +\begin{columns} +\column{3.in} +\begin{figure}[h] +\includegraphics[height=3cm]{plots/vllll_mmm.pdf}{~}{~} +\includegraphics[height=3.2cm]{plots_tauola/LLLL.pdf}\\ +\end{figure} + +\begin{figure} +\includegraphics[height=3cm]{plots/vllrr_mmm.pdf}{~}{~} +\includegraphics[height=3.2cm]{plots_tauola/LLRR.pdf}\\ +\end{figure} + +\column{2in} +\begin{small} +$\tau^{-} \to \mu^{-}_{1} \mu^{-}_{2} \mu^{+}_{3}$\\ +$m_{--}=m_{12}=(p_{\mu^{-}_{1}} + p_{\mu^{-}_{2}})^2$\\ +$m_{+-}m_{23}=(p_{\mu^{-}_{2}} + p_{\mu^{+}_{3}})^2$\\ +$m_{13}=(p_{\mu^{-}_{1}} + p_{\mu^{+}_{3}})^2$ + + +\begin{align} +\Gamma_{LLLL} = Const \dfrac{ (m_{\tau}^2-m_{\mu}^2)^2 }{256 \pi m_{\tau}^3} \nonumber\\ -\dfrac{ (2m_{12}^{2}-m_{\tau}^2 -3 m_{\mu}^2)^2}{256 \pi m_{\tau}^3} +\end{align} + +\end{small} + +See \href{http://arxiv.org/pdf/0707.0988.pdf}{0707.0988}. I don't want to latex all the equations here :P + +\end{columns} + +\end{frame} + + +\begin{frame}\frametitle{New decays: $\tau \to 3\mu$ } +\begin{columns} +\column{3.in} +\begin{figure}[h] +\includegraphics[width=0.45\textwidth]{plots/radlr_mmm.pdf} +\includegraphics[width=0.45\textwidth]{plots_tauola/RAD.pdf}\\ +\end{figure} + +\begin{figure} +\includegraphics[width=0.45\textwidth]{plots/mixlrll_mmm.pdf} +\includegraphics[width=0.45\textwidth]{plots_tauola/LLLLRAD.pdf}\\ +\end{figure} + +\column{2in} +\begin{small} +$\tau^{-} \to \mu^{-}_{1} \mu^{-}_{2} \mu^{+}_{3}$\\ +$m_{--}=m_{12}=(p_{\mu^{-}_{1}} + p_{\mu^{-}_{2}})^2$\\ +$m_{+-}m_{23}=(p_{\mu^{-}_{2}} + p_{\mu^{+}_{3}})^2$\\ +$m_{13}=(p_{\mu^{-}_{1}} + p_{\mu^{+}_{3}})^2$ + +\end{small} +{~}\\ +See \href{http://arxiv.org/pdf/0707.0988.pdf}{0707.0988}. I don't want to latex all the equations here :P + +\end{columns} + +\end{frame} + +\begin{frame}\frametitle{New decays: $\tau \to 3\mu$ } +\begin{columns} +\column{3.in} +\begin{figure}[h] +\includegraphics[width=0.45\textwidth]{plots/mixlrrr_mmm.pdf} +\includegraphics[width=0.45\textwidth]{plots_tauola/LLRRRAD.pdf}\\ +\end{figure} + + +\column{2in} +\begin{small} +$\tau^{-} \to \mu^{-}_{1} \mu^{-}_{2} \mu^{+}_{3}$\\ +$m_{--}=m_{12}=(p_{\mu^{-}_{1}} + p_{\mu^{-}_{2}})^2$\\ +$m_{+-}m_{23}=(p_{\mu^{-}_{2}} + p_{\mu^{+}_{3}})^2$\\ +$m_{13}=(p_{\mu^{-}_{1}} + p_{\mu^{+}_{3}})^2$ + +\end{small} +{~}\\ +See \href{http://arxiv.org/pdf/0707.0988.pdf}{0707.0988}. I don't want to latex all the equations here :P + +\end{columns} + +\end{frame} + +\begin{frame}\frametitle{New decays: $\tau^{-} \to e^{-} \mu^{-} \mu^{+} $ } +\begin{columns} +\column{3.in} +\begin{figure}[h] +\includegraphics[width=0.45\textwidth]{plots/vllrr_emm.pdf} +\includegraphics[width=0.45\textwidth]{plots_tauola/LLRR_emumu_GE.pdf}\\ +\end{figure} +\begin{figure}[h] +\includegraphics[width=0.45\textwidth]{plots/vllrr_mem.pdf} +\includegraphics[width=0.45\textwidth]{plots_tauola/LLRR_emumu_GMU.pdf}\\ +\end{figure} + + +\column{2in} +\begin{small} +$\tau^{-} \to e^{-}_{1} \mu^{-}_{2} \mu^{+}_{3}$\\ +$m_{--}=m_{12}=(p_{e^{-}_{1}} + p_{\mu^{-}_{2}})^2$\\ +$m_{+-}m_{23}=(p_{\mu^{-}_{2}} + p_{\mu^{+}_{3}})^2$\\ +$m_{13}=(p_{e^{-}_{1}} + p_{\mu^{+}_{3}})^2$ + +\end{small} +{~}\\ +See \href{http://arxiv.org/pdf/0707.0988.pdf}{0707.0988}. I don't want to latex all the equations here :P + +\end{columns} + +\end{frame} + +\begin{frame}\frametitle{New decays: $\tau^{-} \to e^{-} \mu^{-} \mu^{+} $ } +\begin{columns} +\column{3.in} +\begin{figure}[h] +\includegraphics[width=0.45\textwidth]{plots/radlr_emm.pdf} +\includegraphics[width=0.45\textwidth]{plots_tauola/RAD_emumu.pdf}\\ +\end{figure} +\begin{figure}[h] +\includegraphics[width=0.45\textwidth]{plots/mixlrll_emm.pdf} +\includegraphics[width=0.45\textwidth]{plots_tauola/LLLLRAD_emumu.pdf}\\ +\end{figure} + + +\column{2in} +\begin{small} +$\tau^{-} \to e^{-}_{1} \mu^{-}_{2} \mu^{+}_{3}$\\ +$m_{--}=m_{12}=(p_{e^{-}_{1}} + p_{\mu^{-}_{2}})^2$\\ +$m_{+-}m_{23}=(p_{\mu^{-}_{2}} + p_{\mu^{+}_{3}})^2$\\ +$m_{13}=(p_{e^{-}_{1}} + p_{\mu^{+}_{3}})^2$ + +\end{small} +{~}\\ +See \href{http://arxiv.org/pdf/0707.0988.pdf}{0707.0988}. I don't want to latex all the equations here :P + +\end{columns} + +\end{frame} + +\begin{frame}\frametitle{New decays: $\tau^{-} \to e^{-} \mu^{-} \mu^{+} $ } +\begin{columns} +\column{3.in} +\begin{figure}[h] +\includegraphics[width=0.45\textwidth]{plots/radlr_emm.pdf} +\includegraphics[width=0.45\textwidth]{plots_tauola/RAD_emumu.pdf}\\ +\end{figure} +\begin{figure}[h] +\includegraphics[width=0.45\textwidth]{plots/mixlrrr_emm.pdf} +\includegraphics[width=0.45\textwidth]{plots_tauola/LLRRRAD_emumu.pdf}\\ +\end{figure} + + +\column{2in} +\begin{small} +$\tau^{-} \to e^{-}_{1} \mu^{-}_{2} \mu^{+}_{3}$\\ +$m_{--}=m_{12}=(p_{e^{-}_{1}} + p_{\mu^{-}_{2}})^2$\\ +$m_{+-}m_{23}=(p_{\mu^{-}_{2}} + p_{\mu^{+}_{3}})^2$\\ +$m_{13}=(p_{e^{-}_{1}} + p_{\mu^{+}_{3}})^2$ + +\end{small} +{~}\\ +See \href{http://arxiv.org/pdf/0707.0988.pdf}{0707.0988}. I don't want to latex all the equations here :P + +\end{columns} + +\end{frame} + +\begin{frame}\frametitle{New decays: $\tau^{-} \to e^{-} \mu^{-} \mu^{+} $ } + +\only<1>{ +\begin{itemize} +\item This grey plots produced by theorists are next to useless. +\item Can't really compare them with my nice ones :P +\item I would say there might be disagreement in some tails. +\item Let's check. +\end{itemize} +} +\only<2>{ +\begin{itemize} +\item Yes! this should be there! +\end{itemize} +\begin{equation} +\Gamma^{LLLL}_{Rad} = Const (\dfrac{m_{12}^2 - 2m_{\mu}^2}{126 \pi^3 m_{\tau}^2}+\frac{m_{\mu}^2}{128\pi^3 \textcolor{red}{m_{23}^2}}) +\end{equation} + + + +} + +\begin{figure}[h] +\includegraphics[width=0.35\textwidth]{plots_tauola/mumue_dalitz.pdf} +\includegraphics[width=0.35\textwidth]{plots_tauola/LLLLRAD_emumu.pdf}\\ +\end{figure} +\only<1>{ +\begin{itemize} +\item Does it make sense? +\end{itemize} +} +\end{frame} + + +%%%%%%%%%%%%%%%%%%%%%%%%% + +\begin{frame}\frametitle{Updates SM physics } +\begin{itemize} +\item Both Babar and Belle had their own versions of TAUOLA where they put theirs FF, Br etc. +\item It would be good if now their knowledge could be merged and be accessible to public. +\item Since Babar was more advanced in this I started from there. +\item Ported all FF from Babar to current framework. +\item Need to be sure I am doing things the correct way(this if FORTRAN code, so hard core dark side of the force). + +\end{itemize} +\end{frame} + +%%%%%%%%%%%%%%%%%%%%%%%%% + +\begin{frame}\frametitle{X-checking understanding of FORTRAN} +\begin{itemize} +\item Generate things with my implementation and take official Babar MC production :) +\item Use \href{http://mc-tester.web.cern.ch/MC-TESTER/}{MC-tester} to test if the simulations are compatible. +\item And do it with 95 decays. +\item This software produces a pdf file with histograms. Just had to compare 500 pages of histograms :) +\item I don't want to bore you so just one example: +\end{itemize} +\begin{figure}[h] +\includegraphics[width=0.45\textwidth]{example.png} +\end{figure} + +\end{frame} + +\begin{frame}\frametitle{Summary} +\begin{itemize} +\item Starting to prepare a new update and publication of TAUOLA. +\item Work will be shown on TAU 2014 conference. +\end{itemize} + + +\end{frame} + +\end{document} diff --git a/Zurich_group/14_07_2014/slides.toc b/Zurich_group/14_07_2014/slides.toc new file mode 100644 index 0000000..1e71ea5 --- /dev/null +++ b/Zurich_group/14_07_2014/slides.toc @@ -0,0 +1,3 @@ +\beamer@endinputifotherversion {3.10pt} +\select@language {english} +\beamer@sectionintoc {1}{Introduction}{2}{0}{1} diff --git a/Zurich_group/14_07_2014/sybila-logo-slide-title-shaded.pdf b/Zurich_group/14_07_2014/sybila-logo-slide-title-shaded.pdf new file mode 100644 index 0000000..670c6a6 --- /dev/null +++ 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{\usebeamerfont{subtitle}\usebeamercolor[fg]{subtitle}\insertsubtitle\par}% + \fi% + \end{beamercolorbox}% + + \vskip1em + + \begin{beamercolorbox}[sep=8pt,center,#1]{author} + \usebeamerfont{author}\insertauthor + \end{beamercolorbox} + + \vskip1em + + {\usebeamercolor[fg]{titlegraphic}\inserttitlegraphic\par} + \begin{beamercolorbox}[sep=8pt,center,#1]{institute} + \usebeamerfont{date}\insertinstitute + \end{beamercolorbox} + + \vskip1em + + \begin{beamercolorbox}[sep=8pt,center,#1]{date} + \usebeamerfont{date}\insertdate + \end{beamercolorbox} + \end{centering} + \vfill +} + +%------------------------------------------------------------------------------- +% Logo +%------------------------------------------------------------------------------- + +\logo{\hspace*{0.6\textwidth}\includegraphics[width=1.2cm]{sybila-logo-paper-shaded}\hspace*{0.3cm}} + +%------------------------------------------------------------------------------- +% Colors +%------------------------------------------------------------------------------- + +\setbeamercovered{dynamic} + +\setbeamercolor{math text}{fg=green!45!black} +\setbeamercolor{title}{bg=white!30!black} +\setbeamercolor{frametitle}{bg=white!45!black} +\setbeamercolor{footline}{bg=black,fg=white} +\setbeamercolor{author in head/foot}{bg=black,fg=white} +\setbeamercolor{title in head/foot}{bg=white!45!black} +\setbeamercolor{block title}{bg=white!45!black} +\setbeamercolor{block title example}{bg=white!45!black} +\setbeamercolor{block title alerted}{bg=white!15!black} + +\colorlet{redshaded}{red!25!bg} +\colorlet{shaded}{black!25!bg} +\colorlet{shadedshaded}{black!10!bg} +\colorlet{blackshaded}{black!40!bg} + +\usecolortheme{whale} +\usecolortheme{orchid} + +%------------------------------------------------------------------------------- +% Fonts +%------------------------------------------------------------------------------- + +\setbeamerfont{block title}{size={}} +\setbeamerfont{date}{size=\small} + +%------------------------------------------------------------------------------- +% Other +%------------------------------------------------------------------------------- + +\titlegraphic{\includegraphics[width=3.0cm]{sybila-logo-slide-title-shaded.pdf}} + +\mode + diff --git a/Zurich_group/14_07_2014/tmp/example.tex b/Zurich_group/14_07_2014/tmp/example.tex new file mode 100644 index 0000000..ce0641b --- /dev/null +++ b/Zurich_group/14_07_2014/tmp/example.tex @@ -0,0 +1,21 @@ +\documentclass[xcolor=svgnames]{beamer} +\usepackage[utf8]{inputenc} +\usepackage[english]{babel} + +\usetheme{Sybila} + +\title[Parallelization of Methods for Dynamic System Analysis]{Parallelization of Methods for Dynamic System Analysis Using CUDA} +\author{Jan Papou\v{s}ek} +\institute{Masaryk University Brno} +\date{\today} + +\begin{document} +% --------------------------- SLIDE -------------------------------------------- +\frame[plain]{\titlepage} +% ------------------------------------------------------------------------------ +% --------------------------- SLIDE -------------------------------------------- +\begin{frame} + \frametitle{Introduction} +\end{frame} +% ------------------------------------------------------------------------------ +\end{document} diff --git a/Zurich_group/14_07_2014/tmp/example/beamerthemeSybila.sty b/Zurich_group/14_07_2014/tmp/example/beamerthemeSybila.sty new file mode 100644 index 0000000..5639601 --- /dev/null +++ b/Zurich_group/14_07_2014/tmp/example/beamerthemeSybila.sty @@ -0,0 +1,104 @@ +\mode + +%------------------------------------------------------------------------------- +% Themes +%------------------------------------------------------------------------------- + +\useoutertheme{split} +\useinnertheme{rounded} +\usefonttheme{structurebold} +%\useoutertheme{shadow} + +%------------------------------------------------------------------------------- +% Templates +%------------------------------------------------------------------------------- + +\beamertemplatenavigationsymbolsempty +\beamertemplateheadempty +\beamertemplateshadowblocks + +%------------------------------------------------------------------------------- +% Own templates +%------------------------------------------------------------------------------- + +% Normal title page. +\defbeamertemplate*{title page}{simple}[1][] +{ + \vfill + \begin{centering} + \begin{beamercolorbox}[center, rounded=true]{title} + \usebeamerfont{title}\inserttitle\par% + \ifx\insertsubtitle\@empty% + \else% + \vskip0.25em% + {\usebeamerfont{subtitle}\usebeamercolor[fg]{subtitle}\insertsubtitle\par}% + \fi% + \end{beamercolorbox}% + + \vskip1em + + \begin{beamercolorbox}[sep=8pt,center,#1]{author} + \usebeamerfont{author}\insertauthor + \end{beamercolorbox} + + \vskip1em + + {\usebeamercolor[fg]{titlegraphic}\inserttitlegraphic\par} + \begin{beamercolorbox}[sep=8pt,center,#1]{institute} + \usebeamerfont{date}\insertinstitute + \end{beamercolorbox} + + \vskip1em + + \begin{beamercolorbox}[sep=8pt,center,#1]{date} + \usebeamerfont{date}\insertdate + \end{beamercolorbox} + \end{centering} + \vfill +} + +%------------------------------------------------------------------------------- +% Logo +%------------------------------------------------------------------------------- + +\logo{\hspace*{0.6\textwidth}\includegraphics[width=1.2cm]{sybila-logo-paper-shaded}\hspace*{0.3cm}} + +%------------------------------------------------------------------------------- +% Colors +%------------------------------------------------------------------------------- + +\setbeamercovered{dynamic} + +\setbeamercolor{math text}{fg=green!45!black} +\setbeamercolor{title}{bg=white!30!black} +\setbeamercolor{frametitle}{bg=white!45!black} +\setbeamercolor{footline}{bg=black,fg=white} +\setbeamercolor{author in head/foot}{bg=black,fg=white} +\setbeamercolor{title in head/foot}{bg=white!45!black} 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b/Zurich_group/14_07_2014/tmp/example/example.snm diff --git a/Zurich_group/14_07_2014/tmp/example/example.synctex.gz b/Zurich_group/14_07_2014/tmp/example/example.synctex.gz new file mode 100644 index 0000000..5bccdb3 --- /dev/null +++ b/Zurich_group/14_07_2014/tmp/example/example.synctex.gz Binary files differ diff --git a/Zurich_group/14_07_2014/tmp/example/example.tex b/Zurich_group/14_07_2014/tmp/example/example.tex new file mode 100644 index 0000000..ce0641b --- /dev/null +++ b/Zurich_group/14_07_2014/tmp/example/example.tex @@ -0,0 +1,21 @@ +\documentclass[xcolor=svgnames]{beamer} +\usepackage[utf8]{inputenc} +\usepackage[english]{babel} + +\usetheme{Sybila} + +\title[Parallelization of Methods for Dynamic System Analysis]{Parallelization of Methods for Dynamic System Analysis Using CUDA} +\author{Jan Papou\v{s}ek} +\institute{Masaryk University Brno} +\date{\today} + +\begin{document} +% --------------------------- SLIDE -------------------------------------------- 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0000000..f22b3e2 --- /dev/null +++ b/Zurich_group/14_07_2014_2/MM.out @@ -0,0 +1,5 @@ +\BOOKMARK [2][]{Outline0.2}{Introduction}{} +\BOOKMARK [2][]{Outline0.3}{Method of Moments - Theory}{} +\BOOKMARK [2][]{Outline0.4}{Moments of Ss}{} +\BOOKMARK [2][]{Outline0.5}{Toy MC study}{} +\BOOKMARK [2][]{Outline0.6}{2 am discovery}{} diff --git a/Zurich_group/14_07_2014_2/MM.pdf b/Zurich_group/14_07_2014_2/MM.pdf new file mode 100644 index 0000000..160ac5e --- /dev/null +++ b/Zurich_group/14_07_2014_2/MM.pdf Binary files differ diff --git a/Zurich_group/14_07_2014_2/MM.snm b/Zurich_group/14_07_2014_2/MM.snm new file mode 100644 index 0000000..e69de29 --- /dev/null +++ b/Zurich_group/14_07_2014_2/MM.snm diff --git a/Zurich_group/14_07_2014_2/MM.synctex.gz b/Zurich_group/14_07_2014_2/MM.synctex.gz new file mode 100644 index 0000000..78b4daf --- /dev/null +++ b/Zurich_group/14_07_2014_2/MM.synctex.gz Binary files differ diff --git a/Zurich_group/14_07_2014_2/MM.tex b/Zurich_group/14_07_2014_2/MM.tex new file mode 100644 index 0000000..2e9ab92 --- /dev/null +++ b/Zurich_group/14_07_2014_2/MM.tex @@ -0,0 +1,1097 @@ +\documentclass[]{beamer} +\setbeamertemplate{navigation symbols}{} +\usepackage{beamerthemesplit} +\useoutertheme{infolines} +\usecolortheme{dolphin} +%\usetheme{Warsaw} +\usetheme{progressbar} +\usecolortheme{progressbar} + +\usefonttheme{progressbar} +\useoutertheme{progressbar} +\useinnertheme{progressbar} +\usepackage{graphicx} +%\usepackage{amssymb,amsmath} +\usepackage[latin1]{inputenc} +\usepackage{amsmath} +\newcommand\abs[1]{\left|#1\right|} +\usepackage{iwona} +\usepackage{hepparticles} +\usepackage{hepnicenames} +\usepackage{hepunits} +\progressbaroptions{imagename=images/lhcb} +%\usetheme{Boadilla}f + +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%5 +\definecolor{mygreen}{cmyk}{0.82,0.11,1,0.25} +\setbeamertemplate{blocks}[rounded][shadow=false] +\addtobeamertemplate{block begin}{\pgfsetfillopacity{0.8}}{\pgfsetfillopacity{1}} +\setbeamercolor{structure}{fg=mygreen} +\setbeamercolor*{block title example}{fg=mygreen!50, +bg= blue!10} +\setbeamercolor*{block body example}{fg= blue, +bg= blue!5} + + + + + +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%\beamersetuncovermixins{\opaqueness<1>{25}}{\opaqueness<2->{15}} +\title{Method of moments for $\PB \to \PKstar \mu \mu$} +\author{\underline{Marcin Chrzaszcz}$^{1,2}$} +\date{\today} + +\begin{document} + +{ +\institute{$^1$ University of Zurich, $^2$ Institute of Nuclear Physics} +\setbeamertemplate{footline}{} +\begin{frame} +\logo{ +\vspace{2 mm} +\includegraphics[height=1cm,keepaspectratio]{images/uzh.jpg}~ +\includegraphics[width=1cm,keepaspectratio]{images/ifj.png}} + + \titlepage +\end{frame} +} +\institute{UZH,IFJ} + +\section[Outline]{} +\begin{frame} +\tableofcontents +\end{frame} + +\section{Introduction} +\begin{frame}\frametitle{Plan} +Why method of moments: +\begin{enumerate} +\item Complementary approach in performing the fit. +\item Allows to extract info measuring quantities in event basis depending on the angular distribution. +\item Used in $\PB \to \rho \Plepton \nu$(SLAC-386 UC-414),\\ $\PJpsi \to \PK \PK \gamma$(PRD 71, 032005 (2005) ), etc. +\end{enumerate} + + +\end{frame} +\section{Method of Moments - Theory} +\begin{frame}\frametitle{Method of moments} +{~} +Let's assume we have our pdf with $k$ unknown parameters :$PDF(x_i, \alpha)$, $dim(\alpha)=k$. One can calculate $k$ moments, which are the functions of $\alpha_i$: +\begin{equation} +\mu_i=f(\alpha_1,..., \alpha_k) = E[W_i] +\end{equation} +If we have $n$ events in our $q^2$ bin, we can estimate: +\begin{equation} +\widehat{\mu}_i=\dfrac{1}{n}\sum_{j=0}^{j=n-1} w_j +\end{equation} +, where $w_j=g(x_i)$ + +\end{frame} + +\begin{frame}\frametitle{Trivial example} +{~} +Lets see how this works in practice: +\begin{equation} +f(x)=\dfrac{x^{a-1}e^{-x/b}} {b^a \Gamma(a)} +\end{equation} +we measure the moments:\\ +\begin{center} $m_1=\dfrac{X_1+X_2+...+X_n}{n}$,\\ $m_2=\dfrac{X_1^2+X_2^2+...+X_n^2}{n}$.\\\end{center} +and calculate them analytically: +\begin{center} $m_1=ab$, $m_2=b^2a(a+1)$\end{center} +So one just needs to solve this and get the answer: +\center $a=\dfrac{m_1^2}{m_2-m_1^2}$, $b=\dfrac{m_2-m_1^2}{m_1}$ +\end{frame} + +\section{Moments of Ss} + + +\begin{frame}\frametitle{Our PDF} +{~} +The angular terms: +\begin{multline} +\dfrac{d^4\Gamma}{dq^2 dcos\theta_k dcos\theta_l d\phi}=\dfrac{9}{32\pi}( \dfrac{3}{4}(1-F_l)\sin^2 \theta_k + F_l \cos^2 \theta_k + (\dfrac{1}{4}(1-F_l)\sin^2 \theta_k \\ -F_l\cos^2) \cos 2\theta_l + J_3 \sin^2 \theta_k \sin^2 \theta_l cos2\phi + J_4 \sin2 \theta_k \sin \theta_l \cos\phi +\\ J_5 \sin 2 \theta_k \sin \theta_l \cos \phi + (J_{6s} \sin^2 \theta_k + J_{6c} \cos^2 \theta_k) \cos \theta_l + \\ J_7 \sin 2\theta_k \sin \theta_l \sin \phi + J_8 \sin 2 \theta_k \sin 2 \theta_l \sin \phi + J_9 \sin^2 \theta_k \sin^2 \theta_l \sin 2 \phi) +\end{multline} +Since we are fitting a PDF we need to ensure it is normalized: +\begin{equation} +\int_{-\pi}^{\pi} d\phi \int_{-1}^{1} d cos\theta_l \int_{-1}^{1} d cos\theta_k \dfrac{d^4\Gamma}{dq^2 dcos\theta_k dcos\theta_l d\phi}=1 +\end{equation} + + +\end{frame} +\begin{frame}\frametitle{Measuring Js} +{~} +From equation 2 we have the following: + +\begin{equation} +\dfrac{1}{4}(3 J_{1c} + 6 J_{1s} - J_{2c} - 2 J_{2s}) =1 +\end{equation} +For now we will consider the following PDF: +\begin{equation} + \dfrac{d^3\Gamma}{\Gamma dcos\theta_k dcos\theta_l d\phi }(cos\theta_k , cos\theta_l, \phi) +\end{equation} + +Becouse our PDF is not normalized and we are measuring $\Gamma+\overline{\Gamma} +$ we are effectively fitting the $S_i$ (aka $J_i \to S_i$) +\end{frame} + + +\begin{frame}\frametitle{Moments for $\PB \to \PKstar \mu \mu$} +{~} +Let's calculate the moments for Ss: +\begin{equation} + \dfrac{d^3\Gamma}{\Gamma dcos\theta_k dcos\theta_l d\phi }sin^2 \theta_k sin^2 \theta_l cos 2 \phi= \dfrac{8 S_3 }{25} +\end{equation} +\begin{equation} + \dfrac{d^3\Gamma}{\Gamma dcos\theta_k dcos\theta_l d\phi } sin 2 \theta_k sin 2 \theta_k cos\phi= \dfrac{8 S_4 }{25} +\end{equation} +\begin{equation} + \dfrac{d^3\Gamma}{\Gamma dcos\theta_k dcos\theta_l d\phi }sin2\theta_k sin\theta_l cos\phi = \dfrac{2 S_5 }{5} +\end{equation} +\begin{equation} + \dfrac{d^3\Gamma}{\Gamma dcos\theta_k dcos\theta_l d\phi} sin 2 \theta_k sin \theta_l sin \phi = \dfrac{2 S_7 }{5} +\end{equation} +\begin{equation} + \dfrac{d^3\Gamma}{\Gamma dcos\theta_k dcos\theta_l d\phi} sin 2 \theta_k sin2 \theta_l sin \phi = \dfrac{8 S_8 }{25} +\end{equation} + + + +\end{frame} +\begin{frame}\frametitle{Moments for $\PB \to \PKstar \mu \mu$} +{~} +\begin{itemize} +\item The simplest solution one could imagine. +\item We are abusing the fact that the basis is orthogonal. +\item Each of the J doesn't know about other. +\item Only $S_{1s}$, $S_{2s}$, $S_{1c}$, $S_{2c}$ and $S_{6s}$, $S_{6c}$ are not orthogonal, but to get the answer you just need to solve a linear equation system so it's not a tragedy. +\end{itemize} +\begin{equation} + \dfrac{d^3\Gamma}{\Gamma dcos\theta_k dcos\theta_l d\phi} sin^2 \theta_k cos \theta_l = 0.1(S_6c+4S_6s) +\end{equation} +\begin{equation} + \dfrac{d^3\Gamma}{\Gamma dcos\theta_k dcos\theta_l d\phi} cos \theta_l = 0.25(S_{6}c+2S_{6s}) +\end{equation} + +solution: $S_{6c}=2 (4 M_{S_{6c}} - 5 M_{S_{6s}})$, $S_{6s}= -2 M_{S_{6c}} + 5 M_{S_{6s}}$ + + + +\end{frame} + + + +\section{Toy MC study} + +\begin{frame}\frametitle{Moments for $\PB \to \PKstar \mu \mu$} +{~} +Lets see if this method actually works. Let's take some random parameters for the PDF and make a toy. +\begin{columns} +\column{2.5in} +\includegraphics[scale=0.25]{images/J5.png} + + + +\column{2.5in} +\includegraphics[scale=0.25]{images/J7.png} + + +\end{columns} +\begin{itemize} +\item let's take 300 signal events as a working case. +\end{itemize} + +\end{frame} + + + + +\begin{frame}\frametitle{Moments for $\PB \to \PKstar \mu \mu$} +{~} +\small Lets see if this method actually works. Let's take some random parameters for the PDF and make a toy. +\begin{columns} +\column{2.5in} +\includegraphics[scale=0.25]{images/J3.png} + + + +\column{2.5in} +\includegraphics[scale=0.25]{images/J4.png} + + +\end{columns} + + +\begin{itemize} +\item let's take 300 signal events as a working case... we might still change the binning +\end{itemize} + +\end{frame} + + + +\begin{frame}\frametitle{Moments for $\PB \to \PKstar \mu \mu$} +{~} +Lets see if this method actually works. Let's take some random parameters for the PDF and make a toy. +\begin{columns} +\column{2.5in} +\includegraphics[scale=0.25]{images/J8.png} + + + +\column{2.5in} +\includegraphics[scale=0.25]{images/J9.png} + + +\end{columns} + +\begin{itemize} +\item let's take 300 signal events as a working case... we might still change the binning +\end{itemize} + +\end{frame} + +\begin{frame}\frametitle{Error Estimation} +{~} +\begin{itemize} +\item Since moment is the mean of a given distribution the error can be estimated as $mean/RMS$ +\item use TOY MC to check this assumption +\end{itemize} + +\includegraphics[scale=0.3]{plots/conw.png}\\ + + +\end{frame} +%%%%%%%%%%%%%%%%%%%%%%%%5 +\begin{frame}\frametitle{Correlation check} +{~} +\begin{itemize} +\item In theory $S_i$ shouldn't be correlated to $S_j$ in the moment calculation. +\item Lets put this to a test. +\end{itemize} + +\begin{columns} +\column{2.5in} +\includegraphics[scale=0.2]{plots/J9J4.png}\\ + + +\column{2.5in} +\includegraphics[scale=0.2]{plots/J8J5.png}\\ + + +\end{columns} + + +\end{frame} + + +%%%%%%%%%%%%%%%%%%%%%%%%5 +\begin{frame}\frametitle{Correlation check 2} +{~} +\begin{itemize} +\item Let's now FIX $J_x$ and simulate different $J_y$ +\item Again theory would suggest that one J shouldn't know about the other, so $J_x$ shouldn't change with scanning $J_y$ parameter +\end{itemize} + +\begin{columns} +\column{2.5in} +\includegraphics[scale=0.24]{plots/J5_vs_J9_300.png}\\ + + +\column{2.5in} +\includegraphics[scale=0.24]{plots/J3_vs_J9_300.png}\\ + + +\end{columns} + + +\end{frame} + + + +\section{2 am discovery} +\begin{frame}\frametitle{What will happen to our problem with an S-wave?} +{~} +Reminder: +\begin{multline} +\dfrac{d^4\Gamma}{dq^2 dcos\theta_k dcos\theta_l d\phi}=\dfrac{9}{32\pi}( J_{1s}sin^2 \theta_k + J_{1c}cos^2 \theta_k + (J_{2s}sin^2 \theta_k + \\ J_{2c}cos^2) cos 2\theta_l + J_3 sin^2 \theta_k sin^2 \theta_l cos2\phi + J_4 sin2 \theta_k sin \theta_l cos\phi +\\ J_5 sin2 \theta_k sin \theta_l cos \phi + (J_{6s} sin^2 \theta_k + J_{6c} cos^2 \theta_k) cos \theta_l + \\ J_7 sin 2\theta_k sin \theta_l sin \phi + J_8 sin 2 \theta_k sin 2 \theta_l sin phi + J_9 sin^2 \theta_k sin^2 \theta_l sin 2 \phi) +\end{multline} +Let's add a very discussing things that keeps us awake at night: +\begin{multline} +W_s =\dfrac{2}{3} F_s \sin^2 \theta_l + \frac{4}{3} A_s \sin^2 \theta_l \cos \theta_k + I_4 sin \theta_k sin 2 \theta_lcos \phi \\+ I_5 sin \theta_k sin \theta_l cos \phi + I_7 sin \theta_k sin \theta_l + sin \phi + I_8 sin \theta_k sin 2\theta_l sin\phi) +\end{multline} + + +\end{frame} + +\begin{frame}\frametitle{What will happen to our problem with an S-wave?} +{~} +So now our PDF is sum of eq. 15 and 16. Of coz we need to require normalization: +\begin{equation} +\dfrac{1}{12}(32 I_{1a} + 9 J_{1c} + 18 J_{1s} - 3 J_{2c} - 6 J_{2s}) =1 +\end{equation} +No surprises here. If we have a S-wave it has to enter in $\Gamma$. +To build up the preasure, what will happen to our Ss? + + + +\end{frame} + + +\begin{frame}\frametitle{NOTHING!!!!!!!!} +{~} +We are completely insensitive to S-wave: +\begin{equation} + \dfrac{d^3\Gamma}{\Gamma dcos\theta_k dcos\theta_l d\phi }sin^2 \theta_k sin^2 \theta_l cos 2 \phi= \dfrac{8 S_3 }{25} +\end{equation} +\begin{equation} + \dfrac{d^3\Gamma}{\Gamma dcos\theta_k dcos\theta_l d\phi } sin 2 \theta_k sin 2 \theta_k cos\phi= \dfrac{8 S_4 }{25} +\end{equation} +\begin{equation} + \dfrac{d^3\Gamma}{\Gamma dcos\theta_k dcos\theta_l d\phi }sin2\theta_k sin\theta_l cos\phi = \dfrac{2 S_5 }{5} +\end{equation} +\begin{equation} + \dfrac{d^3\Gamma}{\Gamma dcos\theta_k dcos\theta_l d\phi} sin 2 \theta_k sin \theta_l sin \phi = \dfrac{2 S_7 }{5} +\end{equation} +\begin{equation} + \dfrac{d^3\Gamma}{\Gamma dcos\theta_k dcos\theta_l d\phi} sin 2 \theta_k sin2 \theta_l sin \phi = \dfrac{8 S_8 }{25} +\end{equation} + + + +\end{frame} + +\begin{frame}\frametitle{Thins get better :)} +{~} +We can even measure directly the S-wave: +\begin{equation} + \dfrac{d^3\Gamma}{\Gamma dcos\theta_k dcos\theta_l d\phi }sin^2 \theta_l cos \theta_k = \dfrac{32 I_{1b} }{45} +\end{equation} +\begin{equation} + \dfrac{d^3\Gamma}{\Gamma dcos\theta_k dcos\theta_l d\phi } sin \theta_k sin 2 \theta_l cos \phi = \dfrac{16 I_4 }{45} +\end{equation} +\begin{equation} + \dfrac{d^3\Gamma}{\Gamma dcos\theta_k dcos\theta_l d\phi } sin\theta_k sin\theta_l cos\phi = \dfrac{4 I_5 }{9} +\end{equation} +\begin{equation} + \dfrac{d^3\Gamma}{\Gamma dcos\theta_k dcos\theta_l d\phi} sin \theta_k sin 2 \theta_l sin \phi = \dfrac{4 I_7 }{9} +\end{equation} +\begin{equation} + \dfrac{d^3\Gamma}{\Gamma dcos\theta_k dcos\theta_l d\phi} sin \theta_k sin2 \theta_l sin \phi = \dfrac{16 S_8 }{45} +\end{equation} + + + +\end{frame} + + +\begin{frame}\frametitle{Conclusions on S-wave} +{~} +\begin{itemize} +\item S-wave components are transparent to method of moments. +\item If they are orthogonal to others all they toy studies holds for them as well(will reapat for robustness but can bet my house that there is nothing going on there). +\item +\end{itemize} + +\end{frame} + + + +\begin{frame}\frametitle{Conclusions} +{~} +\begin{itemize} +\item Implemented moments method for the K*mm and start testing with toy MC +\item The method converge fast and works for the "simple case", i.e. signal only. +\item Method completely insensitive to S-wave component, thanks to orthogonality. +\item Complementary one can measure in-depended S-wave component. +\end{itemize} +TO DO: +\begin{itemize} +\item add realism: backgrounds +\item Do the unfolding +\item Study binning +\end{itemize} + +\end{frame} +%%%%%%%%%%%%%%%%%%%%%%%%%55 +\begin{frame}\frametitle{~} +{~} +\center \Huge BACKUPS + +\end{frame} + +\begin{frame} +{~} + +\begin{columns} +\column{2.5in} +\includegraphics[scale=0.17]{plots/pool_plots/J1c_50.png}\\ +\includegraphics[scale=0.17]{plots/pool_plots/J1c_75.png}\\ + + +\column{2.5in} +\includegraphics[scale=0.17]{plots/pool_plots/J1c_50E.png}\\ +\includegraphics[scale=0.17]{plots/pool_plots/J1c_75E.png} + + +\end{columns} +\end{frame} + +\begin{frame} +{~} + +\begin{columns} +\column{2.5in} +\includegraphics[scale=0.17]{plots/pool_plots/J1c_125.png}\\ +\includegraphics[scale=0.17]{plots/pool_plots/J1c_175.png}\\ + + +\column{2.5in} +\includegraphics[scale=0.17]{plots/pool_plots/J1c_125E.png}\\ +\includegraphics[scale=0.17]{plots/pool_plots/J1c_175E.png} + + +\end{columns} +\end{frame} + +\begin{frame} +{~} + +\begin{columns} +\column{2.5in} +\includegraphics[scale=0.17]{plots/pool_plots/J1c_225.png}\\ +\includegraphics[scale=0.17]{plots/pool_plots/J1c_300.png}\\ + + +\column{2.5in} +\includegraphics[scale=0.17]{plots/pool_plots/J1c_225E.png}\\ +\includegraphics[scale=0.17]{plots/pool_plots/J1c_300E.png} + + +\end{columns} +\end{frame} + + +\begin{frame} +{~} + +\begin{columns} +\column{2.5in} +\includegraphics[scale=0.17]{plots/pool_plots/J1c_400.png}\\ + + + +\column{2.5in} +\includegraphics[scale=0.17]{plots/pool_plots/J1c_400E.png}\\ + + + +\end{columns} +\end{frame} + +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%55 +\begin{frame} +{~} + +\begin{columns} +\column{2.5in} +\includegraphics[scale=0.17]{plots/pool_plots/J1s_50.png}\\ +\includegraphics[scale=0.17]{plots/pool_plots/J1s_75.png}\\ + + +\column{2.5in} +\includegraphics[scale=0.17]{plots/pool_plots/J1s_50E.png}\\ +\includegraphics[scale=0.17]{plots/pool_plots/J1s_75E.png} + + +\end{columns} +\end{frame} + +\begin{frame} +{~} + +\begin{columns} +\column{2.5in} +\includegraphics[scale=0.17]{plots/pool_plots/J1s_125.png}\\ +\includegraphics[scale=0.17]{plots/pool_plots/J1s_175.png}\\ + + +\column{2.5in} +\includegraphics[scale=0.17]{plots/pool_plots/J1s_125E.png}\\ +\includegraphics[scale=0.17]{plots/pool_plots/J1s_175E.png} + + +\end{columns} +\end{frame} + +\begin{frame} +{~} + +\begin{columns} 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+\includegraphics[scale=0.17]{plots/pool_plots/J9_500E.png}\\ + + +\end{columns} +\end{frame} + +%%%%%%%%%%%%%%%%%%%%%%% +\begin{frame} +{~} + +\begin{columns} +\column{2.5in} +\includegraphics[scale=0.2]{plots/J9J8.png}\\ +\includegraphics[scale=0.2]{plots/J9J5.png}\\ + +\column{2.5in} +\includegraphics[scale=0.2]{plots/J9J7.png}\\ +\includegraphics[scale=0.2]{plots/J9J4.png}\\ + +\end{columns} + +\end{frame} + +\begin{frame} +{~} + +\begin{columns} +\column{2.5in} +\includegraphics[scale=0.2]{plots/J9J3.png}\\ +\includegraphics[scale=0.2]{plots/J8J7.png}\\ + +\column{2.5in} +\includegraphics[scale=0.2]{plots/J8J5.png}\\ +\includegraphics[scale=0.2]{plots/J8J4.png}\\ + +\end{columns} + +\end{frame} + + + + + + +\end{document} \ No newline at end of file diff --git a/Zurich_group/14_07_2014_2/MM.toc b/Zurich_group/14_07_2014_2/MM.toc new file mode 100644 index 0000000..77ff2e8 --- /dev/null +++ b/Zurich_group/14_07_2014_2/MM.toc @@ -0,0 +1,6 @@ +\beamer@endinputifotherversion {3.10pt} 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+\newcommand\abs[1]{\left|#1\right|} +\usepackage{hepnicenames} +\usepackage{hepunits} +\usepackage{color} + + + +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%5 +\definecolor{mygreen}{cmyk}{0.82,0.11,1,0.25} + + +\usetheme{Sybila} + +\title[Unfolding for counting experiments]{Unfolding for counting experiments} +\author{Marcin Chrz\k{a}szcz$^{1,2}$, Nicola Serra$^{1}$} +\institute{$^1$~University of Zurich,\\ $^2$~Institute of Nuclear Physics, Krakow} +\date{\today} + +\begin{document} +% --------------------------- SLIDE -------------------------------------------- +\frame[plain]{\titlepage} +\author{Marcin Chrz\k{a}szcz} +% ------------------------------------------------------------------------------ +% --------------------------- SLIDE -------------------------------------------- + +\begin{frame}\frametitle{Quo vadis $\PBzero \to \PKstar \mu \mu$?} + +\center \includegraphics[width=0.8\paperwidth]{diagram.png}\\ + +\end{frame} +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +\begin{frame}\frametitle{Quo vadis $\PBzero \to \PKstar \mu \mu$?} + +\center \includegraphics[width=0.8\paperwidth]{matrix.png}\\ + +\end{frame} + + +\section{Introduction} + +\begin{frame}\frametitle{Reminder} +For now: +\begin{itemize} +\item We have proven that there has to exists unfolding matrix. +\item Shown how to construct transformation matrix: $Gen \to Reco$. +\item Inverting it we can have transformation matrix of $Reco \to Gen$. +\item For details: \href{https://indico.cern.ch/event/316905/session/1/contribution/18/material/slides/0.pdf}{LINK} + +\end{itemize} + +What is missing? +\begin{columns} +\column{1in} +\begin{enumerate} +\item ERROR! +\end{enumerate} +\column{4in} +\includegraphics[width=0.8\textwidth]{err.jpg}\\ +\end{columns} + +\end{frame} + + + +\begin{frame}\frametitle{How to?} +\begin{itemize} +\item So lets say that transformation matrix:$Gen \to Reco$ is $\epsilon_{i,j}$. +\item Of coz it's easy to write the covariance matrix(error matrix): +\end{itemize} +\begin{equation} +cov(\epsilon_{\alpha, \beta},\epsilon_{a,b}) +\end{equation} +\begin{itemize} +\item Then we can calculate the matrix: $\epsilon_{i,j}^{-1}$(assuming it exists). +\item and the 1M dollar question is: $cov(\epsilon_{\alpha, \beta}^{-1},\epsilon_{a,b}^{-1}) =?$ +\end{itemize} + +\end{frame} + +\begin{frame}\frametitle{Answer to 1M dolar quesion} +\begin{itemize} +\item Solution comes from $\tau$ physics :) +\end{itemize} +\begin{equation} +cov(\epsilon_{\alpha, \beta}^{-1},\epsilon_{a,b}^{-1}) = \epsilon^{-1}_{\alpha,i} \epsilon^{-1}_{j,\beta} \epsilon^{-1}_{a,k} \epsilon^{-1}_{l,b} cov( \epsilon_{ij} \epsilon_{kl}) +\end{equation} +\begin{itemize} +\item It's way to late to latex the prove. For prove see: \href{http://arxiv.org/abs/hep-ex/9909031}{arXiv:hep-ex/9909031} +\item Thanks to orthonormal basis lifes gets simpler: +\end{itemize} +\begin{equation} +cov(\epsilon_{ij},\epsilon_{kl} ) = \sigma_{\epsilon,ij} \delta_{ik} \delta_{jl} ( no correlations) +\end{equation} + +\end{frame} + + +\begin{frame}\frametitle{Total error} +\begin{itemize} +\item So let's say: $B=\epsilon^{-1} f$ +\item Then: +\end{itemize} +\begin{equation} +cov(B_i,B_j) = f_a f_b cov(\epsilon_{i \alpha }^{-1} , \epsilon_{j \beta}^{-1} )+ \epsilon^{-1}_{ ik} \epsilon^{-1}_{jl} cov(f_k,f_l) +\end{equation} +\begin{itemize} +\item Looks easy just need to implement! +\end{itemize} + +\end{frame} + + +\begin{frame}\frametitle{Matrix, $0.1-0.98~GeV$} +\tiny{ +$ A_{reco\rightarrow gen}=\begin{pmatrix} + 0.9495 0.008518 0.01522 -0.007362 0.01496 -0.04544 -0.02468 0.002078 + 0.0002651 0.8261 0.00978 -0.001042 0.004382 0.03191 0.01247 0.01886 + -0.0003391 0.009773 1.03 0.008433 -0.002028 0.003 0.02086 0.001549 + -0.00403 -0.001336 0.01047 0.9215 0.006898 -0.0006023 0.003041 -0.004465 + 0.006557 0.005531 -0.002423 0.00691 1.171 -0.01082 -0.0158 -0.003231 + -0.01931 0.03973 0.00342 -0.0006455 -0.01081 0.9452 0.02232 -0.005304 + .008421 0.0124 0.02071 0.002415 -0.01264 0.01785 1.06 0.001084 + 0.000347 0.01886 0.001555 -0.003568 -0.002591 -0.004226 0.001093 0.8204 + + + + + \end{pmatrix}$ +} + + + + + +\end{frame} + +\begin{frame}\frametitle{Constructing Matrix unfolding} +\begin{itemize} +\item We got first column of the unfolding matrix. +\end{itemize} +\small{ +$ \begin{pmatrix} + 1.06 & \cdots & a_{1,8} \\ + 0.01157 & \cdots & a_{2,8} \\ + -0.003547 & \ddots & \vdots \\ + 0.0007841 & \ddots & \vdots \\ + 0.001126 & \ddots & \vdots \\ + 0.001766 & \ddots & \vdots \\ + 0.001664 & \ddots & \vdots \\ + -0.001937 & \cdots & a_{8,8} + \end{pmatrix}$ + + +} +\begin{itemize} +\item How about the others? +\item We can reweight accordingly to $f_x$. +\end{itemize} + +\end{frame} + +\begin{frame}\frametitle{Constructing Matrix unfolding} +\begin{itemize} +\item To get $S_3$ each event $i^{th}$ has has weight $f_{S_3}(\cos \theta_{k_i},\cos \theta_{l_i},\phi_i) $ +\item One can calculate on MC the reweighed moments in PHPS: +\end{itemize} +\begin{equation} +\int PDF*f_{S_3}=\dfrac{32}{225} +\end{equation} +\begin{itemize} +\item Our base vector now is:$v^{T}_{gen}=(0 ,\frac{32}{225},0,0,0,0,0,0)$ +\item So lets see what do we get as reconstructed vector(after multiplying by $\frac{225}{32}$. +\small{$v^{T}_{rec}=( 0.042, 1.105,-0.005,0.003,-0.0023,-0.005,-0.005,-0.006)$ } +\end{itemize} + +\end{frame} + + +\begin{frame}\frametitle{Constructing Matrix unfolding} +\begin{itemize} +\item Now the matrix looks like: +\end{itemize} +\small{ +$ \begin{pmatrix} + 1.06 & 0.042 & \cdots & a_{1,8} \\ + 0.01157 & 1.105 & \cdots & a_{2,8} \\ + -0.003547 & -0.005 & \ddots & \vdots \\ + 0.0007841 &-0.005 & \ddots & \vdots \\ + 0.001126 & 0.003 &\ddots & \vdots \\ + 0.001766 & -0.0023 &\ddots & \vdots \\ + 0.001664 & -0.005 &\ddots & \vdots \\ + -0.001937 & -0.006 &\cdots & a_{8,8} + \end{pmatrix}$ + + +} +\begin{itemize} +\item The others go in the same way. +\item Repenting this exercise from $1^{st}$ year algebra we can get the full matrix +\end{itemize} + + +\end{frame} +\begin{frame}\frametitle{Constructing Matrix unfolding} +\begin{itemize} +\item The full transformation matrix from generator space to reconstructed space: +\end{itemize} +\tiny{ +$ A_{gen\rightarrow reco}=\begin{pmatrix} + 1.06 & 0.0423 & -0.0081 & 0.0022 & 0.0049 & 0.0037 & 0.0028 & -0.0065 \\ + + 0.0115 & 1.105 & -0.0050 & 0.0027 & -0.0018 & -0.0040 &-0.0054 & -0.0065 \\ + -0.0035 & -0.0050 & 0.981 & 0.0005 & -0.0025 & 0.0002 & -0.0037 & -0.0048\\ + 0.00078 & 0.0034 & 0.0006 & 1.002 & -0.0032 & -0.0040 & 0.0003 & 0.0018\\ + 0.001126 & -0.0023 & -0.0032 & -0.0032 & 1.055 & 0.001& -0.004 & 0.0023\\ + 0.00176 & -0.0050 & 0.00036 & -0.0040 & 0.0011 & 0.96 & -0.0057 & 0.0009 \\ + 0.0016 & -0.005 & -0.003 & 0.00029& -0.003 &-0.004 & 0.9543 & 0.0000\\ + -0.0019 & -0.0065 & -0.004 & 0.001 & 0.0018 & 0.0007 & 0.000 & 1.098 \\ + + + + + + \end{pmatrix}$ + + +} +\begin{itemize} +\item Inverting the matrix is simple, and doable +\end{itemize} +\tiny{ +$ A_{reco\rightarrow gen}=\begin{pmatrix} + 0.9434 & -0.036 & 0.007& -0.0020 & -0.0044& -0.0038 & -0.0030 & 0.0054\\ + -0.009 & 0.90 & 0.0045 & -0.0024& 0.0016 & 0.003873 & 0.00527& 0.005 \\ + 0.003 & 0.00454& 1.019 & -0.00058 & 0.0025& -0.000291 & 0.004 & 0.004 \\ +-0.00071 & -0.0030 & -0.0007 & 0.9977 & 0.0030 & 0.004206 &-0.0003 & -0.0017 \\ + -0.001 & 0.0020 & 0.0031& 0.0030 & 0.9483 & -0.0010 & 0.004626 & -0.0019 \\ + -0.001 & 0.004 & -0.0003 & 0.0042 & -0.001087 & 1.037 & 0.0063 & -0.0009\\ + -0.0017 & 0.0053 & 0.0042 & -0.0002 & 0.00370& 0.0050 & 1.048 & 0.0000 \\ + 0.0016& 0.0053& 0.00452 & -0.001 & -0.001582 & -0.0007213 &0.000 & 0.9105 \\ + + + + + \end{pmatrix}$ +} + +\end{frame} + + + +\begin{frame}\frametitle{Sensitivity to unknowns} +\begin{itemize} +\item We are unfolding based on MC. +\item There are MC/Data differences, which can have impact on the unfolding. +\end{itemize} +Let's put small modification: +\begin{equation} +w_j \to \overline{w_j}= \dfrac{1}{eff(\cos \theta_{l~j}, \cos \theta_{k~j}, \phi_{j})} \times corr(\cos \theta_{l~j}, \cos \theta_{k~j}, \phi_{j}) +\end{equation} +Unfortunately God didn't allowed me sneak peak into his cards so I don't know $corr(\cos \theta_{l}, \cos \theta_{k}, \phi)$, but let's try out some functions and see what happens :) + + +\end{frame} + +\begin{frame}\frametitle{Corr1 functions} +\begin{columns} +\column{2in} +\includegraphics[width=\linewidth]{corr/Corr1_cosk.png}\\ +\includegraphics[width=\linewidth]{corr/Corr1_cosl.png}\\ +\column{2.5in} +$ +corr1(\cos_l, \cos_k,\phi)= 1+ 0.032 \cos_l - 0.032 \cos_k + 0.01 \phi +$ +\includegraphics[width=0.8\linewidth]{corr/Corr1_phi.png}\\ + +\end{columns} + +\end{frame} +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +\begin{frame}\frametitle{Corr2 functions} +\begin{columns} +\column{2in} +\includegraphics[width=0.85\linewidth]{corr/corr21.png}\\ +\includegraphics[width=0.85\linewidth]{corr/corr22.png}\\ +\column{2.5in} +$ +corr2(\cos_l, \cos_k,\phi)= -0.02 \cos_l^2 + 0.02 \cos_k^2 - + 0.015 \phi^2+ 1 +$ +\includegraphics[width=0.75\linewidth]{corr/corr23.png}\\ + +\end{columns} + +\end{frame} + +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +\begin{frame}\frametitle{Corr3 functions} +\begin{columns} +\column{2in} +\includegraphics[width=0.85\linewidth]{corr/corr31.png}\\ +\includegraphics[width=0.85\linewidth]{corr/corr32.png}\\ +\column{2.5in} +$ +corr3(\cos_l, \cos_k,\phi)= 0.02 \cos_l \cos_k + 0.01 \cos_k \phi - 0.01 \phi \cos_l + 1 +$ +\includegraphics[width=0.75\linewidth]{corr/corr33.png}\\ + +\end{columns} + +\end{frame} +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +\begin{frame}\frametitle{Corr4 functions} +\begin{columns} +\column{2in} +\includegraphics[width=0.85\linewidth]{corr/corr41.png}\\ +\includegraphics[width=0.85\linewidth]{corr/corr42.png}\\ +\column{2.5in} +$ +corr3(\cos_l, \cos_k,\phi)= 0.01 \cos_k \cos_l \phi + 1 +$ +\includegraphics[width=0.75\linewidth]{corr/corr43.png}\\ + +\end{columns} + +\end{frame} + + + + +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% + + +\begin{frame}\frametitle{Corr1- MM} + + +\begin{tiny} + +\begin{center} + \begin{tabular}{ l l l l l l l l l } + \hline + \multicolumn{8}{c}{Mean of the pull} \\ \hline +$q^2$ & $S_3$ & $S_4$ & $S_5$ & $S_{6s}$ & $S_{6c}$ & $S_7$ & $S_8$ \\ \hline \hline + +0 & \scalebox{0.5}{$0.0085 \pm 0.026(0.3)$} & \scalebox{0.5}{$0.13 \pm 0.027(4.6)$} & \scalebox{0.5}{$-0.025 \pm 0.027(-0.92)$} & \scalebox{0.5}{$0.46 \pm 0.027(17)$} & \scalebox{0.5}{$-0.13 \pm 0.028(-4.7)$} & \scalebox{0.5}{$0.029 \pm 0.028(1)$} & \scalebox{0.5}{$-0.66 \pm 0.027(-25)$} \\ \hline +1 & \scalebox{0.5}{$0.0094 \pm 0.028(0.33)$} & \scalebox{0.5}{$0.078 \pm 0.028(2.8)$} & \scalebox{0.5}{$-0.02 \pm 0.028(-0.73)$} & \scalebox{0.5}{$0.24 \pm 0.028(8.5)$} & \scalebox{0.5}{$-0.075 \pm 0.028(-2.7)$} & \scalebox{0.5}{$-0.016 \pm 0.026(-0.63)$} & \scalebox{0.5}{$-0.39 \pm 0.028(-14)$} \\ \hline +2 & \scalebox{0.5}{$-0.02 \pm 0.027(-0.72)$} & \scalebox{0.5}{$0.027 \pm 0.026(1)$} & \scalebox{0.5}{$-0.024 \pm 0.027(-0.91)$} & \scalebox{0.5}{$0.18 \pm 0.027(6.8)$} & \scalebox{0.5}{$-0.024 \pm 0.027(-0.89)$} & \scalebox{0.5}{$-0.067 \pm 0.027(-2.5)$} & \scalebox{0.5}{$-0.39 \pm 0.028(-14)$} \\ \hline +3 & \scalebox{0.5}{$0.013 \pm 0.028(0.46)$} & \scalebox{0.5}{$-0.0089 \pm 0.027(-0.32)$} & \scalebox{0.5}{$0.055 \pm 0.026(2.1)$} & \scalebox{0.5}{$0.12 \pm 0.027(4.7)$} & \scalebox{0.5}{$0.11 \pm 0.027(3.9)$} & \scalebox{0.5}{$-0.018 \pm 0.028(-0.63)$} & \scalebox{0.5}{$-0.43 \pm 0.027(-16)$} \\ \hline +4 & \scalebox{0.5}{$-0.0054 \pm 0.029(-0.18)$} & \scalebox{0.5}{$-0.066 \pm 0.027(-2.4)$} & \scalebox{0.5}{$0.037 \pm 0.028(1.3)$} & \scalebox{0.5}{$0.22 \pm 0.027(8.1)$} & \scalebox{0.5}{$0.099 \pm 0.027(3.7)$} & \scalebox{0.5}{$-0.1 \pm 0.026(-3.8)$} & \scalebox{0.5}{$-0.41 \pm 0.026(-15)$} \\ \hline +5 & \scalebox{0.5}{$0.06 \pm 0.027(2.2)$} & \scalebox{0.5}{$-0.069 \pm 0.026(-2.6)$} & \scalebox{0.5}{$-0.013 \pm 0.028(-0.49)$} & \scalebox{0.5}{$0.21 \pm 0.027(7.8)$} & \scalebox{0.5}{$0.093 \pm 0.027(3.5)$} & \scalebox{0.5}{$-0.083 \pm 0.028(-3)$} & \scalebox{0.5}{$-0.41 \pm 0.028(-15)$} \\ \hline +6 & \scalebox{0.5}{$0.0064 \pm 0.026(0.25)$} & \scalebox{0.5}{$-0.051 \pm 0.027(-1.9)$} & \scalebox{0.5}{$-0.029 \pm 0.028(-1)$} & \scalebox{0.5}{$0.26 \pm 0.028(9.2)$} & \scalebox{0.5}{$0.14 \pm 0.027(5.1)$} & \scalebox{0.5}{$-0.081 \pm 0.027(-3)$} & \scalebox{0.5}{$-0.45 \pm 0.028(-16)$} \\ \hline +%7 & \scalebox{0.5}{$0.22 \pm 0.027(8)$} & \scalebox{0.5}{$-0.34 \pm 0.028(-12)$} & \scalebox{0.5}{$-0.43 \pm 0.026(-16)$} & \scalebox{0.5}{$2.4 \pm 0.029(82)$} & \scalebox{0.5}{$0.66 \pm 0.027(24)$} & \scalebox{0.5}{$-0.24 \pm 0.028(-8.6)$} & \scalebox{0.5}{$-0.51 \pm 0.027(-19)$} & +8 & \scalebox{0.5}{$0.023 \pm 0.027(0.85)$} & \scalebox{0.5}{$-0.031 \pm 0.028(-1.1)$} & \scalebox{0.5}{$0.0042 \pm 0.028(0.15)$} & \scalebox{0.5}{$0.21 \pm 0.026(7.8)$} & \scalebox{0.5}{$0.12 \pm 0.028(4.2)$} & \scalebox{0.5}{$-0.13 \pm 0.027(-4.8)$} & \scalebox{0.5}{$-0.48 \pm 0.026(-18)$} \\ \hline +9 & \scalebox{0.5}{$-0.017 \pm 0.027(-0.63)$} & \scalebox{0.5}{$-0.015 \pm 0.026(-0.56)$} & \scalebox{0.5}{$-0.0052 \pm 0.026(-0.2)$} & \scalebox{0.5}{$0.27 \pm 0.027(10)$} & \scalebox{0.5}{$0.046 \pm 0.026(1.7)$} & \scalebox{0.5}{$-0.12 \pm 0.026(-4.4)$} & \scalebox{0.5}{$-0.5 \pm 0.026(-19)$} \\ \hline +10 & \scalebox{0.5}{$-0.054 \pm 0.027(-2)$} & \scalebox{0.5}{$-0.056 \pm 0.026(-2.2)$} & \scalebox{0.5}{$0.036 \pm 0.026(1.4)$} & \scalebox{0.5}{$0.16 \pm 0.028(5.7)$} & \scalebox{0.5}{$0.077 \pm 0.028(2.8)$} & \scalebox{0.5}{$-0.034 \pm 0.027(-1.3)$} & \scalebox{0.5}{$-0.39 \pm 0.028(-14)$} \\ \hline +11 & \scalebox{0.5}{$0.023 \pm 0.027(0.88)$} & \scalebox{0.5}{$0.021 \pm 0.027(0.8)$} & \scalebox{0.5}{$-0.011 \pm 0.027(-0.41)$} & \scalebox{0.5}{$0.14 \pm 0.027(5)$} & \scalebox{0.5}{$0.042 \pm 0.027(1.6)$} & \scalebox{0.5}{$-0.098 \pm 0.028(-3.5)$} & \scalebox{0.5}{$-0.3 \pm 0.027(-11)$} \\ \hline + + + \hline + + + \end{tabular} + +\end{center} + + +\end{tiny} +\end{frame} + +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% + + +\begin{frame}\frametitle{Corr2- MM} + + +\begin{tiny} + +\begin{center} + \begin{tabular}{ l l l l l l l l l } + \hline + \multicolumn{8}{c}{Mean of the pull} \\ \hline +$q^2$ & $S_3$ & $S_4$ & $S_5$ & $S_{6s}$ & $S_{6c}$ & $S_7$ & $S_8$ \\ \hline \hline + +0 & \scalebox{0.5}{$-0.21 \pm 0.026(-8.1)$} & \scalebox{0.5}{$0.061 \pm 0.026(2.3)$} & \scalebox{0.5}{$-0.016 \pm 0.026(-0.63)$} & \scalebox{0.5}{$0.048 \pm 0.026(1.8)$} & \scalebox{0.5}{$-0.0062 \pm 0.027(-0.23)$} & \scalebox{0.5}{$-0.012 \pm 0.028(-0.44)$} & \scalebox{0.5}{$0.0091 \pm 0.026(0.36)$} \\ \hline +1 & \scalebox{0.5}{$-0.12 \pm 0.028(-4.5)$} & \scalebox{0.5}{$0.032 \pm 0.027(1.2)$} & \scalebox{0.5}{$-0.0071 \pm 0.026(-0.27)$} & \scalebox{0.5}{$0.02 \pm 0.027(0.75)$} & \scalebox{0.5}{$-0.086 \pm 0.027(-3.2)$} & \scalebox{0.5}{$-0.03 \pm 0.025(-1.2)$} & \scalebox{0.5}{$0.021 \pm 0.027(0.79)$} \\ \hline +2 & \scalebox{0.5}{$-0.15 \pm 0.027(-5.8)$} & \scalebox{0.5}{$-0.013 \pm 0.026(-0.49)$} & \scalebox{0.5}{$0.011 \pm 0.026(0.44)$} & \scalebox{0.5}{$-0.039 \pm 0.026(-1.5)$} & \scalebox{0.5}{$-0.032 \pm 0.027(-1.2)$} & \scalebox{0.5}{$-0.066 \pm 0.027(-2.5)$} & \scalebox{0.5}{$0.018 \pm 0.028(0.64)$} \\ \hline +3 & \scalebox{0.5}{$-0.15 \pm 0.027(-5.6)$} & \scalebox{0.5}{$0.025 \pm 0.026(0.96)$} & \scalebox{0.5}{$0.016 \pm 0.027(0.58)$} & \scalebox{0.5}{$-0.062 \pm 0.027(-2.3)$} & \scalebox{0.5}{$0.037 \pm 0.026(1.4)$} & \scalebox{0.5}{$0.026 \pm 0.027(0.96)$} & \scalebox{0.5}{$-0.016 \pm 0.027(-0.6)$} \\ \hline +4 & \scalebox{0.5}{$-0.12 \pm 0.028(-4.5)$} & \scalebox{0.5}{$-0.024 \pm 0.026(-0.92)$} & \scalebox{0.5}{$0.045 \pm 0.027(1.6)$} & \scalebox{0.5}{$0.0075 \pm 0.026(0.29)$} & \scalebox{0.5}{$0.015 \pm 0.027(0.53)$} & \scalebox{0.5}{$-0.036 \pm 0.026(-1.4)$} & \scalebox{0.5}{$0.037 \pm 0.026(1.4)$} \\ \hline +5 & \scalebox{0.5}{$-0.095 \pm 0.027(-3.6)$} & \scalebox{0.5}{$-0.032 \pm 0.026(-1.2)$} & \scalebox{0.5}{$0.014 \pm 0.026(0.52)$} & \scalebox{0.5}{$-0.013 \pm 0.026(-0.48)$} & \scalebox{0.5}{$-0.0093 \pm 0.027(-0.35)$} & \scalebox{0.5}{$-0.013 \pm 0.026(-0.51)$} & \scalebox{0.5}{$0.042 \pm 0.027(1.6)$} \\ \hline +6 & \scalebox{0.5}{$-0.17 \pm 0.025(-6.5)$} & \scalebox{0.5}{$0.008 \pm 0.027(0.3)$} & \scalebox{0.5}{$0.012 \pm 0.027(0.45)$} & \scalebox{0.5}{$0.029 \pm 0.027(1.1)$} & \scalebox{0.5}{$0.0072 \pm 0.027(0.27)$} & \scalebox{0.5}{$-0.0012 \pm 0.026(-0.046)$} & \scalebox{0.5}{$0.011 \pm 0.027(0.42)$} \\ \hline +%7 & \scalebox{0.5}{$0.078 \pm 0.026(3)$} & \scalebox{0.5}{$-0.3 \pm 0.026(-11)$} & \scalebox{0.5}{$-0.34 \pm 0.026(-13)$} & \scalebox{0.5}{$2.1 \pm 0.028(73)$} & \scalebox{0.5}{$0.47 \pm 0.026(18)$} & \scalebox{0.5}{$-0.17 \pm 0.027(-6.1)$} & \scalebox{0.5}{$0.0051 \pm 0.027(0.19)$} \\ \hline +8 & \scalebox{0.5}{$-0.13 \pm 0.026(-5.1)$} & \scalebox{0.5}{$-0.0077 \pm 0.027(-0.28)$} & \scalebox{0.5}{$0.05 \pm 0.027(1.9)$} & \scalebox{0.5}{$-0.03 \pm 0.026(-1.2)$} & \scalebox{0.5}{$-0.012 \pm 0.028(-0.44)$} & \scalebox{0.5}{$-0.046 \pm 0.026(-1.7)$} & \scalebox{0.5}{$0.031 \pm 0.026(1.2)$} \\ \hline +9 & \scalebox{0.5}{$-0.15 \pm 0.026(-5.7)$} & \scalebox{0.5}{$-0.0083 \pm 0.026(-0.32)$} & \scalebox{0.5}{$0.03 \pm 0.026(1.2)$} & \scalebox{0.5}{$0.044 \pm 0.027(1.6)$} & \scalebox{0.5}{$-0.07 \pm 0.026(-2.7)$} & \scalebox{0.5}{$-0.022 \pm 0.026(-0.84)$} & \scalebox{0.5}{$-0.045 \pm 0.026(-1.7)$} \\ \hline +10 & \scalebox{0.5}{$-0.15 \pm 0.025(-5.8)$} & \scalebox{0.5}{$-0.032 \pm 0.025(-1.3)$} & \scalebox{0.5}{$0.059 \pm 0.026(2.2)$} & \scalebox{0.5}{$-0.072 \pm 0.028(-2.6)$} & \scalebox{0.5}{$-0.029 \pm 0.027(-1.1)$} & \scalebox{0.5}{$0.064 \pm 0.027(2.4)$} & \scalebox{0.5}{$0.014 \pm 0.027(0.51)$} \\ \hline +11 & \scalebox{0.5}{$-0.067 \pm 0.026(-2.6)$} & \scalebox{0.5}{$0.017 \pm 0.026(0.65)$} & \scalebox{0.5}{$-0.015 \pm 0.026(-0.56)$} & \scalebox{0.5}{$-0.051 \pm 0.026(-1.9)$} & \scalebox{0.5}{$-0.0086 \pm 0.026(-0.33)$} & \scalebox{0.5}{$-0.018 \pm 0.028(-0.67)$} & \scalebox{0.5}{$0.017 \pm 0.027(0.62)$} \\ \hline + + + + + + +\hline + + + \end{tabular} + +\end{center} + + +\end{tiny} +\end{frame} + + +\begin{frame}\frametitle{Corr3- MM} + + +\begin{tiny} + +\begin{center} + \begin{tabular}{ l l l l l l l l l } + \hline + \multicolumn{8}{c}{Mean of the pull} \\ \hline +$q^2$ & $S_3$ & $S_4$ & $S_5$ & $S_{6s}$ & $S_{6c}$ & $S_7$ & $S_8$ \\ \hline \hline + +0 & \scalebox{0.5}{$-0.021 \pm 0.026(-0.81)$} & \scalebox{0.5}{$0.041 \pm 0.026(1.5)$} & \scalebox{0.5}{$0.009 \pm 0.027(0.34)$} & \scalebox{0.5}{$0.043 \pm 0.026(1.6)$} & \scalebox{0.5}{$0.13 \pm 0.028(4.8)$} & \scalebox{0.5}{$-0.0072 \pm 0.028(-0.26)$} & \scalebox{0.5}{$0.044 \pm 0.026(1.7)$} \\ \hline +1 & \scalebox{0.5}{$-0.014 \pm 0.028(-0.51)$} & \scalebox{0.5}{$0.03 \pm 0.027(1.1)$} & \scalebox{0.5}{$0.022 \pm 0.027(0.82)$} & \scalebox{0.5}{$0.015 \pm 0.028(0.53)$} & \scalebox{0.5}{$0.078 \pm 0.028(2.8)$} & \scalebox{0.5}{$-0.037 \pm 0.025(-1.4)$} & \scalebox{0.5}{$0.057 \pm 0.027(2.1)$} \\ \hline +2 & \scalebox{0.5}{$-0.037 \pm 0.027(-1.4)$} & \scalebox{0.5}{$-0.0013 \pm 0.027(-0.048)$} & \scalebox{0.5}{$-0.015 \pm 0.027(-0.54)$} & \scalebox{0.5}{$-0.052 \pm 0.026(-2)$} & \scalebox{0.5}{$0.1 \pm 0.027(3.8)$} & \scalebox{0.5}{$-0.051 \pm 0.026(-1.9)$} & \scalebox{0.5}{$0.022 \pm 0.028(0.78)$} \\ \hline +3 & \scalebox{0.5}{$-0.015 \pm 0.027(-0.55)$} & \scalebox{0.5}{$0.036 \pm 0.028(1.3)$} & \scalebox{0.5}{$-0.039 \pm 0.027(-1.4)$} & \scalebox{0.5}{$-0.072 \pm 0.027(-2.7)$} & \scalebox{0.5}{$0.17 \pm 0.027(6.2)$} & \scalebox{0.5}{$-0.0044 \pm 0.028(-0.15)$} & \scalebox{0.5}{$-0.024 \pm 0.027(-0.9)$} \\ \hline +4 & \scalebox{0.5}{$-0.00047 \pm 0.029(-0.017)$} & \scalebox{0.5}{$-0.012 \pm 0.027(-0.43)$} & \scalebox{0.5}{$0.0099 \pm 0.028(0.35)$} & \scalebox{0.5}{$-0.002 \pm 0.026(-0.076)$} & \scalebox{0.5}{$0.17 \pm 0.028(6.2)$} & \scalebox{0.5}{$-0.062 \pm 0.027(-2.3)$} & \scalebox{0.5}{$0.0086 \pm 0.027(0.32)$} \\ \hline + +5 & \scalebox{0.5}{$0.046 \pm 0.027(1.7)$} & \scalebox{0.5}{$-0.02 \pm 0.026(-0.76)$} & \scalebox{0.5}{$-0.04 \pm 0.027(-1.5)$} & \scalebox{0.5}{$-0.012 \pm 0.027(-0.44)$} & \scalebox{0.5}{$0.13 \pm 0.027(4.8)$} & \scalebox{0.5}{$-0.04 \pm 0.027(-1.5)$} & \scalebox{0.5}{$-0.0056 \pm 0.027(-0.21)$} \\ \hline +6 & \scalebox{0.5}{$-0.013 \pm 0.026(-0.52)$} & \scalebox{0.5}{$0.041 \pm 0.027(1.5)$} & \scalebox{0.5}{$-0.033 \pm 0.028(-1.2)$} & \scalebox{0.5}{$-0.0019 \pm 0.027(-0.068)$} & \scalebox{0.5}{$0.15 \pm 0.027(5.4)$} & \scalebox{0.5}{$-0.034 \pm 0.027(-1.3)$} & \scalebox{0.5}{$-0.021 \pm 0.028(-0.75)$} \\ \hline +%7 & \scalebox{0.5}{$0.25 \pm 0.027(9.1)$} & \scalebox{0.5}{$-0.27 \pm 0.027(-10)$} & \scalebox{0.5}{$-0.41 \pm 0.027(-16)$} & \scalebox{0.5}{$2.1 \pm 0.029(73)$} & \scalebox{0.5}{$0.65 \pm 0.027(24)$} & \scalebox{0.5}{$-0.19 \pm 0.028(-7)$} & \scalebox{0.5}{$-0.053 \pm 0.028(-1.9)$} \\ \hline +8 & \scalebox{0.5}{$0.039 \pm 0.026(1.5)$} & \scalebox{0.5}{$0.01 \pm 0.028(0.36)$} & \scalebox{0.5}{$-0.027 \pm 0.028(-0.96)$} & \scalebox{0.5}{$-0.024 \pm 0.026(-0.9)$} & \scalebox{0.5}{$0.12 \pm 0.027(4.3)$} & \scalebox{0.5}{$-0.092 \pm 0.026(-3.5)$} & \scalebox{0.5}{$-0.036 \pm 0.027(-1.3)$} \\ \hline +9 & \scalebox{0.5}{$-0.01 \pm 0.027(-0.38)$} & \scalebox{0.5}{$0.0024 \pm 0.027(0.09)$} & \scalebox{0.5}{$-0.018 \pm 0.026(-0.68)$} & \scalebox{0.5}{$0.022 \pm 0.028(0.79)$} & \scalebox{0.5}{$0.068 \pm 0.027(2.6)$} & \scalebox{0.5}{$-0.069 \pm 0.026(-2.6)$} & \scalebox{0.5}{$-0.078 \pm 0.026(-3)$} \\ \hline +10 & \scalebox{0.5}{$-0.017 \pm 0.027(-0.62)$} & \scalebox{0.5}{$-0.015 \pm 0.026(-0.57)$} & \scalebox{0.5}{$0.012 \pm 0.027(0.46)$} & \scalebox{0.5}{$-0.074 \pm 0.028(-2.6)$} & \scalebox{0.5}{$0.1 \pm 0.027(3.8)$} & \scalebox{0.5}{$-0.003 \pm 0.027(-0.11)$} & \scalebox{0.5}{$-0.043 \pm 0.029(-1.5)$} \\ \hline +11 & \scalebox{0.5}{$0.032 \pm 0.026(1.2)$} & \scalebox{0.5}{$0.024 \pm 0.026(0.91)$} & \scalebox{0.5}{$-0.04 \pm 0.026(-1.5)$} & \scalebox{0.5}{$-0.066 \pm 0.027(-2.5)$} & \scalebox{0.5}{$0.098 \pm 0.027(3.7)$} & \scalebox{0.5}{$-0.043 \pm 0.028(-1.6)$} & \scalebox{0.5}{$-0.0018 \pm 0.028(-0.064)$} \\ \hline + + + +\hline + + + \end{tabular} + +\end{center} + + +\end{tiny} +\end{frame} + +\begin{frame}\frametitle{Corr4- MM} + + +\begin{tiny} + +\begin{center} + \begin{tabular}{ l l l l l l l l l } + \hline + \multicolumn{8}{c}{Mean of the pull} \\ \hline +$q^2$ & $S_3$ & $S_4$ & $S_5$ & $S_{6s}$ & $S_{6c}$ & $S_7$ & $S_8$ \\ \hline \hline + + +0 & \scalebox{0.5}{$-0.019 \pm 0.026(-0.71)$} & \scalebox{0.5}{$0.048 \pm 0.027(1.8)$} & \scalebox{0.5}{$0.018 \pm 0.027(0.67)$} & \scalebox{0.5}{$0.059 \pm 0.027(2.2)$} & \scalebox{0.5}{$-0.015 \pm 0.028(-0.55)$} & \scalebox{0.5}{$0.061 \pm 0.027(2.2)$} & \scalebox{0.5}{$0.012 \pm 0.027(0.44)$} \\ \hline +1 & \scalebox{0.5}{$-0.014 \pm 0.028(-0.51)$} & \scalebox{0.5}{$0.043 \pm 0.027(1.6)$} & \scalebox{0.5}{$0.013 \pm 0.027(0.49)$} & \scalebox{0.5}{$0.024 \pm 0.028(0.86)$} & \scalebox{0.5}{$-0.038 \pm 0.028(-1.4)$} & \scalebox{0.5}{$0.024 \pm 0.026(0.94)$} & \scalebox{0.5}{$0.037 \pm 0.027(1.3)$} \\ \hline +2 & \scalebox{0.5}{$-0.03 \pm 0.027(-1.1)$} & \scalebox{0.5}{$-0.0021 \pm 0.027(-0.076)$} & \scalebox{0.5}{$-0.01 \pm 0.027(-0.39)$} & \scalebox{0.5}{$-0.017 \pm 0.027(-0.61)$} & \scalebox{0.5}{$-0.016 \pm 0.027(-0.58)$} & \scalebox{0.5}{$0.013 \pm 0.027(0.49)$} & \scalebox{0.5}{$0.027 \pm 0.028(0.98)$} \\ \hline +3 & \scalebox{0.5}{$-0.007 \pm 0.027(-0.26)$} & \scalebox{0.5}{$0.03 \pm 0.028(1.1)$} & \scalebox{0.5}{$-0.036 \pm 0.027(-1.3)$} & \scalebox{0.5}{$-0.074 \pm 0.027(-2.8)$} & \scalebox{0.5}{$0.041 \pm 0.027(1.5)$} & \scalebox{0.5}{$0.08 \pm 0.028(2.9)$} & \scalebox{0.5}{$-0.0083 \pm 0.027(-0.31)$} \\ \hline +4 & \scalebox{0.5}{$0.00089 \pm 0.029(0.031)$} & \scalebox{0.5}{$-0.021 \pm 0.027(-0.77)$} & \scalebox{0.5}{$0.0032 \pm 0.028(0.11)$} & \scalebox{0.5}{$0.0031 \pm 0.026(0.12)$} & \scalebox{0.5}{$0.012 \pm 0.027(0.44)$} & \scalebox{0.5}{$0.019 \pm 0.026(0.71)$} & \scalebox{0.5}{$0.034 \pm 0.027(1.3)$} \\ \hline +5 & \scalebox{0.5}{$0.044 \pm 0.028(1.6)$} & \scalebox{0.5}{$-0.022 \pm 0.026(-0.82)$} & \scalebox{0.5}{$-0.041 \pm 0.027(-1.5)$} & \scalebox{0.5}{$-0.014 \pm 0.027(-0.53)$} & \scalebox{0.5}{$-0.029 \pm 0.027(-1.1)$} & \scalebox{0.5}{$0.041 \pm 0.027(1.5)$} & \scalebox{0.5}{$0.042 \pm 0.028(1.5)$} \\ \hline +6 & \scalebox{0.5}{$-0.011 \pm 0.026(-0.42)$} & \scalebox{0.5}{$0.041 \pm 0.027(1.5)$} & \scalebox{0.5}{$-0.045 \pm 0.028(-1.6)$} & \scalebox{0.5}{$0.011 \pm 0.027(0.41)$} & \scalebox{0.5}{$-0.0089 \pm 0.027(-0.33)$} & \scalebox{0.5}{$0.067 \pm 0.027(2.5)$} & \scalebox{0.5}{$0.036 \pm 0.027(1.3)$} \\ \hline +%7 & \scalebox{0.5}{$0.25 \pm 0.027(9.1)$} & \scalebox{0.5}{$-0.26 \pm 0.027(-9.9)$} & \scalebox{0.5}{$-0.42 \pm 0.027(-16)$} & \scalebox{0.5}{$2.1 \pm 0.029(73)$} & \scalebox{0.5}{$0.47 \pm 0.027(18)$} & \scalebox{0.5}{$-0.077 \pm 0.028(-2.8)$} & \scalebox{0.5}{$0.029 \pm 0.028(1)$} \\ \hline +8 & \scalebox{0.5}{$0.05 \pm 0.026(1.9)$} & \scalebox{0.5}{$0.0021 \pm 0.028(0.074)$} & \scalebox{0.5}{$-0.025 \pm 0.028(-0.91)$} & \scalebox{0.5}{$-0.023 \pm 0.026(-0.87)$} & \scalebox{0.5}{$-0.024 \pm 0.028(-0.85)$} & \scalebox{0.5}{$0.022 \pm 0.026(0.82)$} & \scalebox{0.5}{$0.026 \pm 0.026(0.98)$} \\ \hline +9 & \scalebox{0.5}{$-0.0064 \pm 0.027(-0.23)$} & \scalebox{0.5}{$0.012 \pm 0.027(0.44)$} & \scalebox{0.5}{$-0.0075 \pm 0.026(-0.28)$} & \scalebox{0.5}{$0.029 \pm 0.027(1.1)$} & \scalebox{0.5}{$-0.087 \pm 0.027(-3.2)$} & \scalebox{0.5}{$0.036 \pm 0.027(1.3)$} & \scalebox{0.5}{$-0.02 \pm 0.026(-0.76)$} \\ \hline +10 & \scalebox{0.5}{$-0.019 \pm 0.027(-0.71)$} & \scalebox{0.5}{$-0.0051 \pm 0.025(-0.2)$} & \scalebox{0.5}{$0.0081 \pm 0.026(0.31)$} & \scalebox{0.5}{$-0.077 \pm 0.028(-2.7)$} & \scalebox{0.5}{$-0.03 \pm 0.027(-1.1)$} & \scalebox{0.5}{$0.11 \pm 0.027(4.1)$} & \scalebox{0.5}{$0.013 \pm 0.028(0.46)$} \\ \hline +11 & \scalebox{0.5}{$0.027 \pm 0.026(1)$} & \scalebox{0.5}{$0.032 \pm 0.027(1.2)$} & \scalebox{0.5}{$-0.038 \pm 0.027(-1.4)$} & \scalebox{0.5}{$-0.048 \pm 0.026(-1.8)$} & \scalebox{0.5}{$-0.021 \pm 0.027(-0.77)$} & \scalebox{0.5}{$0.019 \pm 0.028(0.69)$} & \scalebox{0.5}{$0.035 \pm 0.027(1.3)$} \\ \hline + + + +\hline + + \end{tabular} + +\end{center} + +\end{tiny} +\end{frame} + + + + +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +\section{Reverse Engineering Unfolding} + +\begin{frame}\frametitle{Reverse Engineering- Corr1} +\begin{itemize} +\item Let's try to understand if we can understand why this happens: +\item Let's calculate what should I expect with the unfolding +\item This is up to normalization! +\begin{itemize} +\item $M_5=0.4 S_5 \to M_5=0.00512 S_3 + 0.4 S_5 - 0.002 S_7$ +\item $M_8=0.32 S_8 \to M_8=0.0016 S_4 + 0.00512 S_7 + 0.32 S_8$ +\item $M_7=0.4 S_7 \to M_7=0.002 S_5 + 0.4 S_7 + 0.00512 S_8$ +\item $M_3=0.32 S_3 \to M_3=0.32 S_3 - 0.0008 S_9$ +\end{itemize} +\item The way you can look at this is that i just shown you how our unfolding matrix works like. +\end{itemize} + + + +\end{frame} + +\begin{frame}\frametitle{Reverse Engineering- Corr2} +\begin{itemize} +\item Let's try to understand if we can understand why this happens: +\item Let's calculate what should I expect with the unfolding +\item This is up to normalization! +\begin{itemize} +\item $M_5=0.4 S_5 \to M_5= 0.4 S_5$ +\item $M_8=0.32 S_8 \to M_8=0.32 S_5$ +\item $M_7=0.4 S_7 \to M_7=0.4 S_7$ +\item $M_3=0.32 S_3 \to M_3=-0.0036 + 0.0012 Fl + 0.32 S_3$ +\end{itemize} +\item The way you can look at this is that i just shown you how our unfolding matrix works like. +\end{itemize} + + + +\end{frame} + + + + +\begin{frame}\frametitle{Summary} +\begin{itemize} +\item Developed a systematic way how to get Unfolding matrix +\item Moments are resistant against variety of unfolding discrepancies. +\item This might lead to reduced systematics in the future. +\end{itemize} + + + + +\end{frame} + + + +\end{document} diff --git a/Zurich_group/14_07_2014_2/MMatrix.toc b/Zurich_group/14_07_2014_2/MMatrix.toc new file mode 100644 index 0000000..1e71ea5 --- /dev/null +++ b/Zurich_group/14_07_2014_2/MMatrix.toc @@ -0,0 +1,3 @@ +\beamer@endinputifotherversion {3.10pt} +\select@language {english} +\beamer@sectionintoc {1}{Introduction}{2}{0}{1} diff --git a/Zurich_group/14_07_2014_2/P5.png b/Zurich_group/14_07_2014_2/P5.png new file mode 100644 index 0000000..7819eef --- /dev/null +++ b/Zurich_group/14_07_2014_2/P5.png Binary files differ diff --git a/Zurich_group/14_07_2014_2/Q2_4_S8.png b/Zurich_group/14_07_2014_2/Q2_4_S8.png new file mode 100644 index 0000000..9176de4 --- /dev/null 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begin /PageSize 3 def end def + { /Duplex true def } if + currentdict end setpagedevice + } { + pop pop + } ifelse +} def +/pdfStartPage { + pdfDictSize dict begin + /pdfFillCS [] def + /pdfFillXform {} def + /pdfStrokeCS [] def + /pdfStrokeXform {} def + /pdfFill [0] def + /pdfStroke [0] def + /pdfFillOP false def + /pdfStrokeOP false def + /pdfLastFill false def + /pdfLastStroke false def + /pdfTextMat [1 0 0 1 0 0] def + /pdfFontSize 0 def + /pdfCharSpacing 0 def + /pdfTextRender 0 def + /pdfTextRise 0 def + /pdfWordSpacing 0 def + /pdfHorizScaling 1 def + /pdfTextClipPath [] def +} def +/pdfEndPage { end } def +% PDF color state +/cs { /pdfFillXform exch def dup /pdfFillCS exch def + setcolorspace } def +/CS { /pdfStrokeXform exch def dup /pdfStrokeCS exch def + setcolorspace } def +/sc { pdfLastFill not { pdfFillCS setcolorspace } if + dup /pdfFill exch def aload pop pdfFillXform setcolor + /pdfLastFill true def /pdfLastStroke false def } def +/SC { pdfLastStroke not { pdfStrokeCS setcolorspace } if + dup /pdfStroke exch def aload pop pdfStrokeXform setcolor + /pdfLastStroke true def /pdfLastFill false def } def +/op { /pdfFillOP exch def + pdfLastFill { pdfFillOP setoverprint } if } def +/OP { /pdfStrokeOP exch def + pdfLastStroke { pdfStrokeOP setoverprint } if } def +/fCol { + pdfLastFill not { + pdfFillCS setcolorspace + pdfFill aload pop pdfFillXform setcolor + pdfFillOP setoverprint + /pdfLastFill true def /pdfLastStroke false def + } if +} def +/sCol { + pdfLastStroke not { + pdfStrokeCS setcolorspace + pdfStroke aload pop pdfStrokeXform setcolor + pdfStrokeOP setoverprint + /pdfLastStroke true def /pdfLastFill false def + } if +} def +% build a font +/pdfMakeFont { + 4 3 roll findfont + 4 2 roll matrix scale makefont + dup length dict begin + { 1 index /FID ne { def } { pop pop } ifelse } forall + /Encoding exch def + currentdict + end + definefont pop +} def +/pdfMakeFont16 { + exch findfont + dup length dict begin + { 1 index /FID ne { def } { pop pop } ifelse } forall + /WMode exch def + currentdict + end + definefont pop +} def +% graphics state operators +/q { gsave pdfDictSize dict begin } def +/Q { + end grestore + /pdfLastFill where { + pop + pdfLastFill { + pdfFillOP setoverprint + } { + pdfStrokeOP setoverprint + } ifelse + } if +} def +/cm { concat } def +/d { setdash } def +/i { setflat } def +/j { setlinejoin } def +/J { setlinecap } def +/M { setmiterlimit } def +/w { setlinewidth } def +% path segment operators +/m { moveto } def +/l { lineto } def +/c { curveto } def +/re { 4 2 roll moveto 1 index 0 rlineto 0 exch rlineto + neg 0 rlineto closepath } def +/h { closepath } def +% path painting operators +/S { sCol stroke } def +/Sf { fCol stroke } def +/f { fCol fill } def +/f* { fCol eofill } def +% clipping operators +/W { clip newpath } def +/W* { eoclip newpath } def +% text state operators +/Tc { /pdfCharSpacing exch def } def +/Tf { dup /pdfFontSize exch def + dup pdfHorizScaling mul exch matrix scale + pdfTextMat matrix concatmatrix dup 4 0 put dup 5 0 put + exch findfont exch makefont setfont } def +/Tr { /pdfTextRender exch def } def +/Ts { /pdfTextRise exch def } def +/Tw { /pdfWordSpacing exch def } def +/Tz { /pdfHorizScaling exch def } def +% text positioning operators +/Td { pdfTextMat transform moveto } def +/Tm { /pdfTextMat exch def } def +% text string operators +/cshow where { + pop + /cshow2 { + dup { + pop pop + 1 string dup 0 3 index put 3 index exec + } exch cshow + pop pop + } def +}{ + /cshow2 { + currentfont /FontType get 0 eq { + 0 2 2 index length 1 sub { + 2 copy get exch 1 add 2 index exch get + 2 copy exch 256 mul add + 2 string dup 0 6 5 roll put dup 1 5 4 roll put + 3 index exec + } for + } { + dup { + 1 string dup 0 3 index put 3 index exec + } forall + } ifelse + pop pop + } def +} ifelse +/awcp { + exch { + false charpath + 5 index 5 index rmoveto + 6 index eq { 7 index 7 index rmoveto } if + } exch cshow2 + 6 {pop} repeat +} def +/Tj { + fCol + 1 index stringwidth pdfTextMat idtransform pop + sub 1 index length dup 0 ne { div } { pop pop 0 } ifelse + pdfWordSpacing pdfHorizScaling mul 0 pdfTextMat dtransform 32 + 4 3 roll pdfCharSpacing pdfHorizScaling mul add 0 + pdfTextMat dtransform + 6 5 roll Tj1 +} def +/Tj16 { + fCol + 2 index stringwidth pdfTextMat idtransform pop + sub exch div + pdfWordSpacing pdfHorizScaling mul 0 pdfTextMat dtransform 32 + 4 3 roll pdfCharSpacing pdfHorizScaling mul add 0 + pdfTextMat dtransform + 6 5 roll Tj1 +} def +/Tj16V { + fCol + 2 index stringwidth pdfTextMat idtransform exch pop + sub exch div + 0 pdfWordSpacing pdfTextMat dtransform 32 + 4 3 roll pdfCharSpacing add 0 exch + pdfTextMat dtransform + 6 5 roll Tj1 +} def +/Tj1 { + 0 pdfTextRise pdfTextMat dtransform rmoveto + currentpoint 8 2 roll + pdfTextRender 1 and 0 eq { + 6 copy awidthshow + } if + pdfTextRender 3 and dup 1 eq exch 2 eq or { + 7 index 7 index moveto + 6 copy + currentfont /FontType get 3 eq { fCol } { sCol } ifelse + false awcp currentpoint stroke moveto + } if + pdfTextRender 4 and 0 ne { + 8 6 roll moveto + false awcp + /pdfTextClipPath [ pdfTextClipPath aload pop + {/moveto cvx} + {/lineto cvx} + {/curveto cvx} + {/closepath cvx} + pathforall ] def + currentpoint newpath moveto + } { + 8 {pop} repeat + } ifelse + 0 pdfTextRise neg pdfTextMat dtransform rmoveto +} def +/TJm { pdfFontSize 0.001 mul mul neg 0 + pdfTextMat dtransform rmoveto } def +/TJmV { pdfFontSize 0.001 mul mul neg 0 exch + pdfTextMat dtransform rmoveto } def +/Tclip { pdfTextClipPath cvx exec clip newpath + /pdfTextClipPath [] def } def +% Level 2 image operators +/pdfImBuf 100 string def +/pdfIm { + image + { currentfile pdfImBuf readline + not { pop exit } if + (%-EOD-) eq { exit } if } loop +} def +/pdfImM { + fCol imagemask + { currentfile pdfImBuf readline + not { pop exit } if + (%-EOD-) eq { exit } if } loop +} def +/pdfImClip { + gsave + 0 2 4 index length 1 sub { + dup 4 index exch 2 copy + get 5 index div put + 1 add 3 index exch 2 copy + get 3 index div put + } for + pop pop rectclip +} def +/pdfImClipEnd { grestore } def +% shading operators +/colordelta { + false 0 1 3 index length 1 sub { + dup 4 index exch get 3 index 3 2 roll get sub abs 0.004 gt { + pop true + } if + } for + exch pop exch pop +} def +/funcCol { func n array astore } def +/funcSH { + dup 0 eq { + true + } { + dup 6 eq { + false + } { + 4 index 4 index funcCol dup + 6 index 4 index funcCol dup + 3 1 roll colordelta 3 1 roll + 5 index 5 index funcCol dup + 3 1 roll colordelta 3 1 roll + 6 index 8 index funcCol dup + 3 1 roll colordelta 3 1 roll + colordelta or or or + } ifelse + } ifelse + { + 1 add + 4 index 3 index add 0.5 mul exch 4 index 3 index add 0.5 mul exch + 6 index 6 index 4 index 4 index 4 index funcSH + 2 index 6 index 6 index 4 index 4 index funcSH + 6 index 2 index 4 index 6 index 4 index funcSH + 5 3 roll 3 2 roll funcSH pop pop + } { + pop 3 index 2 index add 0.5 mul 3 index 2 index add 0.5 mul + funcCol sc + dup 4 index exch mat transform m + 3 index 3 index mat transform l + 1 index 3 index mat transform l + mat transform l pop pop h f* + } ifelse +} def +/axialCol { + dup 0 lt { + pop t0 + } { + dup 1 gt { + pop t1 + } { + dt mul t0 add + } ifelse + } ifelse + func n array astore +} def +/axialSH { + dup 0 eq { + true + } { + dup 8 eq { + false + } { + 2 index axialCol 2 index axialCol colordelta + } ifelse + } ifelse + { + 1 add 3 1 roll 2 copy add 0.5 mul + dup 4 3 roll exch 4 index axialSH + exch 3 2 roll axialSH + } { + pop 2 copy add 0.5 mul axialCol sc + exch dup dx mul x0 add exch dy mul y0 add + 3 2 roll dup dx mul x0 add exch dy mul y0 add + dx abs dy abs ge { + 2 copy yMin sub dy mul dx div add yMin m + yMax sub dy mul dx div add yMax l + 2 copy yMax sub dy mul dx div add yMax l + yMin sub dy mul dx div add yMin l + h f* + } { + exch 2 copy xMin sub dx mul dy div add xMin exch m + xMax sub dx mul dy div add xMax exch l + exch 2 copy xMax sub dx mul dy div add xMax exch l + xMin sub dx mul dy div add xMin exch l + h f* + } ifelse + } ifelse +} def +/radialCol { + dup t0 lt { + pop t0 + } { + dup t1 gt { + pop t1 + } if + } ifelse + func n array astore +} def +/radialSH { + dup 0 eq { + true + } { + dup 8 eq { + false + } { + 2 index dt mul t0 add radialCol + 2 index dt mul t0 add radialCol colordelta + } ifelse + } ifelse + { + 1 add 3 1 roll 2 copy add 0.5 mul + dup 4 3 roll exch 4 index radialSH + exch 3 2 roll radialSH + } { + pop 2 copy add 0.5 mul dt mul t0 add axialCol sc + exch dup dx mul x0 add exch dup dy mul y0 add exch dr mul r0 add + 0 360 arc h + dup dx mul x0 add exch dup dy mul y0 add exch dr mul r0 add + 0 360 arc h f* + } ifelse +} def +end +%%EndResource +%%EndProlog +%%BeginSetup +xpdf begin +%%BeginResource: font CMR12 +%!FontType1-1.0: CMR12 +12 dict begin +/FontInfo 10 dict dup begin +/Notice (Copyright (C) 1997 American Mathematical Society. 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index exec + } forall + } ifelse + pop pop + } def +} ifelse +/awcp { + exch { + false charpath + 5 index 5 index rmoveto + 6 index eq { 7 index 7 index rmoveto } if + } exch cshow2 + 6 {pop} repeat +} def +/Tj { + fCol + 1 index stringwidth pdfTextMat idtransform pop + sub 1 index length dup 0 ne { div } { pop pop 0 } ifelse + pdfWordSpacing pdfHorizScaling mul 0 pdfTextMat dtransform 32 + 4 3 roll pdfCharSpacing pdfHorizScaling mul add 0 + pdfTextMat dtransform + 6 5 roll Tj1 +} def +/Tj16 { + fCol + 2 index stringwidth pdfTextMat idtransform pop + sub exch div + pdfWordSpacing pdfHorizScaling mul 0 pdfTextMat dtransform 32 + 4 3 roll pdfCharSpacing pdfHorizScaling mul add 0 + pdfTextMat dtransform + 6 5 roll Tj1 +} def +/Tj16V { + fCol + 2 index stringwidth pdfTextMat idtransform exch pop + sub exch div + 0 pdfWordSpacing pdfTextMat dtransform 32 + 4 3 roll pdfCharSpacing add 0 exch + pdfTextMat dtransform + 6 5 roll Tj1 +} def +/Tj1 { + 0 pdfTextRise pdfTextMat dtransform rmoveto + 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fCol imagemask + { currentfile pdfImBuf readline + not { pop exit } if + (%-EOD-) eq { exit } if } loop +} def +/pdfImClip { + gsave + 0 2 4 index length 1 sub { + dup 4 index exch 2 copy + get 5 index div put + 1 add 3 index exch 2 copy + get 3 index div put + } for + pop pop rectclip +} def +/pdfImClipEnd { grestore } def +% shading operators +/colordelta { + false 0 1 3 index length 1 sub { + dup 4 index exch get 3 index 3 2 roll get sub abs 0.004 gt { + pop true + } if + } for + exch pop exch pop +} def +/funcCol { func n array astore } def +/funcSH { + dup 0 eq { + true + } { + dup 6 eq { + false + } { + 4 index 4 index funcCol dup + 6 index 4 index funcCol dup + 3 1 roll colordelta 3 1 roll + 5 index 5 index funcCol dup + 3 1 roll colordelta 3 1 roll + 6 index 8 index funcCol dup + 3 1 roll colordelta 3 1 roll + colordelta or or or + } ifelse + } ifelse + { + 1 add + 4 index 3 index add 0.5 mul exch 4 index 3 index add 0.5 mul exch + 6 index 6 index 4 index 4 index 4 index funcSH + 2 index 6 index 6 index 4 index 4 index funcSH + 6 index 2 index 4 index 6 index 4 index funcSH + 5 3 roll 3 2 roll funcSH pop pop + } { + pop 3 index 2 index add 0.5 mul 3 index 2 index add 0.5 mul + funcCol sc + dup 4 index exch mat transform m + 3 index 3 index mat transform l + 1 index 3 index mat transform l + mat transform l pop pop h f* + } ifelse +} def +/axialCol { + dup 0 lt { + pop t0 + } { + dup 1 gt { + pop t1 + } { + dt mul t0 add + } ifelse + } ifelse + func n array astore +} def +/axialSH { + dup 0 eq { + true + } { + dup 8 eq { + false + } { + 2 index axialCol 2 index axialCol colordelta + } ifelse + } ifelse + { + 1 add 3 1 roll 2 copy add 0.5 mul + dup 4 3 roll exch 4 index axialSH + exch 3 2 roll axialSH + } { + pop 2 copy add 0.5 mul axialCol sc + exch dup dx mul x0 add exch dy mul y0 add + 3 2 roll dup dx mul x0 add exch dy mul y0 add + dx abs dy abs ge { + 2 copy yMin sub dy mul dx div add yMin m + yMax sub dy mul dx div add yMax l + 2 copy yMax sub dy mul dx div add yMax l + yMin sub dy mul dx div add yMin l + h f* + } { + exch 2 copy xMin sub dx mul dy div add xMin exch m + xMax sub dx mul dy div add xMax exch l + exch 2 copy xMax sub dx mul dy div add xMax exch l + xMin sub dx mul dy div add xMin exch l + h f* + } ifelse + } ifelse +} def +/radialCol { + dup t0 lt { + pop t0 + } { + dup t1 gt { + pop t1 + } if + } ifelse + func n array astore +} def +/radialSH { + dup 0 eq { + true + } { + dup 8 eq { + false + } { + 2 index dt mul t0 add radialCol + 2 index dt mul t0 add radialCol colordelta + } ifelse + } ifelse + { + 1 add 3 1 roll 2 copy add 0.5 mul + dup 4 3 roll exch 4 index radialSH + exch 3 2 roll radialSH + } { + pop 2 copy add 0.5 mul dt mul t0 add axialCol sc + exch dup dx mul x0 add exch dup dy mul y0 add exch dr mul r0 add + 0 360 arc h + dup dx mul x0 add exch dup dy mul y0 add exch dr mul r0 add + 0 360 arc h f* + } ifelse +} def +end +%%EndResource +%%EndProlog +%%BeginSetup +xpdf begin +%%BeginResource: font CMR12 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pdfTextMat dtransform 32 + 4 3 roll pdfCharSpacing pdfHorizScaling mul add 0 + pdfTextMat dtransform + 6 5 roll Tj1 +} def +/Tj16 { + fCol + 2 index stringwidth pdfTextMat idtransform pop + sub exch div + pdfWordSpacing pdfHorizScaling mul 0 pdfTextMat dtransform 32 + 4 3 roll pdfCharSpacing pdfHorizScaling mul add 0 + pdfTextMat dtransform + 6 5 roll Tj1 +} def +/Tj16V { + fCol + 2 index stringwidth pdfTextMat idtransform exch pop + sub exch div + 0 pdfWordSpacing pdfTextMat dtransform 32 + 4 3 roll pdfCharSpacing add 0 exch + pdfTextMat dtransform + 6 5 roll Tj1 +} def +/Tj1 { + 0 pdfTextRise pdfTextMat dtransform rmoveto + currentpoint 8 2 roll + pdfTextRender 1 and 0 eq { + 6 copy awidthshow + } if + pdfTextRender 3 and dup 1 eq exch 2 eq or { + 7 index 7 index moveto + 6 copy + currentfont /FontType get 3 eq { fCol } { sCol } ifelse + false awcp currentpoint stroke moveto + } if + pdfTextRender 4 and 0 ne { + 8 6 roll moveto + false awcp + /pdfTextClipPath [ pdfTextClipPath aload pop + {/moveto cvx} + {/lineto cvx} + {/curveto cvx} + {/closepath cvx} + pathforall ] def + currentpoint newpath moveto + } { + 8 {pop} repeat + } ifelse + 0 pdfTextRise neg pdfTextMat dtransform rmoveto +} def +/TJm { pdfFontSize 0.001 mul mul neg 0 + pdfTextMat dtransform rmoveto } def +/TJmV { pdfFontSize 0.001 mul mul neg 0 exch + pdfTextMat dtransform rmoveto } def +/Tclip { pdfTextClipPath cvx exec clip newpath + /pdfTextClipPath [] def } def +% Level 2 image operators +/pdfImBuf 100 string def +/pdfIm { + image + { currentfile pdfImBuf readline + not { pop exit } if + (%-EOD-) eq { exit } if } loop +} def +/pdfImM { + fCol imagemask + { currentfile pdfImBuf readline + not { pop exit } if + (%-EOD-) eq { exit } if } loop +} def +/pdfImClip { + gsave + 0 2 4 index length 1 sub { + dup 4 index exch 2 copy + get 5 index div put + 1 add 3 index exch 2 copy + get 3 index div put + } for + pop pop rectclip +} def +/pdfImClipEnd { grestore } def +% shading operators +/colordelta { + 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def +/axialCol { + dup 0 lt { + pop t0 + } { + dup 1 gt { + pop t1 + } { + dt mul t0 add + } ifelse + } ifelse + func n array astore +} def +/axialSH { + dup 0 eq { + true + } { + dup 8 eq { + false + } { + 2 index axialCol 2 index axialCol colordelta + } ifelse + } ifelse + { + 1 add 3 1 roll 2 copy add 0.5 mul + dup 4 3 roll exch 4 index axialSH + exch 3 2 roll axialSH + } { + pop 2 copy add 0.5 mul axialCol sc + exch dup dx mul x0 add exch dy mul y0 add + 3 2 roll dup dx mul x0 add exch dy mul y0 add + dx abs dy abs ge { + 2 copy yMin sub dy mul dx div add yMin m + yMax sub dy mul dx div add yMax l + 2 copy yMax sub dy mul dx div add yMax l + yMin sub dy mul dx div add yMin l + h f* + } { + exch 2 copy xMin sub dx mul dy div add xMin exch m + xMax sub dx mul dy div add xMax exch l + exch 2 copy xMax sub dx mul dy div add xMax exch l + xMin sub dx mul dy div add xMin exch l + h f* + } ifelse + } ifelse +} def +/radialCol { + dup t0 lt { + pop t0 + } { + dup t1 gt { + pop t1 + } if + } ifelse + func n array astore +} def +/radialSH { + dup 0 eq { + true + } { + dup 8 eq { + false + } { + 2 index dt mul t0 add radialCol + 2 index dt mul t0 add radialCol colordelta + } ifelse + } ifelse + { + 1 add 3 1 roll 2 copy add 0.5 mul + dup 4 3 roll exch 4 index radialSH + exch 3 2 roll radialSH + } { + pop 2 copy add 0.5 mul dt mul t0 add axialCol sc + exch dup dx mul x0 add exch dup dy mul y0 add exch dr mul r0 add + 0 360 arc h + dup dx mul x0 add exch dup dy mul y0 add exch dr mul r0 add + 0 360 arc h f* + } ifelse +} def +end +%%EndResource +%%EndProlog +%%BeginSetup +xpdf begin +%%BeginResource: font CMR12 +%!FontType1-1.0: CMR12 +12 dict begin +/FontInfo 10 dict dup begin +/Notice (Copyright (C) 1997 American Mathematical Society. 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