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/dev/null +++ b/Kstmumu/MMatrix2/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/Kstmumu/MMatrix2/MM.pdf b/Kstmumu/MMatrix2/MM.pdf new file mode 100644 index 0000000..160ac5e --- /dev/null +++ b/Kstmumu/MMatrix2/MM.pdf Binary files differ diff --git a/Kstmumu/MMatrix2/MM.snm b/Kstmumu/MMatrix2/MM.snm new file mode 100644 index 0000000..e69de29 --- /dev/null +++ b/Kstmumu/MMatrix2/MM.snm diff --git a/Kstmumu/MMatrix2/MM.synctex.gz b/Kstmumu/MMatrix2/MM.synctex.gz new file mode 100644 index 0000000..78b4daf --- /dev/null +++ b/Kstmumu/MMatrix2/MM.synctex.gz Binary files differ diff --git a/Kstmumu/MMatrix2/MM.tex b/Kstmumu/MMatrix2/MM.tex new file mode 100644 index 0000000..2e9ab92 --- /dev/null +++ b/Kstmumu/MMatrix2/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}\\ 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+\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/Kstmumu/MMatrix2/MM.toc b/Kstmumu/MMatrix2/MM.toc new file mode 100644 index 0000000..77ff2e8 --- /dev/null +++ b/Kstmumu/MMatrix2/MM.toc @@ -0,0 +1,6 @@ +\beamer@endinputifotherversion {3.10pt} +\beamer@sectionintoc 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100644 index 0000000..5eb6bdb --- /dev/null +++ b/Kstmumu/MMatrix2/MMatrix.synctex.gz Binary files differ diff --git a/Kstmumu/MMatrix2/MMatrix.tex b/Kstmumu/MMatrix2/MMatrix.tex new file mode 100644 index 0000000..3d37875 --- /dev/null +++ b/Kstmumu/MMatrix2/MMatrix.tex @@ -0,0 +1,626 @@ +\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)} + +\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~ new file mode 100644 index 0000000..2fc0e58 --- /dev/null +++ b/Kstmumu/MMatrix2/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/MMatrix2/MMatrix.toc b/Kstmumu/MMatrix2/MMatrix.toc new file mode 100644 index 0000000..1e71ea5 --- /dev/null +++ b/Kstmumu/MMatrix2/MMatrix.toc @@ -0,0 +1,3 @@ +\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 new file mode 100644 index 0000000..7819eef --- /dev/null +++ b/Kstmumu/MMatrix2/P5.png Binary files differ diff --git a/Kstmumu/MMatrix2/Q2_4_S8.png b/Kstmumu/MMatrix2/Q2_4_S8.png new file mode 100644 index 0000000..9176de4 --- /dev/null +++ b/Kstmumu/MMatrix2/Q2_4_S8.png Binary files differ diff --git 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\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}{$0.0042 \pm 0.0188(0.22)$} & 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b/Kstmumu/MMatrix2/tables/tables.toc new file mode 100644 index 0000000..e06b51d --- /dev/null +++ b/Kstmumu/MMatrix2/tables/tables.toc @@ -0,0 +1 @@ +\beamer@endinputifotherversion {3.10pt} diff --git a/Kstmumu/MMatrix2/texput.log b/Kstmumu/MMatrix2/texput.log new file mode 100644 index 0000000..f84449f --- /dev/null +++ b/Kstmumu/MMatrix2/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/MMatrix2/tmp.png b/Kstmumu/MMatrix2/tmp.png new file mode 100644 index 0000000..574cb07 --- /dev/null +++ b/Kstmumu/MMatrix2/tmp.png Binary files differ diff --git a/Kstmumu/MMatrix2/tmp/beamerthemeSybila.sty b/Kstmumu/MMatrix2/tmp/beamerthemeSybila.sty new file mode 100644 index 0000000..5639601 --- /dev/null +++ b/Kstmumu/MMatrix2/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/MMatrix2/tmp/example.tex b/Kstmumu/MMatrix2/tmp/example.tex new file mode 100644 index 0000000..ce0641b --- /dev/null +++ b/Kstmumu/MMatrix2/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/MMatrix2/tmp/example/beamerthemeSybila.sty b/Kstmumu/MMatrix2/tmp/example/beamerthemeSybila.sty new file mode 100644 index 0000000..5639601 --- /dev/null +++ b/Kstmumu/MMatrix2/tmp/example/beamerthemeSybila.sty @@ -0,0 +1,104 @@ +\mode + +%------------------------------------------------------------------------------- +% Themes +%------------------------------------------------------------------------------- + +\useoutertheme{split} +\useinnertheme{rounded} +\usefonttheme{structurebold} +%\useoutertheme{shadow} + +%------------------------------------------------------------------------------- +% Templates 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+\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/MMatrix2/tmp/example/example.aux b/Kstmumu/MMatrix2/tmp/example/example.aux new file mode 100644 index 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--------------------------- SLIDE -------------------------------------------- +\begin{frame} + \frametitle{Introduction} +\end{frame} +% ------------------------------------------------------------------------------ +\end{document} diff --git a/Kstmumu/MMatrix2/tmp/example/example.toc b/Kstmumu/MMatrix2/tmp/example/example.toc new file mode 100644 index 0000000..495658f --- /dev/null +++ b/Kstmumu/MMatrix2/tmp/example/example.toc @@ -0,0 +1,2 @@ +\beamer@endinputifotherversion {3.10pt} +\select@language {english} diff --git a/Kstmumu/MMatrix2/tmp/example/sybila-logo-paper-shaded.png b/Kstmumu/MMatrix2/tmp/example/sybila-logo-paper-shaded.png new file mode 100644 index 0000000..f2a2c4e --- /dev/null +++ b/Kstmumu/MMatrix2/tmp/example/sybila-logo-paper-shaded.png Binary files differ diff --git a/Kstmumu/MMatrix2/tmp/example/sybila-logo-slide-title-shaded.pdf b/Kstmumu/MMatrix2/tmp/example/sybila-logo-slide-title-shaded.pdf new file mode 100644 index 0000000..670c6a6 --- /dev/null +++ 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