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The treatmend of the standard: \end{itemize} \begin{equation} -\chi^2 = \Delta cov \Delta +\chi^2 = \Delta^T V^{-1} \Delta \end{equation} - +\begin{itemize} +\item We will have four covariance matrix: $V_{++}$, $V_{-+}$, $V_{+-}$, $V_{--}$. +\end{itemize} \end{frame} \begin{frame}\frametitle{What is missing?} +\begin{itemize} +\item We do not have theory errors in. +\item Started discusion with Nazila about them. +\item This is tricky, we need to properly recalculate the errors from SM values. +\item Limit treatment procedure. We had some discussion about this but we should make a decision here. +\item My personal view: procedure should be as unbias as possible. + +\end{itemize} + \end{frame} + + + + + + \end{document} diff --git "a/Kaggle/\043kagg.tex\043" "b/Kaggle/\043kagg.tex\043" deleted file mode 100644 index 3cd4b9f..0000000 --- "a/Kaggle/\043kagg.tex\043" +++ /dev/null @@ -1,271 +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} -\usepackage{feynmp} -\usepackage{pst-pdf} -\usepackage{hyperref} -\usepackage{xcolor} - -\setbeamertemplate{footline}{\insertframenumber/\inserttotalframenumber} -%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%5 -\definecolor{mygreen}{cmyk}{0.82,0.11,1,0.25} - - - -%\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[Kaggle challenge from LHCb]{Kaggle challenge from LHCb} -\author{Marc-Olivier Bettler$^{1}$, Marcin Chrz\k{a}szcz$^{2,3}$,\\ Andrey Ustyuzhanin$^{4,5}$, Tatiana Likhomanenko$^{4,5}$} - -\institute{ -$^1$~CERN, Geneva \\ -$^2$~University of Zurich \\ -$^3$~Institute of Nuclear Physics, Krakow \\ -$^4$~Yandex School of Data Analysis,~Moscow \\ -$^5$~~NRC ``Kurchatov Institute'',~Moscow -} -\date{27 February 2015} -\begin{document} -% --------------------------- SLIDE -------------------------------------------- -\frame[plain]{\titlepage} -\author{Marcin Chrz\k{a}szcz} -% ------------------------------------------------------------------------------ -% --------------------------- SLIDE -------------------------------------------- - -\institute{~(UZH, IFJ)} - -%-------------------------------------------------------------------- -% OUTLINE -%-------------------------------------------------------------------- - - - - - -\begin{frame}\frametitle{What is kaggle - The Home of Data Science} -\begin{columns} -\column{3.5in} -\begin{itemize} - \item Kaggle is the world's largest community of data scientists. - \item It provides the possibility to data scientists to solve real-world problems across a diverse array of industries including life sciences, financial services, energy, information technology. - \item In addition to the prize money and data, participants use Kaggle to meet, learn, network and collaborate with experts from related fields. -\end{itemize} -\column{0.1in} -{~}\\ - -\column{1.3in} -Who has alrady\\ used Kaggle: \\{~}\\ -\includegraphics[height=0.9cm]{images/NASA.png}\hspace*{0.3cm} -\includegraphics[height=0.9cm]{images/download.png}\hspace*{0.3cm}\\ -%\includegraphics[height=0.9cm]{images/ms.png}\hspace*{0.3cm}\\ -\includegraphics[height=0.9cm]{images/ford.jpg}\hspace*{0.3cm}\\ -\includegraphics[height=0.9cm]{images/fb.jpg}\hspace*{0.3cm} \\ -and many many\\ others including: -\includegraphics[height=0.9cm]{images/ATLAS-chrome-logo-blue_hi.png} - - -\end{columns} - -\end{frame} - - - - - - - - -\begin{frame}\frametitle{How does Kaggle work?} -\begin{itemize} -\item One (ex. LHCb) defines a data analysis problem, provides data sets and rules about the evaluation. -\item For the constests there are allocated prizes. -\item After the constes is over( couple of mounths ) the solutions are made public. -\item Current contests: -\end{itemize} -\begin{center} -\includegraphics[width=10cm]{images/kagg_now.png} -\end{center} - -\end{frame} - -%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% - -\begin{frame}\frametitle{Atlas path to $\color{white}{H \to \tau \tau}$} -\begin{columns} -\column{3in} -\begin{itemize} -\item As we know ATLAS due to poor vertex detector is worse then CMS a in modes like $\PHiggs \to \Ptau \Ptau$ or $\PHiggs \to \PB \APB$ -\item ATLAS gave their datasets (for $\PHiggs \to \Ptau \Ptau$) training the classifiers that can be used for future analysis. -\item After evaluation they gained $\sim10\%$ on sensitivity! -\item This would be great for $\Ptau \to \Pmu \Pmu \Pmu$. -\item This would be great for LHCb and HEP community as well. -\item Also after the challenge they organized a workshop $\to$ other LHCb analysis could benefit from this kind of collaborations, we almost always use MVAs. - -\end{itemize} - -\column{2in} -\includegraphics[width=1.9in]{images/higgs.png}\\ -\includegraphics[width=1.9in]{images/HiggsML-sm.jpg} -\end{columns} - -\end{frame} -%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%55 - -\begin{frame}\frametitle{Future of $\color{white}{\tau \to \mu\mu\mu}$ in LHCb} -\begin{columns} -\column{3in} -\begin{itemize} -\item In $3~\invfb$ we had expected limit of $5.0 \times 10^{-8}$. -\item What can we expect after another $5~\invfb$? -\item $\dfrac{5.0\times 10^{-8}}{ \sqrt{\dfrac{5\times 2}{3} }}=2.7 \times 10^{-8}$ -\item We should aim to do better then Belle $(2.1\times 10^{-8}$)! -\item Help from Kaggle community would be very appreciated! -\end{itemize} - -\column{2in} -\includegraphics[width=1.9in]{images/bananaB.pdf} - -\end{columns} - -\end{frame} - -%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%5 -\begin{frame}\frametitle{Comparison with Higgs Boson Challenge} -{ -\fontsize{10}{12} -\selectfont -Proposed challenge is connected with Higgs Boson challenge, but differs from it, being more realistic (closer to real physics analysis): -\begin{enumerate} - \item training dataset includes not only simulated data but also real data (signal-like events and background-like events have different nature). - \item test dataset includes also normalization channel to do calibration of data. - \item the submission must pass additional checks (classifier must not be correlated with mass and behave similarly on real and simulated data). - \item our quality metric uses predicted probability in all bins as we do in real analysis. - \item all scripts for testing mass correlation, DATA/MC agreement and limit evaluation are provided by us. -\end{enumerate} -} -\end{frame} - -\begin{frame}\frametitle{What would we like to give} -\begin{itemize} -\item MC and DATA\footnote{I will comment on protecting our data in couple of slides} after the preselection. -\item DATA will contain our standard ntuple entries (excluding varaibles, like trigger decisions, BKGCAT, etc.). -\item We want to give as much of thouse as possible as people can then construct their own varaibles (happens often). -\item The size of data that is used for testing and training is up to us. -\end{itemize} - -\end{frame} - -\begin{frame}\frametitle{Evaluation} - -\begin{itemize} - \item Check correlation between mass and model predictions on all test $\tau \to\mu\mu\mu$ sidebands using Cramer-von Mises measure~(\href{http://arxiv.org/abs/1410.4140}{ex. arXiv:1410.4140}) - \item Check agreement between MC and data on $Ds\to\phi\pi$ (test MC and test data) using Kolmogorov-Smirnov distance - \item Calculate of Approximate Binned Median Statistics (ABMS), only if above two tests are passed. - \item We need to use ABMS becaouse the standard $CL_s$ method is computational expensive. - \item ABMS is just value of statistic and shows how well two hypothesis can be distinguished - \item ABMS metric is similar AMS used in Higgs competition, but involves all available statistics, making it more meaningful and stable. Details of this metrix can be found in backups. -\end{itemize} -\begin{itemize} - \item Participants chooses number of bins and bins thresholds themselves (i.e. splitting classifier output) -\end{itemize} -\end{frame} - -%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%5 - -\begin{frame}\frametitle{Evaluation Examples} -Ada Boost, Gradient Boost were trained (as participants can do). Also Ada Boost and Uniform Gradient Boost were trained using mass as input for classifier. (CVM - Cramer-von Mises metric, KS - Kolmogorov-Smirnov metric), - -\begin{center} - \begin{tabular} {| l | r | r | r | r |} - \hline - {~}& ada & ada(mass) & gb & ugb(mass) \\ \hline \hline - CVM metric & 0.005674 & \textcolor{red} {0.061837} &\textcolor{blue}{ 0.005642 }& 0.005714 \\ \hline - CVM p-value & 0.918667 & \textcolor{red}{1.000000} & \textcolor{blue}{0.850000} & 0.970000 \\ \hline - KS distance & 0.028815 & 0.018353 & 0.027854 & \textcolor{blue}{0.025621} \\ \hline - ABMS public & 1.557205 & 1.790282 & \textcolor{blue}{1.564490} & 1.545545 \\ \hline - ABMS private & 1.549253 & 1.785880 & \textcolor{blue}{1.562412} & 1.542357 \\ \hline - \end{tabular} -\end{center} - -\begin{itemize} - -\item We tested already with standard classifiers that this metric work and reject cases where people will try to do something strange (like add mass for training). - -\end{itemize} -\end{frame} - -%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% - -\begin{frame}\frametitle{Protecting our data} -\begin{columns} -\column{3in} -\begin{itemize} -\item We should be of course worried that we are giving to public our data set. -\item However those data are after preselection, without any PID calibration, only selected variables, etc. -\item Plan is to smear the Data, so we can make a statment such as: ''Data was prepared in a way that it can't be used for any physical analysis''. -\item Other tughts are welcome! -\end{itemize} -\column{2in} -{~} -\includegraphics[width=1.9in]{images/images.jpg} -\end{columns} -\end{frame} - -%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% - -\begin{frame}\frametitle{Timescale} -\begin{itemize} - \item Jan/Feb: confirmation from LHCb, allocate prize budget at Yandex - \item Feb: prepare website, explanatory materials, evaluation procedures, test challenge - \item Feb: propose workshop at KDD - \item Mar: announce challenge, start - \item Mar-May: run challenge - \item Jun: announce winners - \item Aug: run KDD workshop, award winners -\end{itemize} -\begin{enumerate} -\item KDD - Conference on Knowledge discovery and Data Mining: 2015 is one of the most important conferneces for data scientists. -\item Plan would be to have a sesion there dedicated to our chalange. -\item Afterwards we could organise workshop at CERN as well to hopefully fruitfull collaboration.Conference on Knowledge discovery and Data -Mining: 2015 - - -\end{enumerate} - - -\end{frame} - - - - - - - -\end{document} diff --git a/Kaggle/beamerthemeSybila.sty b/Kaggle/beamerthemeSybila.sty index abe0338..21f9016 100644 --- a/Kaggle/beamerthemeSybila.sty +++ b/Kaggle/beamerthemeSybila.sty @@ -114,7 +114,7 @@ %------------------------------------------------------------------------------- \titlegraphic{ -%\includegraphics[height=0.9cm]{images/warwic.jpg}\hspace*{0.3cm} +\includegraphics[height=0.9cm]{images/warwic.jpg}\hspace*{0.3cm} \includegraphics[height=0.9cm]{images/CERN-logo.jpg}\hspace*{0.3cm} \includegraphics[width=3.0cm]{images/uzh.jpg}\hspace*{0.3cm} \includegraphics[height=0.9cm,keepaspectratio]{images/ifj.png}\hspace*{0.3cm} diff --git a/Kaggle/kagg.aux b/Kaggle/kagg.aux index 6cdd96e..1f792f9 100644 --- a/Kaggle/kagg.aux +++ b/Kaggle/kagg.aux @@ -42,8 +42,18 @@ \@writefile{nav}{\headcommand {\beamer@framepages {10}{10}}} \@writefile{nav}{\headcommand {\slideentry {0}{0}{11}{11/11}{}{0}}} \@writefile{nav}{\headcommand {\beamer@framepages {11}{11}}} -\@writefile{nav}{\headcommand {\beamer@partpages {1}{11}}} -\@writefile{nav}{\headcommand {\beamer@subsectionpages {1}{11}}} -\@writefile{nav}{\headcommand {\beamer@sectionpages {1}{11}}} -\@writefile{nav}{\headcommand {\beamer@documentpages {11}}} -\@writefile{nav}{\headcommand {\def \inserttotalframenumber {11}}} +\@writefile{nav}{\headcommand {\slideentry {0}{0}{12}{12/12}{}{0}}} +\@writefile{nav}{\headcommand {\beamer@framepages {12}{12}}} +\@writefile{nav}{\headcommand {\slideentry {0}{0}{13}{13/13}{}{0}}} +\@writefile{nav}{\headcommand {\beamer@framepages {13}{13}}} +\@writefile{nav}{\headcommand {\slideentry {0}{0}{14}{14/14}{}{0}}} +\@writefile{nav}{\headcommand {\beamer@framepages {14}{14}}} +\@writefile{nav}{\headcommand {\slideentry {0}{0}{15}{15/15}{}{0}}} +\@writefile{nav}{\headcommand {\beamer@framepages {15}{15}}} +\@writefile{nav}{\headcommand {\slideentry {0}{0}{16}{16/16}{}{0}}} +\@writefile{nav}{\headcommand {\beamer@framepages {16}{16}}} +\@writefile{nav}{\headcommand {\beamer@partpages {1}{16}}} +\@writefile{nav}{\headcommand {\beamer@subsectionpages {1}{16}}} +\@writefile{nav}{\headcommand {\beamer@sectionpages {1}{16}}} +\@writefile{nav}{\headcommand {\beamer@documentpages {16}}} +\@writefile{nav}{\headcommand {\def \inserttotalframenumber {16}}} diff --git a/Kaggle/kagg.log b/Kaggle/kagg.log index feea4e1..c397da9 100644 --- a/Kaggle/kagg.log +++ b/Kaggle/kagg.log @@ -1,4 +1,4 @@ -This is pdfTeX, Version 3.1415926-2.4-1.40.13 (TeX Live 2012/Debian) (format=pdflatex 2014.12.22) 23 JAN 2015 15:43 +This is pdfTeX, Version 3.1415926-2.4-1.40.13 (TeX Live 2012/Debian) (format=pdflatex 2014.12.22) 25 JAN 2015 18:21 entering extended mode restricted \write18 enabled. %&-line parsing enabled. @@ -1199,86 +1199,110 @@ )) Package hyperref Warning: Token not allowed in a PDF string (PDFDocEncoding): -(hyperref) removing `math shift' on input line 45. +(hyperref) removing `math shift' on input line 48. 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LHCb) defines a data analysis problem, provides data sets and rules about the evaluation. +\item One (ex. LHCb) defines a data analysis problem, provides data sets and rules to rank solutions. \item For the constests there are allocated prizes. -\item After the constes is over( couple of mounths ) the solutions are made public. +\item When a contest is over (couple of months) the top solutions are made public. \item Current contests: \end{itemize} \begin{center} @@ -121,12 +127,15 @@ \begin{columns} \column{3in} \begin{itemize} -\item As we know ATLAS due to poor vertex detector is worse then CMS a in modes like $\PHiggs \to \Ptau \Ptau$ or $\PHiggs \to \PB \APB$ -\item ATLAS gave their datasets (for $\PHiggs \to \Ptau \Ptau$) training the classifiers that can be used for future analysis. -\item After evaluation they gained $\sim10\%$ on sensitivity! -\item This would be great for $\Ptau \to \Pmu \Pmu \Pmu$. -\item This would be great for LHCb and HEP community as well. -\item Also after the challenge they organized a workshop $\to$ other LHCb analysis could benefit from this kind of collaborations, we almost always use MVAs. +\item Because of its poorer vertex resolution, ATLAS is less sensitive than CMS in modes like $\PHiggs \to \Ptau \Ptau$ or $\PHiggs \to \PB \APB$ +\item ATLAS gave their MC samples datasets (for $\PHiggs \to \Ptau \Ptau$) to train the classifiers that can be used for future analyses. +\item After evaluation they gained $\sim 10\%$ on sensitivity! +\item Other analysis from ATLAS picked up some open source libraries and are using them. +\item During the constest there are discussions between the participants, which are also avaible for physicist $\rightarrow$ knowledge transfer. +\item Over 1.800 teams pariticipated in this contest! +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%55 +%\item This would be great for $\Ptau \to \Pmu \Pmu \Pmu$, LHCb and HEP community as well. +%\item Also after the challenge they organized a workshop $\to$ other LHCb analysis could benefit from this kind of collaborations, we almost always use MVAs. \end{itemize} @@ -146,7 +155,7 @@ \item What can we expect after another $5~\invfb$? \item $\dfrac{5.0\times 10^{-8}}{ \sqrt{\dfrac{5\times 2}{3} }}=2.7 \times 10^{-8}$ \item We should aim to do better then Belle $(2.1\times 10^{-8}$)! -\item Help from Kaggle community would be very appreciated! +\item Help from Kaggle community would be very appreciated for $\Ptau \to \Pmu \Pmu \Pmu$, LHCb and HEP community as well. \end{itemize} \column{2in} @@ -164,33 +173,39 @@ Proposed challenge is connected with Higgs Boson challenge, but differs from it, being more realistic (closer to real physics analysis): \begin{enumerate} \item training dataset includes not only simulated data but also real data (signal-like events and background-like events have different nature). - \item test dataset includes also normalization channel to do calibration of data. + \item test dataset includes also control channel to access DATA/MC differences. \item the submission must pass additional checks (classifier must not be correlated with mass and behave similarly on real and simulated data). \item our quality metric uses predicted probability in all bins as we do in real analysis. \item all scripts for testing mass correlation, DATA/MC agreement and limit evaluation are provided by us. + \item $\Ptau$ in LHCb comes from five different sources which makes this contest more interesting for machine learning people. \end{enumerate} } \end{frame} \begin{frame}\frametitle{What would we like to give} +\begin{small} \begin{itemize} -\item MC and DATA\footnote{I will comment on protecting our data in couple of slides} after the preselection. -\item DATA will contain our standard ntuple entries (excluding varaibles, like trigger decisions, BKGCAT, etc.). -\item We want to give as much of thouse as possible as people can then construct their own varaibles (happens often). -\item The size of data that is used for testing and training is up to us. + \item Full MC sample of $\PDs \to \phi \pi$ and $\sim 30\%$ data $\PDs \to \phi \pi$. + \item Full MC sample of $\Ptau \to \Pmu \Pmu \Pmu$ and full data of $\Ptau \to \Pmu \Pmu \Pmu$.\footnote{I will comment on protecting our data in couple of slides}. +\item DATA will contain our standard ntuple entries (excluding lumi etc.) +\item We want to give as much of those as possible to allow people to construct their own variables (happens often). +\item The size of the data sets and the split training/testing is up to us. \end{itemize} - +\end{small} +\begin{center} +\includegraphics[scale=0.13]{Diagram1.png} +\end{center} \end{frame} \begin{frame}\frametitle{Evaluation} \begin{itemize} \item Check correlation between mass and model predictions on all test $\tau \to\mu\mu\mu$ sidebands using Cramer-von Mises measure~(\href{http://arxiv.org/abs/1410.4140}{ex. arXiv:1410.4140}) - \item Check agreement between MC and data on $Ds\to\phi\pi$ (test MC and test data) using Kolmogorov-Smirnov distance - \item Calculate of Approximate Binned Median Statistics (ABMS), only if above two tests are passed. - \item We need to use ABMS becaouse the standard $CL_s$ method is computational expensive. + \item Check agreement between MC and data on $\PDs\to\phi\pi$ (test MC and test data) using Kolmogorov-Smirnov distance + \item Calculation of Approximate Binned Median Statistics (ABMS), only if above two tests are passed. + \item We need to use ABMS because the standard CLs method is computationally too expensive. \item ABMS is just value of statistic and shows how well two hypothesis can be distinguished - \item ABMS metric is similar AMS used in Higgs competition, but involves all available statistics, making it more meaningful and stable. Details of this metrix can be found in backups. + \item ABMS is similar to the AMS metric used in Higgs competition, but involves all available statistics, making it more meaningful and stable. Details of the metric can be found in backups. \end{itemize} \begin{itemize} \item Participants chooses number of bins and bins thresholds themselves (i.e. splitting classifier output) @@ -227,10 +242,9 @@ \begin{columns} \column{3in} \begin{itemize} -\item We should be of course worried that we are giving to public our data set. -\item However those data are after preselection, without any PID calibration, only selected variables, etc. -\item Plan is to smear the Data, so we can make a statment such as: ''Data was prepared in a way that it can't be used for any physical analysis''. -\item Other tughts are welcome! +\item We could make our data open without any modifications, as performing any analisis without knowledge of the preselection is not possible. +\item If collaborations feels strong about protecting our data, we can smear/shift it in a way that physcics analysis is not possible, but the training is not distorted. +\item Both scenarios are acceptable for us. \end{itemize} \column{2in} {~} @@ -241,28 +255,94 @@ %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \begin{frame}\frametitle{Timescale} -\begin{itemize} - \item Jan/Feb: confirmation from LHCb, allocate prize budget at Yandex - \item Feb: prepare website, explanatory materials, evaluation procedures, test challenge - \item Feb: propose workshop at KDD - \item Mar: announce challenge, start - \item Mar-May: run challenge - \item Jun: announce winners - \item Aug: run KDD workshop, award winners -\end{itemize} +\begin{itemize} + \item Feb: ask OK from LHCb, allocate prize budget at Yandex (15k \$, more then ATLAS had ;) ) + \item Mar: prepare website, explanatory materials, refine evaluation procedures, test challenge + \item Mar: propose workshop at KDD/NIPS + \item Apr: announce challenge, start + \item Apr-Jun: run challenge + \item July: announce winners + \item Aug/Sep: run KDD/NIPS workshop, award winners +\end{itemize} \begin{enumerate} -\item KDD - Conference on Knowledge discovery and Data Mining: 2015 is one of the most important conferneces for data scientists. -\item Plan would be to have a sesion there dedicated to our chalange. -\item Afterwards we could organise workshop at CERN as well to hopefully fruitfull collaboration. - +\item KDD/NIPS are very well know maschine learning contests. +\item Plan would be to have a sesion there dedicated to our challange (was the case of ATLAS competition). +\item Afterwards we could organise workshop at CERN as well to hopefullys start a fruitfull collaboration. \end{enumerate} \end{frame} +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% + +\begin{frame}\frametitle{Conclusions} +\begin{enumerate} + \item Kaggle constes for LHCb would be very beneficial for us. + \item A lot of work has been put in to make the contest as usable for us as possible(correlations check, MC/DATA disagrement). + \item All scripts are ready and automatised and tested. + \item We look to have feedback from the collaboration. +\end{enumerate} +\begin{center} +\includegraphics[width=1.9in]{pr.jpg} +\end{center} +\end{frame} +\begin{frame}\frametitle{~} + \begin{center} +\begin{Large} +BACKUPS +\end{Large} +\end{center} +\end{frame} + \begin{frame}\frametitle{Approximate Binned Median Statistics (ABMS)} + + In real analysis if you are looking for upper limit you compare null hypothesis $H_0$ (background-only) with a spectrum of other hypotheses representing different branching fractions. Then you choose one with smaller value of branching fraction that gives enough significance. + The measure of significance is CLs, that is computed for statistics + $q$ equal to ratio of likelihoods of your hypotheses. + + For Kaggle to simplify understanding/computation of the metric we do two «tricks»: + \begin{itemize} + + \item instead of comparing $H_0$ with spectrum of hypothesis we compare it with hypothesis with specific branching fraction (taken from the paper on $\tau\rightarrow \mu\mu\mu$) and + \item instead of estimation of significance we just calculate statistics $q$ (the better it is, the better significance classifier can provide) + \end{itemize} + + %From practical point of view it could be shown classifiers with better ROC curve have better ABMS. + + \end{frame} + +\begin{frame} +\frametitle{Approximate Binned Median Statistics (ABMS)-2} +For given classifier $g$, the number of events $n$ found in a bin (a region of input variable space), is assumed to follow a Poisson distribution with mean $\mu_s+\mu_b$ +$$P(n | \mu_s, \mu_b) = \frac{(\mu_s + \mu_b)^n}{n!}e^{-(\mu_s+\mu_b)},$$ +where $\mu_s$ and $\mu_b$ are the expected numbers of events from the signal and background, respectively. To establish the existence of the signal process, we test the $H_0$ of $\mu_s$ = 0 against the alternative $H_1$ with $\mu_s +>0.$ We will use several bins, and assume that for each bin we have independent parameter $\mu_s$. Thus the likelihood ratio looks like: +\begin{equation} +Q= \prod_{bin} \frac{P(n_i|0, \mu_{b}^i)}{P(n_i | \hat{\mu}_s^i, \mu_{b}^i)} = \prod_{bin}\left(\frac{\mu_b^i}{n_i}\right)^{n_i} e^{n_i - \mu_b^i}, +\end{equation} +where $\hat{\mu}_s^i$ is the maximum likelihood estimator of $\mu_s^i$ given that we observe $n_i$ events in the $i$-th bin. $\hat{\mu}_s^i = n_i - \mu_b^i$. +\end{frame} + +\begin{frame}\frametitle{Approximate Binned Median Statistics (ABMS)-3} + +\begin{equation} +q = -2 \ln Q = 2 \sum_{bin} \left(n_i \ln{\frac{n_i}{\mu_b^i}} - n_i +\mu_b^i\right) +\end{equation} + +For empirical estimations we take $\mu_b^i = b_i$, $n_i = s_i + b_i$, where $s_i$ - is estimation of the amount of signal according to the best known upper limit. Then empirical estimation of the statistics is +\begin{equation} +\hat{q}= 2 \sum_{bin} \left((s_i + b_i) \ln{\left(1 + \frac{s_i}{b_i}\right)} - s_i\right) +\end{equation} + +Adding regularization term we can define +\begin{equation} +ABMS = \sqrt{\hat{q}_{regularization}} = \sqrt{\sum_{bin} AMS_i^2} +\end{equation} +where $AMS_i$ is calculated for $i-th$ bin in the same way as in HiggsML challenge: +$$AMS = \sqrt{2 ((s + b + b_{reg}) \ln{(1 + s/(b+b_{reg}))} - s)} \cong \sqrt{2 s^2 / (b + b_{reg})}$$ +\end{frame} diff --git a/Kstmumu/Face2Face_meeting/Systematics/Systematics.aux b/Kstmumu/Face2Face_meeting/Systematics/Systematics.aux index 972daff..250d2ac 100644 --- a/Kstmumu/Face2Face_meeting/Systematics/Systematics.aux +++ b/Kstmumu/Face2Face_meeting/Systematics/Systematics.aux @@ -1,16 +1,19 @@ \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 - +\providecommand\HyperFirstAtBeginDocument{\AtBeginDocument} +\HyperFirstAtBeginDocument{\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{\ifx\hyper@anchor\@undefined +\let\contentsline\oldcontentsline +\let\newlabel\oldnewlabel +\fi} +\fi} +\global\let\hyper@last\relax +\gdef\HyperFirstAtBeginDocument#1{#1} +\providecommand\HyField@AuxAddToFields[1]{} \@writefile{toc}{\beamer@endinputifotherversion {3.10pt}} \@writefile{nav}{\beamer@endinputifotherversion {3.10pt}} \select@language{english} diff --git a/Kstmumu/Face2Face_meeting/Systematics/Systematics.log b/Kstmumu/Face2Face_meeting/Systematics/Systematics.log index 3d8f45d..a8e0778 100644 --- a/Kstmumu/Face2Face_meeting/Systematics/Systematics.log +++ b/Kstmumu/Face2Face_meeting/Systematics/Systematics.log @@ -1,17 +1,21 @@ -This is pdfTeX, Version 3.1415926-1.40.10 (TeX Live 2009/Debian) (format=pdflatex 2014.3.24) 27 MAY 2014 14:36 +This is pdfTeX, Version 3.1415926-2.4-1.40.13 (TeX Live 2012/Debian) (format=pdflatex 2014.12.22) 1 JAN 2015 22:54 entering extended mode + restricted \write18 enabled. %&-line parsing enabled. **Systematics.tex (./Systematics.tex -LaTeX2e <2009/09/24> -Babel and hyphenation patterns for english, usenglishmax, dumylang, noh -yphenation, farsi, arabic, croatian, bulgarian, ukrainian, russian, czech, slov -ak, danish, dutch, finnish, french, basque, ngerman, german, german-x-2009-06-1 -9, ngerman-x-2009-06-19, ibycus, monogreek, greek, ancientgreek, hungarian, san -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, pinyin, loaded. +LaTeX2e <2011/06/27> +Babel and hyphenation patterns for english, dumylang, nohyphenation, et +hiopic, farsi, arabic, pinyin, croatian, bulgarian, ukrainian, russian, slovak, + czech, danish, dutch, usenglishmax, ukenglish, finnish, french, basque, ngerma +n, german, swissgerman, ngerman-x-2012-05-30, german-x-2012-05-30, monogreek, g +reek, ibycus, ancientgreek, hungarian, bengali, tamil, hindi, telugu, gujarati, + sanskrit, malayalam, kannada, assamese, marathi, oriya, panjabi, italian, lati +n, latvian, lithuanian, mongolian, mongolianlmc, nynorsk, bokmal, indonesian, e +speranto, coptic, welsh, irish, interlingua, serbian, serbianc, slovenian, friu +lan, romansh, estonian, romanian, armenian, uppersorbian, turkish, afrikaans, i +celandic, kurmanji, polish, portuguese, galician, catalan, spanish, swedish, th +ai, loaded. 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+\usetheme{Sybila} +\title[Search for Charged Lepton Flavour Violation at LHCb experiment]{Search for Charged Lepton Flavour Violation at LHCb experiment} +\subtitle{Doctoral disertation} + \author[Marcin Chrz\k{a}szcz]{Marcin Chrz\k{a}szcz \\ Supervisor: prof. dr hab. Tadeusz Lesiak \\ Auxiliary supervisor: dr hab. Alberto Lusiani} + + \institute[UZH, IFJ]{ +Henryk Niewodniczanski Institute of Nuclear Physics Polish Academy of Sciences, Cracow, Poland} + + +\date{\today} +\begin{document} + + +% --------------------------- SLIDE -------------------------------------------- +\frame[plain]{\titlepage} +\author{Marcin Chrz\k{a}szcz} +% ------------------------------------------------------------------------------ +% --------------------------- SLIDE -------------------------------------------- + +\institute{~(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} + + +\iffalse + + \begin{frame} + \frametitle{Errata to thesis} + \begin{itemize} + \item Since submision, the HFAG report has been published, so refence: + \end{itemize} + [53] HFAG Collaboration, M.Chrz\k{a}szcz et. al. Averages of $b$-hadron, $c$-hadron, and $\tau$-lepton properties as of summer 2014, arXiv:1412.7515. + \end{frame} + + +\fi + +\section{Lepton Flavour Violation phenomenon} +\begin{frame}\frametitle{Lepton Flavour/Number Violation} +\begin{small} + Lepton Flavour Violation(LFV): +\end{small} + + +\begin{footnotesize} + +After $\Pmuon$ was discovered (1936) 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 there is a nother $\Pnu$. +\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 (oscillations). +\end{itemize} +\end{footnotesize} + + +\begin{footnotesize} + +\begin{columns} +\column{3.5in} +\begin{small} + Lepton Number Violation (LNV) %(see J. Harrison \href{https://indico.cern.ch/event/300387/session/17/contribution/74}{\color{blue}talk}) +\end{small} + +\begin{itemize} +\item Even with LFV, lepton number can be a conserved quantity. +\item Many NP models predict LNV (Majorana neutrinos) +\item LNV searched in s-called neutrinoless double $\beta$ decays. +\end{itemize} + +\column{1.5in} +\includegraphics[width=0.73\textwidth]{Double_beta_decay_feynman.png} + +\end{columns} + +\end{footnotesize} +%Double_beta_decay_feynman.png + + % \textref{M.Chrz\k{a}szcz 2014} +\end{frame} +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% + \begin{frame} + \frametitle{Status of searches for $\color{white} \tau \to \mu \mu \mu$} + \begin{columns} + \begin{column}{.62\textwidth} + + \includegraphics[width=.95\textwidth]{feymn.png} + + {{ + \begin{itemize} + \item Charged Lepton Flavour Violation process. + \item The Standard Model contribution: penguin diagram 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] $2.1\times 10^{-8}$ + \end{description} + \end{alertblock} + \begin{alertblock}{Predictions} + \begin{description} + \item[SM] $ O(10^{-40})$ + \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} +%%%%%%%%%%%%%%%%% + + +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% + \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 Superb particle identification (PID). + \end{itemize} + + + +\end{footnotesize} +\end{columns} + +\end{frame} +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% + \section{Selection} + \begin{frame} \frametitle{Strategy} +\begin{enumerate} +\item Data sample: $1 \invfb~7~\TeV$ and $2 \invfb~8\TeV$. +\item Normalization (control) decay channel: $\PDs\to\Pphi(\Pmu\Pmu)\Ppi$. +\item Blind analysis. +\item Event selection: +\begin{itemize} +\item Preselection of three tracks that combine to give a mass close to $m_{\tau}$, with desplaised vertex. +\item Selection based on three classifiers: +\begin{itemize} +\item Geometry and topology ($\mathcal{M}_{3body}$) +\item PID ($\mathcal{M}_{PID}$) +\item Three muon invariant mass ($m_{\mu\mu\mu}$) +\end{itemize} +\end{itemize} +\item Major background contributions:$\PDs \to \eta(\mu\mu\gamma) \mu \nu$ and $\PD \to \PK \Ppi \Ppi$. +\item Evaluation of the upper limit on $\mathcal{B}(\Ptau \to \Pmu \Pmu \Pmu)$ using $CL_s$. +\end{enumerate} + + + \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{footnotesize} +\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{footnotesize} + + + \begin{itemize} + \item Pythia produces them in wrong propotions + \item Channels were produced seperatly and added in the given proporitons. + \end{itemize} + + + + \end{center} + + + \begin{columns} + \column{0.05\textwidth} + {~} + \column{0.9\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, \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{Triggers at LHCb} +\begin{footnotesize} + +\begin{itemize} +\item LHCb uses complex trigger, $\mathcal{O}(100)$ trigger lines. %\footnote{\href{http://arxiv.org/abs/1211.3055}{\color{blue}arXiv:1211.3055}}, $\mathcal{O}(100)$ trigger lines. +\item Lines change with data taking. +\item Optimized choice of triggers based on $\dfrac{s}{\sqrt{b}}$ FOM, +\end{itemize} +\end{footnotesize} +\begin{tiny} +\begin{columns} +\column{0.66\textwidth} +\begin{equation} +\label{eq:efftrig} +\varepsilon(\beta)^\prime_{\text{evt},\text{line}} = \frac{N(\tau~\text{ MC(BKG) events triggered +line, but not by any better line})}{N(\tau\text{ MC(BKG) events triggered by any line})}, \nonumber +\end{equation} +\begin{small} +\begin{itemize} +\item Evaluated different triggers used in 2012 data taking. +\item Found negligible differences in trigger efficiencies. +\end{itemize} +\end{small} +\column{0.32\textwidth} +\begin{equation} +\text{CTFM}=\frac{\sqrt{\sum\limits_\text{trigger lines} \beta^\prime_{\text{evt},\text{line}}}}{\sum\limits_\text{trigger lines} \varepsilon^\prime_{\text{evt},\text{line}}}\nonumber +\end{equation} + +\end{columns} +\end{tiny} +\begin{footnotesize} + + +\end{footnotesize} +\begin{tiny} + \begin{tabular}{|l|c|c|c|} + \hline + name & $\varepsilon^\prime$ & $\beta^\prime$ & CTFM \\\hline + % here +Hlt2TriMuonTauDecision & 0.880708 & 0.736182 & 0.974228\\ +Hlt2DiMuonDetachedDecision & 0.0669841 & 0.173396 & 1.00636\\ +Hlt2CharmSemilep3bodyD2KMuMuDecision & 0.0206816 & 0.0182935 & 0.99472\\ +Hlt2CharmHadD2HHHDecision & 0.00554351 & 0.00666405 & 0.992604\\ +Hlt2CharmSemilep3bodyD2KMuMuSSDecision & 0.00195444 & 0.00470404 & 0.993106\\ +Hlt2CharmSemilep3bodyD2PiMuMuDecision & 0.00206105 & 0.00679472 & 0.994591\\ +Hlt2TopoMu3BodyBBDTDecision & 0.00394442 & 0.0121521 & 0.996937\\ + \hline + \end{tabular} +\end{tiny} + + + + \end{frame} + + \section{Multivariate technique} + + \begin{frame} + \frametitle{Geometric likelihood} + + \begin{itemize} + \item As mentioned in LHC we have different production sources of $\Ptau$'s. + \item Each source has different detector response signature. + \item To maximise our performance we trained classifiers for each of the $\Ptau$ sources using: + \begin{itemize} + \item Kinematic properties of $\Ptau$ candidate. + \item Geometric properties of $\Ptau$ candidate, like pointing angle, DOCA, Vertex $\chi^2$, flight distance. + \item Isolations, for vertex and individual tracks. + \end{itemize} + \item After training the individual classifiers one that combines all this information in a single classifier on mixed sample of $\Ptau$'s. + \item This technique is known as Blending or Ensemble learning. + \item Using this approach we gain $6\%$ sensitivity! + \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{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} +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%5 +% PID + + \begin{frame} + \frametitle{Particle Identification (PID)} +\begin{itemize} +\item Classifier trained on inclusive MC sample. +\item Using information from: RICH, Calorimeters, Muon system and tracking. +\item Correct for the MC efficiency using control channel: $\PDs \to \Pphi(\Pmu\Pmu) \Ppi$ and $\PB \to \PJpsi(\Pmu\Pmu) \PK$ +\end{itemize} + \begin{columns} + \begin{column}{.45\textwidth} + \includegraphics[width=.95\textwidth]{mPID_2012.pdf} + \end{column} + \end{columns} + \end{frame} +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%5 + \begin{frame} + \frametitle{Binning optimisation} + \begin{itemize} + \item Events are distributed among $\mathcal{M}_{3body}, \mathcal{M}_{PID}$ plane. + \item In 2D we group the events in groups(bins) + \item Bins are optimised using $CL_s$ method. + \item The lowest bins are rejected, because they do not contribute to the limit sensitivity. + \item In rest of the bins a fit to mass side-bands is performed in order to estimate number of expected background in signal window. + \end{itemize} +\begin{columns} +\column{2.2in} +\center{2011}\\ + \includegraphics[width=.99\textwidth]{2D_2011.pdf} +\column{2.2in} +\center{2012}\\ + \includegraphics[width=.99\textwidth]{2D_2012.pdf} +\column{0.5in} +{~} + +\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 efficiency. + \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} + + + + + \section{Backgrounds} + + \begin{frame} + \frametitle{Misidentification} + \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 All contained in the lowest $\mathcal{M}_{PID}$ bin. + % \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]{./trash.pdf}{~}{~}{~}{~}{~}{~}{~}{~}{~}{~}{~}{~}{~}{~} + \includegraphics[width=.45\textwidth]{./mPID_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 Model it + \item \underline{Remove it} with dimuon mass cut: + \begin{itemize} + + + \item Fits better understood. + \item Sensitivity unchanged when removing veto. + \item Smaller uncertainty on expected background. + \end{itemize} + \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{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 \href{http://arxiv.org/abs/0707.0988}{\color{blue}\texttt{arXiv:0707.0988}} by S.Turczyk. + \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} + \begin{center} + \includegraphics[width=.5\textwidth]{./sigDalitz.pdf} + \end{center} + + + } + \only<1>{ +\begin{columns} + \column{0.33\textwidth} + \includegraphics[width=.95\textwidth]{./gammallll2.pdf}\\ + \includegraphics[width=.95\textwidth]{./gammarad-llll2.pdf} + + + \column{0.33\textwidth} + \includegraphics[width=.95\textwidth]{./gammallrr2.pdf}\\ + \includegraphics[width=.95\textwidth]{./gammarad-llrr2.pdf} + + \column{0.33\textwidth} + \includegraphics[width=.95\textwidth]{./gammarad2.pdf}\\ + +% \begin{itemize} +% \item Same models as in Z.Was \href{https://indico.cern.ch/event/300387/session/7/contribution/33}{\color{blue}talk} +% \end{itemize} +{~}\\ {~}\\ {~}\\ {~}\\ {~}\\ + + \end{columns} +} + + \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{Results} + + \begin{frame} + \frametitle{Results} + + \begin{center} + \includegraphics[width=0.7\textwidth]{banana_line.pdf} + \end{center} +\begin{columns} + +\column{0.2in}{~} +\column{2in} +Limits(PHSP):\\ +Observed(Expected)\\ +$\color{red}4.6~(5.0)\times 10^{-8}$ at $90\%$ CL\\ +$\color{pink}5.6~(6.1)\times 10^{-8}$ at $95\%$ CL\\ + + \column{3in} + \includegraphics[width=0.5\textwidth]{model.png} +\end{columns} + \end{frame} + + + +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%5 +\section{LFV limit combination} + + +\begin{frame}\frametitle{Combination of LFV UL 1/2} +\begin{columns} + +\column{1.8in} + \begin{itemize} + + \item Searches for LFV in $\Ptau$ sector is a domain of B factories. + \item Over last years both BaBar and Belle set very strong limits on branching fractions of several rare $\tau$ decays. + + \end{itemize} + + +\column{3.2in} + \includegraphics[width=0.95\textwidth]{TauLFV_UL_2014001.png} + + + +\end{columns} +\begin{itemize} + \item Since thouse limits are used to constraint NP models, their "official" combination is of paramount importance. + \item Various methods of limit computation used in Belle and BaBar's studies. + \item The HFAQ group recomputed consistently all estimates using the $CL_s$ method and the the same approach was involved in the average evaluation. + \end{itemize} + \end{frame} + + +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%5 + +\begin{frame}\frametitle{Combination of LFV UL 2/2} +\begin{itemize} +\item For each measurement take integrated luminosity ($\mathcal{L}$), cross section ($\sigma_{\tau\tau}$), efficiencies ($\epsilon$), background expected($b$) and all systematics. +\item Calculate number of signal: $s = \mathcal{L} \sigma_{\tau\tau} \epsilon^{tot} \mathcal{B}(\Ptau \to LFV)$. +\item Scan the $CL_s$ wrt. $\mathcal{B}(\Ptau \to LFV)$: +\end{itemize} +\begin{columns} +\column{0.15in} +{~} +\column{2in} +\begin{small} +\begin{align} +CL_s = \dfrac{\prod_{i=1}^{N_{\text{chan}}}\sum_{n=0}^{n_i} \dfrac{e^{-(s_i+b_i)} (s_i+b_i)^{n}}{n!} }{\prod_{i=1}^{n_{\text{chan}}} \sum_{n=0}^{n_i} \dfrac{e^{-b_i} b_i^{n}}{n!}} \nonumber~, +\end{align} +\end{small} +\column{2.7in} + \includegraphics[width=0.95\textwidth]{TauLFV_UL_2014001_averaged.png} + + +\end{columns} +\end{frame} + + + + + +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% + + \begin{frame} + \frametitle{"The Rule of Three"} + \begin{columns} + % \column{2.5in} + \begin{column}{1.9in} + \begin{alertblock}{ $\Ptau \to \Pmu \Pmu \Pmu$ limits ($ \color{white} 90\,\%$ CL)} + + \begin{description} + \item[BaBar(FC)] $3.3\times 10^{-8}$ + \item[Belle(FC)] $2.1\times 10^{-8}$ + \item[LHCb(CLs)] $4.6\times 10^{-8}$ + \item[HFAG(CLs)] $1.2 \times 10^{-8}$ + \end{description} + \end{alertblock} +\end{column} + \begin{column}{2.85in} + \includegraphics[width=1\textwidth]{TauLFV_UL_2014001_averaged_zoom.png}\\ + +\end{column} + + \end{columns} + {~}\\ + + + To conclude: + \begin{columns} + \column{3in} +\begin{small} + \begin{itemize} +% \item LHCb result for $\Ptau \to \Pmu \Pmu \Pmu$ with full data set. +% \item We are getting close to B-factories. +% \item Thanks to 3 experiments we have a world limit: $\mathcal{B}(\Ptau \to \Pmu \Pmu \Pmu)< 1.2 \times 10^{-8}$ at 90\% CL. +\item LHCb is reaching B-factories limits. +\item Many new techniques developed to perform this analysis. +\item Combination of UL within HFAG gave the best sensitivity for $\mathcal{B}(\Ptau \to \Pmu \Pmu \Pmu)< 1.2 \times 10^{-8}$ at 90\% CL. + + \end{itemize} + \end{small} +\column{2in} + \includegraphics[width=0.93\textwidth]{banana_tau23mu_hfag.pdf}\\ + + +\end{columns} + + \end{frame} + +\pagenumbering{gobble} + \begin{frame}\frametitle{Backup} + + \includegraphics[width=0.93\textwidth]{ngbbs4f7918ec8ffb8.jpg}\\ + + + \end{frame} + + + + + + \begin{frame}\frametitle{Prof. J.Ciborowski comments} +\begin{enumerate} +\item Podrozdział (4.10) ten jest de facto zapowiedzią większej pracy. Szkoda, że materiał tu przedstawiony +potraktowany został bardzo skrótowo, co wymusiło na mnie konieczność kilkakrotnego przeczytania tego podrozdziału i utrudniło docenienie wyniku +otrzymanego przez autora w konfrontacji z przewidywaniami teoretycznymi. +\end{enumerate} +\begin{itemize} +\item The theory part of this was presented in detail in 2.3.4. This chapter is just a showing how to reweight the distributions to a given NP model, thats why I tried to keep it short, but I agree I over did it. +\end{itemize} + + + \end{frame} + + + + \begin{frame}\frametitle{Prof. J.Ciborowski comments} +\begin{enumerate} +\item Jedyne +rzucające się w oczy uchybienie redakcyjne to pomyłki w numerach +rozdziałów, których zawartość wymieniona jest pod koniec Wstępu. + +\end{enumerate} +\begin{itemize} +\item Mea Cupla. Completly missed that. +\end{itemize} + + + \end{frame} + + %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%5555 + + + +\end{document} diff --git a/Seminars/IFJ/tau23mu_08_02_15/defence.toc b/Seminars/IFJ/tau23mu_08_02_15/defence.toc new file mode 100644 index 0000000..e0540c9 --- /dev/null +++ b/Seminars/IFJ/tau23mu_08_02_15/defence.toc @@ -0,0 +1,11 @@ +\beamer@endinputifotherversion {3.10pt} +\select@language {english} +\beamer@sectionintoc {1}{Lepton Flavour Violation phenomenon}{3}{0}{1} +\beamer@sectionintoc {2}{LHCb detector}{5}{0}{2} +\beamer@sectionintoc {3}{Selection}{6}{0}{3} +\beamer@sectionintoc {4}{Multivariate technique}{9}{0}{4} +\beamer@sectionintoc {5}{Normalisation}{15}{0}{5} +\beamer@sectionintoc {6}{Backgrounds}{16}{0}{6} +\beamer@sectionintoc {7}{Model dependence}{19}{0}{7} +\beamer@sectionintoc {8}{Results}{21}{0}{8} +\beamer@sectionintoc {9}{LFV limit combination}{22}{0}{9} diff --git a/Seminars/IFJ/tau23mu_08_02_15/defence2.aux b/Seminars/IFJ/tau23mu_08_02_15/defence2.aux 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+\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} +\definecolor{darkpastelgreen}{rgb}{0.01, 0.75, 0.24} + + +\usetheme{Sybila} +\title[Search for Charged Lepton Flavour Violation at LHCb experiment]{Search for Charged Lepton Flavour Violation at LHCb experiment} + \author[Marcin Chrz\k{a}szcz]{Marcin Chrz\k{a}szcz } + + \institute[UZH, IFJ]{ +Henryk Niewodniczanski Institute of Nuclear Physics Polish Academy of Sciences, Cracow, Poland} + + +\date{\today} +\begin{document} + + +% --------------------------- SLIDE -------------------------------------------- +\frame[plain]{\titlepage} +\author{Marcin Chrz\k{a}szcz} +% ------------------------------------------------------------------------------ +% --------------------------- SLIDE -------------------------------------------- + +\institute{~(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} + + +\iffalse + + \begin{frame} + \frametitle{Errata to thesis} + \begin{itemize} + \item Since submision, the HFAG report has been published, so refence: + \end{itemize} + [53] HFAG Collaboration, M.Chrz\k{a}szcz et. al. Averages of $b$-hadron, $c$-hadron, and $\tau$-lepton properties as of summer 2014, arXiv:1412.7515. + \end{frame} + + +\fi + +\section{Lepton Flavour Violation phenomenon} +\begin{frame}\frametitle{Lepton Flavour/Number Violation} + + +\begin{enumerate} +\item Lepton Flavour Violation (LFV) found in neutrino sector - the first phenomena outside the Standard Model. +\item The search for charged lepton flavour violation (CLFV) commenced with muon discovery (1936) and its identification as a separate particle. +\end{enumerate} +\begin{columns} +\column{3in} +\begin{itemize} +\item Expected: $B(\mu\to\Pe\gamma) \approx 10^{-4}$ +\item Unless there is another $\Pnu$. +\end{itemize} + +\column{2in} +{~}\includegraphics[width=0.98\textwidth]{rabi.png} + +\end{columns} +\begin{footnotesize} + +\begin{enumerate} +\setcounter{enumi}{2} +\item The observation of CLFV would be a clear signature of New Physics (NP) - paramount importance for flavour physics and the enigma of generations. +\item LFV vs LNV (Lepton Number Violation) +\end{enumerate}\end{footnotesize} +\begin{columns} +\column{3.5in} +\begin{footnotesize} + + +\begin{itemize} +\item Even with LFV, lepton number can be a conserved quantity. +\item Many NP models predict LNV (Majorana neutrinos) +\item LNV searched in so-called neutrinoless double $\beta$ decays. +\end{itemize} +\end{footnotesize} +\column{1.5in} +\includegraphics[width=0.65\textwidth]{Double_beta_decay_feynman.png} + +\end{columns} + + + % \textref{M.Chrz\k{a}szcz 2014} + +\end{frame} +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% + \begin{frame} + \frametitle{Status of searches for $\color{white} \tau \to \mu \mu \mu$} + \begin{columns} + \begin{column}{.55\textwidth} + + \includegraphics[width=.90\textwidth]{feymn.png} + + {{ + \begin{small} + \begin{itemize} + \item Charged Lepton Flavour Violation process. + \item The Standard Model contribution: penguin diagram with neutrino oscillation. + \item Negligible SM branching fraction. + \item Large enhacement from NP models like: SUSY, Little Higgs, Fourth generation, etc. + + % \item SM prediction is beyond experimental reach~$O(10^{-40})$. + + \end{itemize} + \end{small} + }} + \end{column} + \begin{column}{.45\textwidth} + + \begin{alertblock}{Predictions} + \begin{description} + \item[SM] $ O(10^{-40})$ + \item[var.\ SUSY] $10^{-10}$ + \item[non universal $\color{red}{Z'}$] $10^{-8}$ + \item[mSUGRA+seesaw] $10^{-9}$ + \item[and many more...] + \end{description} + \end{alertblock} + + \begin{alertblock}{Current limits ($ \color{white} 90\,\%$ CL)} + + \begin{description} + \item[BaBar] $3.3\times 10^{-8}$ + \item[Belle] $2.1\times 10^{-8}$ + \end{description} + \end{alertblock} + \includegraphics[width=.63\textwidth]{SUSY.png} + + \end{column} + + \end{columns} + + + \end{frame} +%%%%%%%%%%%%%%%%% + + +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% + \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 Superb particle identification (PID). + \end{itemize} + + + +\end{footnotesize} +\end{columns} + +\end{frame} +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% + \section{Selection} + \begin{frame} \frametitle{Strategy} +\begin{enumerate} +\item Data sample: $1 \invfb~7~\TeV$ and $2 \invfb~8\TeV$. +\item Normalization (control) decay channel: $\PDs\to\Pphi(\Pmu\Pmu)\Ppi$. +\item Blind analysis in the region of $| m_{\mu\mu\mu} - m_{\tau} | <20~\MeV/c^2$. +\item Event selection: +\begin{itemize} +\item Preselection of three tracks that combine to give a mass close to $m_{\tau}$, with displaced vertex. +\item Selection based on three classifiers: +\begin{itemize} +\item Geometry and topology ($\mathcal{M}_{3body}$) - multivariate classifier +\item PID ($\mathcal{M}_{PID}$) - multivariate classifier +\item Three muon invariant mass ($m_{\mu\mu\mu}$) +\end{itemize} +\end{itemize} +\item Major background contributions:$\PDs \to \eta(\mu\mu\gamma) \mu \nu$ and $\PD \to \PK \Ppi \Ppi$ decays. +\item Evaluation of the upper limit on $\mathcal{B}(\Ptau \to \Pmu \Pmu \Pmu)$ using $CL_s$ method. +\end{enumerate} + + + \end{frame} + +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% + \begin{frame} + \frametitle{$\color{white} \tau$ production at LHCb} + \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} + + + \begin{itemize} + \item Pythia produces them in wrong proportions + \item The above decay channels were produced separately and added in the given proportions. + \item Taken into account different trigger efficiencies for different channels. + \end{itemize} + + + + \end{center} + + + \end{frame} + + + + \section{Multivariate technique} + + \begin{frame} + \frametitle{Signal and background discrimination} + \begin{itemize} + \item Two multivariate classifiers, $\mathcal{M}_{3body}$ and $\mathcal{M_{PID}}$. + \end{itemize} + \begin{columns} + \column{3in} + \begin{itemize} + \item $\mathcal{M}_{3body}$ trained using vertex and track fit quality, vertex displacement, vertex pointing, vertex isolation and $\Ptau$ $p_T$. + \item Used Blending Technique (see the next slide). + \end{itemize} + +\column{2in} + \includegraphics[width=.98\textwidth]{ver.png} +\end{columns} +\begin{columns} +\column{0.1in} +{~} +\column{2in} + % \includegraphics[width=.95\textwidth]{m3body_2012.pdf} +\includegraphics[width=.98\textwidth]{./mixing.pdf} +\column{3in} +\begin{itemize} +\item Trained on signal and background MC. +\item Calibrated on $\PDs \to \Pphi(\mu\mu) \Ppi$ sample. +\end{itemize} +\end{columns} + \end{frame} +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% + \begin{frame} + \frametitle{Blending technique} + \begin{columns} + \column{3.2in} + + + + \includegraphics[width=.99\textwidth]{diagram.png} + \column{1.8in} + \begin{itemize} +\item Each of the $\Ptau$ lepton production channel have a different signature in terms of kinematic distributions. +\item Signal blending technique improved the discriminating power by $6~\%$ +\end{itemize} + \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 $\PDs \Longrightarrow \Ptau$ from MC. + \item Apply corrections to $\PDs\to\Pphi\Ppi$ on data. + \item Publication in preparation. + \end{itemize} + + \begin{columns} + + \begin{column}{.45\textwidth} + \includegraphics[width=.95\textwidth]{m3body_2012.pdf} + + \end{column} + \begin{column}{.45\textwidth} + \begin{itemize} + \item $\PDs\to\Pphi\Ppi$ decay well modelled in MC.\\ + \includegraphics[width=.9\textwidth]{./dataMC.pdf} + % \item[$\rightarrow$] i.e.\ also badly pointing non-prompt $\PDs$ + \end{itemize} + \end{column} + + \end{columns} + \end{frame} + + +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% + \begin{frame} + + \frametitle{Signal and background discrimination - $\color{white}{\mathcal{M}_{PID}}$} + \begin{columns} + \column{3in} + \begin{itemize} + \item $\mathcal{M}_{PID}$ trained using \color{red}{RICH}, \color{blue}{ECAL} and \color{green}{muon chambers}. + \end{itemize} + +\column{2in} + \includegraphics[width=.98\textwidth]{detcol.png} +\end{columns} +\begin{columns} +\column{0.1in} +{~} +\column{2in} + \includegraphics[width=.95\textwidth]{mPID_2012.pdf} +\column{3in} +\begin{itemize} +\item Trained on signal and background MC. +\item Calibrated on $\PB \to \PJpsi \PK$ and $\PDs \to \Pphi(\mu\mu) \Ppi$ decays. +\end{itemize} +\end{columns} + \end{frame} + + + + + +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% + \begin{frame} + \frametitle{Binning optimisation} + + + \begin{footnotesize} + \begin{itemize} + \item Events are distributed among $\mathcal{M}_{3body}, \mathcal{M}_{PID}$ plane. + \item In 2D we collect the events in groups(bins) + \item Bins are optimised using $CL_s$ method: + \begin{equation} + CL_s = \dfrac{\prod_{i=1}^{N_{\text{chan}}}\sum_{n=0}^{n_i} \dfrac{e^{-(s_i+b_i)} (s_i+b_i)^{n}}{n!} }{\prod_{i=1}^{n_{\text{chan}}} \sum_{n=0}^{n_i} \dfrac{e^{-b_i} b_i^{n}}{n!}} \nonumber~, + \end{equation} + \item The lowest bins are rejected, because they do not contribute to the limit sensitivity. + \end{itemize} + \end{footnotesize} +\begin{columns} +\column{2.2in} +\center{2011}\\ + \includegraphics[width=.87\textwidth]{2D_2011.pdf}\\{~} +\\{~} +\\{~}\\{~}\\{~}\\{~} + +\column{2.2in} +\center{2012}\\ + \includegraphics[width=.87\textwidth]{2D_2012.pdf}\\{~} +\\{~} +\\{~}\\{~}\\{~}\\{~} + +\column{0.5in} +{~} + +\end{columns} + + \end{frame} +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% + + + + \section{Normalisation} + + \begin{frame} + \frametitle{Relative normalisation} + $\boxed{\mathcal{B}(\Ptau\to\Pmu\Pmu\Pmu) = \frac{\mathcal{B}(\PDs\to\Pphi\Ppi)}{\mathcal{B}(\PDs\to\Ptau\Pnut)} \times f_{\PDs}^{\Ptau} \times \frac{\varepsilon_\text{norm} }{\varepsilon_\text{sig} } \times \frac{N_\text{sig}}{N_\text{norm}} = \alpha\times N_\text{sig}}$ + \begin{itemize} + \item where $\varepsilon$ stands for trigger, reconstruction, selection efficiency. + \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 data. + \end{itemize} +\begin{columns} +\column{2.3in} + \center{2011}\\ + + \includegraphics[width=.97\textwidth]{./Ds_data_2011.pdf} + \column{2.3in} + \center{2012}\\ + \includegraphics[width=.97\textwidth]{./Ds_data_2012.pdf} + \end{columns} + \end{frame} + + + + + \section{Backgrounds} + + \begin{frame} + \frametitle{Misidentification (Peaking background)} + \begin{columns} + \column{3in} + \begin{itemize} + \item Dominant: $\PDplus\to\PK\Ppi\Ppi$. + \item Also seen $\PDplus\to\Ppi\Ppi\Ppi$ and $\PDs\to\Ppi\Ppi\Ppi$. + \item All contained in the lowest $\mathcal{M}_{PID}$ bin. + % \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]{./trash.pdf}{~}{~}{~}{~}{~}{~}{~}{~}{~}{~}{~}{~}{~}{~} + \includegraphics[width=.45\textwidth]{./mPID_2012.pdf} + \end{frame} + + + \begin{frame} + \frametitle{Other 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 Model it + \item \underline{Remove it} with dimuon mass cut: + \begin{itemize} + + + \item Fits better understood. + \item Sensitivity unchanged when removing veto. + \item Smaller uncertainty on expected background. + \end{itemize} + \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 the $\pm \unit{30}{\MeV}$ region. + % \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{Model dependence} + + \begin{frame} + \frametitle{Model dependence} + \begin{itemize} + \begin{small} + \item $\Peta$ veto $\Rightarrow$ our limit not constraining to New Physics with small $m_{\APmuon\Pmuon}$. + \item Model description in \href{http://arxiv.org/abs/0707.0988}{\color{blue}\texttt{arXiv:0707.0988}} by S.Turczyk using Effective Field Theory approach. + \item 5 relevant Dalitz distributions: 2 four-point operators, 1 radiative operator, 2 interference terms. + \end{small} + \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 remain stable (within $7\,\%$). + \end{itemize} + \begin{center} + \includegraphics[width=.5\textwidth]{./sigDalitz.pdf} + \end{center} + + + } + \only<1>{ +\begin{columns} + \column{0.33\textwidth} + \includegraphics[width=.78\textwidth]{./LLLL.pdf}\\ + \includegraphics[width=.78\textwidth]{./LLRR.pdf}\\ + + + \column{0.33\textwidth} + \includegraphics[width=.78\textwidth]{./LLLLRAD.pdf}\\ + \includegraphics[width=.78\textwidth]{./LLRRRAD.pdf} + + \column{0.33\textwidth} + \includegraphics[width=.78\textwidth]{./RAD.pdf}\\ +\begin{small} + \begin{itemize} + \item All five cases implemented in TAUOLA. + \item Publication in preparation. + \end{itemize} +\end{small} + + +% \begin{itemize} +% \item Same models as in Z.Was \href{https://indico.cern.ch/event/300387/session/7/contribution/33}{\color{blue}talk} +% \end{itemize} +%{~}\\ {~}\\ + + \end{columns} +} + + \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{Results} + + \begin{frame} + \frametitle{Results} + + \begin{center} + \includegraphics[width=0.7\textwidth]{banana_line.pdf} + \end{center} +\begin{columns} + +\column{0.2in}{~} +\column{2in} +Limits(PHSP):\\ +Observed(Expected)\\ +$\color{red}4.6~(5.0)\times 10^{-8}$ at $90\%$ CL\\ +$\color{pink}5.6~(6.1)\times 10^{-8}$ at $95\%$ CL\\ + + \column{3in} + \includegraphics[width=0.5\textwidth]{model.png} +\end{columns} + \end{frame} + + + +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%5 +\section{LFV limit combination} + + +\begin{frame}\frametitle{Combination of LFV UL and Summary (1)} +\begin{columns} + +\column{1.8in} + \begin{itemize} + + \item Searches for LFV in $\Ptau$ sector is a domain of B factories. + \item Over last years both BaBar and Belle set very strong limits on branching fractions of several rare $\tau$ decays. + + \end{itemize} + + +\column{3.2in} + \includegraphics[width=0.95\textwidth]{TauLFV_UL_2014001.png} + + + +\end{columns} +\begin{itemize} +\item First result from hadron collider comparable with B factories. + \item Since those limits are used to constraint NP models, their "official" combination is of paramount importance. + \item Various methods of limit computation used in Belle and BaBar's studies. + \item The HFAG group recomputed consistently all estimates using the $CL_s$ method and the the same approach was involved in the average evaluation. + \end{itemize} + \end{frame} + + +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%5 + + + + + +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% + + \begin{frame} + \frametitle{Summary (2)} + \begin{columns} + % \column{2.5in} + \begin{column}{1.9in} + \begin{alertblock}{ $\Ptau \to \Pmu \Pmu \Pmu$ limits ($ \color{white} 90\,\%$ CL)} + + \begin{description} + \item[BaBar(FC)] $3.3\times 10^{-8}$ + \item[Belle(FC)] $2.1\times 10^{-8}$ + \item[LHCb(CLs)] $4.6\times 10^{-8}$ + \item[HFAG(CLs)] $1.2 \times 10^{-8}$ + \end{description} + \end{alertblock} +\end{column} + \begin{column}{2.85in} + \includegraphics[width=1\textwidth]{TauLFV_UL_2014001_averaged_zoom.png}\\ + +\end{column} + + \end{columns} + {~}\\ + + + To conclude: + \begin{columns} + \column{3.2in} +\begin{footnotesize} + + + \begin{itemize} +% \item LHCb result for $\Ptau \to \Pmu \Pmu \Pmu$ with full data set. +% \item We are getting close to B-factories. +% \item Thanks to 3 experiments we have a world limit: $\mathcal{B}(\Ptau \to \Pmu \Pmu \Pmu)< 1.2 \times 10^{-8}$ at 90\% CL. +\item LHCb is reaching B-factories limits. +\item Many new techniques developed to perform this analysis. +\item Combination of UL within HFAG gave the best sensitivity for $\mathcal{B}(\Ptau \to \Pmu \Pmu \Pmu)< 1.2 \times 10^{-8}$ at 90\% CL. +\item Erratum to bibliography: + + + \end{itemize} + \end{footnotesize} +\column{2in} + \includegraphics[width=0.93\textwidth]{banana_tau23mu_hfag.pdf}\\ + + +\end{columns} +\begin{footnotesize} + \begin{itemize} +\item $\rm[120]$ HFAG report published:arXiv:1412.7515 (previous cited preliminary web report). +\item $\rm[76]$ accepted for publication in JHEP. +\end{itemize} + \end{footnotesize} + \end{frame} + +\pagenumbering{gobble} + + + + + + %%%%%%%%%%%%%%%%%%%%%%%55 + \begin{frame}\frametitle{Prof. J.Ciborowski comments} +\begin{enumerate} +\item Podrozdział (4.10) ten jest de facto zapowiedzią większej pracy. Szkoda, że materiał tu przedstawiony +potraktowany został bardzo skrótowo, co wymusiło na mnie konieczność kilkakrotnego przeczytania tego podrozdziału i utrudniło docenienie wyniku +otrzymanego przez autora w konfrontacji z przewidywaniami teoretycznymi. +\end{enumerate} +\begin{itemize} +\item The theory part of this was presented in detail in 2.3.4. This chapter is just a showing how to reweight the distributions to a given NP model, that is why I tried to keep it short, but I agree I overdid it. +\end{itemize} + + + \end{frame} + + + + \begin{frame}\frametitle{Prof. J.Ciborowski comments} +\begin{enumerate} +\setcounter{enumi}{1} +\item Jedyne +rzucające się w oczy uchybienie redakcyjne to pomyłki w numerach +rozdziałów, których zawartość wymieniona jest pod koniec Wstępu. + +\end{enumerate} +\begin{itemize} +\item Mea Culpa. Completely missed that. +\end{itemize} + + + \end{frame} + + + \begin{frame}\frametitle{Prof. B.Muryn comments} +\begin{small}\begin{enumerate} + +\item Jest to kwestią subiektywną, ale myślę, że poziom rozprawy wyklucza nieobytego z tymi zagadnieniami czytelnika, a w związku z tym skróciłbym opisywane podstawy poświęcając więcej miejsca na trochę szerszą dyskusję modeli prowadzących do niezachowania liczby leptonowej L. Zgodziłbym się z ewentualną ripostą Autora, że przedstawia modele mające bardziej bezpośredni związek z badaną wartością współczynnika rozgałęzienia dla procesu (będącego w rzeczywistości miarą amplitudy tego procesu), niemniej ogólny niedostatek tych teorii wykazujący silną zależność od nieznanych parametrów modeli a prowadzący do niemożności wyboru żadnego z nich, został trochę pominięty. +\end{enumerate} +\end{small} + +\begin{itemize}\begin{small} +\item I said in Sec. 2.3: ''The violation of charged lepton flavour is predicted in many extensions of the SM (generically named as BSM theories). The inclusion of the CLFV is usually straightforward and follows directly from the models assumptions''. \\ +I however agree that I should said explicitly that there is no way which is correct and that is why we use a ''Model independent'' EFT approach. +\end{small} +\end{itemize} + + + \end{frame} + + + + \begin{frame}\frametitle{Prof. B.Muryn comments} +\begin{small}\begin{enumerate} +\setcounter{enumi}{1} +\item Prezentowane tabele i rysunki dowodzą dbałości o szczegóły i wskazują na samodzielność analizy +przeprowadzonej przez mgr Marcina Chrząszcza. Z drugiej strony uważam, że +jest ich za wiele i cytowanie niektórych tabel mija się z celem (np. tabele 4.13- +4.14, 4.16-4.18 lub 4.34-4.35 oraz 4 strony podobnych w wymowie rozkładów +mas mionów). Zapełniają one miejsca, na których chętnie bym widział szerszy +komentarz dotyczący Blending Technique oraz, co ważne, dyskusji niepewności +systematycznych. +\end{enumerate} +\end{small} + +\begin{itemize}\begin{small} +\item I probably could make Table 4.14-18 shorter and only list most important trigger lines making them substantially shorter. The same goes for Tables 4.34-4.35. I agree that I have been to meticulous in those places. +\end{small} +\end{itemize} + + + \end{frame} + + + + + \begin{frame}\frametitle{Prof. B.Muryn comments continuation} +\begin{itemize}\begin{small} +\item With the limit settings it's not as straightforward to rank the systematics as it is with a measurements. +\item We can group systematics in three categories: +\begin{itemize} +\item Normalization systematics. +\item Signal distribution among $\mathcal{M}_{3body}, \mathcal{M}_{PID}, m_{\mu\mu\mu}$. +\item Background systematics. +\end{itemize} +\item Each of them influences the computation of limit in different way. +\item The main systematic is the normalization, in which the dominant uncertainty comes from $\mathcal{B}(\PDs \to \Pphi(\mu\mu) \Ppi~(7.5\%)$. +\end{small} +\end{itemize} + + + \end{frame} + + \begin{frame}\frametitle{Prof. B.Muryn comments} +\begin{enumerate} +\setcounter{enumi}{2} +\item ''... nie szkodziłoby, gdyby Autor +niniejszej rozprawy w krótkim podsumowaniu wyszczególnił te etapy analizy, w +których grał główną rolę.'' +\end{enumerate} + +\begin{itemize}\begin{small} +\item Apologies about that. I have focued on those things in the talk. +\end{small} +\end{itemize} + + + \end{frame} + + + + + + +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%5 + \begin{frame}\frametitle{Backup} + + \includegraphics[width=0.93\textwidth]{ngbbs4f7918ec8ffb8.jpg}\\ + + + \end{frame} + %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%5555 + \begin{frame} + \frametitle{Triggers at LHCb} +\begin{footnotesize} + +\begin{itemize} +\item LHCb uses complex trigger, $\mathcal{O}(100)$ trigger lines. %\footnote{\href{http://arxiv.org/abs/1211.3055}{\color{blue}arXiv:1211.3055}}, $\mathcal{O}(100)$ trigger lines. +\item Lines change with data taking. +\item Optimized choice of triggers based on $\dfrac{s}{\sqrt{b}}$ FOM, +\end{itemize} +\end{footnotesize} +\begin{tiny} +\begin{columns} +\column{0.66\textwidth} +\begin{equation} +\label{eq:efftrig} +\varepsilon(\beta)^\prime_{\text{evt},\text{line}} = \frac{N(\tau~\text{ MC(BKG) events triggered +line, but not by any better line})}{N(\tau\text{ MC(BKG) events triggered by any line})}, \nonumber +\end{equation} +\begin{small} +\begin{itemize} +\item Evaluated different triggers used in 2012 data taking. +\item Found negligible differences in trigger efficiencies. +\end{itemize} +\end{small} +\column{0.32\textwidth} +\begin{equation} +\text{CTFM}=\frac{\sqrt{\sum\limits_\text{trigger lines} \beta^\prime_{\text{evt},\text{line}}}}{\sum\limits_\text{trigger lines} \varepsilon^\prime_{\text{evt},\text{line}}}\nonumber +\end{equation} + +\end{columns} +\end{tiny} +\begin{footnotesize} + + +\end{footnotesize} +\begin{tiny} + \begin{tabular}{|l|c|c|c|} + \hline + name & $\varepsilon^\prime$ & $\beta^\prime$ & CTFM \\\hline + % here +Hlt2TriMuonTauDecision & 0.880708 & 0.736182 & 0.974228\\ +Hlt2DiMuonDetachedDecision & 0.0669841 & 0.173396 & 1.00636\\ +Hlt2CharmSemilep3bodyD2KMuMuDecision & 0.0206816 & 0.0182935 & 0.99472\\ +Hlt2CharmHadD2HHHDecision & 0.00554351 & 0.00666405 & 0.992604\\ +Hlt2CharmSemilep3bodyD2KMuMuSSDecision & 0.00195444 & 0.00470404 & 0.993106\\ +Hlt2CharmSemilep3bodyD2PiMuMuDecision & 0.00206105 & 0.00679472 & 0.994591\\ +Hlt2TopoMu3BodyBBDTDecision & 0.00394442 & 0.0121521 & 0.996937\\ + \hline + \end{tabular} +\end{tiny} + + + + \end{frame} + \begin{frame} + \frametitle{Geometric likelihood} + + \begin{itemize} + \item As mentioned in LHC we have different production sources of $\Ptau$'s. + \item Each source has different detector response signature. + \item To maximise our performance we trained classifiers for each of the $\Ptau$ sources using: + \begin{itemize} + \item Kinematic properties of $\Ptau$ candidate. + \item Geometric properties of $\Ptau$ candidate, like pointing angle, DOCA, Vertex $\chi^2$, flight distance. + \item Isolations, for vertex and individual tracks. + \end{itemize} + \item After training the individual classifiers one that combines all this information in a single classifier on mixed sample of $\Ptau$'s. + \item This technique is known as Blending or Ensemble learning. + \item Using this approach we gain $6\%$ sensitivity! + \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} + + +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%5 +% PID + + \begin{frame} + \frametitle{Particle Identification (PID)} +\begin{itemize} +\item Classifier trained on inclusive MC sample. +\item Using information from: RICH, Calorimeters, Muon system and tracking. +\item Correct for the MC efficiency using control channel: $\PDs \to \Pphi(\Pmu\Pmu) \Ppi$ and $\PB \to \PJpsi(\Pmu\Pmu) \PK$ +\end{itemize} + \begin{columns} + \begin{column}{.45\textwidth} + \includegraphics[width=.95\textwidth]{mPID_2012.pdf} + \end{column} + \end{columns} + \end{frame} +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%5 + + + \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} + +\begin{frame}\frametitle{Combination of LFV UL 2/2} +\begin{itemize} +\item For each measurement take integrated luminosity ($\mathcal{L}$), cross section ($\sigma_{\tau\tau}$), efficiencies ($\epsilon$), background expected($b$) and all systematics. +\item Calculate number of signal: $s = \mathcal{L} \sigma_{\tau\tau} \epsilon^{tot} \mathcal{B}(\Ptau \to LFV)$. +\item Scan the $CL_s$ wrt. $\mathcal{B}(\Ptau \to LFV)$: +\end{itemize} +\begin{columns} +\column{0.15in} +{~} +\column{2in} +\begin{small} +\begin{align} +CL_s = \dfrac{\prod_{i=1}^{N_{\text{chan}}}\sum_{n=0}^{n_i} \dfrac{e^{-(s_i+b_i)} (s_i+b_i)^{n}}{n!} }{\prod_{i=1}^{n_{\text{chan}}} \sum_{n=0}^{n_i} \dfrac{e^{-b_i} b_i^{n}}{n!}} \nonumber~, +\end{align} +\end{small} +\column{2.7in} + \includegraphics[width=0.95\textwidth]{TauLFV_UL_2014001_averaged.png} + + +\end{columns} +\end{frame} + + + + + + \begin{frame}\frametitle{Variables 1/2} + + \begin{footnotesize} + + + + + The multi-variate classifiers were trained using the following variables: +\begin{itemize} +\item \textbf{DOCA:} the minimum of distances of the closest approach of two muons in each of three possible two muon pairings, +\item \textbf{$\Ptau(\PDs)$ Vertex $\chi^2$:} the quality of the vertex parametrized as the chi square of the $\Ptau$ secondary vertex fit (as defined in, +\item $\mathbf{c\tau}$\textbf{:} The measured decay length of the $\Ptau$ lepton, assuming its production at the primary vertex. To smooth out the distribution, the + decay time is transformed according to the formula $T=\exp{(-1000 \cdot \tau )}$, +\item \textbf{IP $\chi^2$ ($\Ptau$):} $\Ptau$ lepton impact parameter $\chi^2$/ndf, +\item \textbf{Min.\ IP $\chi^2$ ($\Pmu$):} the minimum value of + the three $\Pmu$ impact parameter ($\chi^2$/ndf)s, + \item \textbf{Track $\chi^2$/ndf:} maximum of track's ($\chi^2$)s of the three muons, + + +\end{itemize} + \end{footnotesize} + \end{frame} + + + + \begin{frame}\frametitle{Variables 2/2} + + \begin{footnotesize} + + + + + The multi-variate classifiers were trained using the following variables: +\begin{itemize} + +\item \textbf{Pointing angle $\alpha$:} the angle between the direction of $\Ptau$ momentum and a straight line from the $\Ptau$ decay vertex to the primary vertex, +\item $\mathbf{p_T}$: the $\Ptau$ transverse momentum, +\item \textbf{Track isolation:} the sum of three track isolations variables, each parametrising how far in space is an individual muon candidate w.r.t. the rest of event. + +\item \textbf{BDT (Boosted Decision Tree) isolation:} the response of multivariate analysis~(MVA) working at the charged track level and aimed at discriminating between isolated and non-isolated tracks. +\item \textbf{Cone isolation:} the fraction of the $\Ptau$ candidate transverse + momentum among the sum of all transverse momenta within a certain cone around the + $\Ptau$ candidate. + +\end{itemize} + \end{footnotesize} + \end{frame} + + + + \begin{frame}\frametitle{Isolations 1/2} +\begin{footnotesize} +The track isolation (TI) variable is constructed on the basis of the respective studies performed by the LHCb collaboration for the needs of $B_s^0\to \mu^+ \mu^-$ analysis. The TI is defined as the number of extra tracks (i.e. excluding tracks that are attributed to the $\Ptau \to \mu\mu\mu$ candidate) that can form a vertex with a muon track. +The assignment to the above SV is based on the selection criteria imposed on the following variables: +\begin{itemize} + \item minimum distance between the {\bf\color{red}track} and the PV ({\color{darkpastelgreen}\bf pvdist}), + \item minimum distance between the {\bf\color{red}track} and the $\Ptau \to \mu\mu\mu$ vertex ({\color{darkpastelgreen}\bf svdist}), + \item the distance of the closest approach between the {\bf\color{blue}muon} and the {\bf\color{red}track} (DOCA), + \item IP $\chi^2$,% ($ips$). + \item angle between the {\bf\color{blue}muon} and the {\bf\color{red}track} ({\color{darkpastelgreen}$\mathbf\beta$}), + \item the quantity + \begin{equation} + f_c=\dfrac{\vert \overrightarrow{p}_{\color{blue}h}+ \overrightarrow{p}_{\color{red}trk} \vert {\color{darkpastelgreen}\alpha^{h + trk, PV}} } + { \vert \overrightarrow{p}_{\color{blue}h}+ \overrightarrow{p}_{\color{red}trk} \vert {\color{green} \alpha^{h + trk, PV}} + p_{{\rm T},{\color{blue}h}} + p_{{\rm T},{\color{red}trk}} }, + \end{equation} + where {\color{darkpastelgreen}$\alpha^{h + trk, PV}$} is the angle between the {\bf\color{blue}muon} and the {\bf\color{red}track} candidate, $P_{{\rm T},{\color{blue}h}}$ and $P_{{\rm T},{\color{red}trk}}$ are the transverse momentum with respect to the beam line. +\end{itemize} +\end{footnotesize} + + + + \end{frame} + + + + + + \begin{frame}\frametitle{Isolations 2/2} +\begin{footnotesize} +The track is considered as "isolated" if it satisfies the following requirements (imposed on the above mentioned variables): +\begin{itemize} + \item pvdist $\in [0.5, 40]~\mm$, + \item svdist $\in [-0.15,30]~\mm$, + \item DOCA $< 0.13~\mm$, + \item Track IP significance $>3$, + \item $\beta<0.27~\rad$, + \item $f_c<0.6$. +\end{itemize} +% +% + + \centering{ + \includegraphics[width=0.6\textwidth]{LPHNE_iso2.png} + } + + + + +\end{footnotesize} + + + + \end{frame} + + + + + +\end{document} diff --git a/Seminars/IFJ/tau23mu_08_02_15/defence2.toc b/Seminars/IFJ/tau23mu_08_02_15/defence2.toc new file mode 100644 index 0000000..7ae3a9c --- /dev/null +++ b/Seminars/IFJ/tau23mu_08_02_15/defence2.toc @@ -0,0 +1,11 @@ +\beamer@endinputifotherversion {3.10pt} +\select@language {english} +\beamer@sectionintoc {1}{Lepton Flavour Violation phenomenon}{3}{0}{1} +\beamer@sectionintoc {2}{LHCb detector}{5}{0}{2} +\beamer@sectionintoc {3}{Selection}{6}{0}{3} +\beamer@sectionintoc {4}{Multivariate technique}{8}{0}{4} +\beamer@sectionintoc {5}{Normalisation}{13}{0}{5} +\beamer@sectionintoc {6}{Backgrounds}{14}{0}{6} +\beamer@sectionintoc {7}{Model dependence}{17}{0}{7} +\beamer@sectionintoc {8}{Results}{19}{0}{8} +\beamer@sectionintoc {9}{LFV limit combination}{20}{0}{9} diff --git a/Seminars/IFJ/tau23mu_08_02_15/det.jpg 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\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{$\color{white} \tau$ {\scriptsize production\begin{footnotesize} + {\small •} + \end{footnotesize}}} + \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/Seminars/IFJ/tau23mu_08_02_15/mchrzasz2.toc b/Seminars/IFJ/tau23mu_08_02_15/mchrzasz2.toc new file mode 100644 index 0000000..d909493 --- /dev/null +++ b/Seminars/IFJ/tau23mu_08_02_15/mchrzasz2.toc @@ -0,0 +1,10 @@ +\beamer@endinputifotherversion {3.10pt} +\select@language {english} +\beamer@sectionintoc {1}{Introduction}{4}{0}{1} 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0000000..e4bc5ff --- /dev/null +++ b/Seminars/IFJ/tau23mu_08_02_15/seminar.tex @@ -0,0 +1,1103 @@ +\documentclass[xcolor=svgnames]{beamer} +\usepackage[utf8]{inputenc} + +\usepackage[english]{babel} +\usepackage{polski} +%\usepackage{english} + + +%\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} +\usepackage{xcolor} + + +\setbeamertemplate{footline}{\insertframenumber/\inserttotalframenumber} +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%5 +\definecolor{mygreen}{cmyk}{0.82,0.11,1,0.25} +\definecolor{darkpastelgreen}{rgb}{0.01, 0.75, 0.24} + + +\usetheme{Sybila} +\title[Search for Charged Lepton Flavour Violation at LHCb experiment]{Search for Charged Lepton Flavour Violation at LHCb experiment} + \author[Marcin Chrz\k{a}szcz]{Marcin Chrz\k{a}szcz } + + \institute[UZH, IFJ]{ +Henryk Niewodniczanski Institute of Nuclear Physics Polish Academy of Sciences, Cracow, Poland} + + +\date{\today} +\begin{document} + + +% --------------------------- SLIDE -------------------------------------------- +\frame[plain]{\titlepage} +\author{Marcin Chrz\k{a}szcz} +% ------------------------------------------------------------------------------ +% --------------------------- SLIDE -------------------------------------------- + +\institute{~(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} + + +\iffalse + + \begin{frame} + \frametitle{Errata to thesis} + \begin{itemize} + \item Since submision, the HFAG report has been published, so refence: + \end{itemize} + [53] HFAG Collaboration, M.Chrz\k{a}szcz et. al. Averages of $b$-hadron, $c$-hadron, and $\tau$-lepton properties as of summer 2014, arXiv:1412.7515. + \end{frame} + + +\fi + +\section{Lepton Flavour Violation phenomenon} +\begin{frame}\frametitle{Lepton Flavour/Number Violation} + + +\begin{enumerate} +\item Lepton Flavour Violation (LFV) found in neutrino sector - the first phenomena outside the Standard Model. +\item The search for charged lepton flavour violation (CLFV) commenced with muon discovery (1936) and its identification as a separate particle. +\end{enumerate} +\begin{columns} +\column{3in} +\begin{itemize} +\item Expected: $B(\mu\to\Pe\gamma) \approx 10^{-4}$ +\item Unless there is another $\Pnu$. +\end{itemize} + +\column{2in} +{~}\includegraphics[width=0.98\textwidth]{rabi.png} + +\end{columns} +\begin{footnotesize} + +\begin{enumerate} +\setcounter{enumi}{2} +\item The observation of CLFV would be a clear signature of New Physics (NP) - paramount importance for flavour physics and the enigma of generations. +\item LFV vs LNV (Lepton Number Violation) +\end{enumerate}\end{footnotesize} +\begin{columns} +\column{3.5in} +\begin{footnotesize} + + +\begin{itemize} +\item Even with LFV, lepton number can be a conserved quantity. +\item Many NP models predict LNV (Majorana neutrinos) +\item LNV searched in so-called neutrinoless double $\beta$ decays. +\end{itemize} +\end{footnotesize} +\column{1.5in} +\includegraphics[width=0.65\textwidth]{Double_beta_decay_feynman.png} + +\end{columns} + + + % \textref{M.Chrz\k{a}szcz 2014} + +\end{frame} +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% + \begin{frame} + \frametitle{Status of searches for $\color{white} \tau \to \mu \mu \mu$} + \begin{columns} + \begin{column}{.55\textwidth} + + \includegraphics[width=.90\textwidth]{feymn.png} + + {{ + \begin{small} + \begin{itemize} + \item Charged Lepton Flavour Violation process. + \item The Standard Model contribution: penguin diagram with neutrino oscillation. + \item Negligible SM branching fraction. + \item Large enhacement from NP models like: SUSY, Little Higgs, Fourth generation, etc. + + % \item SM prediction is beyond experimental reach~$O(10^{-40})$. + + \end{itemize} + \end{small} + }} + \end{column} + \begin{column}{.45\textwidth} + + \begin{alertblock}{Predictions} + \begin{description} + \item[SM] $ O(10^{-40})$ + \item[var.\ SUSY] $10^{-10}$ + \item[non universal $\color{red}{Z'}$] $10^{-8}$ + \item[mSUGRA+seesaw] $10^{-9}$ + \item[and many more...] + \end{description} + \end{alertblock} + + \begin{alertblock}{Current limits ($ \color{white} 90\,\%$ CL)} + + \begin{description} + \item[BaBar] $3.3\times 10^{-8}$ + \item[Belle] $2.1\times 10^{-8}$ + \end{description} + \end{alertblock} + \includegraphics[width=.63\textwidth]{SUSY.png} + + \end{column} + + \end{columns} + + + \end{frame} +%%%%%%%%%%%%%%%%% + + +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% + \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 Superb particle identification (PID). + \end{itemize} + + + +\end{footnotesize} +\end{columns} + +\end{frame} +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% + \section{Selection} + \begin{frame} \frametitle{Strategy} +\begin{enumerate} +\item Data sample: $1 \invfb~7~\TeV$ and $2 \invfb~8\TeV$. +\item Normalization (control) decay channel: $\PDs\to\Pphi(\Pmu\Pmu)\Ppi$. +\item Blind analysis in the region of $| m_{\mu\mu\mu} - m_{\tau} | <20~\MeV/c^2$. +\item Event selection: +\begin{itemize} +\item Preselection of three tracks that combine to give a mass close to $m_{\tau}$, with displaced vertex. +\item Selection based on three classifiers: +\begin{itemize} +\item Geometry and topology ($\mathcal{M}_{3body}$) - multivariate classifier +\item PID ($\mathcal{M}_{PID}$) - multivariate classifier +\item Three muon invariant mass ($m_{\mu\mu\mu}$) +\end{itemize} +\end{itemize} +\item Major background contributions:$\PDs \to \eta(\mu\mu\gamma) \mu \nu$ and $\PD \to \PK \Ppi \Ppi$ decays. +\item Evaluation of the upper limit on $\mathcal{B}(\Ptau \to \Pmu \Pmu \Pmu)$ using $CL_s$ method. +\end{enumerate} + + + \end{frame} + \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{$\color{white} \tau$ production at LHCb} + \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{Triggers at LHCb} +\begin{footnotesize} + +\begin{itemize} +\item LHCb uses complex trigger, $\mathcal{O}(100)$ trigger lines. %\footnote{\href{http://arxiv.org/abs/1211.3055}{\color{blue}arXiv:1211.3055}}, $\mathcal{O}(100)$ trigger lines. +\item Lines change with data taking. +\item Optimized choice of triggers based on $\dfrac{s}{\sqrt{b}}$ FOM, +\end{itemize} +\end{footnotesize} +\begin{tiny} +\begin{columns} +\column{0.66\textwidth} +\begin{equation} +\label{eq:efftrig} +\varepsilon(\beta)^\prime_{\text{evt},\text{line}} = \frac{N(\tau~\text{ MC(BKG) events triggered +line, but not by any better line})}{N(\tau\text{ MC(BKG) events triggered by any line})}, \nonumber +\end{equation} +\begin{small} +\begin{itemize} +\item Evaluated different triggers used in 2012 data taking. +\item Found negligible differences in trigger efficiencies. +\end{itemize} +\end{small} +\column{0.32\textwidth} +\begin{equation} +\text{CTFM}=\frac{\sqrt{\sum\limits_\text{trigger lines} \beta^\prime_{\text{evt},\text{line}}}}{\sum\limits_\text{trigger lines} \varepsilon^\prime_{\text{evt},\text{line}}}\nonumber +\end{equation} + +\end{columns} +\end{tiny} +\begin{footnotesize} + + +\end{footnotesize} +\begin{tiny} + \begin{tabular}{|l|c|c|c|} + \hline + name & $\varepsilon^\prime$ & $\beta^\prime$ & CTFM \\\hline + % here +Hlt2TriMuonTauDecision & 0.880708 & 0.736182 & 0.974228\\ +Hlt2DiMuonDetachedDecision & 0.0669841 & 0.173396 & 1.00636\\ +Hlt2CharmSemilep3bodyD2KMuMuDecision & 0.0206816 & 0.0182935 & 0.99472\\ +Hlt2CharmHadD2HHHDecision & 0.00554351 & 0.00666405 & 0.992604\\ +Hlt2CharmSemilep3bodyD2KMuMuSSDecision & 0.00195444 & 0.00470404 & 0.993106\\ +Hlt2CharmSemilep3bodyD2PiMuMuDecision & 0.00206105 & 0.00679472 & 0.994591\\ +Hlt2TopoMu3BodyBBDTDecision & 0.00394442 & 0.0121521 & 0.996937\\ + \hline + \end{tabular} +\end{tiny} + + + + \end{frame} + + + + \section{Multivariate technique} + + \begin{frame} + \frametitle{Signal and background discrimination} + \begin{itemize} + \item Two multivariate classifiers, $\mathcal{M}_{3body}$ and $\mathcal{M_{PID}}$. + \end{itemize} + \begin{columns} + \column{3in} + \begin{itemize} + \item $\mathcal{M}_{3body}$ trained using vertex and track fit quality, vertex displacement, vertex pointing, vertex isolation and $\Ptau$ $p_T$. + \item Used Blending Technique (see the next slide). + \end{itemize} + +\column{2in} + \includegraphics[width=.98\textwidth]{ver.png} +\end{columns} +\begin{columns} +\column{0.1in} +{~} +\column{2in} + % \includegraphics[width=.95\textwidth]{m3body_2012.pdf} +\includegraphics[width=.98\textwidth]{./mixing.pdf} +\column{3in} +\begin{itemize} +\item Trained on signal and background MC. +\item Calibrated on $\PDs \to \Pphi(\mu\mu) \Ppi$ sample. +\end{itemize} +\end{columns} + \end{frame} + + \begin{frame}\frametitle{Variables 1/2} + + \begin{footnotesize} + + + + + The multi-variate classifiers were trained using the following variables: +\begin{itemize} +\item \textbf{DOCA:} the minimum of distances of the closest approach of two muons in each of three possible two muon pairings, +\item \textbf{$\Ptau(\PDs)$ Vertex $\chi^2$:} the quality of the vertex parametrized as the chi square of the $\Ptau$ secondary vertex fit (as defined in, +\item $\mathbf{c\tau}$\textbf{:} The measured decay length of the $\Ptau$ lepton, assuming its production at the primary vertex. To smooth out the distribution, the + decay time is transformed according to the formula $T=\exp{(-1000 \cdot \tau )}$, +\item \textbf{IP $\chi^2$ ($\Ptau$):} $\Ptau$ lepton impact parameter $\chi^2$/ndf, +\item \textbf{Min.\ IP $\chi^2$ ($\Pmu$):} the minimum value of + the three $\Pmu$ impact parameter ($\chi^2$/ndf)s, + \item \textbf{Track $\chi^2$/ndf:} maximum of track's ($\chi^2$)s of the three muons, + + +\end{itemize} + \end{footnotesize} + \end{frame} + + + + \begin{frame}\frametitle{Variables 2/2} + + \begin{footnotesize} + + + + + The multi-variate classifiers were trained using the following variables: +\begin{itemize} + +\item \textbf{Pointing angle $\alpha$:} the angle between the direction of $\Ptau$ momentum and a straight line from the $\Ptau$ decay vertex to the primary vertex, +\item $\mathbf{p_T}$: the $\Ptau$ transverse momentum, +\item \textbf{Track isolation:} the sum of three track isolations variables, each parametrising how far in space is an individual muon candidate w.r.t. the rest of event. + +\item \textbf{BDT (Boosted Decision Tree) isolation:} the response of multivariate analysis~(MVA) working at the charged track level and aimed at discriminating between isolated and non-isolated tracks. +\item \textbf{Cone isolation:} the fraction of the $\Ptau$ candidate transverse + momentum among the sum of all transverse momenta within a certain cone around the + $\Ptau$ candidate. + +\end{itemize} + \end{footnotesize} + \end{frame} + + + + \begin{frame}\frametitle{Isolations 1/2} +\begin{footnotesize} +The track isolation (TI) variable is constructed on the basis of the respective studies performed by the LHCb collaboration for the needs of $B_s^0\to \mu^+ \mu^-$ analysis. The TI is defined as the number of extra tracks (i.e. excluding tracks that are attributed to the $\Ptau \to \mu\mu\mu$ candidate) that can form a vertex with a muon track. +The assignment to the above SV is based on the selection criteria imposed on the following variables: +\begin{itemize} + \item minimum distance between the {\bf\color{red}track} and the PV ({\color{darkpastelgreen}\bf pvdist}), + \item minimum distance between the {\bf\color{red}track} and the $\Ptau \to \mu\mu\mu$ vertex ({\color{darkpastelgreen}\bf svdist}), + \item the distance of the closest approach between the {\bf\color{blue}muon} and the {\bf\color{red}track} (DOCA), + \item IP $\chi^2$,% ($ips$). + \item angle between the {\bf\color{blue}muon} and the {\bf\color{red}track} ({\color{darkpastelgreen}$\mathbf\beta$}), + \item the quantity + \begin{equation} + f_c=\dfrac{\vert \overrightarrow{p}_{\color{blue}h}+ \overrightarrow{p}_{\color{red}trk} \vert {\color{darkpastelgreen}\alpha^{h + trk, PV}} } + { \vert \overrightarrow{p}_{\color{blue}h}+ \overrightarrow{p}_{\color{red}trk} \vert {\color{green} \alpha^{h + trk, PV}} + p_{{\rm T},{\color{blue}h}} + p_{{\rm T},{\color{red}trk}} }, + \end{equation} + where {\color{darkpastelgreen}$\alpha^{h + trk, PV}$} is the angle between the {\bf\color{blue}muon} and the {\bf\color{red}track} candidate, $P_{{\rm T},{\color{blue}h}}$ and $P_{{\rm T},{\color{red}trk}}$ are the transverse momentum with respect to the beam line. +\end{itemize} +\end{footnotesize} + + + + \end{frame} + + + + + + \begin{frame}\frametitle{Isolations 2/2} +\begin{footnotesize} +The track is considered as "isolated" if it satisfies the following requirements (imposed on the above mentioned variables): +\begin{itemize} + \item pvdist $\in [0.5, 40]~\mm$, + \item svdist $\in [-0.15,30]~\mm$, + \item DOCA $< 0.13~\mm$, + \item Track IP significance $>3$, + \item $\beta<0.27~\rad$, + \item $f_c<0.6$. +\end{itemize} +% +% + + \centering{ + \includegraphics[width=0.6\textwidth]{LPHNE_iso2.png} + } + + + + +\end{footnotesize} + + + + \end{frame} + + + + +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% + \begin{frame} + \frametitle{Blending technique} + \begin{columns} + \column{3.2in} + + + + \includegraphics[width=.99\textwidth]{diagram.png} + \column{1.8in} + \begin{itemize} +\item Each of the $\Ptau$ lepton production channel have a different signature in terms of kinematic distributions. +\item Signal blending technique improved the discriminating power by $6~\%$ +\end{itemize} + \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 $\PDs \Longrightarrow \Ptau$ from MC. + \item Apply corrections to $\PDs\to\Pphi\Ppi$ on data. + \item Publication in preparation. + \end{itemize} + + \begin{columns} + + \begin{column}{.45\textwidth} + \includegraphics[width=.95\textwidth]{m3body_2012.pdf} + + \end{column} + \begin{column}{.45\textwidth} + \begin{itemize} + \item $\PDs\to\Pphi\Ppi$ decay well modelled in MC.\\ + \includegraphics[width=.9\textwidth]{./dataMC.pdf} + % \item[$\rightarrow$] i.e.\ also badly pointing non-prompt $\PDs$ + \end{itemize} + \end{column} + + \end{columns} + \end{frame} + + +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% + \begin{frame} + + \frametitle{Signal and background discrimination - $\color{white}{\mathcal{M}_{PID}}$} + \begin{columns} + \column{3in} + \begin{itemize} + \item $\mathcal{M}_{PID}$ trained using \color{red}{RICH}, \color{blue}{ECAL} and \color{green}{muon chambers}. + \end{itemize} + +\column{2in} + \includegraphics[width=.98\textwidth]{detcol.png} +\end{columns} +\begin{columns} +\column{0.1in} +{~} +\column{2in} + \includegraphics[width=.95\textwidth]{mPID_2012.pdf} +\column{3in} +\begin{itemize} +\item Trained on signal and background MC. +\item Calibrated on $\PB \to \PJpsi \PK$ and $\PDs \to \Pphi(\mu\mu) \Ppi$ decays. +\end{itemize} +\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} + + + +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% + \begin{frame} + \frametitle{Binning optimisation} + + + \begin{footnotesize} + \begin{itemize} + \item Events are distributed among $\mathcal{M}_{3body}, \mathcal{M}_{PID}$ plane. + \item In 2D we collect the events in groups(bins) + \item Bins are optimised using $CL_s$ method: + \begin{equation} + CL_s = \dfrac{\prod_{i=1}^{N_{\text{chan}}}\sum_{n=0}^{n_i} \dfrac{e^{-(s_i+b_i)} (s_i+b_i)^{n}}{n!} }{\prod_{i=1}^{n_{\text{chan}}} \sum_{n=0}^{n_i} \dfrac{e^{-b_i} b_i^{n}}{n!}} \nonumber~, + \end{equation} + \item The lowest bins are rejected, because they do not contribute to the limit sensitivity. + \end{itemize} + \end{footnotesize} +\begin{columns} +\column{2.2in} +\center{2011}\\ + \includegraphics[width=.87\textwidth]{2D_2011.pdf}\\{~} +\\{~} +\\{~}\\{~}\\{~}\\{~} + +\column{2.2in} +\center{2012}\\ + \includegraphics[width=.87\textwidth]{2D_2012.pdf}\\{~} +\\{~} +\\{~}\\{~}\\{~}\\{~} + +\column{0.5in} +{~} + +\end{columns} + + \end{frame} + \begin{frame} + \frametitle{Impact of 2D 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} + + + +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% + + + + \section{Normalisation} + + \begin{frame} + \frametitle{Relative normalisation} + $\boxed{\mathcal{B}(\Ptau\to\Pmu\Pmu\Pmu) = \frac{\mathcal{B}(\PDs\to\Pphi\Ppi)}{\mathcal{B}(\PDs\to\Ptau\Pnut)} \times f_{\PDs}^{\Ptau} \times \frac{\varepsilon_\text{norm} }{\varepsilon_\text{sig} } \times \frac{N_\text{sig}}{N_\text{norm}} = \alpha\times N_\text{sig}}$ + \begin{itemize} + \item where $\varepsilon$ stands for trigger, reconstruction, selection efficiency. + \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 data. + \end{itemize} +\begin{columns} +\column{2.3in} + \center{2011}\\ + + \includegraphics[width=.97\textwidth]{./Ds_data_2011.pdf} + \column{2.3in} + \center{2012}\\ + \includegraphics[width=.97\textwidth]{./Ds_data_2012.pdf} + \end{columns} + \end{frame} + + + + + \section{Backgrounds} + + \begin{frame} + \frametitle{Misidentification (Peaking background) 1/2} + \begin{columns} + \column{3in} + \begin{itemize} + \item Dominant: $\PDplus\to\PK\Ppi\Ppi$. + \item Also seen $\PDplus\to\Ppi\Ppi\Ppi$ and $\PDs\to\Ppi\Ppi\Ppi$. + \item All contained in the lowest $\mathcal{M}_{PID}$ bin. + % \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]{./trash.pdf}{~}{~}{~}{~}{~}{~}{~}{~}{~}{~}{~}{~}{~}{~} + \includegraphics[width=.45\textwidth]{./mPID_2012.pdf} + \end{frame} + +\begin{frame} + \frametitle{Misidentification (Peaking background) 2/2} +\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{Other 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 Model it + \item \underline{Remove it} with dimuon mass cut: + \begin{itemize} + + + \item Fits better understood. + \item Sensitivity unchanged when removing veto. + \item Smaller uncertainty on expected background. + \end{itemize} + \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 the $\pm \unit{30}{\MeV}$ region. + % \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{Model dependence} + + \begin{frame} + \frametitle{Model dependence} + \begin{itemize} + \begin{small} + \item $\Peta$ veto $\Rightarrow$ our limit not constraining to New Physics with small $m_{\APmuon\Pmuon}$. + \item Model description in \href{http://arxiv.org/abs/0707.0988}{\color{blue}\texttt{arXiv:0707.0988}} by S.Turczyk using Effective Field Theory approach. + \item 5 relevant Dalitz distributions: 2 four-point operators, 1 radiative operator, 2 interference terms. + \end{small} + \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 remain stable (within $7\,\%$). + \end{itemize} + \begin{center} + \includegraphics[width=.5\textwidth]{./sigDalitz.pdf} + \end{center} + + + } + \only<1>{ +\begin{columns} + \column{0.33\textwidth} + \includegraphics[width=.78\textwidth]{./LLLL.pdf}\\ + \includegraphics[width=.78\textwidth]{./LLRR.pdf}\\ + + + \column{0.33\textwidth} + \includegraphics[width=.78\textwidth]{./LLLLRAD.pdf}\\ + \includegraphics[width=.78\textwidth]{./LLRRRAD.pdf} + + \column{0.33\textwidth} + \includegraphics[width=.78\textwidth]{./RAD.pdf}\\ +\begin{small} + \begin{itemize} + \item All five cases implemented in TAUOLA. + \item Publication in preparation. + \end{itemize} +\end{small} + + +% \begin{itemize} +% \item Same models as in Z.Was \href{https://indico.cern.ch/event/300387/session/7/contribution/33}{\color{blue}talk} +% \end{itemize} +%{~}\\ {~}\\ + + \end{columns} +} + + \end{frame} + + \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{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{Results} + + \begin{frame} + \frametitle{Results} + + \begin{center} + \includegraphics[width=0.7\textwidth]{banana_line.pdf} + \end{center} +\begin{columns} + +\column{0.2in}{~} +\column{2in} +Limits(PHSP):\\ +Observed(Expected)\\ +$\color{red}4.6~(5.0)\times 10^{-8}$ at $90\%$ CL\\ +$\color{pink}5.6~(6.1)\times 10^{-8}$ at $95\%$ CL\\ + + \column{3in} + \includegraphics[width=0.5\textwidth]{model.png} +\end{columns} + \end{frame} + + + +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%5 +\section{LFV limit combination} + + +\begin{frame}\frametitle{Combination of LFV UL 1/2} +\begin{columns} + +\column{1.8in} + \begin{itemize} + + \item Searches for LFV in $\Ptau$ sector is a domain of B factories. + \item Over last years both BaBar and Belle set very strong limits on branching fractions of several rare $\tau$ decays. + + \end{itemize} + + +\column{3.2in} + \includegraphics[width=0.95\textwidth]{TauLFV_UL_2014001.png} + + + +\end{columns} +\begin{itemize} +\item First result from hadron collider comparable with B factories. + \item Since those limits are used to constraint NP models, their "official" combination is of paramount importance. + \item Various methods of limit computation used in Belle and BaBar's studies. + \item The HFAG group recomputed consistently all estimates using the $CL_s$ method and the the same approach was involved in the average evaluation. + \end{itemize} + \end{frame} + + +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%5 + + +\begin{frame}\frametitle{Combination of LFV UL 2/2} +\begin{itemize} +\item For each measurement take integrated luminosity ($\mathcal{L}$), cross section ($\sigma_{\tau\tau}$), efficiencies ($\epsilon$), background expected($b$) and all systematics. +\item Calculate number of signal: $s = \mathcal{L} \sigma_{\tau\tau} \epsilon^{tot} \mathcal{B}(\Ptau \to LFV)$. +\item Scan the $CL_s$ wrt. $\mathcal{B}(\Ptau \to LFV)$: +\end{itemize} +\begin{columns} +\column{0.15in} +{~} +\column{2in} +\begin{small} +\begin{align} +CL_s = \dfrac{\prod_{i=1}^{N_{\text{chan}}}\sum_{n=0}^{n_i} \dfrac{e^{-(s_i+b_i)} (s_i+b_i)^{n}}{n!} }{\prod_{i=1}^{n_{\text{chan}}} \sum_{n=0}^{n_i} \dfrac{e^{-b_i} b_i^{n}}{n!}} \nonumber~ +\end{align} +\begin{align} +\times \dfrac{\prod_{j=1}^{n} s_iS_i(x_{ij})+b_iB_i(x_{ij})}{\prod_{j=1}^{n_i}B_i(x_{ij})} \nonumber~, +\end{align} + +\end{small} +\column{2.7in} + \includegraphics[width=0.95\textwidth]{TauLFV_UL_2014001_averaged.png} + + +\end{columns} +\end{frame} + + + +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% + + \begin{frame} + \frametitle{Summary } + \begin{columns} + % \column{2.5in} + \begin{column}{1.9in} + \begin{alertblock}{ $\Ptau \to \Pmu \Pmu \Pmu$ limits ($ \color{white} 90\,\%$ CL)} + + \begin{description} + \item[BaBar(FC)] $3.3\times 10^{-8}$ + \item[Belle(FC)] $2.1\times 10^{-8}$ + \item[LHCb(CLs)] $4.6\times 10^{-8}$ + \item[HFAG(CLs)] $1.2 \times 10^{-8}$ + \end{description} + \end{alertblock} +\end{column} + \begin{column}{2.85in} + \includegraphics[width=1\textwidth]{TauLFV_UL_2014001_averaged_zoom.png}\\ + +\end{column} + + \end{columns} + {~}\\ + + + To conclude: + \begin{columns} + \column{3.2in} +\begin{footnotesize} + + + \begin{itemize} +% \item LHCb result for $\Ptau \to \Pmu \Pmu \Pmu$ with full data set. +% \item We are getting close to B-factories. +% \item Thanks to 3 experiments we have a world limit: $\mathcal{B}(\Ptau \to \Pmu \Pmu \Pmu)< 1.2 \times 10^{-8}$ at 90\% CL. +\item LHCb is reaching B-factories limits. +\item Many new techniques developed to perform this analysis. +\item Combination of UL within HFAG gave the best sensitivity for $\mathcal{B}(\Ptau \to \Pmu \Pmu \Pmu)< 1.2 \times 10^{-8}$ at 90\% CL. +\item Erratum to bibliography: + + + \end{itemize} + \end{footnotesize} +\column{2in} + \includegraphics[width=0.93\textwidth]{banana_tau23mu_hfag.pdf}\\ + + +\end{columns} +\begin{footnotesize} + \begin{itemize} +\item $\rm[120]$ HFAG report published:arXiv:1412.7515 (previous cited preliminary web report). +\item $\rm[76]$ accepted for publication in JHEP. +\end{itemize} + \end{footnotesize} + \end{frame} + +\pagenumbering{gobble} + + + + + +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%5 + \begin{frame}\frametitle{Backup} + + \includegraphics[width=0.93\textwidth]{ngbbs4f7918ec8ffb8.jpg}\\ + + + \end{frame} + %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%5555 + + \begin{frame} + \frametitle{Geometric likelihood} + + \begin{itemize} + \item As mentioned in LHC we have different production sources of $\Ptau$'s. + \item Each source has different detector response signature. + \item To maximise our performance we trained classifiers for each of the $\Ptau$ sources using: + \begin{itemize} + \item Kinematic properties of $\Ptau$ candidate. + \item Geometric properties of $\Ptau$ candidate, like pointing angle, DOCA, Vertex $\chi^2$, flight distance. + \item Isolations, for vertex and individual tracks. + \end{itemize} + \item After training the individual classifiers one that combines all this information in a single classifier on mixed sample of $\Ptau$'s. + \item This technique is known as Blending or Ensemble learning. + \item Using this approach we gain $6\%$ sensitivity! + \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} + + +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%5 +% PID + + \begin{frame} + \frametitle{Particle Identification (PID)} +\begin{itemize} +\item Classifier trained on inclusive MC sample. +\item Using information from: RICH, Calorimeters, Muon system and tracking. +\item Correct for the MC efficiency using control channel: $\PDs \to \Pphi(\Pmu\Pmu) \Ppi$ and $\PB \to \PJpsi(\Pmu\Pmu) \PK$ +\end{itemize} + \begin{columns} + \begin{column}{.45\textwidth} + \includegraphics[width=.95\textwidth]{mPID_2012.pdf} + \end{column} + \end{columns} + \end{frame} +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%5 + + + + + + + + +\end{document} diff --git a/Seminars/IFJ/tau23mu_08_02_15/seminar.toc b/Seminars/IFJ/tau23mu_08_02_15/seminar.toc new file mode 100644 index 0000000..2d151f6 --- /dev/null +++ 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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/Seminars/IFJ/tau23mu_08_02_15/trash.pdf b/Seminars/IFJ/tau23mu_08_02_15/trash.pdf new file mode 100644 index 0000000..8f7415e --- /dev/null +++ b/Seminars/IFJ/tau23mu_08_02_15/trash.pdf Binary files differ diff --git a/Seminars/IFJ/tau23mu_08_02_15/ver.png b/Seminars/IFJ/tau23mu_08_02_15/ver.png new file mode 100644 index 0000000..b390d91 --- /dev/null +++ b/Seminars/IFJ/tau23mu_08_02_15/ver.png Binary files differ diff --git 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