\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}


\usetheme{Sybila} 
\title[Lepton Flavour Violation at LHCb ]{Lepton Flavour Violation at LHCb}
\author{Marcin Chrz\k{a}szcz$^{1,2}$ \\ \footnotesize{on behalf of the LHCb collaboration}}
\institute{$^1$~University of Zurich,\\ $^2$~Institute of Nuclear Physics, Krakow \\{~}\\  International Workshop on Tau Lepton Physics 2014,\\ Aachen, Germany }
\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}

\section{LHCb detector}

\begin{frame}\frametitle{LHCb detector}
\begin{columns}
\column{3.in}
\begin{center}
\includegraphics[width=0.98\textwidth]{det.jpg}
\end{center}

\column{2.0in}
\begin{footnotesize}


      LHCb is a forward spectrometer:
        	\begin{itemize}
        	\item Excellent vertex resolution.
        	\item Efficient trigger.
        	\item High acceptance for $\Ptau$ and $\PB$.
        	\item Great Particle ID
        	\end{itemize}	
        


\end{footnotesize}
\end{columns}

\end{frame}


\section{Lepton Flavour Violation status}
\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 another $\Pnu$, in intermediate vector boson loop, cancels. 
\end{itemize}

\column{2in}
{~}\includegraphics[width=0.98\textwidth]{rabi.png}

\end{columns}
\begin{columns}
\column{0.5in}
{~}
\column{3in}
\begin{block}{I.I.Rabi:}
"Who ordered that?"
\end{block}
\column{0.3in}{~}
\column{2in}
{~}\includegraphics[scale=0.08]{II_Rabi.jpg}

\end{columns}


\begin{itemize}
\item Up to this day charged LFV is being searched for in various decay modes.
\item LFV was already found in neutrino sector (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 it violation(Majorana neutrinos)
\item Searched in so 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 $\color{white} \tau \to \mu \mu \mu$ in Tau 2012}

\begin{columns}
         \begin{column}{.6\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] $8.0\times 10^{-8}~(1 \invfb)$
              \end{description}
            \end{alertblock}
{~}\\
 \includegraphics[width=.95\textwidth]{TauLFV_UL_2013001_old.pdf}


          \end{column}
   \begin{column}{.4\textwidth}
 \includegraphics[width=.45\textwidth]{275px-Nagoya_Castle.jpg}{~}
 \includegraphics[width=.45\textwidth]{taushodo.jpg}\\{~}\\{~}\\
  \includegraphics[width=.93\textwidth]{Fig3a.png}
        \end{column}
\end{columns}
\begin{Large}
Today: Update with full LHCb data sample $(3\invfb)$!
\end{Large}


      \end{frame}


 \begin{frame}
         \section{Selection}
        \frametitle{Strategy}
        \begin{itemize}
          \item Blind analysis.
          \item Loose selection.
          \item Multivariate classification in: mass, PID($\mathcal{M}_{PID}$), geometry($\mathcal{M}_{3body}$).
          \item Binning optimisation.
          \item Consider 2012($8~\TeV$) and 2011($7~\TeV$) data separately.
          \item Relative normalisation ($\PDs\to\Pphi(\Pmu\Pmu)\Ppi$).
          \item Invariant mass fit for expected background in each likelihood bin: fit in $\left| m-m_{\Ptau} \right| >\unit{30}{\MeV}$.
          \item ``middle sidebands'' for classifier evaluation and tests: ($\unit{20}{\MeV}<\left| m-m_{\Ptau}\right| <\unit{30}{\MeV}$).
          \item CLs for limit calculation.
        \end{itemize}
       
      \end{frame}

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
      \begin{frame}
        \frametitle{$\color{white} \tau$ production}
        \begin{itemize}
          \item $\Ptau$'s in LHCb come from five main sources:
            \end{itemize}
            \begin{center}
            
         
\begin{tabular}{| c | c | c | }
\hline
  Mode & $7~\TeV$ & $8~\TeV$ \\ \hline
  Prompt $\PDs\to\Ptau$  & $71.1\pm3.0\,\%$ & $72.4\pm2.7\,\%$ \\
  Prompt $\PDplus\to\Ptau$  & $4.1\pm0.8\,\%$  & $4.2\pm0.7\,\%$ \\
  Non-prompt $\PDs\to\Ptau$ & $9.0\pm2.0\,\%$ & $8.5\pm1.7\,\%$ \\
  Non-prompt $\PDplus\to\Ptau$ &  $0.18\pm0.04\,\%$  & $0.17\pm0.04\,\%$ \\
  $X_{\Pbottom}\to\Ptau$   & $15.5\pm2.7\,\%$  & $14.7\pm2.3\,\%$ \\ \hline
  
\end{tabular}
             \end{center}

       
        \begin{columns}
        \column{0.8\textwidth}
        \begin{exampleblock}{$\mathcal{B}(\PDplus\to\Ptau)$}
          \begin{itemize}
            \item There is no measurement of $\mathcal{B}(\PDplus\to\Ptau)$.
            \item One can calculate it from: $\mathcal{B}(\PDplus\to\Pmu\Pnum)$ + helicity suppression + phase space.
            \item \texttt{hep-ex:0604043}.
            \item $\mathcal{B}(\PDplus\to\Ptau\Pnut)=(1.0\pm0.1) \times10^{-3}$.
          \end{itemize}
        \end{exampleblock}
        \column{0.2\textwidth}
        {~}
           \end{columns}
           
      \end{frame}
 
      \begin{frame}
        \frametitle{Triggers at LHCb}
\begin{itemize}
\item LHCb uses complex trigger\footnote{\href{http://arxiv.org/abs/1211.3055}{\color{blue}arxiv 1211.3055}}
\item $\mathcal{O}(100)$ trigger lines.
\item Lines change with data taking.
\item Optimized choice of triggers based on $\dfrac{s}{\sqrt{b}}$ FOM.
\item Evaluated different triggers used in 2012 data taking.
\item Found negligible differences in trigger efficiencies.
\end{itemize}
   
   
   
   
        \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{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{2.5in}
\center{2011}\\
 \includegraphics[width=.85\textwidth]{2D_2011.pdf}
\column{2.5in}
\center{2012}\\
 \includegraphics[width=.85\textwidth]{2D_2012.pdf}


\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}  
      
 \begin{frame}
        \frametitle{"The Rule of Three"}
 \begin{columns}
   %     \column{2.5in}
   \begin{column}{2.1in}
            \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}{2.5in}    
          \includegraphics[width=1\textwidth]{zom.png}\\
     {~}From A.Lusiani \href{https://indico.cern.ch/event/300387/session/6/contribution/12}{\color{blue}talk}

\end{column}

 \end{columns}
 {~}\\
 To conclude:
    \begin{itemize}
    \item LHCb updated $\Ptau \to \Pmu \Pmu \Pmu$ 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.
         \end{itemize}    
 

      \end{frame}        
      
      
      
\end{document}
