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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}
 \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}
