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\usetheme{Sybila} 
\title[Lepton Flavour Violation at $\color{white}\tau$ decays]{Lepton Flavour Violation at $\color{white}\tau$ decays}
\author{Marcin Chrz\k{a}szcz$^{1,2}$}
\institute{$^1$~University of Zurich,\\ $^2$~Institute of Nuclear Physics, Krakow \\{~}\\  FCC WG on experiments with the CERN injectors }
\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{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) 
\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}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\section{LFV at B-factories}
\begin{frame}\frametitle{LFV at B-factories}
\begin{columns}
\column{0.2in}
{~}
\column{2.5in}
$\sigma(\Pelectron \APelectron \to \Ptau^+ \Ptau^-)=0.919~\nanobarn$
\begin{itemize}
\item Clean environment.
\end{itemize}
\includegraphics[width=0.73\textwidth]{upsilon4s.png}
\begin{itemize}
\item High efficiency: $5-10\%$
\item Background free.
\item Efficient and simple tag.
\end{itemize}

\column{2.5in}
Signal extraction:
$M_{\mu\gamma}=\sqrt{(E^{CM}_{sig})^2 - (p_{sig}^{CM})^2}$
$\Delta E = E_{sig}^{CM}-E_{beam}^{CM}$
$H_l = \sum_{ij} \dfrac{|\overrightarrow{p_j}||\overrightarrow{p_i}| P_l(\cos \Omega_{ij}) }{s}$
\includegraphics[width=0.73\textwidth]{dedm.png}


\end{columns}


\end{frame}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%


\section{LHCb detector}

\begin{frame}\frametitle{Hadron collider - LHCb}
\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}


\begin{frame}\frametitle{Analysis approach}
\begin{columns}
\column{0.2in}
{~}
\column{2.5in}
B factories


\column{2.5in}
LHCb, ($7-8 TeV$, 2011-2012 data)

\end{columns}
\begin{columns}
\column{2.5in}


\begin{enumerate}
		\item Clean signal: $\APelectron\Pelectron\to\APtauon\Ptauon$   
		\item Calculate the thrust axis   
		\item "Partial tag" of the other $\tau$   
		\item Small cross section $0.919nb$    
\end{enumerate}

\column{2.5in}

\begin{enumerate}
\item	Inclusive $\tau$ cross section: \newline $\sim80{\micro\barn}$.  
	\item	 $~\sim 10^{11} \tau$ produced.
	\item	 Dominant contribution: \newline $\PDs\to\Ptau\Pnut$ ($78\%$)   
		\item	 No tag possible.   
\end{enumerate}


\end{columns}
\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 the remaining 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 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}    
   \begin{frame}
        %\frametitle{More nasty background}
\begin{center}
\begin{Huge}

Future of $\Ptau \to 3\Pmu$ at hadron colliders.
\end{Huge}
\end{center}



      \end{frame}   
      
      
      
      
          
\section{Future of LFV at hadron colliders}      
            \begin{frame}
        \frametitle{More nasty background}
\includegraphics[width=1\textwidth]{b1.png}\\

      \end{frame}
      
              \begin{frame}
        \frametitle{More nasty background}
\includegraphics[width=1\textwidth]{b2.png}\\

      \end{frame}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
              \begin{frame}
        \frametitle{LFV at SHIP experiment}
\begin{columns}
\column{2.5in}
\begin{center}
\includegraphics[width=0.2\textwidth]{SHIP-Full_Black_146x195.png}

\end{center}
\begin{itemize}
\item Beam dump experiment from SPS.
\item Designed to study long living particles e.g.. HNL.
\item Main interest are particles coming from  charm decays.
\item Charm decays are also an excellent source of $\Ptau$ decays:\\
$Br(\PDsplus \to \APtauon \Pnut )= (5.6 \pm 0.4 )\%$
\\{~}\\{~}\\{~}\\{~}\\


\end{itemize}

\column{2.5in}

%\begin{center}
\includegraphics[width=0.98\textwidth]{setup-sketch.pdf}\\
\includegraphics[width=0.98\textwidth]{ship.png}\\
{~}{~}{~}{~}
\\{~}\\{~}\\{~}\\{~}\\
%\end{center}
\end{columns}

      \end{frame}
         
         
   %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
 \begin{frame}
\frametitle{LFV at SHIP experiment: Idea 1}
\begin{columns}
\column{2.5in}
\begin{itemize}
\item Put a specific $\Ptau \to 3 \Pmu$ detector just after the target.
\item Huge number of $\Ptau$ produced: $1.2 \times 10^{15}$!
\item The numbers are very encouraging!
\item What is the mass resolution?
\end{itemize}
%\includegraphics[width=0.65\textwidth]{tungsten.png}\\
\column{2.5in}
{~}\\
Based on SHIP $\Ptau \to 3\Pmu$ WG:\\
\begin{small}
L.Shchutska, G.Mitselmakher, J.Harrison, C.Parkes, N.Serra, E. Rodrigues, B.Storaci, A.Golutvin ,M.Chrz\k{a}szcz\\\end{small}
\includegraphics[width=0.98\textwidth]{setup-sketch1.png}\\
%{~}\\{~}\\{~}\\{~}\\{~}\\{~}\\{~}\\{~}\\
%\includegraphics[width=0.7\textwidth]{carbon.png}\\
\end{columns}

\begin{columns}
\column{0.1in}
{~}\\
\column{1.7in}
\includegraphics[width=0.95\textwidth]{tungsten.png}\\
\column{1.7in}
\includegraphics[width=0.95\textwidth]{carbon.png}\\
\column{1.5in}
{~}\\
\end{columns}


      \end{frame}
  
          
   %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
 \begin{frame}
\frametitle{Momentum correction}
\includegraphics[width=0.95\textwidth]{corrections.png}\\
\begin{itemize}
\item With correction of momentum after the target the resolution is better.
\item However still not good enough to perform this measurement.
\item Conclusions: momentum of the muons needs to be measured before absorber and on thin target.
\end{itemize}
      \end{frame}
    
  
      %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
 \begin{frame}
\frametitle{LFV at SHIP experiment: Idea 2}
\begin{columns}
\column{2.5in}
\includegraphics[width=0.95\textwidth]{ship2.png}\\
\includegraphics[width=0.95\textwidth]{det.png}\\
\column{2.5in}
\begin{itemize}
\item Multiple scattering is negligible.
\item $\Ptau$ vertex outside the target.
\item Reduce $\Ptau$ flux by a factor of $100$.
\item First estimate of sensor \\
radius :$\sim 2.5~\mm$
\item Evaluated acceptance: $33\%$
\item Work ongoing.
\end{itemize}


\end{columns}
  
      \end{frame}
      %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
 \begin{frame}
\frametitle{LFV at injectors for FCC}
\begin{itemize}
\item First thought: Detector similar to LHCb.
\item Lets try to make ,,zero approximation'' using LHCb analysis.
\item Ingredients:
\begin{itemize}
\item Acceptance:$\sim10~\%$.
\item Pre-Selection and tracking:$\sim10~\%$.
\item Trigger:$\sim40~\%$.
\item Selection(trash bins):$\sim50~\%$.
\item In total: $0.2~\%$.
\end{itemize}
\item Not bad so far!
\end{itemize}

   \begin{exampleblock}{Observation:}
The total efficiency can be increased by factor $2-5$ if detector is optimised for $\Ptau$'s.
   \end{exampleblock}



\end{frame}
          %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

          
\begin{frame}
\frametitle{LFV at injectors for FCC - Pileup}

\begin{columns}
\column{3in}
\includegraphics[width=0.95\textwidth]{multvsgeo.pdf}
\column{2in}
\begin{itemize}
\item Not clear correlation with multiplicity.
\item Good for pile-up increase.
\end{itemize}

\end{columns}


   \begin{exampleblock}{Observation:}
  Pile up in LHCb regime is not a problem.
   \end{exampleblock}

\end{frame}
    
            %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

          
\begin{frame}
\frametitle{LFV at injectors for FCC - Idea to shoot at}
\begin{columns}
\column{2.5in}
\begin{itemize}
\item Let's assume that FCC will be a $\Pelectron \APelectron$ collider.\\ LHC tunnel - $\Pelectron \APelectron$ booster.
\item We would collect $10^{12-13}~\PZ$ decays.
\item $Br(\PZ \to \Ptauon \APtauon) = 3.370 \pm0.008\%$.
\item Number of $\Ptau$: $6.7\times 10^{10-11}$.
\only<2>
{
\item Belle2: $50 \invab \times 2 \times 0.919 \nanobarn = 9.2 \times  10^{10}~\tau$'s

}

\end{itemize}
\column{2.5in}
\includegraphics[width=0.95\textwidth]{lumi.png}


\end{columns}

\only<2>
{
\begin{columns}
\column{0.3in}
{~}
\column{2.5in}
\begin{alertblock}{Reminder:}
\begin{itemize}
\item $\epsilon_{\Ptau\to 3\mu}^{BaBar}= 6.6\pm0.6\%$
\item $\epsilon_{\Ptau\to 3\mu}^{Belle}= 7.6\pm0.6\%$
\item $\epsilon_{\Ptau}^{ALEPH}= \sim 50\%$

\end{itemize}
\end{alertblock}  
           
 \column{2.5in}
\begin{itemize}
\item There is a factor of $8$ to gain \\ just in efficiency!

\end{itemize}
 \end{columns}

}
\only<3>
{
\begin{columns}
\column{0.3in}
{~}
\column{2.5in}
       \includegraphics[width=0.95\textwidth]{emumu1.png}    
 \column{2.0in}
\begin{exampleblock}{Reminder 2:}
\begin{itemize}
\item \small{In $\Pelectron \APelectron$ machines in contrast to hadron colliders the limit doesn't necessary follow $\sqrt{\mathcal{L}}$}.
\item Another factor to gain.



\end{itemize}
\end{exampleblock}  
 \end{columns}

}




\end{frame}



    %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame}
\frametitle{Beyond LFV}

\begin{columns}
\column{0.2in}
{~}
\column{3in}
$\Ptau$'s at hadron collider have limit use! 
At $\Pelectron \APelectron$  we get for free:
\begin{itemize}
\item All LFV(at hadron colliders most decays are not possible).
\item $V_{us}$ from $\Ptau$.
\item Lepton universality tests\\(anomally from LEP):\\ \begin{footnotesize}$\dfrac{2BR(\PW\to \Ptau \Pnut)}{BR(\PW\to \Pmu \Pnum)+ BR(\PW\to e \Pnue)}$=1.077(0.026). \end{footnotesize}
\item Hadronic spectral functions.
\item etc.
\end{itemize}
\column{2.0in}
  \includegraphics[width=0.95\textwidth]{Vus.png}    
\end{columns}
\end{frame}
    %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame}
\frametitle{Conclusions}

\begin{itemize}
\item LFV is possible at hadron machines!
\item LHCb already caught up with B-factories.
\item In future there are many different possibilities for $\Ptau$ factories.
\item Many studies ongoing.

\end{itemize}



\end{frame}
    
      
    
    
    
      
\end{document}
