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\author{ {\fontspec{Trebuchet MS}Marcin Chrz\k{a}szcz} (Universit\"{a}t Z\"{u}rich)}
\institute{UZH}
\title[$\tau \to \mu\mu\mu$ in LHCb]{$\tau \to \mu\mu\mu$ in LHCb}
\date{25 September 2014}


\begin{document}
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\begin{center}
\begin{center}
	\begin{columns}
		\begin{column}{0.9\textwidth}
			\flushright\fontspec{Trebuchet MS}\bfseries \Huge {$\tau \to \mu\mu\mu$ in LHCb}
		\end{column}
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	\quad
	\vspace{3em}
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\flushright \vspace{-1.8em} {\fontspec{Trebuchet MS} \Large Marcin Chrząszcz\\\vspace{-0.1em}\small \href{mailto:mchrzasz@cern.ch}{mchrzasz@cern.ch}}

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\vspace{1em}
%		\footnotesize\textcolor{gray}{With N. Serra, B. Storaci\\Thanks to the theory support from M. Shaposhnikov, D. Gorbunov}\normalsize\\
\vspace{0.5em}
	\textcolor{normal text.fg!50!Comment}{Kaggle Seminar, San Francisco\\August 21, 2015}
\end{center}
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\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}


%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
      \begin{frame}
        \frametitle{$\tau$ 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{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[angle=-90,width=.98\textwidth]{images/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[angle=-90,width=.95\textwidth]{images/m3body_2012.pdf}

        \end{column}
        \begin{column}{.45\textwidth}
          \begin{itemize}
              \item $\PDs\to\Pphi\Ppi$ decay well modelled in MC.\\
          \includegraphics[angle=-90,width=.9\textwidth]{images/dataMC.pdf}  
                        %       \item[$\rightarrow$] i.e.\ also badly pointing non-prompt $\PDs$
          \end{itemize}
        \end{column}

        \end{columns}
      \end{frame}


\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[angle=-90,width=.97\textwidth]{images/Ds_data_2011.pdf}
       \column{2.3in}
  \center{2012}\\     
       \includegraphics[angle=-90,width=.97\textwidth]{images/Ds_data_2012.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 $\pm 30~\MeV$ 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}


  \begin{frame}
        \frametitle{Results}

      \begin{center}
    \includegraphics[angle=-90,width=0.7\textwidth]{images/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=0.45\textwidth]{model.png} 
\end{columns}
      \end{frame}  
      

  \begin{frame}
        \frametitle{Why are we not putting the mass in the classifier?}

$\Rrightarrow$ Why don't we put mass in the classifier?\\
$\rightrightarrows$ Many reasons:\\
\begin{itemize}
\item Our normalization channel is in different mass range!
\item Mass resolution is wrongly modelled in MC.
\item Easily to interpret:
\end{itemize}
\begin{columns}
\column{0.05\textwidth}

\column{0.45\textwidth}
\includegraphics[width=0.95\textwidth]{mass2.png}
\column{0.45\textwidth}
\includegraphics[angle=-90, width=0.95\textwidth]{{images/10500_11000_y_bin_2_4.5}.pdf}

\column{0.05\textwidth}


\end{columns}



      \end{frame}  
      

  \begin{frame}
        \frametitle{Data agreement check, why do we bother?}
$\Rrightarrow$ It all boils down to our equation:
 $\boxed{\mathcal{B}(\Ptau\to\Pmu\Pmu\Pmu) = \frac{\mathcal{B}(\PDs\to\Pphi\Ppi)}{\mathcal{B}(\PDs\to\Ptau\Pnut)} \times f_{\PDs}^{\Ptau} \times \frac{\varepsilon_\text{norm}    }{\varepsilon_\text{sig}     }  \times \frac{N_\text{sig}}{N_\text{norm}} = \alpha\times N_\text{sig}}$\\{~}\\
There are 3 variables that we need to terminate: $\varepsilon_\text{sig}$, $\varepsilon_\text{norm}$ and $N_\text{norm}$.
\begin{itemize}
\item $\varepsilon_\text{norm}$; determine from data, by a cut and count method.
\item $N_\text{norm}$; determined from data by a simple fit.
\item $\varepsilon_\text{sig}$; calibrated on data: 
\end{itemize}
\begin{align*}
\varepsilon_\text{sig}=\varepsilon_\text{sig}^\text{MC} \frac{\varepsilon_\text{norm}^\text{DATA}}{\varepsilon_\text{norm}^\text{MC}}
\end{align*}
The hack that is used here is: $\varepsilon_\text{sig}$ is ok, but $N_\text{norm}$ is smaller, so alpha is bigger $\Rightarrow$ worse sensitivity.

      \end{frame}  




\begin{frame}\frametitle{Wrap up}

\begin{enumerate}
\item Physics has a different application of ML than computer science.  
\item There are physics consequance of what you use!                    
\item Blindly taking all varaibles is the bad solution.                 

\end{enumerate}

   \end{frame}  

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