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% title slide definition
\title{Report on $\tau \to p \Plepton \Plepton$}
%\subtitle{a bias report}
\author{Marcin Chrz\k{a}szcz, Alberto Lusiani}
\institute[Institute of Nuclear Physics]
{
Institute of Nuclear Physics, INFN, Scuola Normale Superiore
}


\date{$27^{th}$ March 2013}

%--------------------------------------------------------------------
%                           Introduction
%--------------------------------------------------------------------

\begin{document}



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%--------------------------------------------------------------------
%                          OUTLINE
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\section[Outline]{}
\begin{frame}
\tableofcontents
\end{frame}







%-------------------------------------------------------------------
%                          Introduction
%-------------------------------------------------------------------
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\title{Report on $\tau \to p \Plepton \Plepton$}


%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

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\section{Motivation}
\begin{frame}\frametitle{Motivation}
\begin{small}
\begin{itemize}
\item Each of studied decay: $\tau^- \to p \Plepton^- \Plepton^-$ or $\tau^- \to \bar{p} \Plepton^- \Plepton^+$ violates Lepton and Baryon numbers.  
\item However the quantity: $\Delta \vert B-L \vert = 0$, which is predicted by many NP models, ex. R-parity violating SUSY.
\item LHCb searched for this decays($\Plepton=\mu$) using 2011 data.  
\end{itemize}
\end{small}
\begin{figure}[h]
\begin{center}
\mbox{
  {\includegraphics[scale=0.15]{pic/OS_banan_un.png}}
  {\includegraphics[scale=0.15]{pic/SS_banan_un.png}}
}
\end{center}
\end{figure}
\small Limits 90\% CL:  (can we do better?)\\
 $\mathcal{B}(\tau^- \to p^+ \mu^- \mu^-) < 4.4 \times 10^{-7}$\\
 $\mathcal{B}(\tau^- \to \bar{p}^+ \mu^+ \mu^-) < 3.3 \times 10^{-7}$\\	

\end{frame}

\section{MC \& data}
\begin{frame}

\frametitle{Data Set used in this analysis.}
{~}

Available data:
\only<1>{

The MC signal samples used:
\begin {table}[h]
\begin{center}
    \begin{tabular}{ l | l }
    \hline
    Decay & Generated events \\ \hline  \hline
 	$\tau^{-} \rightarrow p \mu^- \mu^{-}$ & 207000  \\ \hline
 	$\tau^{+} \rightarrow \overline{p} \mu^+ \mu^{+}$ & 212000 \\ \hline
 	$\tau^{-} \rightarrow \overline{p} \mu^+ \mu^{-}$ &  212000\\ \hline
 	$\tau^{+} \rightarrow p \mu^- \mu^{+}$ & 217000 \\ \hline	
 	%%%%%%%%%%%%%%%%%%%%%%5 electrons now 
 	$\tau^{-} \rightarrow p e^- e^{-}$ &  185000 \\ \hline
 	$\tau^{+} \rightarrow \overline{p} e^+ e^{+}$ & 198000 \\ \hline
 	$\tau^{-} \rightarrow \overline{p} e^+ e^{-}$ & 191000 \\ \hline
 	$\tau^{+} \rightarrow p e^- e^{+}$ & 187000 \\ \hline	
    
    \end{tabular}
\end{center}

\caption {Simulated MC signal samples.}

\end {table}


}

\only<2>{
Data: $472 fb^{-1}$ (run 1-6, on and off peak).  \\
MC bck samples: Run 1-6 
\begin {table}[h]
\begin{center}
    \begin{tabular}{  l | l | l }
    \hline
    Background type & $\sigma [nb]$ & $L [ fb^{-1} ] $   \\ \hline  \hline
	$e^{-} e^{+} \to \tau \tau$ & 0.92 & 471 \\  \hline
    $e^{-} e^{+} \to uu/dd/ss$ & 1.09 & 746 \\  \hline 
    $e^{-} e^{+} \to cc$ &1.3 & 860 \\  \hline 
	$e^{-} e^{+} \to B\bar{B}$ & 1.1 & 1190 \\  \hline 
	

    \end{tabular}
\end{center}


\caption {MC background samples used in this analysis.}

\end {table}

%The luminosity is not used in the analysis.
}

\end{frame}

\section{Preselection}
\begin{frame}\frametitle{Preselection}
We divide our pre selection cuts into two categories:
\begin{itemize}
\item Geometric \& Topology
\item PID
\end{itemize}
\end{frame}

\subsection{Geometric \& Topology}
\begin{frame}\frametitle{Geometric \& Topology}
\only<1>{
The following selections are applied to data and MC samples:

\begin{itemize}
\item Trigger logic: (L3OutDch $\Vert$ L3OutEmc)$\&$BGFMultiHadron.
\item Pass the 1N skim.
\item Events are divided into two hemispheres using the thrust axis:
	\begin{equation}
 thr= MAX (   \dfrac{\sum^n_{i=0} \vert A \cdot P_i  \vert }{\sum^n_{i=0}\sqrt{ P_i \cdot P_i }} )
\end{equation}
\item Total charge =0 and opposite sign of the two hemispheres is required.
\end{itemize}
}

\only<2>{
The following selections are applied to data and MC samples:

\begin{itemize}
\item On the signal side we require 3 charged tracks from GoodChargeLoose list.
\item Tag side is single charge track form the same list. $85\%$ eff. in SM decays.
\item A loose kinematic cuts are also applied:
\end{itemize}


\begin{table}[h]
\begin{center}
    \begin{tabular}{| l | l |}
    \hline
    Variable & Cut \\ \hline  \hline
 	$P_t$ & $>0.1GeV$ \\ \hline
 	$P$ & <$10GeV$ \\ \hline
 	$\theta$ & $(0.41;2.46)$\\ \hline
    \hline
    \end{tabular}
\end{center}
   \caption{Cuts applied for each track in the event.}
\end{table}

}


\only<3>{
we found the following efficiencies:
\begin{table}
\begin{center}
    \begin{tabular}{ l | l | l }
    \hline
	Decay & $\epsilon_{Geo}$  & $\pm \delta\epsilon_{Geo}$ \\ \hline  \hline
 	$\tau \rightarrow p e^- e^{-}$ & 35.3 \% & 0.1 \%  \\ \hline
 	$\tau \rightarrow \overline{p} e^+ e^{-}$ & 35.3 \%& 0.1  \% \\ \hline
 	$\tau \rightarrow \overline{p} \mu^- \mu^{-}$ &  39.4 \% & 0.1 \% \\ \hline
 	$\tau \rightarrow p \mu^- \mu^{+}$ & 39.3 \% & 0.1 \% \\ \hline \hline	
 	%%%%%%%%%%%%%%%%%%%%%%5 electrons now \%
 	 	 
    \end{tabular}
\end{center}
    \caption{Efficiencies for signal MC.}

\end{table}

where we used:

$
\varepsilon  = \dfrac{n+0.5}{k+1} 
$, 
$
\delta \varepsilon  = \sqrt{\dfrac{(n+0.5)(k-b+0.5)}{(k+2)(k+1)^2} }
$ \footnote{arXiv0908.0130}



}
\end{frame}


\begin{frame}\frametitle{Energy constrain fit}

We applied an Energy constrain fit for $\tau$ reconstruction(signal hemisphere is constrain to have $E_{cm}/2$ energy. This improves the mass resolution by $5-10 \%$ depending on the decay mode.
\begin{figure}[h]
\begin{center}
\mbox{
  {\includegraphics[scale=0.16]{pic/eeOS_fit_energy.png}}
  {\includegraphics[scale=0.16]{pic/eeOS_fit_geo.png}}
}
\caption
{Fits to $\tau \to p e^- e^+$ mass. Left- with energy constrain. Right with Geo constrain.}
\end{center}
\end{figure}

\end{frame}

\begin{frame}\frametitle{Signal distribution.}

\begin{figure}[h]
\begin{center}
\mbox{
  {\includegraphics[scale=0.1]{pic/dE_dM_tau2mumuOS.png}}
  {\includegraphics[scale=0.1]{pic/dE_dM_tau2eeOS.png}}
}
\mbox{
  {\includegraphics[scale=0.1]{pic/dE_dM_tau2mumuSS.png}}
  {\includegraphics[scale=0.1]{pic/dE_dM_tau2eeSS.png}}
}
\end{center}
\end{figure}

\end{frame}

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%}


\subsection{PID}
\begin{frame}\frametitle{PID}
%\begin{small}
\begin{itemize}
\item We used the standard BaBar classifiers for the PID cuts. 
\end{itemize}
\begin{table}[h]
\begin{center}
    \begin{tabular}{ l | l | l | l | l }
    \hline
	Decay & e Classifier & $\mu$ Classifier & p Classifier & $\epsilon_{PID|GEO}$\\ \hline  \hline
	$\tau \rightarrow p \mu^- \mu^{-}$ &  DNA & BDTLoose &  LooseKM & $34.5 \pm 0.1\%$ \\ \hline
 	$\tau \rightarrow \overline{p} \mu^+ \mu^{-}$  & DNA & BDTLoose & LooseKM & $35.3 \pm 0.1\%$\\ \hline

 	%%%%%%%%%%%%%%%%%%%%%%5 electrons now 
 	$\tau \rightarrow p e^- e^{-}$   & TightKM & DNA  & LooseKM & $54.7 \pm 0.1\%$\\ \hline

 	$\tau \rightarrow \overline{p} e^+ e^{-}$ & TightKM & DNA & LooseKM& $55.1 \pm 0.1\%$ \\ \hline \hline
    \end{tabular}
\end{center}
    \caption{Classifiers and efficiencies after the PID cut. DNA = does not apply}
\end{table}


\end{frame}


\section{Selection}
\begin{frame}\frametitle{Selection}
%\begin{small}
\begin{itemize}
\item Selection was optimised in order to get the best upper limit. For the optimisation the CLs method was used.
\item
The optimisation is done to reach the best separation of signal+background like hypothesis and background only hypothesis. We used the following figure of merit:
\end{itemize}
\[\Delta LQ = 2ln(Q_{SB})-2ln(Q_{B})\]

\only<1>{
where,
\begin{align*}
Q_{SB}&= \prod \frac{P(s_{i}+b_{i},s_{i}+b_{i})}{P(s_{i}+b_{i},b_{i})}\\
Q_{B} &= \prod \frac{P(b_{i},s_{i}+b_{i})}{P(b_{i},b_{i})}.
\end{align*}
}

\only<2>{
\begin{figure}[h]
\begin{center}
\mbox{
	 {\includegraphics[scale=0.12]{pic/cls.png}}
}
\end{center}
\end{figure}


}

\end{frame}



\begin{frame}\frametitle{Optimisation results}
%\begin{small}


\begin{figure}[h]
\begin{center}
\mbox{
 {\includegraphics[scale=0.07]{pic/cos31_eeOS.png}}
 {\includegraphics[scale=0.07]{pic/tagmass_eeOS.png}}
 {\includegraphics[scale=0.07]{pic/thrust_eeOS.png}}	
}
\end{center}
\end{figure}

\begin{figure}[h]
\begin{center}
\mbox{
 {\includegraphics[scale=0.07]{pic/cos31_mumuOS.png}}
 {\includegraphics[scale=0.07]{pic/tagmass_mumuOS.png}}
 {\includegraphics[scale=0.07]{pic/thrust_mumuOS.png}}	
}
\end{center}
\end{figure}


\end{frame}


\begin{frame}\frametitle{Efficiency after the selection}
%\begin{small}
\begin{table}[h]
\begin{center}
    \begin{tabular}{ l | l | l }
    \hline
	Decay & $\epsilon_{Sel|PID}$  & $ \pm  \delta\epsilon_{Sel|PID}$ \\ \hline  \hline
 	$\tau \rightarrow p e^- e^{-}$ & $41.8 \%$ & $0.2 \%$  \\ \hline
 	$\tau \rightarrow \overline{p} e^+ e^{-}$ & $47.7 \%$ & $0.2  \%$ \\ \hline
 	$\tau \rightarrow \overline{p} \mu^+ \mu^{-}$ & $ 75.2 \%$ & $0.2 \%$ \\ \hline
 	$\tau \rightarrow p \mu^- \mu^{+}$ & $79.0 \%$ & $0.2 \% $ \\ \hline	
 	%%%%%%%%%%%%%%%%%%%%%%5 electrons now \%
 	  
    \end{tabular}
\end{center}
    \caption{Efficiencies for signal MC.}

\end{table}
\end{frame}

\section{Fits}
\begin{frame}\frametitle{Background and fits}
\begin{itemize}
\item Because only few events from $B\bar{B}$ background survive the geometric cut we will not consider this in further analysis. 
\item We used the PID weighting procedure as in $\tau \to \mu \mu \mu$ to determined the pdf shape. We consider 3 types of background: QED, $udsc$ , $\tau \tau$. 
\item QED samples are evaluated directly on data.
\item We sum the bck pdf and preform an Unbinned maximum likelihood fit to data side band to determine the expected number of bck events.

\end{itemize}
\end{frame}


\begin{frame}\frametitle{Fits to MC background}

\begin{figure}[h]
\begin{center}
\mbox{
 {\includegraphics[scale=0.15]{pic/tautaumumuOS_before_out_DM.png}}
 {\includegraphics[scale=0.15]{pic/tautaumumuSS_before_out_DE.png}}
}
\mbox{ 
 {\includegraphics[scale=0.15]{pic/udsmumuOS_before_out_DE.png}}	
  {\includegraphics[scale=0.15]{pic/udsmumuOS_before_out_DM.png}}	
}
\end{center}
\end{figure}

\end{frame}
\begin{frame}\frametitle{Fits to data}

\begin{figure}[h]
\begin{center}
\mbox{
 {\includegraphics[scale=0.15]{pic/DEmumuOS.png}}
 {\includegraphics[scale=0.15]{pic/DMmumuOS.png}}
}
\end{center}
\end{figure}
\end{frame}


\begin{frame}\frametitle{Expected background}


\begin{table}[h]
\begin{center}
    \begin{tabular}{ l | l | l }
    \hline
	Decay & Expected & Error  \\ \hline  \hline
 	$\tau^- \rightarrow p e^- e^{-}$ & $0.30$  &  $0.09$  \\ \hline
 	$\tau^- \rightarrow \overline{p} e^+ e^{-}$ & $1.08$ & $0.13$ \\ \hline
 	$\tau^- \rightarrow \overline{p} \mu^+ \mu^{-}$ & $0.81$ & $0.15$ \\ \hline
 	$\tau^- \rightarrow p \mu^- \mu^{-}$ & $ 0.49 $   &$0.14  $ \\ \hline	
 	%%%%%%%%%%%%%%%%%%%%%%5 electrons now \%
 	  
    \end{tabular}
\end{center}
    \caption{Number of expected events in the signal window.}

\end{table}
\end{frame}

\section{systematics}
\begin{frame}\frametitle{Systematics}
We define three types of systematics:
\begin{itemize}
\item MC related
\item Background systematics
\item Luminosity systematics.

\end{itemize}

\end{frame}


\subsection{MC systematics}
\begin{frame}\frametitle{MC Systematics}
\only<1>{
Considered systematics:  

\begin{itemize}
\item Signal systematics, limited MC statistics.
\item $\tau$ BR.
\item PID
\item Tracking efficiency.

\end{itemize}
}

\only<2>{
{ \Large $\tau$ BR. } \\
TAUOLA takes the SM branching fractions from PDG 2006. The systematic uncertainty
related to the branching fraction errors is evaluated as a quadrature sum of the individual BF uncertainties weighted by their relative fraction. 


}

\only<3>{
{ \Large PID efficiency } \\ 
	The PID systematics is evaluated in a conservative way. We sum squared errors for each track on the tag side. Because the distribution is asymmetric the error is defined at 68\% coverage. 

\begin{figure}[h]
\begin{center}
\mbox{
 {\includegraphics[scale=0.15]{pic/eeSS.png}}
 {\includegraphics[scale=0.15]{pic/MUMUSS.png}}
}
\end{center}
\end{figure}

}
\only<4>{
\begin{table}[h]
\begin{center}
    \begin{tabular}{ l | l | l | l | l }
    \hline 
	--- & $\tau \rightarrow \bar{p} e^+ e^{-}$ & $\tau \rightarrow p e^{-} e^{-}$ & $\tau \rightarrow \bar{p} \mu^{+} \mu^{-}$  & $\tau \rightarrow p \mu^{-} \mu^{-}$ \\ \hline \hline
	Total eff.    & $9.3  $ &  $8.1$  & $ 11.0$ & $10.3$  \\ \hline 	\hline		
	MC statistics & $0.46  $ &  $0.54$  & $  0.39 $ & $3.8$  \\ \hline
	Tau BR        & $0.7  $  & $0.7  $   & $0.7  $ & $0.7  $ \\ \hline
	PID sig side  & $2.34 $  &  $3.1 $  &  $ 7.0$ &  $7.8 $\\ \hline
	PID tag side  &	$0.9 $   &  $0.9 $ &  $0.0$ &  $0.0$\\ \hline
	Tracking eff. & $ 1.0  $  &   $ 1.0  $ & $ 1.0$ & $ 1.0$\\ \hline \hline
	Total 	      & $2.7$   &  $3.4$ & $7.1 $ & $7.9$      \\ \hline \hline
 	%%%%%%%%%%%%%%%%%%%%%%5 electrons now \% 
    \end{tabular}
\end{center}
    \caption{Total efficiency and systematic uncertainties expressed in relative percent
}
\end{table}


}
\end{frame}
\section{Results}
\begin{frame}\frametitle{Expected UL at 90\% CL}

\begin{table}[h]
\begin{center}
    \begin{tabular}{ l | l }
    \hline
	Decay & Expected UL  \\ \hline  \hline
 	$\tau^- \rightarrow p e^- e^{-}$ & $3.2 \times 10^{-8}$  \\ \hline
 	$\tau^- \rightarrow \overline{p} e^+ e^{-}$ & $4.0 \times 10^{-8}$ \\ \hline
 	$\tau^- \rightarrow \overline{p} \mu^+ \mu^{-}$ & $3.5 \times 10^{-8}$ \\ \hline
 	$\tau^- \rightarrow p \mu^- \mu^{-}$ & $ 2.5 \times 10^{-8} $ \\ \hline	
 	%%%%%%%%%%%%%%%%%%%%%%5 electrons now \%
 	  
    \end{tabular}
\end{center}
    \caption{Expected upper limits at $90\%$ CL.}

\end{table}

\end{frame}

\begin{frame}\frametitle{Conclusions}



\begin{itemize}
\item Analysis in pretty  good shape.
\item Supporting documentation 20, pages, needs just polishing. 
\item With this presentation we ask to start an AWG review.

\end{itemize}

\end{frame}

\end{document}
