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\title{$\tau \rightarrow \mu \mu \mu$ at LHCb }  
\author{Marcin Chrzaszcz}

\date{\today} 

\begin{document}

{
\institute{Institute of Nuclear Physics PAN}
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  \titlepage
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\institute{IFJ PAN}



%tutaj mamy pierwsza strone


\section[Outline]{}
\begin{frame}
\tableofcontents
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%normal slides
\section{General rewiew of LHCb}
\subsection{First Informations}

\begin{frame}\frametitle{General Informations}
\begin{itemize}
\item Fresh analyses! Aproved less than 24h ago.
\item Premision to only speak generally without going to any details.
\item Will try to be clouse to the boundry of what I can say


\begin{block}{Appologyse}
All details will be avaible avaible on FPCP conference so stay tune!
\end{block}

\end{itemize}

\end{frame}


\subsection{Detector}
\begin{frame}\frametitle{LHCb detector}
\begin{center}

\includegraphics[scale=0.3]{detector.png}

\end{center}
\end{frame}

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\begin{frame}\frametitle{LHCb detector}
Strong features of LHCb detector:
\begin{itemize}
\item Good particle indentyfication due to RICH detectors.
\item State of the art strip detector provides good 
\item High luminosity. Nowadays operating $4$ $10^{-32} cm^{-2}s^{-1}$. We target to get $1.5fb$ in 2012.

\end{itemize}

\end{frame}
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\subsection{Theoretical and experimental status}
\begin{frame}\frametitle{Theoretical and experimental status}
Strong features of LHCb detector:
\begin{itemize}
\item LFV has been observed in neutrino oscillations.
\item Never saw in charge sector.
\item Depending on the model $\tau \rightarrow \mu\mu\mu$ can be dominant over $\tau \rightarrow \mu \gamma$

\end{itemize}

\begin{columns}[c]

\column{2in}
	
SM prediction: BR $\sim 10^{-54}$
\newline Best limits (90 \%CL):
\newline BaBar: 3.3 x 10-8 ($468fb^{-1}$)
\newline Belle: 2.1 x 10-8 ($782fb^{-1}$)


\column{3in}
	\includegraphics[scale=0.35]{sm.png}

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\section{Analysys strategy}
\subsection{General informations}

\begin{frame}\frametitle{General informations}

\begin{enumerate}
\item Three separate Likelihoods to discriminate background
\begin{itemize}
\item Geometry and topology
\item Particle indentyfication
\item Three body invariant mass
\end{itemize}
\item Training done on MC samples:
\begin{itemize}
\item $\tau \rightarrow \mu \mu \mu$
\item $b \bar{b} \rightarrow \mu \mu X$ and $c \bar{c} \rightarrow \mu \mu X$
\end{itemize}
\item Different input variables, MVA operators and training methods
examined, choice: ~highest performance \& simplest 

\end{enumerate}

\end{frame}
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\subsection{$\tau$ production}

\begin{frame}\frametitle{$\tau$ production}

\includegraphics[scale=0.35]{table.png}

MC signal sample generated with phase space distribution


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\subsection{Binning optimisation}
\begin{frame}\frametitle{Binning optimisation}
The mentioned 3D plane(mass, kinematics, and geometry with topology) was divided into bins. The optimisation of that binning was done using CLs method.

\includegraphics[scale=0.15]{geolq.png}
\includegraphics[scale=0.15]{pidlq.png}

 $\Delta LQ = 2ln(Q_{SB})-2ln(Q_{B})$
where, 
\newline $Q_{SB}= \prod \frac{P(s_{i}+b_{i},s_{i}+b_{i})}{P(s_{i}+b_{i},b_{i})}$
\newline $Q_{SB}= \prod \frac{P(s_{i}+b_{i},s_{i}+b_{i})}{P(s_{i}+b_{i},b_{i})}$
\newline $P(a,b)$ is the propabylity that expected number of 
backgound a \newline fluctuated (by Poisson distribution) to b, and i is the bin bumber.


\end{frame}
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\subsection{MVA parameter space}
\begin{frame}\frametitle{MVA parameter space}
For the geometry and kinematics MVA is callibrated using $D_{s} \rightarrow \phi(\mu\mu) \pi$.
 \includegraphics[scale=0.35]{geo-out.pdf}


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\subsection{Normalization}

\begin{frame}\frametitle{Normalization}
$\tau$ BR was normalized to $D_{s} \rightarrow \phi(\mu\mu) \pi$


\begin{center}
 \includegraphics[scale=0.25]{alpha.png}
\newline \includegraphics[scale=0.25]{ds.pdf}
\end{center}
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\section{Background}
\subsection{SM background}


\begin{frame}\frametitle{SM background}
LHCb is not a B factory. We have ireducable background! And we have to life with it.
\begin{center}
 \includegraphics[scale=0.23]{table2.png}

\end{center}
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\subsection{SM background}


\begin{frame}\frametitle{$D_{s} \rightarrow (\eta \rightarrow \mu \mu \gamma) \mu \nu$}
This decay was badly simulated in current version of MC. For proper simulation new method in EvtGen was written.
It took into account form factors comming from NA60 experiment.
\newline arXiv:1108.0968
\begin{center}
 \includegraphics[scale=0.23]{old_new.png}

\end{center}
For the purpouse of this analyses 5M events were simulated in a private production in IFJ computing cloud.
Many thanks to Mariusz Witek for computing resourses!


\end{frame}
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\subsection{Background extraction}
\begin{frame}\frametitle{Background extraction}

There are 3 possibilities to deal with background.
\begin{itemize}
\item Treat it as normal combinatorical background.
\item Veto the $\eta$.
\item Parametrize the $\eta$ background and fit with combinatorical.	
\end{itemize}
\begin{center}
\includegraphics[scale=0.25]{1stbin.pdf}
\end{center}
\end{frame}


\subsection{Results}
\begin{frame}\frametitle{Results}

\begin{center}

\includegraphics[scale=0.5]{cen.png}
\end{center}
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\section{Summary}

\begin{frame}\frametitle{Summary}
\begin{itemize}
\item LHCb is capable of performing $\tau \rightarrow \mu \mu \mu$ measurements.
\item Method is completly different from the one used in B factories. We are cuting the phase space
\item Looking for perticular model of decay could increase our sensetiwity. Need MC generators for that.




\end{itemize}

Thank you for your attention.

\end{frame}




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