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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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\institute{IFJ PAN}



%tutaj mamy pierwsza strone


\section[Outline]{}
\begin{frame}
\tableofcontents
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%normal slides
\section{Brief review of LHCb}
\subsection{Introduction}

\begin{frame}\frametitle{Introduction}
\begin{itemize}
\item Fresh analysis! Approved less than 24hrs ago.
\item Permission to speak only in general sense without going into any details.
\item Will try to give a closed talk with as much information as possible.  


\begin{block}{Apologise}
All the details will be available on the FPCP conference so stay tuned!
\end{block}

\end{itemize}

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

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

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\begin{frame}\frametitle{LHCb detector}
Strong features of the LHCb detector:
\begin{itemize}
\item Good particle identification thanks to the RICH detectors.
\item State of the art silicon strip detector provides good vertex resolution. 
\item High luminosity: currently operating $4 \times 10^{-32} cm^{-2}s^{-1}$; we target to get $1.5fb$ in 2012.

\end{itemize}

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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 seen in the charged lepton 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 ($782fb^{-1}$)
\newline LHCb:  X.Y         ($1fb^{-1}$)


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

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\section{Analysis strategy}
\subsection{General information}

\begin{frame}\frametitle{General information}

\begin{enumerate}
\item Three separate likelihoods to discriminate background
\begin{itemize}
\item Geometry and topology
\item Particle identification
\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}

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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 3D plane(mass, kinematics, and geometry with topology) mentioned 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 probability that the expected number of 
background a \newline fluctuates (by Poisson distribution) to b, and i is the bin number.


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\subsection{MVA parameter space}
\begin{frame}\frametitle{MVA parameter space}
For the geometry and kinematics MVA is calibrated 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}
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\section{Background}
\subsection{SM background}


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

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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 has been written.
It takes into account of the factors from the NA60 experiment.
\newline arXiv:1108.0968
\begin{center}
 \includegraphics[scale=0.23]{old_new.png}

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


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

There are 3 possibilities to deal with the 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}
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\subsection{Results}
\begin{frame}\frametitle{Results}

\begin{center}

As mentioned before I can't give the number. Please see slides from FPCP conference.

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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 completely different from that used in the B factories. We are cutting the phase space. 
\item Looking for particular model of decay could increase our sensitivity. Need MC generators for that.




\end{itemize}

Thank you for your attention.

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