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\title{ $\tau$ Physics at $\tau$ - $c$ factory }
\author{Alberto Lusiani, Marcin Chrz\k{a}szcz}
\institute[SNS, INFN, IFJ]



\date{30th November 2012}

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%                           Introduction
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\begin{document}


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\section[Outline]{}
\begin{frame}
\tableofcontents
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%                          Section 1
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\section{$\Upsilon(4S)$ vs $\Psi(3770)$ in $\tau$ sector}

\begin{frame}\frametitle{$\Upsilon(4S)$ vs $\Psi(3770)$ in $\tau$ sector}
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        \circled{1} $\tau \overline{\tau}$ cross section
        	\begin{itemize}
        	\item  $\sigma_{\tau \overline{\tau}}(m_{\tau \overline{\tau}})=0.1 nb$
        	\item  $\sigma_{\tau \overline{\tau}}(\Upsilon(4S))=0.9 nb$
        	\item  $\sigma_{\tau \overline{\tau}}(\Upsilon(2S))=2.5 nb$
        	\item  	 $\sigma_{\tau \overline{\tau} MAX}(4.25 \GeV)=3.5 nb$
        	\end{itemize}
      \hspace{1cm} 
       	 \colorbox{white}{\color{blue}   $\sigma_{\tau \overline{\tau}}=\dfrac{4 \Pi \alpha^{2}}{3s} \dfrac{3\beta -\beta^{2}}{2}$,} 
 \hspace{1cm}
 		{\newline	 $\beta$ velocity of $\tau$  }
                  
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 \only<2>{
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        \circled{2} SuperB $75 ab^{-1}$:
        	\begin{itemize}
        	\item  Number of $\tau \overline{\tau}$ produced:
        	$0.9nb \times 75 ab^{-1} = 6.8 \times 10^{10}$
        	
        	\end{itemize}
        	 \circled{3} $\tau - c$ factory $7.5 ab^{-1} $:
        	 
        	\begin{itemize}
        	\item  Number of $\tau \overline{\tau}$ produced:
	          $3 \times 7.5 ab^{-1} = 2.3 \times 10^{10}$	
        	
        	\end{itemize}
                  
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  \textref{A.Lusiani, M.Chrz\k{a}szcz 2012}
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\section{Lepton Flavour Violation(LFV)}
\begin{frame}\frametitle{Current Status of LFV}

\begin{block}{}
        \circled{1} Theoretical considerations:
        	\begin{itemize}
        	\item LFV predicted in many NP models(SUSY, Majorana neutrinos).
        	\item In SM negligibly small $\mathcal{B}<10^{-54}$  \footnote{T.P Cheng, L.Li, Phys. Rev. Lett. 45 (1980) 1908}.
        	\item Any observation clear sign of NP.
        	\end{itemize}	
        \circled{2} Experimental status:   
       	   	\begin{itemize}
        	\item Limits for LFV channels set by BaBar, Belle and Cleo in range of $10^{-7} - 10^{-8}$ depending on the decay channel.
        	\item Most promising channels: $\tau \to \mu \gamma$ and $\tau \to 3 \mu$.
        	\end{itemize}	  
                  
    \end{block}



  \textref{A.Lusiani, M.Chrz\k{a}szcz 2012}
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\subsection{$\tau \to \mu \gamma$ at $\tau -c$ factory }
\begin{frame}\frametitle{$\tau \to \mu \gamma$  at $\tau -c$ factory }
SM background for $\tau \to \mu \gamma$ :
\begin{itemize}
\item $\tau \to \mu \gamma \nu_{\mu} \nu_{\tau}$
\item $\tau \to \pi \pi^{0} \nu_{\tau}$
\item $\tau\tau \to \mu  \nu_{\mu} \nu_{\tau} + \pi \pi^{0} \nu_{\tau} \to \mu \gamma \pi^{+}\gamma \mu_{\nu} \nu_{\tau}\nu_{\overline{\tau}}$
\item Initial state radiation: $e^{+} e^{-} \to \tau \overline{\tau} \gamma$
\item Initial state radiation: $e^{+} e^{-} \to \mu \overline{\mu} \gamma$
\end{itemize}
ISR strongly suppress the the sensitivity in $\mathcal{B}$ factories.
  \textref{A.Lusiani, M.Chrz\k{a}szcz 2012}
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\begin{frame}\frametitle{Suppression ISR at charm threshold}
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\color{red}{$E_{\gamma}$ FSR}


\hspace{1cm}   \color{black}{$E_{\gamma} \tau \to \mu \gamma$}
\\
ISR vanishes for $E \approx 4 GeV $

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\begin{center}
\includegraphics[scale=0.2 ]{pic/ISF.png}
\end{center}

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  \textref{A.Lusiani, M.Chrz\k{a}szcz 2012}
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\begin{frame}\frametitle{Expected sensitivity for $\tau \to \mu \gamma$}

From MC studies \footnote{A.V. Bobrov, A.E Boundar, arxiv: 1206.1909} one can estimate the background in the $\mathcal{c} - \tau$ factory using KK2F with TAUOLA generator.
\begin{center}
\includegraphics[scale=0.18 ]{pic/idiots.png}
\end{center}
A full data set of $7.5 ab^{-1}$ is sufficient to put an exclusion limit on  $\tau \to \mu \gamma$ of order of $10^{-9}$.


  \textref{A.Lusiani, M.Chrz\k{a}szcz 2012}
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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%


\section{QCD probe}
\begin{frame}\frametitle{Probe QCD}

\begin{itemize}
\item Using analytical constraints and the Operator Product Expansion one can compute ration between harmonic and leptonic decays:
\newline $R_{\tau} \equiv \dfrac{\Gamma( \tau \to \nu hadrons(\gamma)) }{\Gamma( \tau \to e \nu_{\tau} \nu_{e})} = R_{\tau, V} + R_{\tau, A}+ R_{\tau, S}$
\item Which can be further devided to contributions coming form different quarks and currents:
$R_{\tau} \equiv \dfrac{\Gamma( \tau \to \nu hadrons(\gamma)) }{\Gamma( \tau \to e \nu_{\tau} \nu_{e})} =  R_{\tau, V} + R_{\tau, A}+ R_{\tau, S}$
\item Theoretical prediction can be wrote in a form:
$R_{\tau, V+A}=N_{c} \vert V_{ud} \vert^{2} S_{EW}(1+\delta_{P}+\delta_{NP})$ \footnote{W.A. Rolke and A.M. Lopez, Nucl. Instr. Meth. in Phys. Res. A458, 745 (2001).}
\item Biggest correction comes from $\delta_{P}$.


\end{itemize}

  \textref{A.Lusiani, M.Chrz\k{a}szcz 2012}
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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%5
\section{CP Violation}
\begin{frame}\frametitle{CP Violation}
\begin{itemize}
\item CP violation in $\tau$ sector is becoming a popular subject in light that the CKM matrix cannot explain matter-antimatter asymmetry.
\item Much more decay modes than in $\mu$ sector.
\item Possible contributions from charge Higgs at loop level.
\end{itemize}
The most promising channel is: $\tau \to K_{s} \pi \nu$
\begin{enumerate}
\item SM in 3rd loops generates asymmetry.
\item Numerical studies showed that NP can contribute in $1\%$
\item Expected sensitivity with full data set is expected to be of the order of  $0.01\%$

\end{enumerate} 




  \textref{A.Lusiani, M.Chrz\k{a}szcz 2012}
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