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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%\beamersetuncovermixins{\opaqueness<1>{25}}{\opaqueness<2->{15}}
\title{Update on $\tau \to \mu \mu \mu$ searches}  
\author{J.Albrecht$^1$, M.Calvi$^2$, \underline{M.Chrzaszcz}$^{3,4}$, L. Gavardi$^2$, J.Harrison$^5$,\\ B. Khanji$^2$,G. Lafferty$^5$, E. Rodrigues$^5$, N. Serra$^4$, P. Seyfert$^6$
}

%\date{\today} 
\begin{document}

{
\institute{$^1$ Dortmund, $^2$ Milano, $^3$ Zurich, $^4$ Krakow,\\ $^5$ Manchester, $^6$ Heidelberg}
\setbeamertemplate{footline}{} 
\begin{frame}
\logo{
\vspace{2 mm}
\includegraphics[height=1cm,keepaspectratio]{images/ifj.png}~
\includegraphics[height=1cm,keepaspectratio]{images/uzh.jpg}}

  \titlepage
\end{frame}
}

\institute{UZH,IFJ} 


\section[Outline]{}
\begin{frame}
\tableofcontents
\end{frame}

\begin{frame}\frametitle{Status}
\begin{columns}
\column{2in}
\begin{center}
$1 $fb$^{-1}$ analysis of  \textcolor{violet}{$\tau \to \mu \mu \mu$} and \textcolor{blue}{$\tau \to p \mu \mu$} appeared in PLB.

\end{center}


\column{3in}

 \includegraphics[scale=0.197]{RD_meeting/PLB.png}
\end{columns}

\begin{exampleblock}{2011 results:} \begin{enumerate}
\item Obtained limit for $\tau \to \mu \mu \mu$: $8.0 \times 10^{-8}$. 
\item Belle(BaBar) results: $2.1 (3.2) \times 10^{-8}$ at $90\%$ CL.
\item For 2012 + 2011 planned to implement several improvements.

\end{enumerate}
\end{exampleblock}


%	\textref {M.Chrz\k{a}szcz 2013}

\end{frame}

\section{MC Samples}

\begin{frame}\frametitle{Generated MC samples }
\only<1>
{

\begin{enumerate}
\item In 2011 analysis one of the biggest contributions to the systematic error from MC was the reweighting the MC signal for the correct cross section.
\item For 2012 we solved this problem by simulating signal in 5 parts. One for each production channel:
\end{enumerate}

}

\begin{center}

 \fcolorbox{blue}{yellow}{
%\begin{equation}NUmber of ne

$\tau \to \mu \mu \mu =  \begin{cases}
\PB \to \Ptau \to \mu \mu \mu     &   11.6\% \\
\PB \to \PDs \to \tau \to \mu \mu \mu &  8.7\% \\
\PB \to \PD \to \tau \to \mu \mu \mu & 0.2\% \\
\PDs \to \tau \to \mu \mu \mu & 75.0\% \\
\PD \to \tau \to \mu \mu \mu & 4.4\% \\

\end{cases}$
%\end{equation}

 }
% $\HepParticle{B}{}{\pm} \to \HepParticle{D}{}{(\ast)} \tau^{\pm} \nu$}
\end{center}

	%\textref {M.Chrz\k{a}szcz 2013}

\end{frame}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%55
\begin{frame}\frametitle{MC Generator Cuts}
\only<1>
{
In order to use computing resources in more efficient way we introduced generator level cuts.
\begin{center}
  \begin{tabular}{ | c | c || l | c |}
    \hline
    \multicolumn{2}{|c|| }{Signal sample\footnote{$X \to \tau\to 3\mu$, $\PDs \to \eta(\mu\mu \gamma) \mu \nu$, $\PDs \to \phi(\mu\mu) \pi$ }} & \multicolumn{2}{|c| }{Background sample(Dimuon)\footnote{$c\bar{c}$, $b\bar{b}$ }} \\ \hline \hline
    $p_{t\mu}$ & $>250MeV$ & $p_{t\mu}$ & $>280MeV$ \\ \hline
    $p_{\mu}$ & $>2.5GeV$ & $p_{\mu}$ & $>2.9GeV$ \\     \cline{3-4}  
    & & $m(\mu\mu)$ & $<4.5GeV$\\  \cline{3-4}  
    & & DOCA$(\mu\mu)$ & $<0.35mm$\\ \hline
  \end{tabular}
\end{center}
}
Gain a factor of $\sim 2-3$ in signal statistics compared to 2011.

	%\textref {M.Chrz\k{a}szcz 2013}

\end{frame}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame}\frametitle{Trigger lines}
\only<1>
{
In 2011 we took all trigger lines into account. Studies shown we can gain on limiting our self to specific lines (2011 data sample).


\begin{center}
  \begin{tabular}{| c | c | c | c | c | }
    \hline
    Line Name & $\epsilon [\%]$ & $\epsilon' [\%]$ & $\beta [\%]$ &  $\beta' [\%]$ \\ \hline \hline
  Hlt2CharmSemilepD2HMuMu & $81.7$ & $81.7$ & $56.8$ & $56.8$ \\ \hline
  Hlt2DiMuonDetached & $75.0$ & $12.5$ & $54.1$ & $17.6$ \\ \hline
  Hlt2TriMuonTau & $66.3$ & $2.9$ & $60.0$ & $12.2$ \\ \hline 
  Others & - & $2.2$ & - & $11.6$ \\ \hline
  \end{tabular}
	  
\end{center}
, where $\epsilon$ is the signal efficiency, $\epsilon'$ is the gain of the efficiency, $\beta$ is the efficiency of background and $\beta'$ is the gain of the bck efficiency\\

Rule of thumb (using Punzi FOM) tells us that we can gain $\mathcal{O}(5\%)$. 

}


	%\textref {M.Chrz\k{a}szcz 2013}

\end{frame}


%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%55
\section{Normalization}
\begin{frame}\frametitle{Normalization channel}
\only<1>
{
  As last year we will use \textcolor{blue}{$\PDs \to \phi(\mu\mu) \pi$}.Similar as signal channels we produced them with correct proportion:
 \begin{exampleblock}{~}
\begin{enumerate}
\item $cc \to \PDs \to \phi (\mu\mu) \pi$   $89.7\%$ 
\item $bb \to \PDs \to \phi (\mu\mu) \pi$   $10.3\%$
\end{enumerate}
\end{exampleblock}
We avoid reweighing of the samples as in 2011.
 
}

	%\textref {M.Chrz\k{a}szcz 2013}

\end{frame}
\begin{frame}\frametitle{Mass correction}
\only<1>
{
\begin{center}
\begin{tiny}
	\begin{columns}
\column{2.5in}
\begin{center}
	$D_s \to \phi(\mu\mu)\pi$ in data.\\
  \includegraphics[scale=0.13]{Ds_Mass/Ds_mass_data.png} \\
  \begin{itemize}
  \item mean = $1970.3 \pm 0.9 MeV$
  \end{itemize}
\end{center}

\column{2.5in}
\begin{center}
$D_s \to \phi(\mu\mu)\pi$ in MC.\\
 \includegraphics[scale=0.13]{Ds_Mass/D_mass_base.png}\\
   \begin{itemize}
  \item mean = $1969.1 \pm 0.60 MeV$
  \end{itemize}
\end{center}
\end{columns}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%5
	\begin{columns}
\column{2.5in}
\begin{center}
\begin{small}
   \begin{itemize}
  \item $m_{\tau \to 3\mu} = \dfrac{1970.3}{1969.1} \times 1777.7  =$\textcolor{blue}{$ 1778.8 \pm 1.1 MeV$}
  \end{itemize}
{~} \\ In agreement with 2011.
\end{small}
\end{center}


\column{2.5in}
\begin{center}
	Fit $\tau \to \mu\mu\mu$ in MC. \\
 \includegraphics[scale=0.11]{Ds_Mass/tau_mass_base.png}\\
%   \begin{itemize}
%  \item mean = $1777.7 \pm 0.4 MeV$ \\
%  \end{itemize} 
 
\end{center}
\end{columns}

\end{tiny}
\end{center}

}




	% \textref {M.Chrz\k{a}szcz 2013}

\end{frame}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame}\frametitle{Cross section update}
\only<1>
{
Analysis uses the knowledge of $c\overline{c}$ and $b\overline{b}$ cross sections. In 2011 both were measured by LHCb. For 2012 for the moment we assume:
\begin{itemize}
\item $\sigma_{b\overline{b}}^{8TeV}=298\pm36 \mu b$ form LHCB-PAPER-2013-016 
\item $\sigma_{c\overline{c}}^{8TeV}=\sigma_{c\overline{c}}^{7TeV}\times \dfrac{8}{7} = 6950 \pm 1100 \mu b$

\end{itemize}

\begin{exampleblock}{Cross checks on $c\overline{c}$} 

\begin{enumerate}
\item Comparing $D_s$ yields in data.
\item Pythia cross section calculation.
\end{enumerate}
\end{exampleblock}


}

	%\textref {M.Chrz\k{a}szcz 2013}

\end{frame}

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%5

\begin{frame}\frametitle{Background samples normalization}
\only<1>
{
	For the normalization of background samples($c\bar{c}$ and $b\bar{b}$) we used generator cuts efficiencies and corrected the nominal cross section accordingly:\\
	\begin{center}
 		$\mathcal{L} = \dfrac{N_{MC}}{\varepsilon_{acc} \times \varepsilon_{gen} \times \sigma_{LHCb}}$
 	\end{center}
The obtained luminosities(per 1M events):
\begin{exampleblock}{~}
\begin{enumerate}
\item $\mathcal{L}_{cc} = 0.25 \pm 0.04 pb^{-1}$
\item $\mathcal{L}_{bb} = 1.20 \pm 0.15 pb^{-1}$
 \end{enumerate}
 \end{exampleblock}
 
}
Dominant uncertainty from the cross section.


	% \textref {M.Chrz\k{a}szcz 2013}

\end{frame}




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

\section{Peaking backgrounds}
\begin{frame}\frametitle{$\PDs \to \eta(\mu \mu \gamma) \mu \nu$}
\only<1>
{
 \begin{exampleblock}{~}
\begin{enumerate}
\item The dominant background source of peaking background in this analysis is  \textcolor{blue}{$\PDs \to \eta(\mu\mu\gamma) \mu \nu$}\\
\item In 2011 we suffered from lack of MC statistics.
\item Thanks to generator cuts our pdfs became more stable.
 \end{enumerate}
 \end{exampleblock}

	\begin{columns}
\column{2.5in}
\begin{center}

  \includegraphics[scale=0.11]{RD_meeting/pid_0_65_0_725geo-0_48_0_05.png} \\
\begin{tiny} PID:$0.65;0.725$,GEO:$-0.48;0.05$ \end{tiny}
\end{center}

\column{2.5in}
\begin{center}
 \includegraphics[scale=0.11]{RD_meeting/pid_0_725_0_86geo0_35_0_65.png}\\
\begin{tiny} PID:$0.725;0.0.86$,GEO:$0.35;0.65$ \end{tiny}

\end{center}
\end{columns}
}

%	\textref {M.Chrz\k{a}szcz 2013}

\end{frame}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame}\frametitle{$D \to \Ph \Ph \Ph $}
\only<1>
{
In 2011 we saw a triple miss-ID background: $\PDp \to \PK \Ppi \Ppi$. Luckily this background was in trash-bins that were not used in the analysis. 

	\begin{columns}
\column{1.6in}
\begin{center}
 \includegraphics[scale=0.17]{images/pipipi_peak_2011.pdf}\\
     \begin{itemize}
  \item 2011 data
  \end{itemize}
\end{center}
\column{1.6in}
\begin{center}
 \includegraphics[scale=0.17]{images/pipipi_peak_2012.pdf}\\
      \begin{itemize}
  \item 2012 data
  \end{itemize}
\end{center}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%55
\column{1.6in}
\begin{center}
 \includegraphics[scale=0.19]{images/FittoDkpipi_2012.pdf}\\{~}\\
      \begin{itemize}
  \item 2012 data
  \end{itemize}
\end{center}


\end{columns}
{~}\\
In 2012 there is still no significant amount of triple mis-ID background in the bins important to the analysis.




}

%	\textref {M.Chrz\k{a}szcz 2013}

\end{frame}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%5




\section{MVA development}
\begin{frame}\frametitle{Isolating parameters}
{~}


\only<1>
{	

\begin{enumerate}

\item	In 2011 we used the isolation parameter developed for $\PBs \to \mu\mu$. For 2012 data we optimised the isolation parameter for our channel based on MVA(BDT).
\item We follow two approaches: train a MVA on signal vs. bkg tracks, and the isolating vs. non-isolating tracks.
\item We see big improvement compared to old isolation.
 \end{enumerate}
 }
	\begin{columns}
\column{1.6in}
\begin{center}

  \includegraphics[scale=0.15]{RD_meeting/mva_BDT.png} \\

\end{center}

\column{1.6in}
\begin{center}
 \includegraphics[scale=0.15]{RD_meeting/rejBvsS.png}\\

\end{center}

\column{1.6in}
\begin{center}
 \includegraphics[scale=0.15]{images/Laura/rejBvsS.png}\\

\end{center}

\end{columns}


	% \textref {M.Chrz\k{a}szcz 2013}

\end{frame}


\begin{frame}\frametitle{Ensemble Selection}
{~}
\only<1>
{	
\begin{exampleblock}{~}
\begin{enumerate}
\item In the last few years people winning leading machine learning contests started to combine their classifiers to squeeze the best out of them.
\item This technique/method is know as Ensemble Selection or Blending.
\item The plan for $\tau \to \mu \mu \mu$ is to take it to the next level.
\item Combine not only different signal sources, but also different $\tau$ sources(slide 4).
\item Allows for usage different isolating parameters for each channel.
 \end{enumerate}
 \end{exampleblock}	
		
}
\only<2>
{

	\begin{columns}
\column{1.6in}
\begin{center}
  \includegraphics[scale=0.15]{RD_meeting/rejBvsS_21513000.png}\\
   \begin{itemize}
  \item $\PB \to \PD \to \tau$
  \end{itemize}
\end{center}

\column{1.6in}
\begin{center}
 \includegraphics[scale=0.15]{RD_meeting/rejBvsS_21513001.png}\\
    \begin{itemize}
  \item $\PD \to \tau$
  \end{itemize}
\end{center}

\column{1.6in}
\begin{center}
 \includegraphics[scale=0.15]{RD_meeting/rejBvsS_23513000.png}\\
     \begin{itemize}
  \item $\PB \to \PDs \to \tau$
  \end{itemize}
\end{center}


%\column{2.5in}
%\begin{center}
% \includegraphics[scale=0.15]{RD_meeting/rejBvsS_23513001.png}\\
%      \begin{itemize}
 % \item $\PDs \to \tau$
%  \end{itemize}
%\end{center}
\end{columns}


}
\only<3>{

%	\begin{columns}
%\column{2.5in}
%	  \includegraphics[scale=0.2]{RD_meeting/rejBvsS_oryginal.png}
%	\column{2.5in}
%		  \includegraphics[scale=0.2]{RD_meeting/rejBvsS_blend.png}
%	\end{columns}



\begin{center}
  \includegraphics[scale=0.3]{images/BDT_comparison.png}
\end{center}
}


%	\textref {M.Chrz\k{a}szcz, N.Serra 2013}

\end{frame}

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%5555
\section{Binning optimisation}

\begin{frame}\frametitle{Binning optimisation}
{~}
\only<1>
{	
For the 2011 analysis we had two classifiers: $PIDNN$ and $M_{GEO}$. Each of them we optimised separately. For the 2012 analysis we are performing a simultaneous 2D optimisation.

	\begin{columns}
\column{2.5in}


	  \includegraphics[scale=0.13]{inflaton/punzi1.png}
	    \begin{itemize}
  \item FOM as a function of N. of bins.
  \end{itemize}
	\column{2.5in}
		  \includegraphics[scale=0.27]{RD_meeting/2d-data.pdf}
	    \begin{itemize}
  \item Signal efficiency in 2011 binning.
  \end{itemize}
	\end{columns}
	
}

\end{frame}

\section{Model dependence}
\begin{frame}\frametitle{Model dependence}
\begin{exampleblock}{Minimal Lepton Flavour Violation Model\footnote{arXiv:0707.0988}}
\begin{itemize}
\item In effective-field-theory we introduce new operators that at electro-weak scale are compatible with $SU(2)_L \times U(1)$.
\item Left handed lepton doublets add right handed lepton singlets follow the group symmetry: $G_{LF} = SU(3)_L \times SU(3)_E$.
\item LFV arises from breaking this group.
\item We focus on three operators that have dominant contribution to NP:
\begin{enumerate}
\item Purely left handed iterations: $(\overline{L} \gamma_{\mu} L)(\overline{L} \gamma^{\mu} L)$
\item Mix term: $(\overline{R}\gamma_{\mu} R)(\overline{L} \gamma^{\mu} L)$
\item Radiative operator: $g'(\overline{L}H\sigma_{\mu\nu}R)B^{\mu\nu}$
\end{enumerate}
\end{itemize}
 \end{exampleblock}	

\end{frame}


\begin{frame}\frametitle{Reweighting  MC samples}
\only<1>{
\begin{center}
\begin{columns}
\column{2.5in}
{~}Reconstruction:\\
	{~}\includegraphics[scale=0.22]{images/acceptance.png}

\column{2.5in}
Offline:\\
	 \includegraphics[scale=0.22]{images/offline.png}


\end{columns}
\end{center}
}

\only<2>{
\begin{center}
\begin{columns}
\column{1.6in}
{~}$(\overline{L} \gamma_{\mu} L)(\overline{L} \gamma^{\mu} L)$\\
	{~}\includegraphics[scale=0.22]{images/gammallll.png}

\column{1.6in}
$(\overline{R}\gamma_{\mu} R)(\overline{L} \gamma^{\mu} L)$\\
	 \includegraphics[scale=0.22]{images/gammallrr.png}
\column{1.6in}
$g'(\overline{L}H\sigma_{\mu\nu}R)B^{\mu\nu}$\\
	 \includegraphics[scale=0.22]{images/gammarad.png}

\end{columns}
\end{center}
}

\begin{equation}
\epsilon_{gen\&rec} = C\epsilon^{LHCbMC}_{gen\&rec} \sum \rho^{model}(m_{12},m_{23})
\end{equation}

\only<1>{
\begin{itemize}
\item Simulated signal events with PHSP
\item Take into account reconstruction and selection.
\item Reweigh accordingly to a given distribution.
\end{itemize}


}


\only<2>{
\begin{itemize}
\item Simulated signal events with PHSP
\item Take into account reconstruction and selection.
\item Reweigh accordingly to a given distribution.
\end{itemize}


}

\end{frame}











\section{Conclusions}

\begin{frame}\frametitle{Conclusions}
{~}
\only<1>
{	
\begin{exampleblock}{~}
\begin{enumerate}
\item Analysis is well underway.
\item More efficient use of computing resources and increased MC
      statistics helps at all ends
\item Hope to improve the selection.
%\item $\tau \to p \mu \mu$ mode will be studied in parallel.
 \end{enumerate}
 \end{exampleblock}	
}
 \includegraphics[scale=0.4]{RD_meeting/phd052805.png}\\



\end{frame}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

\begin{frame}
{~}
\begin{Huge}
BACKUP
\end{Huge}


\end{frame}


%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%55

\begin{frame}\frametitle{$B \to \tau$}
{~}\\
We really suck in selecting this channel.

\includegraphics[scale=0.4]{tmva/ROC_31113002.png}



	% \textref {M.Chrz\k{a}szcz 2013}
\end{frame}

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%5
\begin{frame}\frametitle{$B \to D_s \to \tau$}
{~}\\
On the biggest contributing channel we are quite optimal.


\includegraphics[scale=0.4]{tmva/ROC_23513000.png}



	% \textref {M.Chrz\k{a}szcz 2013}
\end{frame}

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%5
\begin{frame}\frametitle{$D_s \to \tau$}
{~}\\
On the biggest contributing channel we are quite optimal.


\includegraphics[scale=0.4]{tmva/ROC_23513001.png}



	%\textref {M.Chrz\k{a}szcz 2013}
\end{frame}

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%5
\begin{frame}\frametitle{$B \to D^+ \to \tau$}
{~}\\
On the biggest contributing channel we are quite optimal.


\includegraphics[scale=0.4]{tmva/21513000_roc2.png}



	% \textref {M.Chrz\k{a}szcz 2013}
\end{frame}

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%5
\begin{frame}\frametitle{$D^+ \to \tau$}
{~}\\
On the biggest contributing channel we are quite optimal.


\includegraphics[scale=0.4]{tmva/ROC_21513001.png}



	%\textref {M.Chrz\k{a}szcz 2013}
\end{frame}

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%5

\begin{frame}\frametitle{Comparison on mix sample}
{~}\\
On the biggest contributing channel we are quite optimal.


\includegraphics[scale=0.4]{tmva/mix.png}



	%\textref {M.Chrz\k{a}szcz 2013}
\end{frame}

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%5


%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%5
\begin{frame}\frametitle{Conclusions on TMVA}
{~}\\
\begin{itemize}
\item Each of the signal components is enormously larger than MVA trained on mix.
\item Method looks very promising if we can find a nice blending method(work for next week).
\item Mayby discusion on TMVA/MatrixNet/Neurobayes is next to leading order effect compared to this method?


\end{itemize}


%	\textref {M.Chrz\k{a}szcz 2013}
\end{frame}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%5
\begin{frame}\frametitle{Comparison on mix sample}
{~}\\
	\begin{columns}
\column{2.5in}


	  \includegraphics[scale=0.27]{RD_meeting/rejBvsS_oryginal.png}
	
	\column{2.5in}
		  \includegraphics[scale=0.27]{RD_meeting/rejBvsS_blend.png}

	\end{columns}


	%\textref {M.Chrz\k{a}szcz 2013}
\end{frame}



\end{document}