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% title slide definition
\title{Updates on $\eta$ treatment in $\tau \to \mu \mu \mu$}
\author{Marcin Chrz\k{a}szcz}
\institute[Institute of Nuclear Physics]
{
Institute of Nuclear Physics,
\newline Polish Academy of Science
}



\date{\today}

%--------------------------------------------------------------------
%                           Introduction
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\begin{document}


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  \titlepage
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\section[Outline]{}
\begin{frame}
\tableofcontents
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%-------------------------------------------------------------------
%                          Section 1
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\section{Limit studies}
\subsection{Present status}
\begin{frame}\frametitle{Where are we?}

 \vspace{1.1cm}
\begin{columns}
\column{2.0in}
 \begin{itemize}
 \item $5 \times 5$ bins in PID and GEO. 
 \item $4 \times 4$ have meaning according to binning optimisation.
 \item ''Trash bins'' are rejected in the binning optimisation procedure.
 \item ''Trash bins'' have unfortunately SM background.
 \end{itemize}

\column{3.0in}
\includegraphics[scale=0.26]{pic/pid_-1_-0p25geo0p55_0p75.png}
\end{columns} 
\begin{exampleblock}{To be, or not to be: that is the question.}
{
Do we really need the trash bin and what is the impact on the limit?
}
\end{exampleblock}


  
  \textref{M.Chrz\k{a}szcz 2012}
\end{frame}

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%55
\subsection{Throwing away garbage}
\begin{frame}\frametitle{Throwing away garbage}
 \vspace{1.1cm}
To fully evaluate the impact of trash bins on the limit:
\begin{itemize}
\item Kick off all trash bins.
\item New $\alpha$ from Paul
\item Calculate the limit again(with the same script!) with and without garbage.
\end{itemize}
Results:
\begin{itemize}	
  \item Expected limit with garbage: $8.18 \times 10^{-8}$.
  \item Expected limit w/o garbage: $8.21 \times 10^{-8}$.
  	\end{itemize}
\begin{exampleblock}{Conclusion}
{
Let's once and for always take out the garbage.
}
\end{exampleblock}
\textref{M.Chrz\k{a}szcz 2012}
\end{frame}


\subsection{Problem!}
\begin{frame}\frametitle{Problem}
 \vspace{1.1cm}
Unfortunately even tho the expected limit doesn't change:
\begin{columns}\column{2.5in}
\includegraphics[scale=0.26]{pic/trash_banana.png}
Observed limit: $6.33 \times 10^{-8}$
\column{2.5in}
\includegraphics[scale=0.26]{pic/no_trash_banana.png}
Observed limit: $7.89 \times 10^{-8}$


\end{columns}
\textref{M.Chrz\k{a}szcz 2012}
\end{frame}






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


\section{Getting ride of $\eta$ }
\subsection{$\eta$ contamination }
\begin{frame}\frametitle{$\eta$ contamination}
 \vspace{0.5cm}
In the note you can find the updated table with eta contribution in each bin. 
\newline The only change was that I changed R form $R=0.1748$ to $R=0.1798$. 
The discrepancy remains between me and Marta.
\begin{tiny}
\begin{columns}
\column{2.5in}

\begin{tabular}{|c|c|c|c|}
\hline
\textbf{PID} & \textbf{GEO}  & \textbf{Marta} & \textbf{Me} \\\hline 

 \\\hline 
 $ -1.1,  -0.25$ & $ -1.1,  0.05$ & $ 36.63 $ & $  58.4975$   \\\hline    
 $ -1.1,  -0.25$ & $ 0.05,  0.35$ & $ 21.38 $ & $  27.776$  \\\hline    
 $ -1.1,  -0.25$ & $ 0.35,  0.55$ & $ 18.58 $ &  $  21.8781$ \\\hline    
 $ -1.1,  -0.25$ & $ 0.55,  0.75$ & $ 14.05. $ &  $  14.0586$   \\\hline    
 $ -1.1,  -0.25$ & $ 0.75,  1.00001$ & $ 0$  & $  0$   \\\hline    
 $ -0.25,  -0.125$ & $ -1.1,  0.05$ & $  35.24$  & $  35.557$   \\\hline    
 $ -0.25,  -0.125$ & $ 0.05,  0.35$ & $ 32.92$  & $  33.1856$   \\\hline    
 $ -0.25,  -0.125$ & $ 0.35,  0.55$ & $ 44.97$  & $  45.4749$  \\\hline    
 $ -0.25,  -0.125$ & $ 0.55,  0.75$ & $ 11.77$  & $  11.7761$   \\\hline    
 $ -0.25,  -0.125$ & $ 0.75,  1.00001$ & $ 2.12$  & $  2.11926$   \\\hline    
 $ -0.125,  -0.025$ & $ -1.1,  0.05$ & $ 60.09$  & $  60.3985$   \\\hline    
 $ -0.125,  -0.025$ & $ 0.05,  0.35$ & $ 83.36$ & $  85.07$   \\\hline    
 $ -0.125,  -0.025$ & $ 0.35,  0.55$ & $ 75.04 $  & $  75.0836$   \\\hline    
 $ -0.125,  -0.025$ & $ 0.55,  0.75$ & $ 35.01 $  & $  35.2021$   \\\hline    
 $ -0.125,  -0.025$ & $ 0.75,  1.00001$ & $ 5.61 $  & $  5.61795$   \\\hline    
 $ -0.025,  0.05$ & $ -1.1,  0.05$ & $ 35.39 $  & $  35.7631$   \\\hline    
 $ -0.025,  0.05$ & $ 0.05,  0.35$ & $ 58.80$ & $  59.245$   \\\hline    
 $ -0.025,  0.05$ & $ 0.35,  0.55$ & $ 45.13 $  & $  45.155$  \\\hline    
\hline
\end{tabular} 


\column{2.5in}
\begin{tabular}{|c|c|c|c|}
\hline
\textbf{PID} & \textbf{GEO}  & \textbf{Marta} & \textbf{Me} \\\hline 

 $ -0.025,  0.05$ & $ 0.55,  0.75$ & $ 44.68$  & $  44.9531$  \\\hline    
 $ -0.025,  0.05$ & $ 0.75,  1.00001$ & $ 3.98$  & $  3.98138$   \\\hline    
 $ 0.05,  1$ & $ -1.1,  0.05$ & $ 10.65$  & $  10.6573$   \\\hline    
 $ 0.05,  1$ & $ 0.05,  0.35$ & $ 15.58$  & $  15.5424$   \\\hline    
 $ 0.05,  1$ & $ 0.35,  0.55$ & $ 14.88$  & $  14.888$   \\\hline    
 $ 0.05,  1$ & $ 0.55,  0.75$ & $ 13.48$  & $  13.5751$   \\\hline    
 $ 0.05,  1$ & $ 0.75,  1.00001$ & $ 0.805$  & $  0.80517$\\\hline    
\hline

\end{tabular} 
Comments:
\begin{itemize}
\item Marta's ''low'' bins have always less events. ''High'' bins are ok.
\item Maybe one file is missing?
\item My script(plug and play):
\newline \href{http://nz11-agh1.ifj.edu.pl/public_users/mchrzaszcz/tau23mu/Per_Marta/}{CLIC}.
\item I think in the end this will not matter(next slides).
\end{itemize}
\end{columns}

\end{tiny}

\textref{M.Chrz\k{a}szcz 2012}
\end{frame}


\subsection{Dalitz}
\begin{frame}\frametitle{Dalitz}
 \vspace{1.1cm}
\begin{Large}  EVERYWHERE I APPLIED STANDARD VETOES AND CUTS \end{Large}
\newline Let's look into Dalitz plots of $\eta$ and signal MC.

\begin{columns}\column{2.5in}
\includegraphics[scale=0.12]{pic/ds_all_bins.png}
\newline $ D_{s} \to \eta \mu \nu$
\column{2.5in}
\includegraphics[scale=0.12]{pic/mc_tau_allbins.png}
\newline $ \tau \to \mu \mu \mu$
\end{columns}

Looks like this can be used.
But here comes a problem: How to evaluate the cut?


\textref{M.Chrz\k{a}szcz 2012}
\end{frame}

\begin{frame}\frametitle{Data after stripping}
 \vspace{1.1cm}

\begin{columns}\column{2.5in}
\includegraphics[scale=0.12]{pic/mc_tau_allbins.png}
\newline $ \tau \to \mu \mu \mu$
\column{2.5in}
\includegraphics[scale=0.12]{pic/str_all.png}
\newline Stripping data.
\end{columns}


\textref{M.Chrz\k{a}szcz 2012}
\end{frame}



\begin{frame}\frametitle{\begin{normalsize}''Learn from yesterday, live for today, hope for tomorrow'', A.Einstein \end{normalsize}}
 \vspace{1.1cm}
The Dalitz may be different in different mass windows:


\begin{columns}\column{2.5in}
\includegraphics[scale=0.12]{pic/mc_tau_allbins.png}
\newline $ \tau \to \mu \mu \mu$
\column{2.5in}
\includegraphics[scale=0.12]{pic/str_signal_window.png}
\newline Stripping data in signal window.
\end{columns}

Looks promising. But this is sample that has ''potentially'' signal. Where to get a calibration sample?

\textref{M.Chrz\k{a}szcz 2012}
\end{frame}


\subsection{Calibration sample}
\begin{frame}\frametitle{Calibration sample}
 \vspace{1.1cm}
We have unused space =)


\center \includegraphics[scale=0.3]{pic/windows.png}



\textref{M.Chrz\k{a}szcz 2012}
\end{frame}

\begin{frame}\frametitle{Calibration sample}
Study to determine how big can we have the calibration sample:
\begin{itemize}
\item Changing the size \textcolor{purple}{purple} of the purple mass windows.
\item Fit (simple exponent this time) and calculate the new PDF. 
\item Calculate the limit expected limit(no systematics).
\end{itemize}

Results: 

 Changing the window from $\pm 15 to \pm50$ changes makes the limit fluctuate by: $\pm0.05$.

 Conclusion:
 We can use this data =)
\textref{M.Chrz\k{a}szcz 2012}
\end{frame}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%5
\begin{frame}\frametitle{Calibration sample vs signal window}


\begin{columns}\column{2.5in}
\includegraphics[scale=0.11]{pic/dalitz_control_left_side.png}
\newline Mass: $(M_{\tau}-40, M_{\tau}-20)$
\column{2.5in}
\includegraphics[scale=0.25]{pic/dalitz_control_right_side.png}
\newline Mass: $(M_{\tau}+20, M_{\tau}+40)$
\end{columns}
To be compared with:
\includegraphics[scale=0.08]{pic/str_signal_window.png}

Looks good =)
\textref{M.Chrz\k{a}szcz 2012}
\end{frame}












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


\subsection{Tricks and tips}
\begin{frame}\frametitle{Tricks and tips}
 \vspace{1.1cm}
Are we really interested in removing $\eta$ in all bins? 
As a rule of thumb I choosd the bins in which we have expected $\eta$ more than $10\%$ of all events. You will end up with bins:

\center \includegraphics[scale=0.3]{pic/good_bins.png}

From now this bins I will call ''high bins''


\textref{M.Chrz\k{a}szcz 2012}
\end{frame}





\subsection{TMVA for $\eta$}
\begin{frame}\frametitle{TMVAing}
 \vspace{1.1cm}
Using data in high bins train MLP:

\center \includegraphics[scale=0.3]{pic/roc.png}

Very efficient!

\textref{M.Chrz\k{a}szcz 2012}
\end{frame}



\begin{frame}\frametitle{TMVAing}
 \vspace{1.1cm}

\begin{columns}\column{2.5in}
\includegraphics[scale=0.25]{pic/MPL_ds_good_bins.png}
\newline \center $D_{s}$
\column{2.5in}
\includegraphics[scale=0.25]{pic/MLP_tau_good_bins.png}
\newline \center $\tau$
\end{columns}

 Looks promising =)
\textref{M.Chrz\k{a}szcz 2012}
\end{frame}



\begin{frame}\frametitle{Cut}
 \vspace{1.1cm}

A good cut is found to be: $0.92$. Removes $90\%$ of $\eta$  

To Do:

\begin{itemize}
\item calculate eff from calibration sample
\item calculate $\alpha$ and new limit
\item pray that it will be better
\end{itemize}



\textref{M.Chrz\k{a}szcz 2012}
\end{frame}


\end{document}
