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%\beamersetuncovermixins{\opaqueness<1>{25}}{\opaqueness<2->{15}}
\title{Toy MC Results}  
\author{\underline{Marcin Chrzaszcz}$^{1,2}$, Nicola Serra$^{1}$}
\date{\today} 

\begin{document}

{
\institute{$^1$ University of Zurich, $^2$ Institute of Nuclear Physics}
\setbeamertemplate{footline}{} 
\begin{frame}
\logo{
\vspace{2 mm}
\includegraphics[height=1cm,keepaspectratio]{images/uzh.jpg}~
\includegraphics[height=1cm,keepaspectratio]{images/ifj.png}}

  \titlepage
\end{frame}
}
\institute{UZH,IFJ} 

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

\section{Debugging MC}
\begin{frame}\frametitle{Plan}
\begin{enumerate}
\item Before we begin to explore the TOY MC let's see if we understand.
\item To X-Check:
\begin{enumerate}
\item Check EOS SM parameters.
\item Check unfolding.
\end{enumerate}
\item Test various methods with data bins and statistics

\end{enumerate}

\end{frame}


\subsection{SM parameters}
\begin{frame}\frametitle{Plan}
\begin{itemize}
\item Take the full MC(without acceptance) and fit + count events.
\item See if the results are consistent.
\item Here we just fit signal(\texttt{bkgcat==0})
\item In \textcolor{yellow}{yellow} $>3~\sigma$ fluctuations, \textcolor{red}{red} $>5~\sigma$ fluctuations,
 
\end{itemize}
\end{frame}


\begin{frame}\frametitle{$S_4$ results}


\begin{tiny}

\begin{center}
  \begin{tabular}{| c | c|  c | c | c | c | }
    \hline
$q^2$ & $S_4^{true}$ & $S_4^{fit}$ & $S_4^{fold}$  &  $S_4^{MM}$ \\  \hline \hline

$[0.1,1.0]$& $ -0.0884 $ & $ -0.0869  \pm 0.0009(1.6)$ & $-0.0874  \pm 0.0010 (1.0)$  &  $-0.0873 \pm 0.0010 (1.1)$ \\  \hline 

$[1.1,2.0]$& $-0.0481$ &  $-0.0447  \pm 0.0015(2.3)$ & $-0.0462  \pm 0.0017 (1.1)$  &  $-0.0477 \pm 0.0018 (0.2)$ \\  \hline 

$[2.0,3.0]$& $ 0.0480$ & $0.0465  \pm 0.0015(1.0)$ & $ 0.0476  \pm 0.0016 (0.25)$  &  $0.0478 \pm 0.0019 (0.1)$ \\  \hline 

$[3.0,4.0]$& $0.1255$ & $ 0.1229  \pm 0.0014(1.9)$  & $ 0.1253  \pm 0.0016 (0.1)$  &  $0.1262 \pm 0.0019 (0.4)$ \\  \hline 

$[4.0,5.0]$& $0.1765$ & $ 0.1731 \pm 0.0013 (2.6)$ & $0.1742  \pm 0.0015 (1.5)$  &  $0.1760 \pm 0.0018 (0.3)$ \\  \hline

$[5.0,6.0]$& $0.2089$ & $0.2058 \pm 0.0012 (2.3)$ &$ 0.2065  \pm 0.0015 (1.6)$  &  $0.2081 \pm 0.0017 (0.9)$ \\  \hline

$[6.0,7.0]$& $0.2295$ & $0.2279 \pm 0.0011 (1.5) $ & $ 0.2283  \pm 0.0014 (0.9)$  &  $0.2313 \pm 0.0016 (1.1) $ \\  \hline

$[7.0,8.0]$ & $0.2609$ & \textcolor{red}{$ 0.2422  \pm 0.0010 (18.7)$} & \textcolor{red}{$ 0.2428  \pm 0.0014 (13)$}  &  \textcolor{red}{$0.2441 \pm 0.0016 (10.5)$} \\  \hline

$[15.0,16.0]$ & $0.2822$ & $0.2820  \pm 0.0008 (0.3)$ & $ 0.2817  \pm 0.0012 (0.4)$ &  $0.2819 \pm 0.0014 (0.2)$ \\  \hline

$[16.0,17.0]$ & $0.2888$ & $ 0.2884  \pm 0.0008 (0.5)$ & $  0.2878  \pm 0.0013 (0.8)$  &  $0.2890 \pm 0.0015 (0.1)$ \\  \hline

$[17.0,18.0]$ & $0.2987$ & $0.2991 \pm 0.0008 (0.5)$ & $ 0.2987  \pm 0.0013 (0.0)$&  $0.2980 \pm0.0016 (0.4)$ \\  \hline

$[18.0,19.0]$ & $0.3139$ & $ 0.3152 \pm 0.0011(1.2)$ & $ 0.3150  \pm 0.0015 (0.7)$  &  $0.3156 \pm 0.0020 (0.85)$ \\  \hline
    \hline
  \end{tabular}
\end{center}


\end{tiny}
\end{frame}



\begin{frame}\frametitle{$S_5$ results}


\begin{tiny}

\begin{center}
  \begin{tabular}{| c | c|  c | c | c | c | }
    \hline
$q^2$ & $S_5^{true}$ & $S_5^{fit}$ & $S_5^{fold}$  &  $S_5^{MM}$ \\  \hline \hline

$[0.1,1.0]$& $0.2253 $ & $0.2238  \pm 0.0008 (1.9)$ & $0.2253  \pm 0.0009 (0.0)$  &  $0.2260 \pm 0.0009 (0.8)$ \\  \hline 
$[1.1,2.0]$& $0.1652 $ & $0.1673  \pm 0.0016 (1.3)$ & $0.1674  \pm 0.0016 (1.4)$  &  $0.1671 \pm 0.0018 (1.1)$ \\  \hline 
$[2.0,3.0]$& $-0.0287 $ & $ -0.0298  \pm 0.0016 (0.7)$ & $ -0.0301  \pm0.0017 (0.8)$  &  $-0.0300 \pm 0.0019 (0.7)$ \\  \hline 
$[3.0,4.0]$& $-0.1897$ & $ -0.1911  \pm 0.0015 (0.9) $ & $-0.1919  \pm 0.0016 (1.4)$  &  $-0.1891 \pm 0.0019 (0.3)$ \\  \hline 
$[4.0,5.0]$& $-0.2969 $ & $ -0.2966  \pm 0.0014 (0.2) $ & $-0.2971 \pm 0.0015 (0.1)$  &  $-0.2966 \pm 0.0018 (0.3)$ \\  \hline 
$[5.0,6.0]$& $-0.3654 $ & $ -0.3678  \pm 0.0013 (1.8) $ & $-0.3682 \pm 0.0014 (2.0)$  &  $-0.3700 \pm 0.0017 (2.7)$ \\  \hline 
$[6.0,7.0]$& $-0.4084 $ & $ -0.4089  \pm 0.0012 (0.4) $ & $-0.4092  \pm 0.0013 (0.6)$  &  $-0.4096 \pm 0.0016 (0.8)$ \\  \hline 
$[7.0,8.0]$& $-0.4113 $ & \textcolor{red}{$ -0.4356  \pm 0.0010  (24.3)$} & \textcolor{red}{$ -0.4364  \pm 0.0012 (21) $}  & \textcolor{red}{ $-0.4356 \pm 0.0015 (16)$} \\  \hline 
$[15.0,16.0]$& $-0.3654 $ & $ -0.3651  \pm 0.0008  (0.6)$ & $-0.3650 \pm 0.0011 (0.4)$  &  $-0.3646 \pm 0.0012 (0.3)$ \\  \hline 
$[16.0,17.0]$& $-0.3356 $ & $ -0.3347  \pm 0.0008  (1.1)$ & $-0.3349 \pm 0.0011 (0.6)$  &  $-0.3359 \pm 0.0013 (0.2)$ \\  \hline 
$[17.0,18.0]$& $-0.2911 $ & $ -0.2907  \pm 0.0009 (0.4) $ & $-0.2903 \pm 0.0013 (0.6)$  &  $-0.2896 \pm 0.0014 (1.1)$ \\  \hline 
$[18.0,19.0]$& $-0.2124 $ & $ -0.2153 \pm 0.0012 (2.4) $ & $-0.2152 \pm 0.0016 (1.8)$  &  $-0.2158 \pm 0.0018 (1.9)$ \\  \hline 



    \hline
  \end{tabular}
\end{center}


\end{tiny}
\end{frame}

\begin{frame}\frametitle{$S_7$ results}


\begin{tiny}

\begin{center}
  \begin{tabular}{| c | c|  c | c | c | c | }
    \hline
$q^2$ & $S_7^{true}$ & $S_7^{fit}$ & $S_7^{fold}$  &  $S_7^{MM}$ \\  \hline \hline

$[0.1,1.0]$& $0.0212 $ & $ 0.0206  \pm 0.0009 (0.7)$ & $0.0214  \pm0.0009 (0.2)$  &  $0.0208 \pm 0.0009 (0.4)$ \\  \hline 
$[1.1,2.0]$& $0.0386 $ & $ 0.0353  \pm 0.0016 (2.1)$ & $0.0352  \pm 0.0016 (2.1)$  &  $0.0348 \pm 0.0018 (2.1)$ \\  \hline 
$[2.0,3.0]$& $0.0379 $ & $ 0.0349  \pm 0.0016 (1.6) $ & $ 0.0351  \pm 0.0017 (1.6)$  &  $0.0353 \pm 0.0019 (1.4) $ \\  \hline 
$[3.0,4.0]$& $0.0341$ & $ 0.0365  \pm 0.0016 (0.5) $ & $0.0368  \pm 0.0017 (1.6)$ &  $0.0363 \pm 0.0019 (1.2)$ \\  \hline 
$[4.0,5.0]$& $0.0306 $ & $ 0.0293 \pm 0.0016 (0.8)$ & $0.0293  \pm 0.0016 (0.8)$  &  $0.0303 \pm 0.0018 (0.6)$ \\  \hline 
$[5.0,6.0]$& $0.0284 $ & $ 0.0261 \pm 0.0015 (1.5)$ & $ 0.0262  \pm 0.0016 (1.4)$  &  $0.0263 \pm 0.0018 (1.2)$ \\  \hline 
$[6.0,7.0]$& $0.0278 $ & $ 0.0282  \pm 0.0014 (0.3)$ & $0.0286  \pm 0.0015 (0.5)$  &  $0.0287 \pm 0.0017 (0.5)$ \\  \hline 
$[7.0,8.0]$& $0.0000 $ &\textcolor{red}{ $ 0.0293  \pm 0.0014 (20.9) $} & \textcolor{red}{$0.0290 \pm 0.0015 (19.3)$ } &  \textcolor{red}{$0.0287 \pm 0.0016 (18)$} \\  \hline 
$[15.0,16.0]$& $0.0000 $ & $ -0.0024  \pm 0.0013 (1.8) $ & $-0.0007 \pm 0.0014 (0.5)$  &  $-0.0008 \pm 0.0014 (0.6)$ \\  \hline 
$[16.0,17.0]$& $0.0000 $ & $ -0.0016  \pm 0.0014 (1.1) $ & $-0.0026 \pm 0.0015 (1.6)$  &  $-0.0026 \pm 0.0015 (1.7)$ \\  \hline 
$[17.0,18.0]$& $0.0000 $ & $ -0.0021 \pm 0.0015 (1.4) $ & $-0.0023  \pm 0.0016 (1.6)$  &  $-0.0021 \pm 0.0017 (1.2)$ \\  \hline 
$[18.0,19.0]$& $0.0000 $ & $ -0.0006  \pm 0.0019 (0.3) $ & $-0.0021 \pm 0.0021 (1.0)$ &  $-0.0015 \pm 0.0021 (0.6)$ \\  \hline

    \hline
  \end{tabular}
\end{center}


\end{tiny}
\end{frame}


\begin{frame}\frametitle{$S_8$ results}
\begin{tiny}
\begin{center}
  \begin{tabular}{| c | c|  c | c | c | c | }
    \hline
$q^2$ & $S_8^{true}$ & $S_8^{fit}$ & $S_8^{fold}$  &  $S_8^{MM}$ \\  \hline \hline

$[0.1,1.0]$& $-0.0038 $ & $-0.0061  \pm0.0010 (2.3) $ & $-0.0042  \pm0.0010 (0.4)$  &  $-0.0040 \pm 0.0010 (0.2)$ \\  \hline 
$[1.1,2.0]$& $-0.0107 $ & $ -0.0133  \pm 0.0015 (1.7)$ & $-0.0142  \pm 0.0017 (2.1)$  &  $-0.0135 \pm 0.0018 (1.5)$ \\  \hline 
$[2.0,3.0]$& $-0.0123 $ & $ -0.0141  \pm 0.0015 (1.2) $ & $-0.0144 \pm0.0017 (1.2)$  &  $-0.0149 \pm 0.0019 (0.3)$ \\  \hline 
$[3.0,4.0]$& $-0.0121$ & $ -0.0109  \pm 0.0016  (0.8)$ & $-0.0112  \pm 0.0016 (0.6)$  &  $-0.0117 \pm  0.0019 (0.2)$ \\  \hline 
$[4.0,5.0]$& $-0.0114 $ & $ -0.0125  \pm 0.0015  (0.8)$ & $-0.0123 \pm 0.0016 (0.6)$  &  $-0.0129 \pm 0.0018 (0.8)$ \\  \hline 
$[5.0,6.0]$& $-0.0110 $ & $ -0.0115  \pm 0.0015  (0.3)$ & $-0.0118  \pm 0.0016 (0.5)$  &  $-0.0115 \pm 0.0018 (0.3)$ \\  \hline 
$[6.0,7.0]$& $-0.0110 $ & $ -0.0104  \pm 0.0014  (0.4)$ & $-0.0110  \pm 0.0016 (0.0)$  &  $-0.0107 \pm 0.0017 (0.2)$ \\  \hline 
$[7.0,8.0]$& $0.0007 $ & \textcolor{red}{$ -0.0112  \pm 0.0013  (8.1)$} & \textcolor{red}{$-0.0112 \pm 0.0015 (7.0)$ } & \textcolor{red}{ $-0.0113 \pm 0.0016 (6.6)$} \\  \hline 
$[15.0,16.0]$& $0.0003 $ & $ 0.0006  \pm 0.0012  (0.3)$ & $-0.0015  \pm 0.0015 (0.8)$  &  $-0.0016 \pm 0.0015 (0.9)$ \\  \hline 
$[16.0,17.0]$& $0.0003 $ & $ -0.0023 \pm 0.0013  (0.8)$ & $-0.0020 \pm 0.0016 (1.1)$  &  $-0.0022 \pm 0.0016 (1.2)$ \\  \hline 
$[17.0,18.0]$& $0.0002 $ & $ 0.0009  \pm 0.0015  (0.5)$ & $0.0023  \pm 0.0018 (1.2)$  &  $0.0022 \pm 0.0018 (1.1)$ \\  \hline 
$[18.0,19.0]$& $0.0002 $ & $ -0.0019 \pm 0.0019  (0.9)$ & $-0.0007  \pm 0.0022 (0.2)$ &  $-0.0012 \pm- 0.0022 (0.5)$ \\  \hline
    \hline
  \end{tabular}
\end{center}
\end{tiny}

\end{frame}



\begin{frame}\frametitle{What is going on in that bin?}

\begin{itemize}
\item Following Einstein:
\end{itemize}
\begin{alertblock}{~}
A scientific person will never understand why he should believe opinions only because they are written in a certain book. \underline{Furthermore, he will never believe that the results 
 of his own attempts}  \underline{are final}.
   \end{alertblock}

\begin{itemize}
\item I start debugging my code.
\item After several hours I said to Einstein to go to hell and start debugging EOS

\end{itemize}
\end{frame}
\begin{frame}\frametitle{WTH is going on with $[7.0,8.0]$ ? 1/3}
\begin{itemize}
\item With those parameters from EOS the PDF is negative? <- checked , no
\item Some boundary conditions? <- checked by simulating my toy, no thing going on there.  
\item The parametrs that EOS gives you are not the one they simulated? <- YES!
\end{itemize}




\end{frame}

\begin{frame}\frametitle{WTH is going on with $[7.0,8.0]$ ? 2/3}
\begin{itemize}
\item First I simulated MY toy MC:
\end{itemize}
\begin{tiny}
\lstinputlisting[label=samplecode,caption=My unofficial MC:]{out.log}
\end{tiny}
\begin{itemize}
\item PDF is fine, can be fitted(here MM).
\end{itemize}


\end{frame}


\begin{frame}\frametitle{WTH is going on with $[7.0,8.0]$ ? 3/3}
\begin{itemize}
\item Let's say if the predictions are internally consistent!
\end{itemize}
\begin{tiny}

\lstinputlisting[label=samplecode,caption=TABLE from email:]{table1.log}
\end{tiny}


\end{frame}

\begin{frame}\frametitle{Conclusions part1}
\begin{itemize}
\item EOS gives wrong prediction to the last bin before $cc$ resonances region. 
\item Rest is consistent. 
\end{itemize}



\end{frame}

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\subsection{Check unfolding}


\begin{frame}\frametitle{More x-checks}
\begin{itemize}
\item Christoph also performed an unfolding.
\item He parametrized the acceptance corrections using $7^{th}$ order polynomials.
\item Also made a check of this.
\item On his official TOY MC
\item Reweighed events($1/\epsilon$) to get back the true distribution.
\item For details see \href{https://indico.cern.ch/event/290851/contribution/0/material/slides/0.pdf}{\underline{Christoph's talk}}




\end{itemize}





\end{frame}




\begin{frame}\frametitle{More x-checks}

\begin{columns}

\column{2.5in}
  \includegraphics[scale=0.15 ]{plots/SMcosthetak.png}
\column{2.5in}
\includegraphics[scale=0.15 ]{plots/SMcosthetak.png}


\end{columns}
\begin{columns}

\column{2.5in}
  \includegraphics[scale=0.15 ]{plots/SMphi.png}
\column{2.5in}
\includegraphics[scale=0.15 ]{plots/SMq2.png}


\end{columns}

\end{frame}



\begin{frame}\frametitle{More x-checks}
\begin{itemize}
\item Official TOY MC internally is consistent.
\item For sanity reasons, let's try the official MC.

\end{itemize}





\end{frame}


\begin{frame}\frametitle{Not good!}


\begin{columns}

\column{2.5in}
  \includegraphics[scale=0.15 ]{plots/lhcbcosthetak.png}
\column{2.5in}
\includegraphics[scale=0.15 ]{plots/lhcbcosthetal.png}


\end{columns}
\begin{columns}

\column{2.5in}
  \includegraphics[scale=0.15 ]{plots/lhcbphi.png}
\column{2.5in}
\includegraphics[scale=0.15  ]{plots/lhcbq2.png}


\end{columns}



\end{frame}



\begin{frame}\frametitle{Magic happens when i don't require $\PBzero$ trueID}


\begin{columns}

\column{2.5in}
  \includegraphics[scale=0.15 ]{plots/lhcb_NO_TRUTHcosthetak.png}
\column{2.5in}
\includegraphics[scale=0.15  ]{plots/lhcb_NO_TRUTHcosthetal.png}


\end{columns}
\begin{columns}

\column{2.5in}
  \includegraphics[scale=0.15  ]{plots/lhcb_NO_TRUTHphi.png}
\column{2.5in}
\includegraphics[scale=0.15  ]{plots/lhcb_NO_TRUTHq2.png}


\end{columns}
\end{frame}

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

\begin{frame}\frametitle{Unfolding conclusions}
\begin{itemize}
\item MC was not truth matched for unfolding!
\item Official TOY MC Internally is consistent but need to be careful for the future!
\end{itemize}


\end{frame}
\section{Results with toys}



%\subsection{Method of moments 1/3}
\begin{frame}\frametitle{Strategy 1/3}
\begin{itemize}
\item Divide the big OFFICIAL TOY MC in bins of $q^2$ that have number of events the same as data.
\item For each of them make fit and counting experiment.
\item See errors and pulls.

\end{itemize}
\end{frame}



\begin{frame}\frametitle{Strategy 2/3}
\begin{itemize}
\item To estimate number of signal and background events we fit the events:
\item For signal, I have assumed the PDF given by Christoph: \href{https://indico.cern.ch/event/290854/contribution/1/material/slides/0.pdf}{\underline{LINK}}
\item All parameters are for this pdf are fixed. 
\item For background I assume exponential, with free parameter.
\item In summary the fit has 3 free parameters, $n_{sig}$, $n_{bkg}$, $\lambda$. 
\item Fit is done in region $5170,5700MeV$.
\end{itemize}
\end{frame}



\begin{frame}\frametitle{Strategy 3/3}
To get Signal moments($S_x$) we do the following:
\begin{itemize}
\item Calculate background moments for $m$ in $(5350,5700)~MeV$
\item Calculate "mixed" moments for $m$ in $(5230,5330)~MeV$
\item Extract signal moments:\\
\end{itemize}

$S_{sig}=\dfrac{S_{mix} (n_{sig} + n_{bck}) }{n_{sig}} - \dfrac{ n_{bck} S_{bck} }{n_{sig}}$

\end{frame}




\begin{frame}\frametitle{Fits}
\begin{columns}
\column{2.5in}
\begin{itemize}
\item All fits converged without any problem
\item Got correlations Matrix.
\end{itemize}
\column{2.5in}
 \includegraphics[scale=0.12 ]{fits_MM/SM_Q2_0_265.png} \\
 \includegraphics[scale=0.12 ]{fits_MM/SM_Q2_11_1348.png}
\end{columns}


\end{frame}

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



\begin{frame}\frametitle{Pull plots S3}
\begin{columns}
\column{2.5in}
 \includegraphics[scale=0.15 ]{PLOTS_SM/Q2_0_S3.png} \\
 $Q^2 (0.1,1)$\\
 \includegraphics[scale=0.15 ]{PLOTS_SM/Q2_1_S3.png} \\
  $Q^2 (1.1,2)$\\
\column{2.5in}
 \includegraphics[scale=0.15 ]{PLOTS_SM/Q2_2_S3.png} \\
   $Q^2 (2,3)$\\
 \includegraphics[scale=0.15 ]{PLOTS_SM/Q2_3_S3.png}\\
    $Q^2 (3,4)$\\
  
\end{columns}


\end{frame}

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame}\frametitle{Pull plots S3}
\begin{columns}
\column{2.5in}
 \includegraphics[scale=0.15 ]{PLOTS_SM/Q2_4_S3.png} \\
 $Q^2 (4,5)$\\
 \includegraphics[scale=0.15 ]{PLOTS_SM/Q2_5_S3.png} \\
  $Q^2 (5,6)$\\
\column{2.5in}
 \includegraphics[scale=0.15 ]{PLOTS_SM/Q2_6_S3.png} \\
   $Q^2 (6,7)$\\
 \includegraphics[scale=0.15 ]{PLOTS_SM/Q2_7_S3.png}\\
    $Q^2 (7,8)$\\
  
\end{columns}

\end{frame}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame}\frametitle{Pull plots S3}
\begin{columns}
\column{2.5in}
 \includegraphics[scale=0.15 ]{PLOTS_SM/Q2_8_S3.png} \\
 $Q^2 (15,16)$\\
 \includegraphics[scale=0.15 ]{PLOTS_SM/Q2_9_S3.png} \\
  $Q^2 (16,17)$\\
\column{2.5in}
 \includegraphics[scale=0.15 ]{PLOTS_SM/Q2_10_S3.png} \\
   $Q^2 (17,18)$\\
 \includegraphics[scale=0.15 ]{PLOTS_SM/Q2_11_S3.png}\\
    $Q^2 (18,19)$\\
  
\end{columns}

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

\begin{frame}\frametitle{Pull plots S4}
\begin{columns}
\column{2.5in}
 \includegraphics[scale=0.15 ]{PLOTS_SM/Q2_0_S4.png} \\
 $Q^2 (0.1,1)$\\
 \includegraphics[scale=0.15 ]{PLOTS_SM/Q2_1_S4.png} \\
  $Q^2 (1.1,2)$\\
\column{2.5in}
 \includegraphics[scale=0.15 ]{PLOTS_SM/Q2_2_S4.png} \\
   $Q^2 (2,3)$\\
 \includegraphics[scale=0.15 ]{PLOTS_SM/Q2_3_S4.png}\\
    $Q^2 (3,4)$\\
  
\end{columns}


\end{frame}

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame}\frametitle{Pull plots S4}
\begin{columns}
\column{2.5in}
 \includegraphics[scale=0.15 ]{PLOTS_SM/Q2_4_S4.png} \\
 $Q^2 (4,5)$\\
 \includegraphics[scale=0.15 ]{PLOTS_SM/Q2_5_S4.png} \\
  $Q^2 (5,6)$\\
\column{2.5in}
 \includegraphics[scale=0.15 ]{PLOTS_SM/Q2_6_S4.png} \\
   $Q^2 (6,7)$\\
 \includegraphics[scale=0.15 ]{PLOTS_SM/Q2_7_S4.png}\\
    $Q^2 (7,8)$\\
  
\end{columns}

\end{frame}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame}\frametitle{Pull plots S4}
\begin{columns}
\column{2.5in}
 \includegraphics[scale=0.15 ]{PLOTS_SM/Q2_8_S4.png} \\
 $Q^2 (15,16)$\\
 \includegraphics[scale=0.15 ]{PLOTS_SM/Q2_9_S4.png} \\
  $Q^2 (16,17)$\\
\column{2.5in}
 \includegraphics[scale=0.15 ]{PLOTS_SM/Q2_10_S4.png} \\
   $Q^2 (17,18)$\\
 \includegraphics[scale=0.15 ]{PLOTS_SM/Q2_11_S4.png}\\
    $Q^2 (18,19)$\\
  
\end{columns}

\end{frame}




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

\begin{frame}\frametitle{Pull plots S5}
\begin{columns}
\column{2.5in}
 \includegraphics[scale=0.15 ]{PLOTS_SM/Q2_0_S5.png} \\
 $Q^2 (0.1,1)$\\
 \includegraphics[scale=0.15 ]{PLOTS_SM/Q2_1_S5.png} \\
  $Q^2 (1.1,2)$\\
\column{2.5in}
 \includegraphics[scale=0.15 ]{PLOTS_SM/Q2_2_S5.png} \\
   $Q^2 (2,3)$\\
 \includegraphics[scale=0.15 ]{PLOTS_SM/Q2_3_S5.png}\\
    $Q^2 (3,4)$\\
  
\end{columns}


\end{frame}

\begin{frame}\frametitle{Pull plots S5}
\begin{columns}
\column{2.5in}
 \includegraphics[scale=0.15 ]{PLOTS_SM/Q2_4_S5.png} \\
 $Q^2 (4,5)$\\
 \includegraphics[scale=0.15 ]{PLOTS_SM/Q2_5_S5.png} \\
  $Q^2 (5,6)$\\
\column{2.5in}
 \includegraphics[scale=0.15 ]{PLOTS_SM/Q2_6_S5.png} \\
   $Q^2 (6,7)$\\
 \includegraphics[scale=0.15 ]{PLOTS_SM/Q2_7_S5.png}\\
    $Q^2 (7,8)$\\
  
\end{columns}

\end{frame}
\begin{frame}\frametitle{Pull plots S5}
\begin{columns}
\column{2.5in}
 \includegraphics[scale=0.15 ]{PLOTS_SM/Q2_8_S5.png} \\
 $Q^2 (15,16)$\\
 \includegraphics[scale=0.15 ]{PLOTS_SM/Q2_9_S5.png} \\
 $Q^2 (16,17)$\\
\column{2.5in}
 \includegraphics[scale=0.15 ]{PLOTS_SM/Q2_10_S5.png} \\
 $Q^2 (17,18)$\\
 \includegraphics[scale=0.15 ]{PLOTS_SM/Q2_11_S5.png}\\
 $Q^2 (18,19)$\\
  
\end{columns}

\end{frame}


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

\begin{frame}\frametitle{Pull plots S6}
\begin{columns}
\column{2.5in}
 \includegraphics[scale=0.15 ]{PLOTS_SM/Q2_0_S6s.png} \\
 $Q^2 (0.1,1)$\\
 \includegraphics[scale=0.15 ]{PLOTS_SM/Q2_1_S6s.png} \\
  $Q^2 (1.1,2)$\\
\column{2.5in}
 \includegraphics[scale=0.15 ]{PLOTS_SM/Q2_2_S6s.png} \\
   $Q^2 (2,3)$\\
 \includegraphics[scale=0.15 ]{PLOTS_SM/Q2_3_S6s.png}\\
    $Q^2 (3,4)$\\
  
\end{columns}


\end{frame}

\begin{frame}\frametitle{Pull plots S6}
\begin{columns}
\column{2.5in}
 \includegraphics[scale=0.15 ]{PLOTS_SM/Q2_4_S6s.png} \\
 $Q^2 (4,5)$\\
 \includegraphics[scale=0.15 ]{PLOTS_SM/Q2_5_S6s.png} \\
  $Q^2 (5,6)$\\
\column{2.5in}
 \includegraphics[scale=0.15 ]{PLOTS_SM/Q2_6_S6s.png} \\
   $Q^2 (6,7)$\\
 \includegraphics[scale=0.15 ]{PLOTS_SM/Q2_7_S6s.png}\\
    $Q^2 (7,8)$\\
  
\end{columns}

\end{frame}
\begin{frame}\frametitle{Pull plots S6}
\begin{columns}
\column{2.5in}
 \includegraphics[scale=0.15 ]{PLOTS_SM/Q2_8_S6s.png} \\
 $Q^2 (15,16)$\\
 \includegraphics[scale=0.15 ]{PLOTS_SM/Q2_9_S6s.png} \\
  $Q^2 (16,17)$\\
\column{2.5in}
 \includegraphics[scale=0.15 ]{PLOTS_SM/Q2_10_S6s.png} \\
   $Q^2 (17,18)$\\
 \includegraphics[scale=0.15 ]{PLOTS_SM/Q2_11_S6s.png}\\
    $Q^2 (18,19)$\\
  
\end{columns}

\end{frame}


\begin{frame}\frametitle{Conclusions}
\begin{itemize}
\item Method of moments works perfectly with the TOY with our statistics.
\item No bias seen in toys.
\end{itemize}
\end{frame}



\subsection{Unfolding for method of moments}
\begin{frame}\frametitle{General way}

\begin{itemize}
\item The natural way of unfolding the method of moments is to reweigh events by $\frac{1}{\epsilon}$
\item Similar to likelihood the normalization doesn't matter.
\item Error is also calculated based on weights:
\end{itemize}
\begin{equation}
var=\dfrac{\sum_i w_i^2 \sigma_i}{(\sum_i w_i)^2}
\end{equation}

\end{frame}

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

\begin{frame}\frametitle{Pull plots S3}
\begin{columns}
\column{2.5in}
 \includegraphics[scale=0.15 ]{PLOTS_SM_ACC/Q2_0_S3_ACC.png} \\
 $Q^2 (0.1,1)$\\
 \includegraphics[scale=0.15 ]{PLOTS_SM_ACC/Q2_1_S3_ACC.png} \\
  $Q^2 (1.1,2)$\\
\column{2.5in}
 \includegraphics[scale=0.15 ]{PLOTS_SM_ACC/Q2_2_S3_ACC.png} \\
   $Q^2 (2,3)$\\
 \includegraphics[scale=0.15 ]{PLOTS_SM_ACC/Q2_3_S3_ACC.png}\\
    $Q^2 (3,4)$\\
  
\end{columns}


\end{frame}

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame}\frametitle{Pull plots S3}
\begin{columns}
\column{2.5in}
 \includegraphics[scale=0.15 ]{PLOTS_SM_ACC/Q2_4_S3_ACC.png} \\
 $Q^2 (4,5)$\\
 \includegraphics[scale=0.15 ]{PLOTS_SM_ACC/Q2_5_S3_ACC.png} \\
  $Q^2 (5,6)$\\
\column{2.5in}
 \includegraphics[scale=0.15 ]{PLOTS_SM_ACC/Q2_6_S3_ACC.png} \\
   $Q^2 (6,7)$\\
 \includegraphics[scale=0.15 ]{PLOTS_SM_ACC/Q2_7_S3_ACC.png}\\
    $Q^2 (7,8)$\\
  
\end{columns}

\end{frame}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame}\frametitle{Pull plots S3}
\begin{columns}
\column{2.5in}
 \includegraphics[scale=0.15 ]{PLOTS_SM_ACC/Q2_8_S3_ACC.png} \\
 $Q^2 (15,16)$\\
 \includegraphics[scale=0.15 ]{PLOTS_SM_ACC/Q2_9_S3_ACC.png} \\
  $Q^2 (16,17)$\\
\column{2.5in}
 \includegraphics[scale=0.15 ]{PLOTS_SM_ACC/Q2_10_S3_ACC.png} \\
   $Q^2 (17,18)$\\
 \includegraphics[scale=0.15 ]{PLOTS_SM_ACC/Q2_11_S3_ACC.png}\\
    $Q^2 (18,19)$\\
  
\end{columns}

\end{frame}

\begin{frame}\frametitle{Conclusions}
\begin{itemize}
\item Preliminary things look ok.
\item However we plan to use a matrix method for unfolding $\rightarrow$ smaller errors.
\end{itemize}

\end{frame}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\section{Fitting toys}

\begin{frame}\frametitle{Fitting strategy}
\begin{itemize}
\item Performed fit on folded data set.
\item Signal PDFs are like in 2011.
\item Background PDFs are $2^{nd}$ order Chebyshev.
\item PDF is parametrized:
\end{itemize}
$
PDF=PDF_{sig}(\cos \theta_k, \cos \theta_l, \phi) \times PDF_{sigm}(m) + PDF_{bkg}(\cos \theta_k, \cos \theta_l, \phi) \times PDF_{bkgm}(m)
$

\begin{itemize}
\item Fit the angles and mass in the full region
\end{itemize}
\end{frame}

\begin{frame}\frametitle{Fitting strategy}
\begin{itemize}
\item Performed fit on folded data set.
\item Signal PDFs are like in 2011.
\item Background PDFs are $2^{nd}$ order Chebyshev.
\item PDF is parametrized:
\end{itemize}
$
PDF=PDF_{sig}(\cos \theta_k, \cos \theta_l, \phi) \times PDF_{sigm}(m) + PDF_{bkg}(\cos \theta_k, \cos \theta_l, \phi) \times PDF_{bkgm}(m)
$

\begin{itemize}
\item Fit the angles and mass in the full region
\end{itemize}
\end{frame}


\begin{frame}\frametitle{Examp}
 \includegraphics[scale=0.35 ]{SM_Q2_4_995.png} 

\end{frame}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame}\frametitle{Pull plots S4}
\begin{columns}
\column{2.5in}
 \includegraphics[scale=0.15 ]{PLOTS_FOLDING/Q2_0_S4.png} \\
 $Q^2 (0.1,1)$\\
 \includegraphics[scale=0.15 ]{PLOTS_FOLDING/Q2_1_S4.png} \\
  $Q^2 (1.1,2)$\\
\column{2.5in}
 \includegraphics[scale=0.15 ]{PLOTS_FOLDING/Q2_2_S4.png} \\
   $Q^2 (2,3)$\\
 \includegraphics[scale=0.15 ]{PLOTS_FOLDING/Q2_3_S4.png}\\
    $Q^2 (3,4)$\\
  
\end{columns}


\end{frame}

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame}\frametitle{Pull plots S3}
\begin{columns}
\column{2.5in}
 \includegraphics[scale=0.15 ]{PLOTS_FOLDING/Q2_4_S5.png} \\
 $Q^2 (4,5)$\\
 \includegraphics[scale=0.15 ]{PLOTS_FOLDING/Q2_5_S5.png} \\
  $Q^2 (5,6)$\\
\column{2.5in}
 \includegraphics[scale=0.15 ]{PLOTS_FOLDING/Q2_6_S5.png} \\
   $Q^2 (6,7)$\\
 \includegraphics[scale=0.15 ]{PLOTS_FOLDING/Q2_7_S5.png}\\
    $Q^2 (7,8)$\\
  
\end{columns}

\end{frame}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame}\frametitle{Pull plots S3}
\begin{columns}
\column{2.5in}
 \includegraphics[scale=0.15 ]{PLOTS_FOLDING/Q2_8_S5.png} \\
 $Q^2 (15,16)$\\
 \includegraphics[scale=0.15 ]{PLOTS_FOLDING/Q2_9_S5.png} \\
  $Q^2 (16,17)$\\
\column{2.5in}
 \includegraphics[scale=0.15 ]{PLOTS_FOLDING/Q2_10_S5.png} \\
   $Q^2 (17,18)$\\
 \includegraphics[scale=0.15 ]{PLOTS_FOLDING/Q2_11_S5.png}\\
    $Q^2 (18,19)$\\
  
\end{columns}

\end{frame}



%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame}\frametitle{Conclusions of fitting}
\begin{itemize}
\item Preliminary I see small bias, and error problems in the fits. To be x-checked.
\item Need to check that unfolding doesn't do any harm.
\item Hight fail rate! To be investigated.
\end{itemize}

\end{frame}


%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame}\frametitle{Error summary}
\begin{columns}
\column{1.5in}
  \begin{tabular}{| c | c|  c |  }
    \hline
$q^2$ & $Err. S_5^{MM}$ & $Err. S_5^{fit}$  \\  \hline \hline
$0$ & $0.047$ & $0.044$ \\  \hline
$1$ & $0.093$ & $0.079$ \\  \hline
$2$ & $0.097$ & $0.080$ \\  \hline
$3$ & $0.099$ & $0.080$ \\  \hline
$4$ & $0.092$ & $0.072$ \\  \hline
$5$ & $0.091$ & $0.069$ \\  \hline
$6$ & $0.087$ & $0.063$ \\  \hline
$7$ & $0.074$ & $0.053$ \\  \hline
$8$ & $0.071$ & $0.058$ \\  \hline
$9$ & $0.072$ & $0.061$ \\  \hline
$10$ & $0.067$ & $0.072$ \\  \hline
$11$ & $0.088$ & $0.094$ \\  \hline

    \hline
  \end{tabular}
\column{2.0in}
\begin{itemize}
\item On average MM are $18\%$ worse here(improvement from 25\% reported by Christoph).
\item Still errors do not have full systematics. 
\item One expects the difference to shrink even more.
\end{itemize}

\end{columns}
\end{frame}


%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame}\frametitle{To do list}
Before the Easter:
\begin{itemize}
\item Do include unfolding inside the fits.
\item Repeat all the fits without folding.
\item Compare all numbers!
\end{itemize}

\end{frame}



\end{document}
