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\author{ {\fontspec{Trebuchet MS}Marcin Chrz\k{a}szcz} (Universit\"{a}t Z\"{u}rich)}
\institute{UZH}
\title[Update of Method of Moments in $\PBzero \to \PKstar \Pmuon \APmuon$]{Update of Method of Moments in $\PBzero \to \PKstar \Pmuon \APmuon$}
\date{25 September 2014}


\begin{document}
\tikzstyle{every picture}+=[remember picture]

{
\setbeamertemplate{sidebar right}{\llap{\includegraphics[width=\paperwidth,height=\paperheight]{bubble2}}}
\begin{frame}[c]%{\phantom{title page}}
\begin{center}
\begin{center}
	\begin{columns}
		\begin{column}{0.75\textwidth}
			\flushright\fontspec{Trebuchet MS}\bfseries \Huge {Update of \\ Method of Moments \\in $\PBzero \to \PKstar \Pmuon \APmuon$}
		\end{column}
                \begin{column}{0.02\textwidth}
                  {~}
                  \end{column}
                \begin{column}{0.23\textwidth}
                 % \hspace*{-1.cm}
                  \vspace*{-3mm}
                  \includegraphics[width=0.6\textwidth]{lhcb-logo}
                  \end{column}

	\end{columns}
\end{center}
	\quad
	\vspace{3em}
\begin{columns}
\begin{column}{0.44\textwidth}
\flushright \vspace{-1.8em} {\fontspec{Trebuchet MS} \Large Marcin Chrząszcz\\\vspace{-0.1em}\small \href{mailto:mchrzasz@cern.ch}{mchrzasz@cern.ch}}

\end{column}
\begin{column}{0.53\textwidth}
\includegraphics[height=1.3cm]{uzh-transp}
\end{column}
\end{columns}

\vspace{1em}
%		\footnotesize\textcolor{gray}{With N. Serra, B. Storaci\\Thanks to the theory support from M. Shaposhnikov, D. Gorbunov}\normalsize\\
\vspace{0.5em}

	\textcolor{normal text.fg!50!Comment}{Referee meeting, CERN\\August 19, 2015}
\end{center}
\end{frame}
}



\begin{frame}{MoM - where do we stand?}
$\Rrightarrow$ From last time the only remaining issue as far as we saw was the calculation of $P_i$ from $S_i$ observables.\\
$\Rrightarrow$ Today we give some of the methods that we studied and explain what we would like to do.


\end{frame}



\begin{frame}[c]{Jacobian transformation }
\begin{itemize}
\item Now how does the new space look like.
\item Important to take into account the boundary as without all my theorems fall down.
\item The white point is the value from which the toy was generated.
\end{itemize}
\begin{center}

\begin{columns}
\column{2.5in}
\begin{small}
Scatter plot $F_L:P_2$, no Jacobian
\end{small}

\column{0.5in}
{~}
\column{2.2in}

\begin{small}
Scatter plot $F_L:P_2$, with Jacobian
\end{small}

\end{columns}
\includegraphics[width=1.1\textwidth]{images/2DZ2.png}

\end{center}

\end{frame}


%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame}\frametitle{Re parametrization of pdf}



\begin{itemize}
\item Re parametrization of the pdf gives exactly the same answer as toys taking into account the jacobian:
\end{itemize}
{~}\\{~}\\

\begin{columns}
\column{2.5in}
\begin{small}
Profile likelihood from re-parametrised pdf.
\end{small}
\includegraphics[width=0.9\textwidth]{images/LL_pdf.png}
\column{2.5in}
\begin{small}
Profile likelihood from toys with Jacobian
\end{small}
\includegraphics[width=0.9\textwidth]{images/LL_toys.png}
\end{columns}

\end{frame}



%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame}\frametitle{Profile likelihoods}

\includegraphics[width=0.9\textwidth]{images/profile.png}\\{~}\\
$\Rrightarrow$ Gives the same answer as the Jacobian.


\end{frame}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame}\frametitle{Quantiles}                                     
\begin{itemize}                                                         
\item Apparently quantiles stay invariant under transformations....     
\item One can just calculate the $68\%$ around the median.              
\item This is our prefered option.                                    
\end{itemize}                                                           
\only<1>{                                                               
\includegraphics[angle=-90,width=0.23\textwidth]{images/S9_4.0_5.0.pdf} 
\includegraphics[angle=-90,width=0.23\textwidth]{images/S5_4.0_5.0.pdf} 
\includegraphics[angle=-90,width=0.23\textwidth]{images/S8_4.0_5.0.pdf} 
\includegraphics[angle=-90,width=0.23\textwidth]{images/S7_4.0_5.0.pdf} 
}                                                                       
\only<2>{                                                               
\includegraphics[angle=-90,width=0.23\textwidth]{images/P5_4.0_5.0.pdf} 
\includegraphics[angle=-90,width=0.23\textwidth]{images/P4_4.0_5.0.pdf} 
\includegraphics[angle=-90,width=0.23\textwidth]{images/P3_4.0_5.0.pdf} 
\includegraphics[angle=-90,width=0.23\textwidth]{images/P2_4.0_5.0.pdf} 
}                                                                       
                                                                        
                                                                        
\end{frame}                                                             


\begin{frame}\frametitle{Unphysical values of $F_L$}   
$\Rrightarrow$ One of the problems is that for some cases $F_L$ goes beyond $1$. This might be a problem for some of the $P_i$ (ex. $P_5 = \frac{S_5}{\sqrt{F_L (1-F_L)}}$.\\
{~}
$\Rrightarrow$ We propose to put thouse bootstraps in the $\pm \infty$:

\includegraphics[width=0.9\textwidth]{images/p1.png}


\end{frame}   


\begin{frame}\frametitle{Conclusions}

\begin{itemize}
\item We have all the numbers in the note.
\item We decided to use the Quantiles for error propagation.
\item If referees agree with this we would like to get this aproved.

\end{itemize}
 


\end{frame} 




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



\backupbegin

\begin{frame}\frametitle{Backup}
\topline

\end{frame}

\backupend

\end{document}
