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\author{ {\fontspec{Trebuchet MS}Marcin Chrz\k{a}szcz} (Universit\"{a}t Z\"{u}rich)}
\institute{UZH}
\title[Partial moments for $\PBzero \to \PKstar \Pmuon \APmuon$]{Partial moments for $\PBzero \to \PKstar \Pmuon \APmuon$}
\date{4 August 2015}


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		\begin{column}{0.9\textwidth}
			\flushright\fontspec{Trebuchet MS}\bfseries \Huge {Partial moments for $\PBzero \to \PKstar \Pmuon \APmuon$}  
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		  %\includegraphics[width=\textwidth]{SHiP-2}
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	\quad
	\vspace{3em}
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\flushright \vspace{-1.8em} {\fontspec{Trebuchet MS} \Large Marcin Chrząszcz\\\vspace{-0.1em}\small \href{mailto:mchrzasz@cern.ch}{mchrzasz@cern.ch}}

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\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}{Zurich meeting, CERN\\August 4, 2015}
\end{center}
\end{frame}
}

\iffalse
\begin{frame}[c]{Deriving amplitudes}
\topline
	\begin{minipage}{\textwidth}
\topline  
One can write the amplitude:
\begin{equation}
\mathcal{A}(\PB \to \PKstar (\to \PK \Ppi) \Pphoton_J (\Pmuon \Pmuon)) \sim  \sum_{-J_{K}}^{J_{K}} \bar{D}^{J_K}_{\lambda,0}  \bar{D}^{J_{\gamma}}_{\lambda,\lambda_l}  \mathcal{A}_{\lambda, \lambda_1, \lambda_2}^{J_{\gamma}}
\end{equation}
Skipping the math because don't have time to latex all of this things. Here is the full moments:
\begin{
		
	\end{minipage}
		\vspace*{2.cm}
\end{frame}
\fi


\begin{frame}[c]{Full moments}
\begin{itemize}
\item Work based on {\it{arXiv:1506.03970}} by Roman Zwicky and James Gratex.
\item So to make long story short: if there is a discrepancy between MoM and LL due to physics missmodeling we should see it in the higher and partial moments.
\item Let's work in Romans framework of notation:
\end{itemize}

\begin{align}
I_{\PKstar}=\Re [ G^{00}_0 \Omega^{00}_0 + G^{01}_0 \Omega^{01}_0 + G^{02}_0 \Omega^{02}_0 \\ + G^{20}_0 \Omega^{20}_0 + G^{21}_0 \Omega^{21}_0 + G^{21}_1 \Omega^{21}_1 \\ + G^{22}_0 \Omega^{22}_0+  G^{22}_1 \Omega^{22}_1 +  G^{22}_2 \Omega^{22}_2 ,
\end{align}
where 
\begin{align}
\Omega^{l_K, L_l}_m=  \bar{D}^{l_K}_{m,0} \bar{D}^{l_l}_{m,0}
\end{align}
\begin{itemize} 
\item This basis is just a linear combination of what we use in the paper. Nothin really fancy here.
\end{itemize}    

\end{frame} 


\begin{frame}[c]{Partial moments}    
\begin{itemize}
\item Now the fun begins, when you leave one angle to float.
\item We can define:
\end{itemize}

\begin{equation}
l_m^{l_{k}} \sim \sum_{l_{l}} \bar{D}^{l_l}_{m,0}
\end{equation}                

The $\bar{D}^{l_l}_{m,0}$ function depends here only on $\theta_K$ and $\phi$. 
\begin{itemize}  
\item Why is this importnant?
\end{itemize}
Beacuse on of thouse moments is euqal just to $S_{6c}$. And remember :
\begin{columns}
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\includegraphics[width=0.9\textwidth, angle=-90]{images/S6c_NC_4.0_5.0.pdf}
\column{1.in}                                                     
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\column{1.in}                                                     
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\column{1.in}                                                     
\includegraphics[width=0.9\textwidth, angle=-90]{images/S6c_NC_7.0_8.0.pdf}  


\end{columns}


\end{frame}                                                                 
              
\begin{frame}[c]{Partial moments toy studies}  
\begin{itemize}                    
\item I run some toys last night.
\item The results look very promissing: On the raw moments the error on partial moments is smaller then on the normal moments.
\item One needs to do the math but looks like we can gain sensitivity to certain observables.
\end{itemize} 

\begin{columns}
\column{2.5in} 
\includegraphics[width=0.9\textwidth]{images/K111re.png}
\column{2.5in}
\includegraphics[width=0.9\textwidth]{images/G200re.png}

 \end{columns}  


\end{frame}   

                                                                                                                                                              
\begin{frame}[c]{Conclusions}
\begin{itemize}
\item Work just started.
\item Need to do all the math $\rightarrow$ there might be many more relations :)
\item If this turn out to gain any sensitivity to certain observables, this will be a super fast paper.
\end{itemize}


\end{frame}  




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