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\title[$\PBzero \to \PKstar \mu\mu$ update]{$\PBzero \to \PKstar \mu\mu$ update}
\author{Marcin Chrz\k{a}szcz$^{1}$}
\institute{$^1$~University of Zurich}
\date{\today}

\begin{document}
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\frame[plain]{\titlepage}
\author{Marcin Chrz\k{a}szcz{~}}
\institute{(UZH)}
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\begin{frame}\frametitle{Reminder}
\begin{itemize}
\item Last time I show you how to get the $P_x$ distributions by simulating the bifurcated Gaussian.
\item Now how to get the mean and error on this distribution.
\end{itemize}



\end{frame}

\begin{frame}\frametitle{Basics}
\begin{itemize}
\item We cannot just take the expected $S_x$ and expected $F_l$ and calculate: $P_x =\dfrac{S_x}{\sqrt{F_l(1-F_l)}}$ to get expected $P_x$.
\item This will work only for Gaussian distributions(but not for bifurcated).
\item Proposal: Fit a parabola in range $[-0.5 \rm{RMS}, 0.5\rm{RMS}]$
\item Get the mean.
\end{itemize}
\begin{columns}
\column{2.5in}
\includegraphics[width=0.95\textwidth]{images/P1.pdf}
\column{2.5in}
\includegraphics[width=0.95\textwidth]{images/P5.pdf}

\end{columns}




\end{frame}

 \begin{frame}\frametitle{Confidence interval}
 \begin{small}
 

\begin{itemize}
\item Now just need to find the $68.27\%$ interval.
\item Draw a horizontal line $y=y_{max} \times 0.9$
\item Iterate among all bins and select bins with events that have $y_{i~bin}>y$.
\item Find $y_{68}$ for which $68.27\%$ have the property$\sum y_{i~bin>y_{68}}=0.6827 $
\item Find the two spots where the $y_{68}$ line crosses the distribution. 
\item With current statistics I have $\mathcal{O}(10^{-4}$ error on the input $S_x$ and $\mathcal{O}(10^{-3})$ on output $P_x$. I am not a pharmacist and don't need more.
\end{itemize}
 \end{small}
\begin{columns}
\column{2.5in}
\includegraphics[width=0.95\textwidth]{images/P1.pdf}
\column{2.5in}
\includegraphics[width=0.95\textwidth]{images/P5.pdf}

\end{columns}


\end{frame}
              
      \begin{frame}\frametitle{Systematics}
 \begin{small}
 

\begin{itemize}
\item To access systematics due to unfolding procedure we use the higher($+2$) order acceptance correction function on high statistics MC.
\item I noticed that some of the weights ($1/eff$) are super large ($>100$) or even negative which fucks up our distributions and creates larger systematics then it should be.
\item Repeated this study rejecting this events.
\end{itemize}
 \end{small}
\begin{tiny}
\begin{tabular}{|c|c|c|c|c|c|c|c|c|}
$q^2$ & $F_l$ & $S_3$ & $S_4$ & $S_5$ & $S_6$ & $S_7$ & $S_8$ & $S_9$ \\ \hline
0 & 0.0022 & 0.005 & 0.0003 & 0.0077 & 0.00664993 & 0.00805836 & 0.000222794 & 0.00325143 \\ 
1 & 0.0048 & 0.001 & 0.0014 & 0.0051 & 0.0088697 & 0.00362942 & 0.00485902 & 0.000377345 \\ 
2 & 0.0004 & 0.0001 & 0.00013 & 0.0056 & 0.00466685 & 0.00142986 & 0.000377415 & 0.00220193 \\ 
3 & 0.0002 & 0.0012 & 0.0007 & 0.0017 & 6.60946e-05 & 0.00167783 & 0.00110383 & 0.00211203 \\ 
4 & 0.002 & 0.0004 & 0.0005 & 0.0015 & 0.000386727 & 0.000966386 & 0.000230578 & 0.00101049 \\ 
5 & 0.006 & 0.0011 & 0.0007 & 0.0026 & 0.00147745 & 0.00164066 & 0.00157731 & 0.000490769 \\ 
6 & 0.008 & 0.0019 & 0.0008 & 0.0024 & 0.0029359 & 0.00333371 & 0.00191923 & 1.9902e-05 \\ 
7 & 0.0062 & 0.0015 & 0.0002 & 0.0011 & 0.00369644 & 0.00283867 & 0.00161656 & 0.000536357 \\ 
8 & 0.0035 & 0.0037 & 0.0017 & 0.0046 & 0.00378288 & 0.000535576 & 0.00400356 & 0.00407972 \\ 
9 & 0.005 & 0.0001 & 0.0004 & 0.0010 & 0.000953251 & 0.00501146 & 0.00438955 & 0.00337069 \\ 
10 & 0.0011 & 0.0044 & 0.002 & 0.0060 & 0.00595211 & 0.0101793 & 3.03904e-05 & 0.00129358 \\ 
11 & 0.0021 & 0.0018 & 0.0001 & 0.0020 & 0.000494505 & 0.00524494 & 0.00823059 & 0.00597133 \\ 

\end{tabular}
\end{tiny}


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