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\title[1D Bose-Einstein correlations]{1D Bose-Einstein correlations}
\author{Marcin Chrz\k{a}szcz$^{1}$}
\institute{$^1$~University of Zurich}
\date{\today}

\begin{document}
% --------------------------- SLIDE --------------------------------------------
\frame[plain]{\titlepage}
\author{Marcin Chrz\k{a}szcz{~}}
\institute{(UZH)}
% ------------------------------------------------------------------------------
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\begin{frame}\frametitle{Fast reminder}

\begin{columns}
\column{2.8in}
\begin{itemize}
\item HBT interferometry can be used to study the diameters of source.
\item For indistinguishable particles the phenomena is know as Bose-Einstein Correlations(BEC).
\item BEC correlations occur as enhancement of same particles in the low $Q$ region.
\item We already observed the effects.
\item For now I want to make BEC for pions, kaons are for future(less statistics).
\item Use 2011 sample.
\end{itemize}

\column{2.2in}
\includegraphics[height=3.cm,keepaspectratio]{images/HBT.png}

\end{columns}
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\end{frame}


\begin{frame}\frametitle{Pre-Selection}
\begin{center}
\begin{tabular}{|c|c|}
\hline
 &  Cut \\
\hline
\hline
track $\chi^{2}$ & $< 2.6$ GeV \\
\hline
track momentum & $> 3.0$ GeV \\
\hline
track $p_{T}$ & $> 0.1$ GeV \\
\hline
track IP & $< 0.2 \rm ~mm$ \\
\hline
track IP $\chi^{2}$ & $< 2.6$ \\
\hline
PID NN (pion, kaon) & $> 0.25$ \\
\hline
track probability to be a ghost  & $< 0.3$ \\
\hline
\end{tabular}
\end{center}

\end{frame}  


\begin{frame}\frametitle{Selection}

\begin{Large}
Hard cuts, as we have enough statistics.
\end{Large}

\begin{center}

\begin{tabular}{|c|c|}
\hline
 &  Cut \\
\hline
\hline
PID NN (pion, kaon)\footnote{No double counting with this cut} & $> 0.9$ \\
\hline
track IP & $< 0.05 \rm ~mm$ \\
\hline
track IP $\chi^2$ & $< 2$ \\
\hline
track probability to be a ghost  & $< 0.2$ \\
\hline
n. PV  & $== 1$ \\
\hline
\end{tabular}

\end{center}
\end{frame}  


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\begin{frame}\frametitle{How to measure correlations?}

\begin{itemize}
\item Define a correlations function:
\end{itemize}
\begin{equation}
C(q_1, q_2) = \dfrac{\rho(q_1, q_2)}{\rho(q_1) \rho(q_2)}
\end{equation}
\begin{itemize}
\item There are many kinematic variables where BEC can occur. Canonical choice $Q=\sqrt{-(q_1 -q_2)^2}$.
\item $\rho(q_1, q_2)$ is easy. For each pair of same sign particles calculate Q and plot.
\item $\rho(q_1) \rho(q_2)$ is a bit more tricky. One way is to take opposite sign particles or mix events. Both by construction kill the BEC effects.
\end{itemize}



\end{frame}  


\begin{frame}\frametitle{Opposite sign}

\begin{columns}
\column{2.5in}
$Q$ Distribution.
\includegraphics[width=0.9\textwidth]{images/q2.png}


\column{2.5in}
$C(q_1, q_2)$ Distribution.
\includegraphics[width=0.9\textwidth]{images/corr.png}

\end{columns}

\begin{itemize}
\item Here I just took $1\%$ of data not to bias myself afterwards.
\end{itemize}


\end{frame}  



\begin{frame}\frametitle{Mix sample}

\begin{columns}
\column{2.5in}
$Q$ Distribution.
\includegraphics[width=0.9\textwidth]{images/q2.png}


\column{2.5in}
$C(q_1, q_2)$ Distribution.
\includegraphics[width=0.9\textwidth]{images/corr.png}

\end{columns}

\begin{itemize}
\item Here I just took $1\%$ of data not to bias myself afterwards.
\end{itemize}


\end{frame}  



              
\end{document}