\section{Dataset}

The data used in the analysis was collected at the \lhcb experiment in the year 2011, which corresponds to an integrated luminosity of $1\invfb$ recorded at a centre-of-mass energy $\sqs = 7\tev$.

Three different decay channels are considered in this analysis.
\begin{itemize}
	\item \Btojpsikpipimumu : a control channel that is used to correct for the largest discrepancies between data and simulation. 
	\item \Btojpsikpipiee : the normalisation channel which is used for some minor kinematic corrections.
	\item \Btokpipiee : the signal mode under study.
\end{itemize}

\subsection{Signal simulation}

The Monte Carlo simulated samples (MC) are generated using \pythia8 with a specific \lhcb configuration\cite{LHCb-PROC-2010-056}. An average number of \proton\proton interactions per bunch crossing\footnote{This also includes the number of not visible (for the detector) interactions and is therefore only used in the context of simulated events.} of 2 is used and a constraint is applied on the generator level to limit the $\Kp\pip\pim$ invariant mass. In order to reduce possible systematic effects from the detector and surrounding, the magnetic polarity is switched during the data taking. Therefore also both magnetic polarities are generated and then merged.


\subsection{Stripping}

For the \jpsi resonant decays Stripping21r0p1 with the Bu2LLK line was used whereas for the rare decay Stripping20r1 was used. The cuts which are applied to the sample are listed in Table \ref{tab:stripping:electron_cuts}.


%\begin{table}[t]
%	\caption[Trigger requirements for candidates with electrons or muons in the final state.]{Trigger requirements for candidates with electrons (left) or muons (right) in the final state. The \texttt{TOS} and \texttt{TIS} requirements are referred to the mother particle.}
%	\begin{center}
%		\begin{tabular}{lll}
%			\hline
%			Trigger level & Electron candidates & Muon candidates \\
%			\hline
%			\texttt{L0} & \texttt{L0Electron TOS} & \texttt{L0Muon TOS} \\
%			& \texttt{L0Hadron TOS} & \\
%			& \texttt{L0Global TIS} & \\
%			\hline
%			\texttt{HLT1} & \texttt{Hlt1TrackAllL0 TOS} & \texttt{Hlt1TrackAllL0 TOS} \\
%			& & \texttt{Hlt1TrackMuon TOS} \\
%			\hline
%			\texttt{HLT2} & \texttt{Hlt2Topo2[3,4]BodyBBDT TOS} & \texttt{Hlt2Topo2[3,4]BodyBBDT TOS} \\
%			& \texttt{Hlt2TopoE2[3,4]BodyBBDT TOS} & \texttt{Hlt2TopoMu2[3,4]BodyBBDT TOS} \\
%			& & \texttt{Hlt2DiMuonDetached TOS}\\
%			\hline
%		\end{tabular}
%	\end{center}
%	\label{tab:Trigger}
%\end{table}

%The distribution of the events can depend on the category they were triggered by. All events from the different triggers are merged into one sample for this study.
%The three trigger categories are defined as follows:
%\begin{itemize}
%	\item \texttt{L0 Electron} contains candidates that are \texttt{TOS} with respect to the \texttt{L0 Electron} trigger line;
%	\item \texttt{L0 Hadron} contains candidates that are \texttt{TOS} with respect to the \texttt{L0 Hadron} trigger line and do not belong to the above category;
%	\item \texttt{L0 TIS} contains candidates that are \texttt{TIS} with respect to the \texttt{L0 Global} trigger line (that is, the corresponding event has been triggered by other particles) and do not belong to none of the two above categories.
%\end{itemize}
%It is additionally required that the particle triggering the \LzeroElectron (\LzeroHadron) trigger line is  a lepton (hadron). So events triggered by the \LzeroElectron and \LzeroHadron trigger line that have been hadrons and electrons, respectively, are removed from the samples.


\begin{table}[t]
	\caption[Stripping requirements]{Stripping requirements.}
	\begin{center}
		\begin{tabularx}{0.5\textwidth}{ll}
			\hline
			Object	& Requirement \\
			\hline
			Event 	& $N_\mathrm{PV} > 1$ \\
			& $n_{\spd} < 600$ \\
			\hline
			\kaon 	& \texttt{hasRICH} \\
			& $\dllkpi > -5$ \\
			& \chisqip PV $> 9$ \\
			& $\chisq_{track} < 3$ \\
			& $GhostProba < 0.4$ \\
			\hline
			\pion 	& \texttt{hasRICH} \\
			& \chisqip PV $> 9$ \\
			& $\chisq_{track} < 3$ \\
			& $GhostProba < 0.4$ \\
			\hline
			\electron & \texttt{hasCalo} \\
			& $\dllepi > 0$ \\
			& $\pt > 300$\mev \\
			& \chisqip PV $> 9$ \\
			\hline
			\muon 	& \texttt{isMuon} \\
			& $\pt > 300$\mev \\
			& \chisqip PV $> 9$ \\
			\hline
			\lepton\lepton & $m < 5500$\mev \\
			& \chisqvtxndf $<9$ \\
			& origin vertex \chisq separation $> 16$ \\
			\hline
			\B & $|m-m_\Bd^\mathrm{PDG}| < 1000$\mev \\
			& \texttt{DIRA} $> 0.9995$ \\
			& \chisqip PV $< 25$ \\
			& \chisqvtxndf $< 9$ \\
			& PV \chisq separation $> 100$ \\
			\hline
			$\kaon_1$ & $0 < m < 6000\mev$ \\
				& $\chisqvtx < 12$ \\
				& sum hadron $\pt > 800\mev$ \\
				& sum hadron $\chisqip > 48$ \\
			\hline
			
		\end{tabularx}
	\end{center}
	\label{tab:stripping:electron_cuts}
\end{table}




\subsection{Preselection}
\label{sec:preselection}

For this study, only the central \qsq region is analysed corresponding to $1 < m^2_{\epem} < 6\gev$. This is chosen in order to reduce the contribution from the resonant mode.

The signal candidates in this analysis are triggered by three different trigger categories and merged into one sample. The categories are exclusive and are evaluated in the following order:
\begin{itemize}
	\item \LzeroElectron\ requires events to be \TOS\ with respect to the \LzeroElectron\ trigger line.
	\item \LzeroHadron\ requires events to be \TOS\ with respect to the \LzeroHadron\ trigger line.
	\item \Lzero\ \TIS\ requires events to be \TIS\ with respect to the \LzeroGlobal\ trigger line and therefore to be triggered by other particles.
\end{itemize}

It is additionally required that the particle triggering the \LzeroElectron\ (\LzeroHadron) trigger line is  a lepton (hadron). So events triggered by the \LzeroElectron\ and \LzeroHadron\ trigger line that have been hadrons and electrons, respectively, are removed from the samples.

Finally, only events passing the \hltone as well as the \hlttwo trigger decision for TOS are kept.

With those requirements applied, still a sizeable amount of background is in our sample. To further remove that, a multivariate analysis (MVA) to discriminate between our signal and the combinatorial background is applied as described in Sect. \ref{sec:selection:mva}.
In order to be able to perform the MVA as well as to get an unbiased yield estimation later on, any physical background reaching into our region of interest has to be removed. Therefore strong preselection cuts are proposed as listed in Table \ref{tab:preselection}.


%define explanations
\def \chisqvtxndfexpl {Reconstruction quality of the vertex per number of degrees of freedom}
\def \chisqvtxexpl {Quality of the vertex reconstruction}
\def \ptexpl {Transverse momentum}
\def \chisqfdexpl {Significance of the flight distance with respect to the PV}

\def \firstghostprobaexpl{{Probability\tablefootnote{Probability to be a ghost obtained from a multivariate classifier trained on misreconstructed tracks and good tracks using information from different stages of the track reconstruction and global event properties.} that track is a ghost}}
\def \ghostprobaexpl{Probability obtained from a MVA algorithm that track is a ghost}
%\def \ghostprobaexpl {Probability to be a ghost obtained from a multivariate classifier trained on misreconstructed tracks and good tracks using information from different stages of the track reconstruction and global event properties.}
\def \amaxdocaexpl {Maximum distance of closest approach with all tracks}
\def \diraexpl {DIRection Angle; the cosine of the angle between the reconstructed momentum of the \Bu and its direction of flight.}
\def \chisqipexpl {Difference in the vertex-fit \chisq of a given PV reconstructed with and without the current track}
\def \thetaexpl {The angle $\theta$ is between the particles flight direction and the beam axis}
\newcommand{\probnnexpl}[1]{Neural network based particle identification probability to be a #1}
\newcommand{\probnn}[1]{$ProbNN_{#1}$}

\begin{table}[t]
	\caption{
		%\small %captions should be a little bit smaller than main text
		Preselection cuts}
	\begin{center}\begin{tabularx}{\textwidth}{lrlX}
			\hline
			Particle& Variable 		& Cut 		& Explanation      \\ 
			\hline
			\Bu		& \chisqvtxndf	& $<6$		& \chisqvtxndfexpl\\
			& AMAXDOCA		& $<4$		& \amaxdocaexpl\\
			& \pt		& $>3\gev$	& Transverse momentum\\
			& $DIRA$	& $>0.9998$	& \diraexpl\\
			& ${\chisq}_{FD}$	& $>150$	& \chisqfdexpl\\
			
			\hline
			\jpsi	& \chisqip PV & $>1$		& \chisqipexpl \\
			& \chisqvtxndf	& $<6$		& \chisqvtxndfexpl\\
			
			\hline
			$\kaon_1$&\chisqip PV & $>3$	& \chisqipexpl		 \\
			
			\hline
			\Kp     & ProbNNk 		& $>0.02$	& \probnnexpl{\kaon} \\
			& GhostProb & $<0.3$	& \ghostprobaexpl \\
			
			\hline
			\pip and \pim & probNNpi		& $>0.02$	& \probnnexpl{\pion} \\
			& GhostProb & $<0.3$	& \ghostprobaexpl\\
			
			
			\hline
			\pip, \pim and \Kp & sum of \chisqip & $>200$ & \chisqipexpl \\
			
			\hline
			\ep and \en & sum of \chisqip & $>200$	& \chisqipexpl \\
			& GhostProb & $<0.3$ & \ghostprobaexpl \\
			
			
			\hline
		\end{tabularx}\end{center}
		\label{tab:preselection}
	\end{table}
 