\subsection{Checks for possible backgrounds}

The main background source in this decay is combinatorial background. However, other background contributions could significantly shift the angular distributions and therefore need to be removed. It is shown already in \refSec{sel-KplusVeto} that the combinatorial background above the mass of the \Bu meson is dominated by \BuToKpmm decays, which are vetoed accordingly. Another check is performed to show that $\Bd\to\piz\mu\mu$ decays do not contribute to the signal. Contrary to the \BuToKpmm contribution, the reconstructed \piz\mumu mass does not peak in the \Bu mass (see \refFig{BuTopizmm} and compare to \refFig{BuToKpmm}).

\begin{figure}[hbt!]
	\centering
	\includegraphics[width=0.54\textwidth]{./Data/Background/Pizmumu_2018Data.eps}
	\captionof{figure}[Reconstructed \piz\mumu mass in the 2018 data sample after cut-based selection.]{Reconstructed \piz\mumu mass in the 2018 data sample after cut-based selection. The red band represents region $\pm$100\mev around the \Bu mass. These events are vetoed. There is no peak suggesting a significant contribution of the $\Bd\to\piz\mu\mu$ sample to the selected data. Compare with \refFig{BuToKpmm}.} \label{fig:BuTopizmm}
\end{figure}

\subsubsection[Study of the \texorpdfstring{${\BuToXJpsi}$}{B to XJpsi} sample]{Study of the \texorpdfstring{\BuToXJpsiBF}{B to XJpsi} sample}

A validation of the selection is performed using a simulated sample of inclusive \BuToXJpsi decays. This simulation is available for the years 2011, 2012 and 2016. The full selection identical to the signal selection is performed. After the selection, the true ID of the particles is checked in order to identify possible background contributions. A small contribution from $\Bu^{\ast}$ is found. However, as this very quickly decays into \Bu meson and cannot be distinguished from the \emph{true} signal, these events are considered as signal. In \refFig{BuToXmm}, the \Bu mass distribution from the sample of inclusive \BuToXJpsi decay is shown, comparing the mass distribution from \emph{true} \BuToKstJpsi events to background events. No peaking background is observed. A similar check is successfully performed in the \Kstar mass distribution (\refFig{BuToXmm_Kstar}).

\begin{figure}[hbt!]
	\centering
	\includegraphics[width=0.44\textwidth]{./Data/Background/Inclusive_MC_Run_1.eps} \hspace{10pt}
	\includegraphics[width=0.44\textwidth]{./Data/Background/Inclusive_MC_Run_2.eps}
	\captionof{figure}[Reconstructed \Bu meson mass in the \BuToXJpsi decay simulation.]{Reconstructed \Bu meson mass in the simulation sample of inclusive \BuToXJpsi decay. The black line represents all candidates passing the whole selection, including  the MLP response cut. The red line represents the events that are identified as background in the ID based truth-matching.} \label{fig:BuToXmm}
\end{figure}



\begin{figure}[hbt!]
	\centering
	\includegraphics[width=0.44\textwidth]{./Data/Background/Inclusive_MC_Run_1_Kstar.eps} \hspace{10pt}
	\includegraphics[width=0.44\textwidth]{./Data/Background/Inclusive_MC_Run_2_Kstar.eps}
	\captionof{figure}[Reconstructed \Kstar mass in the simulation sample of   \BuToXJpsi.]{Reconstructed \Kstar mass in the simulation sample of  inclusive \BuToXJpsi decay. The black line represents all candidates passing the whole selection, including the MLP response cut. The red line represents the events that are identified as background in the ID based truth-matching.} \label{fig:BuToXmm_Kstar}
\end{figure}



Despite no clear contribution of peaking backgrounds, thorough checks revealed the presence of two background components: $\Bu\to K^{**}\jpsi$ and $\Bu\to\Kp (Y_{\ccbar}\to\jpsi X)$. Both of these decays pass the selection if a \piz meson or a photon from the decay of the excited $K^{**}$ or charmonium $Y_{\ccbar}$ meson is missed. Note that both of these decays have $\jpsi$ in their final state: they do not contribute to the signal channel, but to the reference channel only!

The shape of the \piz\mumu mass distribution typical for these decays is shown in \refFig{BuToXmm_peaking}. While the $\Bu\to K^{**}\jpsi$ mass distribution shape  is similar to the $\BuToKstJpsi$ mass distribution shape, there is a clear peak at $\sim3650\mev$ in the $\Bu\to\Kp (Y_{\ccbar}\to\jpsi X)$ case. However, the overall contribution of this background is several percent, as can be seen in \refFig{BuToXmm_peakingCut}. In order to virtually eliminate this background and push it to a 2\% level only, a cut on the \piz\mumu mass is proposed. This cut, corresponding to removing any event with $m_{\piz\mumu}<3700\mev$ would also remove $\sim12\%$ of the actual reference channel signal. Furthermore, this cut also removes virtually all events with soft \piz mesons and therefore all events with $\ctk\sim1$. This cut would then skew the angular distribution of the reference channel. This background accounts for $\sim$15\% of all candidates with $\ctk>0.25$.  Given the small number of such events and the already low selection efficiency in $\ctk\sim1$, this peaking background is modeled as a part of the combinatorial background.

\begin{figure}[hbt!]
	\centering
	\includegraphics[width=0.45\textwidth]{./Data/Background/JpsiX_mpi0mumu.pdf}
	\includegraphics[width=0.45\textwidth]{./Data/Background/JpsiX_cosThetaK_norm.pdf}
	\captionof{figure}
	[Background contributions in reconstructed \piz\mumu mass and \ctk.]
	{Normalized reconstructed \piz\mumu mass (left) and \ctk (right) with different background contributions. The blue line represents the event candidates identified as signal, the orange line represents events coming from \decay{\Bu}{K^{**}\jpsi} and the green line represents the contribution from higher \cquark\cquarkbar resonances $Y_{\cquark\cquarkbar}$ decaying further into \jpsi and a meson. The \decay{\Bu}{K^{**}\jpsi} contamination accounts for 15\% of all signal candidates with $\ctk>0.25$. } \label{fig:BuToXmm_peaking}
\end{figure}

\begin{figure}[hbt!]
	\centering
	\includegraphics[width=0.54\textwidth]{./Data/Background/nice_pollutioncurve.png} \hspace{10pt}
	\captionof{figure}[The $\Bu\to\Kp (Y_{\ccbar}\to\jpsi X)$  pollution vs. the \BuToKstJpsi efficiency.]{The $\Bu\to\Kp (Y_{\ccbar}\to\jpsi X)$  pollution against the \BuToKstJpsi efficiency. In order to reduce the background contribution to 2\%, the signal efficiency would drop to $\sim$87\%. This figure is produced using the inclusive ${\BuToXJpsi}$ simulation sample. } \label{fig:BuToXmm_peakingCut}
\end{figure}