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\subsection{Fit results}
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As previously mentioned, we first perform a fit to determine lifetimes and total yields. In Fig.~\ref{fig:proBsM}
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and Fig.~\ref{fig:proBsCt} the fitted distributions of $M_B$ and $c\tau$ for the $B_s$ sample are shown assuming an
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integrated luminosity of $3$ $pb^{-1}$. The plots show the total contribution from signal and background components
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(solid blue line) and the different components. Table 12 summarizes the fitted yields and lifetime for the sample considered.
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\begin{table}[htbp]
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\centering
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\vspace{0.3cm}
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\begin{tabular}{cc}
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\hline\hline
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Components & $B_s\rightarrow J/ \psi \phi$ \\
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\hline
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Signal & $179 \pm 17$ \\
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$\lambda$ ($\mu$m) & $424\pm 41$\\
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Generated $\lambda$ ($\mu$m) & $423$\\
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B background & $244\pm 63$ \\
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Prompt $J/ \psi$ & $664\pm 64$ \\
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Bias & $-1.29 \pm 0.43$ \\
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Scaling factor & $1.06 \pm 0.44$ \\
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\hline\hline
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\end{tabular}
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\caption{Summary of the ML fit on the MC dataset.}
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\end{table}
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\begin{figure}[!h!t]
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\vspace{0.5cm}
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\begin{minipage}[b]{0.5\linewidth}
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\centering
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\includegraphics[scale=0.4]{figure/proj_BsM.eps}
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\caption{Projection of the fit onto the $B_s$ invariant mass variable (solid blue) with the different components:
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signal (dashed red), B background (dashed blue) and prompt $J/ \psi$ background (dashed green).}
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\label{fig:proBsM}
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\end{minipage}
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\hspace{0.5cm}
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\begin{minipage}[b]{0.5\linewidth}
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\centering
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\includegraphics[scale=0.4]{figure/proj_ctauL.eps}
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\caption{Projection of the fit onto the $B_s$ proper decay length variable (solid blue) with the different components:
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signal (dashed red), B background (dashed blue) and prompt $J/ \psi$ background (dashed green).}
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\label{fig:proBsCt}
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\end{minipage}
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\end{figure}
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\clearpage
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