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\subsection{\boldmath{$B$} Background Studies}
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We studied the main sources of $B$ background in an earlier MC dataset
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generated for a collision energy of 10~TeV~(Summer'09).
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We do not expect that the mixture of the different sources changes
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dramatically for a lower collision energy of 7~TeV.
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We list sources that contribute at least one event with a preliminary
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estimate of their contribution in the present sample.
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The final estimate of the contribution for a given integrated luminosity
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still needs to be performed on a consistently generated cocktail sample for 7~TeV.
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The main categories are:
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\begin{itemize}
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\item $B_d\rightarrow J/ \psi K^*$: the signature of this channel is very similar to
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the signal $B_s\rightarrow J/ \psi \phi$ by replacing a kaon with a pion. This is
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the most important source of background and the selection has been done to optimize
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the discrimination between this channel and our signal.
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\item $B_d\rightarrow J/ \psi K_1^0$: one of the feeddown channel for
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$B_s\rightarrow J/ \psi \phi$. The $K_1^0$ meson primarily decays into
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$\rho $ and a charged $K$.
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The misreconstruction occurs when the two charged pions from the $\rho$
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meson are, the first, identified as a charged $K$, the latter, lost.
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\item $B_d\rightarrow J/ \psi K^0_S$: decay channel with $K_s^0$ decaying
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into two charged pions. The misreconstruction occurs where both charged
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pions are misidentified as charged kaons.
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%\item $B_s\rightarrow J/ \psi K^+K^-$: same signature as our signal but the
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%charged kaons do not make the $\phi$ resonance.
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\item $B_s\rightarrow J/ \psi \eta$: one of the main background coming from
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$B_s$ mesons. The knowledge of only the upper limit for the branching fraction
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make us overestimate this background channel.
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\item $B^+\rightarrow J/ \psi K^+$: one of the feedup channel for
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$B_s\rightarrow J/ \psi \phi$. The charged $K$ is matched to a flying
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$K$ from the background to make a $\phi$ meson.
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\item Other $B_s$: all the decay of the $B_s$ with daughter a $J/ \psi$ and any
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other particle
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\item Other $B_d$: all the decay of the $B_d$ with daughter a $J/ \psi$ and
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any other particle
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\item Other: all the remaining decays from the hadronization of $b\bar{b}$ quarks
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\end{itemize}
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Table~\ref{tab:bsbkg} lists potential background from other $B_s$ decays,
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Table~\ref{tab:bdbkg} from $B_d$ decays, and Table~\ref{tab:bplusbkg}
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from $B^+$ decays.
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\begin{table}[htp]
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\begin{center}
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\begin{tabular}{|l|c|c|}
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\hline
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\multicolumn{3}{|c|}{$B_s$ background} \\
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\hline
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Decay channel & $\#$ Ev. & BF \\ \hline
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\hline
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$J/ \psi \eta$ & 8 & $<3.8\times 10^{-3}$ \\ \hline
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$J/ \psi \eta'$ & 2 & $<3.8\times 10^{-3*}$ \\ \hline
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$D_s^{*+}e\bar{\nu_e}$ & 2 & $(7.9 \pm 2.4)\%$ \\ \hline
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$D_s^{*+}\mu^+\nu_{\mu}$ & 2 & $(7.9 \pm 2.4)\%$ \\ \hline
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$D_s^{*+}D_s^-$ & & $<12.1 \%$ \\ \hline
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$D_s^{*+}D_s^{*-}$ & & $<25.7 \%$\\ \hline
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$D_{s1}^{'-}\mu^+\nu_{\mu}$ & & $(2.3 \pm 0.7)\times 10^{-3}$\\ \hline
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$J/ \psi (2S)K^+K^-$ & & $(6.8 \pm 3.0) \times 10^{-4}$\\ \hline
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$D_s^{*+}\bar{D^0}K^{*-}$ & & \\ \hline
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$D^*(2010)^-\Delta^0 \Sigma^-$ & & \\ \hline
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$D_s^{+}D^- \bar{K^0}$ & & \\ \hline
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$\chi_{c1}(1P)\eta '$ & & \\ \hline
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$\bar{K^0}\pi^+D^*(2010)^-$ & & \\ \hline
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$a_1^+D_s^{-}$ & & \\ \hline
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$D_s^-\eta \rho^+$ & & \\ \hline
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$\chi_{c1}\phi$ & & \\ \hline
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$D_s^-\pi^0\pi^+$ & & \\ \hline
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$D_s^{*-}\rho^{+}\rho^0$ & & \\ \hline
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$K^*\pi^0 D^{*0}$ & & \\ \hline
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$D_s^{*-}\eta\rho^+$ & & \\ \hline
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$\#$ of events & 30 & \\ \hline
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$\#$ of events with $\ge$ 4 daughters & 9 & \\ \hline
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Total & 39 & \\ \hline
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\end{tabular}
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\caption{\sl Potential $B_s$ background channels}
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\label{tab:bsbkg}
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\end{center}
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\end{table}
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\begin{table}[htp]
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\begin{center}
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\begin{tabular}{|l|c|c|}
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\hline
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\multicolumn{3}{|c|}{$B_d$ background} \\
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\hline
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Decay channel & $\#$ Ev. & BF \\ \hline
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\hline
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$J/ \psi K_1^0$ & 34 & $(1.3 \pm 0.5)\times 10^{-3}$\\ \hline
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$\rightarrow K\rho $ & 22 & \\ \hline
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$\rightarrow K^*(892)\pi $ & 5 & \\ \hline
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$\rightarrow K^+ \pi^- \pi^0$ & 4 & \\ \hline
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$\rightarrow K^0 \pi^+ \pi^- $ & 3 & \\ \hline
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$J/ \psi K^0$ & 5 & $(8.71\pm 0.32)\times 10^{-4}$\\ \hline
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$D^*(2010)^- e^+ \nu_e$ & 3 & $(5.16 \pm 0.11) \%$ \\ \hline
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$\chi_{c1} K^{*0}$ & 3 & $(2.0 \pm 0.3)\times 10^{-4}$\\ \hline
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$J/ \psi K^+ \pi^-$ & 3 & $(1.2 \pm 0.6)\times 10^{-3}$\\ \hline
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$J/ \psi(2S) K^+\pi^-$ & 2 & $<1 \times 10^{-3}$ \\ \hline
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$J/ \psi K_2^{*0}$ & 2 & \\ \hline
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$D^+ D^*(2010)^- \bar{K^0}$ & 2 & $(6.5 \pm 1.6)\times 10^{-3}$ \\ \hline
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$D^*(2010)^+ D_s^{*-} $ & & $(1.78 \pm 0.14) \%$\\ \hline
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$D^*(2010)^+ \rho^0 \rho^- $ & & $(1.76 \pm 0.27)\%$\\ \hline
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$D^*(2010)^- \eta \pi^+ $ & & $(1.76 \pm 0.27)\%$\\ \hline
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$J/ \psi \rho^0$ & & $(2.7 \pm 0.4)\times 10^{-5}$\\ \hline
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$\chi_{c1} K^- \pi^+$ & & $(3.8 \pm 0.4)\times 10^{-4}$\\ \hline
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$D^*(2010)^+ \bar{D^*(2007)^0 K^-}$ & &$(1.18 \pm 0.20)\%$ \\ \hline
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$D^*(2010)^-\omega \pi^+$ & &$(2.89 \pm 0.30)\times 10^{-3}$ \\ \hline
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$D^*(2010)^- D_s^{*+}$ & & $(8.2\pm 1.1)\times 10^{-3}$\\ \hline
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$D^*(2007)^0 \pi^+ K^-$ & & $<6.9 \times 10^{-5}$\\ \hline
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$\bar{D^*(2007)^0} D^0 \bar{K^{0}}$ & &$<6.6 \times 10^{-3}$ \\ \hline
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$\bar{D^*(2007)^0} \pi^+ \pi^-$ & & $(6.2 \pm 2.2)\times 10^{-4}$\\ \hline
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$J/ \psi K^{*0} \pi^0$ & & $(6.6 \pm 2.2)\times 10^{-4}$\\ \hline
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$D_s^{*+}D^-$ & &$(7.5 \pm 1.6)\times 10^{-3}$ \\ \hline
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$D^*(2010)^+ \omega \pi^-$ & & $(2.89\pm 0.30)\times 10^{-3}$\\ \hline
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$\chi_{c2} K^- \pi^+$ & & $< 3.6\times 10^{-5}$\\ \hline
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$D^*(2007)^0 D^- K^+$ & &$(4.6 \pm 1.0)\times 10^{-3}$ \\ \hline
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$J/ \psi \omega$ & & $<2.7 \times 10^{-4}$\\ \hline
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$D_0^{*-}\tau\bar{\nu_{\tau}}$ & & \\ \hline
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$D_1^+ e \bar{\nu_e}$ & & \\ \hline
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$D^+ e^- \bar{\nu_e}$ & & \\ \hline
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$D_1(2420)^- D_s^{*+}$ & & \\ \hline
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$D^*(2010)^-\mu^+\nu_{\mu}$ & & \\ \hline
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$D^*(2010)^- K^+ K^{*0}$ & & \\ \hline
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$D^+ \rho^0 \pi^-$ & & \\ \hline
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$D^- \pi^+ \pi^0$ & & \\ \hline
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$D_2^*(2460)^+ \tau \bar{\nu_{\tau}}$ & & \\ \hline
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$\bar{D^*(2007)^0} \Sigma^{*0} \bar{\Sigma^{*0}}$ & & \\ \hline
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$\chi_{c1} \bar{K^{0}} \pi^0$ & & \\ \hline
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$D^*(2010)^+ a_1^-$ & & \\ \hline
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$D^*(2010)^+ \tau \bar{\nu_{\tau}}$ & & \\ \hline
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$D_1^{'*-} \mu^+ \nu_{\mu}$ & & \\ \hline
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$\eta' K^+ D_s^-$ & & \\ \hline
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$D_1(2420)^+\mu^+ \nu_{\mu}$ & & \\ \hline
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$D^*(2010)^+ \rho^+ \eta$ & & \\ \hline
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$\#$ of events & 88 & \\ \hline
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$\#$ of events with $\ge$ 4 daughters & 22 & \\ \hline
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Total & 110 & \\ \hline
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\end{tabular}
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\caption{\sl Potential $B_d$ bacjground channels.}
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\label{tab:bdbkg}
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\end{center}
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\end{table}
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\begin{table}[htp]
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\begin{center}
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\begin{tabular}{|l|c|c|}
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\hline
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\multicolumn{3}{|c|}{Other background} \\
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\hline
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Decay channel & $\#$ Ev. & BF \\ \hline
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$B^+\rightarrow J/ \psi K_1^+ $ & 17 & $(1.8 \pm 0.5)\times 10^{-3}$\\ \hline
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$B^+\rightarrow J/ \psi K^{*+} $ & 4 &$(1.43\pm 0.08)\times 10^{-3}$ \\ \hline
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$B^+\rightarrow J/ \psi K^+$ & 4 & $(1.007\pm 0.035)\times 10^{-3}$\\ \hline
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$B^+\rightarrow D^*(2007)^0 \tau^+ \nu_{\tau}$ & 3 & $(2.2\pm 0.6)\%$\\ \hline
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$B^-\rightarrow D^0 e \bar{\nu_e} $ & 2 &$(2.24\pm 0.11)\%$ \\ \hline
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$B^+\rightarrow D^*(2007)^0 e^+ \nu_{e}$ & 2 &$(5.68\pm 0.19)\% $ \\ \hline
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$B^+\rightarrow D^*(2007)^0 \mu^+ \nu_{\mu}$ & 2 & $(5.68\pm 0.19)\%$\\ \hline
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$B^-\rightarrow J/ \psi(2S) K^{-} $ & 2 & $(6.48\pm 0.35)\times 10^{-4}$\\ \hline
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$B^-\rightarrow \chi_{c1} K^{*-}$ & 2 &$(3.6\pm 0.9)\times 10^{-4}$ \\ \hline
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$B^+\rightarrow \chi_{c1} K^+$ & &$(5.1\pm 0.5)\times 10^{-4}$\\ \hline
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$B^+\rightarrow D_s^{*+} \bar{D^0}$ & &$(7.8\pm 1.6)\times 10^{-3}$ \\ \hline
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$B^+\rightarrow J/ \psi pi^{+} $ & & $(4.9\pm 0.6)\times 10^{-5}$\\ \hline
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$B^-\rightarrow D^*(2007)^0 D^*(2010)^- \bar{K^0}$ & &$(7.8\pm 2.6)\times 10^{-3}$ \\ \hline
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$B^-\rightarrow D^*(2007)^0 \bar{D^*(2007)^0} K^-$ & &$(5.3\pm 1.6)\times 10^{-3}$ \\ \hline
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$B^+\rightarrow D_0^{*0} e^+ \nu_{e}$ & & $(2.5\pm 0.5)\times 10^{-3}$\\ \hline
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$B^-\rightarrow D_s^{*+} \bar{D^*(2007)^0}$ & & $(1.74\pm 0.23)\%$\\ \hline
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$B^-\rightarrow D_s^{*-} D^+ \pi^-$ & & \\ \hline
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$B^+\rightarrow J/ \psi K_1^{'+} $ & & \\ \hline
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$B^+\rightarrow D_2^*(2460)^0 D_s^+$ & & \\ \hline
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$\Lambda_b\rightarrow J/ \psi(2S) \Lambda$ & & \\ \hline
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$B^+\rightarrow D^*(2007)^0 D_{s1}(H)^+$ & & \\ \hline
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$\Lambda_b\rightarrow J/ \psi \Lambda$ & & \\ \hline
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$B^+\rightarrow D_s^+ \bar{D^0} \pi^0$ & & \\ \hline
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$B^+\rightarrow \rho^0 \Sigma_c^- \Delta^{++}$ & & \\ \hline
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$\Lambda_b\rightarrow \Lambda_c^+ D_s^{*-}$ & & \\ \hline
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$B^-\rightarrow J/ \psi D_{s0}^{*-}$ & & \\ \hline
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$\#$ of events & 55 & \\ \hline
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$\#$ of events with $\ge$ 4 daughters & 10 & \\ \hline
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Total & 65 & \\ \hline
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\end{tabular}
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\caption{\sl Potential background $B^+$ decay channels.}
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\label{tab:bplusbkg}
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\end{center}
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\end{table}
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\clearpage
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