Measurement of the Ratios of Branching Fractions $\mathcal{B}(B_s^0\to D_s^{-}{\pi }^{+}{\pi }^{+}{\pi }^{-})/\mathcal{B}(B^0\to D^{-}{\pi }^{+}{\pi }^{+}{\pi }^{-})$ and $\mathcal{B}(B_s^0\to D_s^{-}{\pi }^{+})/\mathcal{B}(B^0\to D^{-}{\pi }^{+})$

Using $355{\mathrm{pb}}^{-1}$ of data collected by the CDF II detector in $p\overline{p}$ collisions at $\sqrt{s}=1.96\mathrm{TeV}$ at the Fermilab Tevatron, we study the fully reconstructed hadronic decays $B_{(s)}^0\to D_{(s)}^{-}{\pi }^{+}$ and $B_{(s)}^0\to D_{(s)}^{-}{\pi }^{+}{\pi }^{+}{\pi }^{-}$. We present the first measurement of the ratio of branching fractions $\mathcal{B}(B_s^0\to D_s^{-}{\pi }^{+}{\pi }^{+}{\pi }^{-})/\mathcal{B}(B^0\to D^{-}{\pi }^{+}{\pi }^{+}{\pi }^{-})=1.05\pm 0.10(\mathrm{stat})\pm 0.22(\mathrm{syst})$. We also update our measurement of $\mathcal{B}(B_s^0\to D_s^{-}{\pi }^{+})/\mathcal{B}(B^0\to D^{-}{\pi }^{+})$ to $1.13\pm 0.08(\mathrm{stat})\pm 0.23(\mathrm{syst})$, improving the statistical uncertainty by more than a factor of 2. We find $\mathcal{B}(B_s^0\to D_s^{-}{\pi }^{+})=[3.8\pm 0.3(\mathrm{stat})\pm 1.3(\mathrm{syst})]\times {10}^{-3}$ and $\mathcal{B}(B_s^0\to D_s^{-}{\pi }^{+}{\pi }^{+}{\pi }^{-})=[8.4\pm 0.8(\mathrm{stat})\pm 3.2(\mathrm{syst})]\times {10}^{-3}$.

Figure 1

Comparison of the sideband subtracted mass spectrum of ${\pi }^{+}{\pi }^{+}{\pi }^{-}$ from $B^0$ and $B_s^0$ decays. Only the $D_s^{-}\to \varphi \pi$ channel is used for $B_s^0$. The $B^0$ histogram is normalized to $B_s^0$.

Figure 2

Mass spectra for (a) $B_s^0\to D_s^{-}{\pi }^{+}$, (b) $B_s^0\to D_s^{-}(\varphi {\pi }^{-}){\pi }^{+}{\pi }^{+}{\pi }^{-}$, (c) $B_s^0\to D_s^{-}(K^{*0}{K}^{-}){\pi }^{+}{\pi }^{+}{\pi }^{-}$, (d) $B_s^0\to D_s^{-}({\pi }^{-}{\pi }^{-}{\pi }^{+}){\pi }^{+}{\pi }^{+}{\pi }^{-}$, (e) $B^0\to D^{-}{\pi }^{+}$, and (f) $B^0\to D^{-}{\pi }^{+}{\pi }^{+}{\pi }^{-}$. The “other physics” category corresponds to the inclusive $B\to D_s^{-}X$ and $B\to D^{-}X$ decays.