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

We report an observation of the decay $B_s^0\to D_s^{-}{\pi }^{+}$ in $p\overline{p}$ collisions at $\sqrt{s}=1.96\mathrm{TeV}$ using $115{\mathrm{pb}}^{-1}$ of data collected by the CDF II detector at the Fermilab Tevatron. We observe $83\pm 11(\mathrm{stat})$ $B_s^0\to D_s^{-}{\pi }^{+}$ candidates, representing a large increase in statistics over previous measurements and the first observation of this decay at a $p\overline{p}$ collider. We present the first measurement of the relative branching fraction $\mathcal{B}(B_s^0\to D_s^{-}{\pi }^{+})/\mathcal{B}(B^0\to D^{-}{\pi }^{+})=1.32\pm 0.18(\mathrm{stat})\pm 0.38(\mathrm{syst})$. We also measure $\mathcal{B}(B^{+}\to {\overline{D}}^0{\pi }^{+})/\mathcal{B}(B^0\to D^{-}{\pi }^{+})=1.97\pm 0.10(\mathrm{stat})\pm 0.21(\mathrm{syst})$, which is consistent with previous measurements.

Figure 1

Different Feynman diagrams which contribute to $B\to D\pi$ decays.

Figure 2

Invariant mass spectra for (a) $D_s^{-}{\pi }^{+}$, (b) $D^{-}{\pi }^{+}$, and (c) ${\overline{D}}^0{\pi }^{+}$ for data, with ${\chi }^2$ fits overlaid. The main background under the signal peak is combinatorial, modeled with a combination of a linear and exponential function. The shaded peak corresponds to $B\to DK$ decays, and is modeled with a Gaussian. The additional background component in the low mass region is due to partially reconstructed $B$ decays. This background component is modeled using shapes determined by inclusive $B\to DX$ Monte Carlo simulations. A sample Monte Carlo mass distribution for $B^{+}\to {\overline{D}}^0{\pi }^{+}$ events is shown in (d). Contributions from different sources in (d) are ordered by peak position, from right to left.