Measurements of branching fractions for $B^0\to D_s^{+}{\pi }^{-}$ and ${\overline{B}}^0\to D_s^{+}{K}^{-}$

We present improved measurements of the branching fractions for the decays $B^0\to D_s^{+}{\pi }^{-}$ and ${\overline{B}}^0\to D_s^{+}{K}^{-}$ using a data sample of $657\times {10}^6$ $B\overline{B}$ events collected at the ${\rm Y}(4S)$ resonance with the Belle detector at the KEKB asymmetric-energy $e^{+}{e}^{-}$ collider. The results are $\mathcal{B}(B^0\to D_s^{+}{\pi }^{-})=(1.99\pm 0.26\pm 0.18)\times {10}^{-5}$ and $\mathcal{B}({\overline{B}}^0\to D_s^{+}{K}^{-})=(1.91\pm 0.24\pm 0.17)\times {10}^{-5}$, where the uncertainties are statistical and systematic, respectively. Based on these results, we determine the ratio between amplitudes of the doubly Cabibbo suppressed decay $B^0\to D^{+}{\pi }^{-}$ and the Cabibbo favored decay $B^0\to D^{-}{\pi }^{+}$, $R_{D\pi }=[1.71\pm 0.11(\mathrm{stat})\pm 0.09(\mathrm{syst})\pm 0.02(\mathrm{theo})]\%$, where the last term denotes the theory error.

Figure 1

Feynman diagrams for (a) $B^0\to D_s^{+}{\pi }^{-}$; (b) the Cabibbo favored decay $B^0\to D^{-}{\pi }^{+}$; (c) the doubly Cabibbo suppressed decay $B^0\to D^{+}{\pi }^{-}$; and the color suppressed $W$-exchange contribution to (d) ${\overline{B}}^0\to D_s^{+}{K}^{-}$, (e) $B^0\to D^{-}{\pi }^{+}$, and (f) $B^0\to D^{+}{\pi }^{-}$.

Figure 2

Projections of the simultaneous fit to (a, c) $B^0\to D_s^{+}{\pi }^{-}$ and (b, d) ${\overline{B}}^0\to D_s^{+}{K}^{-}$. (a, b) correspond to $\Delta E$ and (c, d) are the $D_s^{+}$ mass distributions. Points with error bars show the data, the blue solid curves are the total fit result, the red solid curves are the signal component, the magenta filled curves represent the crossfeed contribution, the green dotted curves are the combinatorial background, and the blue dashed curves correspond to the charmless $B$ background.