Measurement of the branching fractions for $B^0\to D_s^{*+}{\pi }^{-}$ and $B^0\to D_s^{*-}{K}^{+}$ decays

We present a study of $B^0\to D_s^{*+}{\pi }^{-}$ and $B^0\to D_s^{*-}{K}^{+}$ decays based on a sample of $657\times {10}^6$ $B\overline{B}$ events collected with the Belle detector at the KEKB asymmetric-energy $e^{+}{e}^{-}$ collider. We measure the branching fractions to be $\mathcal{B}(B^0\to D_s^{*+}{\pi }^{-})=(1.75\pm 0.34(\mathrm{stat})\pm 0.17(\mathrm{syst})\pm 0.11(\mathcal{B}))\times {10}^{-5}$ and $\mathcal{B}(B^0\to D_s^{*-}{K}^{+})=(2.02\pm 0.33(\mathrm{stat})\pm 0.18(\mathrm{syst})\pm 0.13(\mathcal{B}))\times {10}^{-5}$, with significances of 6.1 and 8.0 standard deviations, respectively. The first uncertainty is statistical, the second is due to the experimental systematics, and the third is from uncertainties in the $D_s^{+}$ decay branching fractions. From our measurements, we obtain the most precise determination so far of $R_{D^{*}\pi }$, where $R_{D^{*}\pi }$ is the ratio between amplitudes of the doubly Cabibbo-suppressed decay $B^0\to D^{*+}{\pi }^{-}$ and the Cabibbo-favored $B^0\to D^{*-}{\pi }^{+}$ decay.

Figure 1

Feynman diagrams for (a) Cabibbo-favored decay $B^0\to D^{*-}{\pi }^{+}$, (b) doubly Cabibbo-suppressed decay $B^0\to D^{*+}{\pi }^{-}$, (c) SU(3) flavor symmetric $B^0\to D_s^{*+}{\pi }^{-}$; color suppressed $W$-exchange contributions (d) to $B^0\to D^{*-}{\pi }^{+}$, (e) to $B^0\to D^{*+}{\pi }^{-}$, and (f) to the decay $B^0\to D_s^{*-}{K}^{+}$.

Figure 2

The simultaneous fit in the $B^0\to D_s^{*+}{\pi }^{-}$ [(a) $\varphi \pi$, (b) ${\overline{K}}^{*0}K$, and (c) $K_S^{0}K$ modes] and the $B^0\to D_s^{*-}{K}^{+}$ [(d)–(f)] signal modes. Signal peaks are shown by the solid curves, while the solid-filled curves represent the cross-feed contributions from the other $B^0$ signal modes. The long-dashed curves correspond to the contribution from the $B\to D_s\pi$ ($B\to D_{s}K$) and the dash-dotted curves to that from $B^0\to D_s^{(*)+}{\rho }^{-}$ ($B^{+}\to D_s^{(*)-}{K}^{+}{\pi }^{+}$). The dotted curves correspond to the combinatorial background.