Study of the Rare Decays $B^0\to D_s^{(*)+}{\pi }^{-}$ and $B^0\to D_s^{(*)-}{K}^{+}$

We report evidence for the decays $B^0\to D_s^{+}{\pi }^{-}$ and $B^0\to D_s^{-}{K}^{+}$ and the results of a search for $B^0\to D_s^{*+}{\pi }^{-}$ and $B^0\to D_s^{*-}{K}^{+}$ in a sample of $84\times {10}^6$ ${\rm Y}(4S)$ decays into $B\overline{B}$ pairs collected with the BABAR detector at the PEP-II asymmetric-energy $e^{+}{e}^{-}$ storage ring. We measure the branching fractions $\mathcal{B}(B^0\to D_s^{+}{\pi }^{-})=[3.2\pm 0.9(\mathrm{s}\mathrm{t}\mathrm{a}\mathrm{t})\pm 1.0(\mathrm{s}\mathrm{y}\mathrm{s}\mathrm{t})]\times {10}^{-5}$ and $\mathcal{B}(B^0\to D_s^{-}{K}^{+})=[3.2\pm 1.0(\mathrm{s}\mathrm{t}\mathrm{a}\mathrm{t})\pm 1.0(\mathrm{s}\mathrm{y}\mathrm{s}\mathrm{t})]\times {10}^{-5}$. We also set 90% C.L. limits $\mathcal{B}(B^0\to D_s^{*+}{\pi }^{-})<4.1\times {10}^{-5}$ and $\mathcal{B}(B^0\to D_s^{*-}{K}^{+})<2.5\times {10}^{-5}$.

Figure 1

The Feynman diagrams for the decays (a) $B^0\to D^{(*)-}{\pi }^{+}$, (b) $B^0\to D^{(*)+}{\pi }^{-}$, (c) $B^0\to D_s^{(*)+}{\pi }^{-}$, and (d) $B^0\to D_s^{(*)-}{K}^{+}$.

Figure 2

The $\Delta E$ distribution for $B^0\to D_s^{+}{\pi }^{-}$ (top) and $B^0\to D_s^{-}{K}^{+}$ (bottom) candidates in data compared with the distributions of the combinatorial background, estimated from the $m_{\mathrm{E}\mathrm{S}}$ sideband, the cross contamination, estimated from the $M_{D_s}^{\mathrm{c}\mathrm{a}\mathrm{n}\mathrm{d}}$ sidebands, and the simulation of the signal, normalized to the observed yield. The inset shows the $\Delta E$ distribution of the separate contributions to the cross contamination to the $B^0\to D_s^{+}{\pi }^{-}$ signal as predicted by simulation. The reflection backgrounds are normalized to the known branching fractions [13], while the normalization of the charmless background is arbitrary.

Figure 3

The $m_{\mathrm{E}\mathrm{S}}$ distributions for the $B^0\to D_s^{+}{\pi }^{-}$ (top left), $B^0\to D_s^{-}{K}^{+}$ (top right), $B^0\to D_s^{*+}{\pi }^{-}$ (bottom left), and $B^0\to D_s^{*-}{K}^{+}$ (bottom right) candidates within the $\Delta E$ band in data after all selection requirements. The fits used to obtain the signal yield are described in the text. The contribution from each $D_s^{+}$ mode is shown separately.