Measurement of $B^0\to D_s^{-}{K}_S^0{\pi }^{+}$ and $B^{+}\to D_s^{-}{K}^{+}{K}^{+}$ branching fractions

We report a measurement of the $B^0$ and $B^{+}$ meson decays to the $D_s^{-}{K}_S^0{\pi }^{+}$ and $D_s^{-}{K}^{+}{K}^{+}$ final states, respectively, using $657\times 10^{6}B\overline{B}$ pairs collected at the $\mathrm{{\rm Y}}(4S)$ resonance with the Belle detector at the KEKB asymmetric-energy $e^{+}{e}^{-}$ collider. Using the $D_s^{-}\to \varphi {\pi }^{-}$, $K^{*}(892{)}^0{K}^{-}$ and $K_S^0{K}^{-}$ decay modes for the $D_s$ reconstruction, we measure the following branching fractions: $\mathcal{B}(B^0\to D_s^{-}{K}_S^0{\pi }^{+})=[0.47\pm 0.06(\text{stat})\pm 0.05(\text{syst})]\times 10^{-4}$ and $\mathcal{B}(B^{+}\to D_s^{-}{K}^{+}{K}^{+})=[0.93\pm 0.22(\text{stat})\pm 0.10(\text{syst})]\times 10^{-5}$. We find the ratio of the branching fraction of $B^{+}\to D_s^{-}{K}^{+}{K}^{+}$ to that of the analogous Cabibbo-favored $B^{+}\to D_s^{-}{K}^{+}{\pi }^{+}$ decay to be ${\mathcal{R}}_{\mathcal{B}}=0.054\pm 0.013(\text{stat})\pm 0.006(\text{syst})$, which is consistent with the naive factorization model. We also observe a deviation of the $D_{s}K$ invariant-mass distribution from the three-body phase-space model for both studied decays.

Figure 1

Dominant Feynman diagram for the (a) $B^{+}\to D_s^{-}{K}^{+}{K}^{+}$ and (b) $B^0\to D_s^{-}{K}_S^0{\pi }^{+}$ decay.

Figure 2

Distributions of $\mathrm{\Delta }E$, $M_{\text{bc}}$ and $M(D_s)$ for (top) $B^0\to D_s^{-}(\to \varphi {\pi }^{-})K_S^0{\pi }^{+}$, (middle) $B^0\to D_s^{-}(\to K^{*0}{K}^{-})K_S^0{\pi }^{+}$, and (bottom) $B^0\to D_s^{-}(\to K_S^0{K}^{-})K_S^0{\pi }^{+}$ decays. The distribution for each quantity is shown in the signal region of the remaining two. The blue solid curves show the results of the overall fit described in the text, the green dotted curves correspond to the signal component, the red long-dashed curves indicate the combinatorial background (including the peaking $D_s$ component) and the pink dot-dashed curves represent the peaking $B^0$ background.

Figure 3

Distributions of $\mathrm{\Delta }E$, $M_{\text{bc}}$ and $M(D_s)$ for (top) $B^{+}\to D_s^{-}(\to \varphi {\pi }^{-})K^{+}{K}^{+}$, (middle) $B^{+}\to D_s^{-}(\to K^{*0}{K}^{-})K^{+}{K}^{+}$, and (bottom) $B^{+}\to D_s^{-}(\to K_S^0{K}^{-})K^{+}{K}^{+}$ decays. The distribution for each quantity is shown in the signal region of the remaining two. The blue solid curves show the results of the overall fit described in the text, the green dotted curves correspond to the signal component, the red long-dashed curves indicate the combinatorial background (including the peaking $D_s$ component) and the pink dot-dashed curves represent the $B\to D_s^{(*)}K\pi$ contribution.

Figure 4

Invariant mass distributions of (left) $D_s^{-}{K}_S^0$ for the $B^0\to D_s^{-}{K}_S^0{\pi }^{+}$ and (right) $D_s^{-}{K}_{\text{low}}^{+}$ for $B^{+}\to D_s^{-}{K}^{+}{K}^{+}$ decay events in the signal region of $\mathrm{\Delta }E$, $M_{\text{bc}}$ and $M_{D_s}$ after applying all selection criteria. Points with error bars represent the data after subtraction of the background contribution, estimated from the $M_{\text{bc}}$ sideband ($5.22\mathrm{GeV}/c^2<M_{\text{bc}}<5.26\mathrm{GeV}/c^2$). The histograms show the phase-space distribution of the signal MC sample normalized to the data luminosity.