Measurement of the Decay $B_s^0\to D_s^{-}{\pi }^{+}$ and Evidence for $B_s^0\to D_s^{\mp }{K}^{\pm }$ in $e^{+}{e}^{-}$ Annihilation at $\sqrt{s}\approx 10.87\mathrm{GeV}$

We have studied $B_s^0\to D_s^{-}{\pi }^{+}$ and $B_s^0\to D_s^{\mp }{K}^{\pm }$ decays using $23.6{\mathrm{fb}}^{-1}$ of data collected at the ${\rm Y}(5S)$ resonance with the Belle detector at the KEKB $e^{+}{e}^{-}$ collider. This highly pure $B_s^0\to D_s^{-}{\pi }^{+}$ sample is used to measure the branching fraction, $\mathcal{B}(B_s^0\to D_s^{-}{\pi }^{+})=[{3.67}_{-0.33}^{+0.35}(\mathrm{stat}{)}_{-0.42}^{+0.43}(\mathrm{syst})\pm 0.49(f_s)]\times {10}^{-3}$ ($f_s=N_{B_s^{(*)}{\overline{B}}_s^{(*)}}/N_{b\overline{b}}$) and the fractions of $B_s^0$ event types at the ${\rm Y}(5S)$ energy, in particular $N_{B_s^{*}{\overline{B}}_s^{*}}/N_{B_s^{(*)}{\overline{B}}_s^{(*)}}=({90.1}_{-4.0}^{+3.8}\pm 0.2)\%$. We also determine the masses $M(B_s^0)=(5364.4\pm 1.3\pm 0.7)\mathrm{MeV}/c^2$ and $M(B_s^{*})=(5416.4\pm 0.4\pm 0.5)\mathrm{MeV}/c^2$. In addition, we observe $B_s^0\to D_s^{\mp }{K}^{\pm }$ decays with a significance of $3.5\sigma$ and measure $\mathcal{B}(B_s^0\to D_s^{\mp }{K}^{\pm })=[{2.4}_{-1.0}^{+1.2}(\mathrm{stat})\pm 0.3(\mathrm{syst})\pm 0.3(f_s)]\times {10}^{-4}$.

Figure 1

$(M_{\mathrm{bc}},\Delta E)$ scatter plots for $B_s^0\to D_s^{-}{\pi }^{+}$ (top) and $B_s^0\to D_s^{\mp }{K}^{\pm }$ (bottom) candidates. The three boxes in the top plot are the $\pm 2.5\sigma$ signal regions ($B_s^{*}{\overline{B}}_s^{*}$, $B_s^{*}{\overline{B}}_s^0$, and $B_s^0{\overline{B}}_s^0$, from top to bottom) while those in the bottom plot are the $\pm 2.5\sigma$ $B_s^{*}{\overline{B}}_s^{*}$ regions for signal (solid) and for $B_s^0\to D_s^{-}{\pi }^{+}$ background (dashed).

Figure 2

(a) $M_{\mathrm{bc}}$ distribution of the $B_s^0\to D_s^{-}{\pi }^{+}$ candidates with $\Delta E$ in the $B_s^{*}{\overline{B}}_s^{*}$ signal region $[-80,-17]\mathrm{MeV}$. (b) $\Delta E$ distribution of the $B_s^0\to D_s^{-}{\pi }^{+}$ candidates with $M_{\mathrm{bc}}$ in the $B_s^{*}{\overline{B}}_s^{*}$ signal region $[5.41,5.43]\mathrm{GeV}/c^2$. The different fitted components are shown with dashed curves for the signal, dotted curves for the $B_s^0\to D_s^{*-}{\pi }^{+}$ background, and dash-dotted curves for the continuum. (c),(d) show the same distributions but using the $B_s^{*}{\overline{B}}_s^0$ signal region ($\Delta E\in [-57,9]\mathrm{MeV}$ and $M_{\mathrm{bc}}\in [5.38,5.40]\mathrm{GeV}/c^2$).

Figure 3

Fitted distribution of the cosine of the angle between the $B_s^0$ momentum and the beam axis in the c.m. frame for the ${\rm Y}(5S)\to B_s^{*}{\overline{B}}_s^{*}$ signal.

Figure 4

Left: $M_{\mathrm{bc}}$ distribution of $B_s^0\to D_s^{\mp }{K}^{\pm }$ candidates with $\Delta E$ in the $B_s^{*}{\overline{B}}_s^{*}$ signal region. Right: $\Delta E$ distribution of the $B_s^0\to D_s^{\mp }{K}^{\pm }$ candidates with $M_{\mathrm{bc}}$ in the $B_s^{*}{\overline{B}}_s^{*}$ signal region; the left (right) peak is the $B_s^0\to D_s^{\mp }{K}^{\pm }$ ($B_s^0\to D_s^{-}{\pi }^{+}$) component. The dashed curves, dotted curves, and dash-dotted curves represent the signal, $B_s^0\to D_s^{(*)-}{\pi }^{+}$ backgrounds, and continuum, respectively.