Measurement of the inclusive branching fractions for $B_s^0$ decays into $D$ mesons via hadronic tagging

We report measurements of the absolute branching fractions $\mathcal{B}(B_s^0\to D_s^{\pm }X)$, $\mathcal{B}(B_s^0\to D^0\mathrm{/}{\bar{D}}^{0}X)$, and $\mathcal{B}(B_s^0\to D^{\pm }X)$, where the latter is measured for the first time. The results are based on a 121.4,fb${}^{-1}$ data sample collected at the $\mathrm{{\rm Y}}(10860)$ resonance by the Belle detector at the KEKB asymmetric-energy $e^{+}{e}^{-}$ collider. We reconstruct one $B_s^0$ meson in $e^{+}{e}^{-}\to \mathrm{{\rm Y}}(10860)\to B_s^{\ast }{\bar{B}}_s^{\ast }$ events and measure yields of $D_s^{+}$, $D^0$, and $D^{+}$ mesons in the rest of the event. We obtain $\mathcal{B}(B_s^0\to D_s^{\pm }X)=(68.6\pm 7.2\pm 4.0)\mathrm{\%}$, $\mathcal{B}(B_s^0\to D^0\mathrm{/}{\bar{D}}^{0}X)=(21.5\pm 6.1\pm 1.8)\mathrm{\%}$, and $\mathcal{B}(B_s^0\to D^{\pm }X)=(12.6\pm 4.6\pm 1.3)\mathrm{\%}$, where the first uncertainty is statistical and the second is systematic. Averaging with previous Belle measurements gives $\mathcal{B}(B_s^0\to D_s^{\pm }X)=(63.4\pm 4.5\pm 2.2)\mathrm{\%}$ and $\mathcal{B}(B_s^0\to D^0\mathrm{/}{\bar{D}}^{0}X)=(23.9\pm 4.1\pm 1.8)\mathrm{\%}$. For the $B_s^0$ production fraction at the $\mathrm{{\rm Y}}(10860)$, we find $f_s=(21.4_{-1.7}^{+1.5})\mathrm{\%}$.