Semi-inclusive studies of semileptonic $B_s$ decays at Belle

We present an analysis of the semi-inclusive decays $B_s \to D_s^- X \ell^+ \nu$and$B_s \to D_s^{-} X \ell^+ \nu$,where$X$ denotes a final state that may consist of additional hadrons or photons and $\mathrm{\ell }$ is an electron or muon. The studied $B_s$ decays are contained in the $121.4{\mathrm{f}\mathrm{b}}^{-1}$ $\mathrm{{\rm Y}}(5S)$ data sample collected by the Belle detector at the KEKB asymmetric-energy $e^{+}{e}^{-}$ collider. The branching fractions of the decays are measured to be $$\mathcal{B}$(B_s \to D_s^- X \ell^+ \nu) = [8.2 \pm 0.2 ($\text{stat}$) \pm 0.6 ($\text{syst}$) \pm 1.4 ($\text{ext}$)]%$and$$\mathcal{B}$(B_s \to D_s^{-} X \ell^+ \nu) = [5.4 \pm 0.4 ($\text{stat}$) \pm 0.4 ($\text{syst}$) \pm 0.9 ($\text{ext}$)]%$, where the first two uncertainties are statistical and systematic and the last is due to external parameters. The measurement also provides an estimate of the $B_s^{(\ast )}{\bar{B}}_s^{(\ast )}$ production cross-section, $\sigma(e^+e^- \to B_s^{()}\bar{B}_s^{()}) = (53.8 \pm 1.4 ($\text{stat}$) \pm 4.0 ($\text{syst}$) \pm 3.4 ($\text{ext}$)),{\rm pb}$, at the center-of-mass energy $\sqrt{s}=10.86\mathrm{G}\mathrm{e}\mathrm{V}$.