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 $\ell$ is an electron or muon. The studied $B_s$ decays are contained in the $121.4{\mathrm{fb}}^{-1}$ $\mathrm{{\rm Y}}(5S)$ 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 $\mathcal{B}(B_s\to D_s^{-}X{\ell }^{+}\nu )=[8.2\pm 0.2(\mathrm{stat})\pm 0.6(\mathrm{syst})\pm 1.4(\mathrm{ext})]\%$ and $\mathcal{B}(B_s\to D_s^{*-}X{\ell }^{+}\nu )=[5.4\pm 0.4(\mathrm{stat})\pm 0.4(\mathrm{syst})\pm 0.9(\mathrm{ext})]\%$, 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 $B_s^{(*)}{\overline{B}}_s^{(*)}$ production cross section, $\sigma (e^{+}{e}^{-}\to B_s^{(*)}{\overline{B}}_s^{(*)})=[53.8\pm 1.4(\mathrm{stat})\pm 4.0(\mathrm{syst})\pm 3.4(\mathrm{ext})]\mathrm{pb}$, at the center-of-mass energy $\sqrt{s}=10.86\mathrm{GeV}$.

• Received 8 April 2015

DOI:https://doi.org/10.1103/PhysRevD.92.072013