Measurement of the inclusive semileptonic branching fraction $\mathcal{B}(B_s^0 \to X^- \ell^+ \nu_{\ell})$ at Belle

We report a measurement of the inclusive semileptonic $B_s^0$ branching fraction in a $121~fb^{-1}$ data sample collected near the $\Upsilon(5S)$ resonance with the Belle detector at the KEKB asymmetric energy $e^+ e^-$ collider. Events containing $B_s^0$ pairs are selected by reconstructing a tag side $D_s^+$ and identifying a signal side lepton $\ell^+$ ($\ell = e, \mu$) that is required to have the same-sign charge to ensure that both originate from different $B_s^0$ mesons. The $B_s^0 \rightarrow X^- \ell^+ \nu_\ell$ branching fraction is extracted from the ratio of the measured yields of $D_s^+$ mesons and $D_s^+ \ell^+$ pairs and the known production and branching fractions. The inclusive semileptonic branching fraction is measured to be $[9.6 \pm 0.4\text{(stat)} \pm 0.7\text{(syst)}]~\%$.