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

We report a measurement of the inclusive semileptonic $B_s^0$ branching fraction in a $121f{b}^{-1}$ data sample collected near the $\mathrm{{\rm Y}}(5S)$ 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 ${\mathrm{\ell }}^{+}$ ($\mathrm{\ell }=e,\mu$) that is required to have the same-sign charge to ensure that both originate from different $B_s^0$ mesons. The $B_s^0\to X^{-}{\mathrm{\ell }}^{+}{\nu }_{\mathrm{\ell }}$ branching fraction is extracted from the ratio of the measured yields of $D_s^{+}$ mesons and $D_s^{+}{\mathrm{\ell }}^{+}$ pairs and the known production and branching fractions. The inclusive semileptonic branching fraction is measured to be $[9.6\pm 0.4\text{(stat)}\pm 0.7\text{(syst)}]\mathrm{\%}$.