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

Here, we report a measurement of the inclusive semileptonic $B_s^0$ branching fraction in a $121{\mathrm{fb}}^{-1}$ data sample collected near the ${\rm Y}\left(5S\right)$ resonance with the Belle detector at the KEKB asymmetric energy $e^{+}{e}^{-}$ collider. Events with $B_s^{0(*)}{\overline{B}}_s^{0(*)}$ 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 $B_s^0\to X^{-}{\ell }^{+}{\nu }_{\ell }$ 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 $[10.6\pm 0.5(\mathrm{stat})\pm 0.7(\mathrm{syst}\left)\right]\%$.