Measurement of the branching fraction of $D_s$ inclusive semileptonic decay $D_s^{+}\to e^{+}X$

The absolute inclusive semileptonic branching fraction of the $D_s$ meson has been measured based on $22.3{\mathrm{pb}}^{\mathrm{-}1}$ of $e^{+}{e}^{-}$ collision data collected with the Beijing Spectrometer at $\sqrt{s}=4.03\mathrm{}\mathrm{GeV}.$ At this energy, the $D_s$ are produced in pairs: $e^{+}{e}^{-}\to D_s^{+}{D}_s^{-}.$ We reconstructed $171\pm 21\pm 15$ $D_s$ events in five hadronic decay modes. In the recoil system of these events, several $D_s$ inclusive semileptonic decays were observed and the branching fraction is estimated to be ${B(D}_s^{+}\to e^{+}{X)=(7.7\mathrm{}}_{-4.3-2.1}^{+5.7+2.4\mathrm{}})\%.\mathrm{}$