Measurement of the absolute branching fraction of the inclusive semileptonic $Lambda_c^+$ decay

Using a data sample corresponding to an integrated luminosity of 567 pb$^{-1}$ collected at a center-of-mass energy of $sqrt{s}=4.6$ GeV with the BESIII detector, we measure the absolute branching fraction of the inclusive semileptonic $Lambda_c^+$ decay with a double-tag method. We obtain $mathcal{B}(Lambda_c^+ rightarrow X e^+ u_e) = (3.95pm0.34pm0.09)%$, where the first uncertainty is statistical and the second systematic. Using the known $Lambda_c^+$ lifetime and the charge-averaged semileptonic decay width of nonstrange charmed measons ($D^0$ and $D^+$), we obtain the ratio of the inclusive semileptonic decay widths $Gamma(Lambda_c^+ rightarrow X e^+ u_e)/bar{Gamma}(Drightarrow X e^+ u_e)= 1.26pm0.12$.