Measurement of the absolute branching fraction of inclusive semielectronic ${D}_{s}^{+}$ decays

We measure the inclusive semielectronic decay branching fraction of the ${D}_{s}^{+}$ meson. A double-tag technique is applied to ${e}^{+}{e}^{-}$ annihilation data collected by the BESIII experiment at the BEPCII collider, operating in the center-of-mass energy range 4.178–4.230 GeV. We select positrons from ${D}_{s}^{+}\to X{e}^{+}{\nu }_{e}$ with momenta greater than $200\text{}\text{}\mathrm{MeV}/c$ and determine the laboratory momentum spectrum, accounting for the effects of detector efficiency and resolution. The total positron yield and semielectronic branching fraction are determined by extrapolating this spectrum below the momentum cutoff. We measure the ${D}_{s}^{+}$ semielectronic branching fraction to be $\left(6.30±0.13\left(\mathrm{stat}.\right)±0.09\left(\mathrm{syst}.\right)±0.04\left(\mathrm{ext}.\right)\right)%$, showing no evidence for unobserved exclusive semielectronic modes. We combine this result with external data taken from literature to determine the ratio of the ${D}_{s}^{+}$ and ${D}^{0}$ semielectronic widths, $\frac{\Gamma \left({D}_{s}^{+}\to X{e}^{+}{\nu }_{e}\right)}{\Gamma \left({D}^{0}\to X{e}^{+}{\nu }_{e}\right)}=\phantom{\rule{0ex}{0ex}}0.790±0.016\left(\mathrm{stat}.\right)±0.011\left(\mathrm{syst}.\right)±0.016\left(\mathrm{ext}.\right)$. Our results are consistent with and more precise than previous measurements.