Measurement of the branching fraction of ${D}_{s}^{+}\to {\ell }^{+}{\nu }_{\ell }$ via ${e}^{+}{e}^{-}\to {D}_{s}^{*+}{D}_{s}^{*-}$

Based on $10.64\text{}\text{}{\mathrm{fb}}^{-1}$ of ${e}^{+}{e}^{-}$ collision data taken at center-of-mass energies between 4.237 and 4.699 GeV with the BESIII detector, we study the leptonic ${D}_{s}^{+}$ decays using the ${e}^{+}{e}^{-}\to {D}_{s}^{*+}{D}_{s}^{*-}$ process. The branching fractions of ${D}_{s}^{+}\to {\ell }^{+}{\nu }_{\ell }\left(\ell =\mu ,\tau \right)$ are measured to be ${B}_{{D}_{s}^{+}\to {\mu }^{+}{\nu }_{\mu }}=\left(0.547±0.02{6}_{\mathrm{stat}}±0.01{6}_{\mathrm{syst}}\right)%$ and ${B}_{{D}_{s}^{+}\to {\tau }^{+}{\nu }_{\tau }}=\left(5.60±0.1{6}_{\mathrm{stat}}±0.2{0}_{\mathrm{syst}}\right)%$, respectively. The product of the decay constant and Cabibbo-Kobayashi-Maskawa matrix element $|{V}_{cs}|$ is determined to be ${f}_{{D}_{s}^{+}}|{V}_{cs}|=\left(246.5±{5.9}_{\mathrm{stat}}±{3.6}_{\mathrm{syst}}±{0.5}_{\text{input}}{\right)}_{\mu \nu }$ and ${f}_{{D}_{s}^{+}}|{V}_{cs}|=\left(252.7±{3.6}_{\mathrm{stat}}±{4.5}_{\mathrm{syst}}±{0.6}_{\text{input}}{\right)}_{\tau \nu }\text{}\text{}\mathrm{MeV}$, respectively. Taking the value of $|{V}_{cs}|$ from a global fit in the Standard Model, we obtain ${f}_{{D}_{s}^{+}}=\left(253.2±{6.0}_{\mathrm{stat}}±{3.7}_{\mathrm{syst}}±{0.6}_{\text{input}}{\right)}_{\mu \nu }$ and ${f}_{{D}_{s}^{+}}=\left(259.6±{3.7}_{\mathrm{stat}}±{4.6}_{\mathrm{syst}}±{0.6}_{\text{input}}{\right)}_{\tau \nu }\text{}\text{}\mathrm{MeV}$, respectively. Conversely, taking the value for ${f}_{{D}_{s}^{+}}$ from the latest lattice quantum chromodynamics calculation, we obtain $|{V}_{cs}|=\left(0.986±0.02{3}_{\mathrm{stat}}±0.01{4}_{\mathrm{syst}}±0.00{3}_{\text{input}}{\right)}_{\mu \nu }$ and $|{V}_{cs}|=\left(1.011±0.01{4}_{\mathrm{stat}}±0.01{8}_{\mathrm{syst}}±0.00{3}_{\text{input}}{\right)}_{\tau \nu }$, respectively.