Measurement of the branching fraction of ${D}_{s}^{+}$ → τ + ν τ via τ + → μ + ν μ $\overline{\nu }$ τ

Utilizing 7.33 fb −1 of e + e − collision data taken at the center-of-mass energies of 4.128, 4.157, 4.178, 4.189, 4.199, 4.209, 4.219, and 4.226 GeV with the BESIII detector, the branching fraction of the leptonic decay ${D}_{s}^{+}$ → τ + ν τ via τ + → μ + ν μ $\overline{\nu }$ τ is measured to be ${B}_{{D}_{s}^{+}\to {\tau }^{+}{\nu }_{\tau }}$ = (5.37 ± 0.17stat ± 0.15syst)%. Combining this branching fraction with the world averages of the measurements of the masses of τ + and ${D}_{s}^{+}$ as well as the lifetime of ${D}_{s}^{+}$ , we extract the product of the decay constant of ${D}_{s}^{+}$ and the c → s Cabibbo-Kobayashi-Maskawa matrix element to be ${f}_{{D}_{s}^{+}}$ |V cs | = (246.7 ± 3.9stat ± 3.6syst) MeV. Taking |V cs | from a global fit in the standard model we obtain ${f}_{{D}_{s}^{+}}$ = (253.4 ± 4.0stat ± 3.7syst) MeV. Conversely, taking ${f}_{{D}_{s}^{+}}$ from lattice quantum chromodynamics calculations, we obtain |V cs | = 0.987 ± 0.016stat ± 0.014syst.