Measurement of the branching fraction of ${\textrm{D}}_{\textrm{s}}^{+}$ → 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 ${\mathcal{B}}_{D_s^{+}\to {\tau}^{+}{\nu}_{\tau }}$ = (5 . 37 ± 0 . 17 stat ± 0 . 15 syst )%. 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 . 9 stat ± 3 . 6 syst ) MeV. Taking |V cs | from a global fit in the standard model we obtain ${f}_{D_s^{+}}$ = (253 . 4 ± 4 . 0 stat ± 3 . 7 syst ) MeV. Conversely, taking ${f}_{D_s^{+}}$ from lattice quantum chromodynamics calculations, we obtain |V cs | = 0 . 987 ± 0 . 016 stat ± 0 . 014 syst .