Measurement of the branching fraction of $$ {\textrm{D}}_{\textrm{s}}^{+} $$ → τ+ντ via τ+ → μ+νμ$$ \overline{\nu} $$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 Ds+ → τ+ ντ via τ+ → μ+ νμ ν¯τ is measured to be BDs+→τ+ντ = (5.37 ± 0.17stat ± 0.15syst)%. Combining this branching fraction with the world averages of the measurements of the masses of τ+ and Ds+ as well as the lifetime of Ds+ , we extract the product of the decay constant of Ds+ and the c → s Cabibbo-Kobayashi-Maskawa matrix element to be fDs+ |Vcs | = (246.7 ± 3.9stat ± 3.6syst) MeV. Taking |Vcs | from a global fit in the standard model we obtain fDs+ = (253.4 ± 4.0stat ± 3.7syst) MeV. Conversely, taking fDs+ from lattice quantum chromodynamics calculations, we obtain |Vcs | = 0.987 ± 0.016stat ± 0.014syst.