Measurement of the branching fraction of D_s⁺ →ℓ⁺ν_ℓ via e⁺e^- → D_s^∗+ D_s^∗-

Based on 10.64 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 Ds+ decays using the e+e-→Ds∗+Ds∗- process. The branching fractions of Ds+→ℓ+νℓ(ℓ=μ,τ) are measured to be BDs+→μ+νμ=(0.547±0.026stat±0.016syst)% and BDs+→τ+ντ=(5.60±0.16stat±0.20syst)%, respectively. The product of the decay constant and Cabibbo-Kobayashi-Maskawa matrix element |Vcs| is determined to be fDs+|Vcs|=(246.5±5.9stat±3.6syst±0.5input)μν and fDs+|Vcs|=(252.7±3.6stat±4.5syst±0.6input)τν MeV, respectively. Taking the value of |Vcs| from a global fit in the Standard Model, we obtain fDs+=(253.2±6.0stat±3.7syst±0.6input)μν and fDs+=(259.6±3.7stat±4.6syst±0.6input)τν MeV, respectively. Conversely, taking the value for fDs+ from the latest lattice quantum chromodynamics calculation, we obtain |Vcs|=(0.986±0.023stat±0.014syst±0.003input)μν and |Vcs|=(1.011±0.014stat±0.018syst±0.003input)τν, respectively.