Measurement of the branching fraction of D⁺ₛ→ ⁺ν_ 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 D⁺ₛ decays using the e⁺e⁻→ D*+ₛ D*-ₛ process. The branching fractions of Dₛ⁺→⁺ν_\,(=μ,τ) are measured to be B(Dₛ⁺→μ⁺ν_μ)=(0.547±0.026ₛₜₐₜ±0.016syst)% and B(Dₛ⁺→τ⁺ν_τ)=(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~MeV and fDₛ⁺|Vcs|=(252.7±3.6ₛₜₐₜ±4.5syst±0.6ᵢₙₚᵤₜ))τ ν~MeV, respectively. Taking the value of |Vcs| from a global fit in the Standard Model, we obtain fD⁺ₛ=(252.8±6.0ₛₜₐₜ±3.7syst±0.6ᵢₙₚᵤₜ)μν MeV and fD⁺ₛ=(259.2±3.6ₛₜₐₜ±4.5syst±0.6ᵢₙₚᵤₜ)τ ν 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)τ ν, respectively.