Measurement of the branching fraction of D^+ₛ ^+_ via e^+e^- D^*+ₒ D^*-ₒ

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^*+ₒ D^*-ₒ process. The branching fractions of Dₛ^+^+_\, (=, ) are measured to be B (Dₛ^+^+_) = (0. 5470. 026 ₒₓ₀ₓ0. 016 ₒₘₒₓ) \% and B (Dₛ^+^+_) = (5. 600. 16 ₒₓ₀ₓ0. 20 ₒₘₒₓ) \%, respectively. The product of the decay constant and Cabibbo-Kobayashi-Maskawa matrix element |V₂ₒ| is determined to be f₃䂺^+|V₂ₒ|= (246. 55. 9 ₒₓ₀ₓ3. 6 ₒₘₒₓ0. 5 ₈₍₏ₔₓ) _~MeV and f₃䂺^+|V₂ₒ|= (252. 73. 6 ₒₓ₀ₓ4. 5 ₒₘₒₓ0. 6 ₈₍₏ₔₓ) ) ~MeV, respectively. Taking the value of |V₂ₒ| from a global fit in the Standard Model, we obtain f₃^+䂺= (252. 86. 0 ₒₓ₀ₓ3. 7 ₒₘₒₓ0. 6 ₈₍₏ₔₓ) _ MeV and f₃^+䂺= (259. 23. 6 ₒₓ₀ₓ4. 5 ₒₘₒₓ0. 6 ₈₍₏ₔₓ) MeV, respectively. Conversely, taking the value for f₃䂺^+ from the latest lattice quantum chromodynamics calculation, we obtain |V₂ₒ| = (0. 9860. 023 ₒₓ₀ₓ0. 014 ₒₘₒₓ0. 003 ₈₍₏ₔₓ) _ and |V₂ₒ| = (1. 0110. 014 ₒₓ₀ₓ0. 018 ₒₘₒₓ0. 003 ₈₍₏ₔₓ), respectively.