Measurements of the branching fractions of semileptonic D^+ₛ decays via e^+e^- Dₛ^*+Dₛ^*-

We measure the absolute branching fractions of semileptonic D^+ₛ decays via the e^+e^- Dₛ^*+Dₛ^*- process using e^+e^- collision data corresponding to an integrated luminosity of 10. 64~fb^-1 collected by the BESIII detector at center-of-mass energies between 4. 237 and 4. 699 GeV. The branching fractions are B (Dₛ^+ e^+ₑ) = (2. 350. 11 ₒₓ₀ₓ 0. 10 ₒₘₒₓ) \%, B (Dₛ^+ ^ e^+ₑ) = (0. 820. 09 ₒₓ₀ₓ 0. 04 ₒₘₒₓ) \%, B (Dₛ^+ e^+ₑ) = (2. 210. 16 ₒₓ₀ₓ 0. 11 ₒₘₒₓ) \%, B (Dₛ^+ f₀ (980) e^+ₑ, f₀ (980) ^+^-) = (0. 150. 02 ₒₓ₀ₓ 0. 01 ₒₘₒₓ) \%, B (Dₛ^+ K⁰ e^+ₑ) = (0. 240. 04 ₒₓ₀ₓ 0. 01 ₒₘₒₓ) \%, and B (Dₛ^+ K^*0 e^+ₑ) = (0. 190. 03 ₒₓ₀ₓ 0. 01 ₒₘₒₓ) \%. These results are consistent with those measured via the e^+e^- Dₛ^*Dₛ^ process by BESIII and CLEO. The hadronic transition form factors D^+ₛ e^+ₑ, D^+ₛ ^ e^+ₑ, and D^+ₛ K⁰ e^+ₑ at four-momentum transfer squared q² = 0 are determined to be f^_+ (0) = 0. 482 0. 011 ₒₓ₀ₓ 0. 009 ₒₘₒₓ0. 004 ₈₍₏ₔₓ, f^^{}_+ (0) = 0. 562 0. 031 ₒₓ₀ₓ 0. 014 ₒₘₒₓ0. 003 ₈₍₏ₔₓ, and f^K⁰_+ (0) = 0. 624 0. 052 ₒₓ₀ₓ 0. 013 ₒₘₒₓ0. 002 ₈₍₏ₔₓ.