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⁺→ η e⁺νₑ)=(2.35±0.11ₛₜₐₜ± 0.10syst)%, B(Dₛ⁺→ η^ e⁺νₑ)=(0.82±0.09ₛₜₐₜ± 0.04syst)%, B(Dₛ⁺→ φ e⁺νₑ)=(2.21±0.16ₛₜₐₜ± 0.11syst)%, B(Dₛ⁺→ f₀(980) e⁺νₑ,f₀(980)→π⁺π⁻)=(0.15±0.02ₛₜₐₜ± 0.01syst)%, B(Dₛ⁺→ K⁰ e⁺νₑ)=(0.24±0.04ₛₜₐₜ± 0.01syst)%, and B(Dₛ⁺→ K*0 e⁺νₑ)=(0.19±0.03ₛₜₐₜ± 0.01syst)%. 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→ η e⁺νₑ, D⁺ₛ→ η^ e⁺νₑ, and D⁺ₛ→ K⁰ e⁺νₑ at four-momentum transfer squared q² = 0 are determined to be fη₊(0) = 0.482 ± 0.011ₛₜₐₜ ± 0.009syst±0.004ᵢₙₚᵤₜ, f^η^₊(0) = 0.562 ± 0.031ₛₜₐₜ ± 0.014syst±0.003ᵢₙₚᵤₜ, and fK⁰₊(0) = 0.624 ± 0.052ₛₜₐₜ ± 0.013syst±0.002ᵢₙₚᵤₜ.