Precision Measurements of Dₛ⁺ → ηe⁺ νₑ and Dₛ⁺ → η^ e⁺ νₑ

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Precision measurements of the semileptonic decays Dₛ⁺ → ηe⁺ νₑ and Dₛ⁺ → η^ e⁺ νₑ are performed with 7.33\,fb⁻¹ of e⁺e⁻ collision data collected at center-of-mass energies between 4.128 and 4.226 GeV with the BESIII detector. The branching fractions obtained are B(Dₛ⁺ → ηe⁺ νₑ) = (2.255±0.039ₛₜₐₜ± 0.051syst)% and B(Dₛ⁺ → η^ e⁺ νₑ) = (0.810±0.038ₛₜₐₜ± 0.024syst)%. Combining these results with the B(D⁺→ηe⁺ νₑ) and B(D⁺→η^ e⁺ νₑ) obtained from previous BESIII measurements, the η-η^ mixing angle in the quark flavor basis is determined to be ϕP = (40.0±2.0ₛₜₐₜ±0.6syst)^∘. Moreover, from the fits to the partial decay rates of Dₛ⁺ → ηe⁺ νₑ and Dₛ⁺ → η^ e⁺ νₑ, the products of the hadronic transition form factors f₊^η⁽⁾(0) and the modulus of the c→ s Cabibbo-Kobayashi-Maskawa matrix element |Vcs| are determined by using different hadronic transition form factor parametrizations. Based on the two-parameter series expansion, the products f^η₊(0)|Vcs| = 0.4519±0.0071ₛₜₐₜ±0.0065syst and fη^₊(0)|Vcs| = 0.525±0.024ₛₜₐₜ±0.009syst are extracted. All results determined in this work supersede those measured in the previous BESIII analyses based on the 3.19 fb⁻¹ subsample of data at 4.178 GeV.