Precision measurements of the semileptonic decays D+s→ηe+νe and D+s→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(D+s→ηe+νe)=(2.255±0.039stat±0.051syst)% and B(D+s→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 D+s→ηe+νe and D+s→η′e+νe, the products of the hadronic transition form factors fη(')+(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 fη+(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.
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