Measurement of the Dynamics of the Decays Ds+ → η(′)e+νe

Using e+e− annihilation data corresponding to an integrated luminosity of 3.19 fb−1 collected at a center-of-mass energy of 4.178 GeV with the BESIII detector, we measure the absolute branching fractions BDs+→ηe+νe = (2.323±0.063stat ± 0.063syst)% and BDs+→η′e+νe = (0.824±0.073stat ± 0.027syst)% via a tagged analysis technique, where one Ds is fully reconstructed in a hadronic mode. Combining these measurements with previous BESIII measurements of BD+→η(′)e+νe, the η−η′ mixing angle in the quark flavor basis is determined to be ϕP = (40.1±2.1stat ± 0.7syst)°. From the first measurements of the dynamics of Ds+ → η(′)e+νe decays, the products of the hadronic form factors f+η(′)(0) and the Cabibbo-Kobayashi-Maskawa matrix element |Vcs| are determined with different form factor parametrizations. For the two-parameter series expansion, the results are f+η(0)|Vcs| = 0.4455±0.0053stat±0.0044syst and f+η′(0)|Vcs|=0.477±0.049stat±0.011syst.