Measurement of the Form Factors in the Decay D⁺ → ωe⁺ν_e and Search for the Decay D⁺ → φe⁺ν_e.

Using 2.92 fb⁻¹ of electron-positron annihilation data collected at a center-of-mass energy of √s = 3.773 GeV with the BESIII detector, we present an improved measurement of the branching fraction ℬ(D⁺ → ωe⁺ν_e) = (1.63 ± 0.11 ± 0.08) x 10⁻³. The parameters defining the corresponding hadronic form factor ratios at zero momentum transfer are determined for the first time; we measure them to be r_V = 1.24 ± 0.09 ± 0.06 and r_2 = 1.06 ± 0.15 ± 0.05. The first and second uncertainties are statistical and systematic, respectively. We also search for the decay D⁺ → ωe⁺ν_e. An improved upper limit ℬ(D⁺ → φe⁺ν_e < 1.3 x 10⁻⁵ is set at 90% confidence level.