Measurement of the form factors in the decay $D^+ to omega e^+ u_{e}$ and search for the decay $D^+ to phi e^+ u_{e}$

Using 2.92 fb$^{-1}$ of electron-positron annihilation data collected at a center-of-mass energy of $sqrt{s}= 3.773$ GeV with the BESIII detector, we present an improved measurement of the branching fraction $mathcal{B}(D^+ to omega e^+ u_{e}) = (1.63pm0.11pm0.08)times 10^{-3}$. The parameters defining the corresponding hadronic form factor ratios at zero momentum transfer are determined for the first time, we measure them to be $r_V = 1.24pm0.09pm0.06$ and $r_2 = 1.06pm0.15 pm 0.05$. The first and second uncertainties are statistical and systematic, respectively. We also search for the decay $D^+ to phi e^+ u_{e}$. An improved upper limit $mathcal{B}(D^+ to phi e^+ u_{e}) < 1.3 times 10^{-5}$ is set at 90% confidence level.