Study of $D^{+} to K^{-} pi^+ e^+ u_e$

We present an analysis of the decay $D^{+} to K^{-} pi^+ e^+ u_e$ based on data collected by the BESIII experiment at the $psi(3770)$ resonance. Using a nearly background-free sample of 18262 events, we measure the branching fraction $mathcal{B}(D^{+} to K^{-} pi^+ e^+ u_e) = (3.71 pm 0.03 pm 0.08)%$. For $0.8<m_{Kpi}<1.0$ GeV/$c^{2}$ the partial branching fraction is $mathcal{B}(D^{+} to K^{-} pi^+ e^+ u_e)_{[0.8,1]} = (3.33 pm 0.03 pm 0.07)%$. A partial wave analysis shows that the dominant $bar K^{*}(892)^{0}$ component is accompanied by an emph{S}-wave contribution accounting for $(6.05pm0.22pm0.18)%$ of the total rate and that other components are negligible. The parameters of the $bar K^{*}(892)^{0}$ resonance and of the form factors based on the spectroscopic pole dominance predictions are also measured. We also present a measurement of the $bar K^{*}(892)^{0}$ helicity basis form factors in a model-independent way.