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We present an analysis of the decay $D^{+} \to K^{-} \pi^+ e^+ \nu_e$ basedon data collected by the BESIII experiment at the $\psi(3770)$ resonance. Usinga nearly background-free sample of 18262 events, we measure the branchingfraction $\mathcal{B}(D^{+} \to K^{-} \pi^+ e^+ \nu_e) = (3.71 \pm 0.03 \pm0.08)\%$. For $0.8<m_{K\pi}<1.0$ GeV/$c^{2}$ the partial branching fraction is$\mathcal{B}(D^{+} \to K^{-} \pi^+ e^+ \nu_e)_{[0.8,1]} = (3.33 \pm 0.03 \pm0.07)\%$. A partial wave analysis shows that the dominant $\bar K^{*}(892)^{0}$component is accompanied by an \emph{S}-wave contribution accounting for$(6.05\pm0.22\pm0.18)\%$ of the total rate and that other components arenegligible. The parameters of the $\bar K^{*}(892)^{0}$ resonance and of theform factors based on the spectroscopic pole dominance predictions are alsomeasured. We also present a measurement of the $\bar K^{*}(892)^{0}$ helicitybasis form factors in a model-independent way.

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