We present an analysis of the decay $D^{+}\to K^{-}{\pi }^{+}{e}^{+}{\nu }_e$ 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 $\mathcal{B}(D^{+}\to K^{-}{\pi }^{+}{e}^{+}{\nu }_e)=(3.77\pm 0.03\pm 0.08)\%$. For $0.8<m_{K\pi }<1.0\mathrm{GeV}/c^2$, the partial branching fraction is $\mathcal{B}(D^{+}\to K^{-}{\pi }^{+}{e}^{+}{\nu }_e{)}_{[0.8,1.0]}=(3.39\pm 0.03\pm 0.08)\%$. A partial wave analysis shows that the dominant ${\overline{K}}^{*}(892{)}^0$ component is accompanied by an $S$-wave contribution accounting for $(6.05\pm 0.22\pm 0.18)\%$ of the total rate and that other components are negligible. The parameters of the ${\overline{K}}^{*}(892{)}^0$ resonance and of the form factors based on the spectroscopic pole dominance predictions are also measured. We also present a measurement of the ${\overline{K}}^{*}(892{)}^0$ helicity basis form factors in a model-independent way.

• Received 26 December 2015

DOI:https://doi.org/10.1103/PhysRevD.94.032001