Semileptonic $D_{e4}$ decays: hadronic dynamics and the determination of $|V_{cs}|$

Abstract

The four-body decays $D^{+}\to K^{-}{\pi }^{+}{e}^{+}{\nu }_e$ ($D_{e4}^{+}$) and $D^0\to \overline{K^0}{\pi }^{-}{e}^{+}{\nu }_e$ ($D_{e4}^0$) are studied in a model where the momentum-dependence of the hadronic matrix elements are described in terms of $K^{\ast }(892)$ and $D^{\ast }(2010)$ pole contributions. From fits to the recent data of the BESIII collaboration we find that the $D^{\ast }$-pole can mimic the effect of the $S$-wave contribution of the $K\pi$ system to the branching fraction. Implications for the determination of the $|V_{cs}|$ quark mixing matrix element are discussed.

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