Semileptonic $D_{e4}$ decays: hadronic dynamics and the determination of $\mathrm{\mid }{V}_{cs}\mathrm{\mid }$

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, which has been suggested as an observational evidence for the light scalar strange resonance. Implications for the determination of the $\mathrm{\mid }{V}_{cs}\mathrm{\mid }$ quark mixing matrix element are discussed.