Semileptonic Dₑ₄ decays: hadronic dynamics and the determination of |Vcs|

The four-body decays D⁺ → K⁻π ⁺e⁺ν ₑ D + → K - π + e + ν e ( Dₑ₄⁺ D e 4 + ) and D⁰→ K⁰̄π ⁻e⁺ν ₑ D 0 → K 0 ¯ π - e + ν e ( D⁰ₑ₄ D e 4 0 ) are studied in a model where the momentum-dependence of the hadronic matrix elements are described in terms of K^*(892) K ∗ ( 892 ) and D^*(2010) D ∗ ( 2010 ) pole contributions. From fits to the recent data of the BESIII collaboration we find that the D^* D ∗ -pole can mimic the effect of the S -wave contribution of the Kπ K π system to the branching fraction. Implications for the determination of the |Vcs| | V cs | quark mixing matrix element are discussed.