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

TL;DR

This paper analyzes four-body semileptonic D meson decays using a pole model to understand hadronic dynamics and improve the extraction of the CKM matrix element |V_{cs}| from recent experimental data.

Contribution

It introduces a pole-based model for hadronic form factors in D_{e4} decays and examines its impact on determining |V_{cs}|, highlighting the role of D* and K* resonances.

Findings

D* pole can mimic S-wave effects in Kπ system

Implications for |V_{cs}| extraction are discussed

Model fits to BESIII data support the resonance contributions

Abstract

The four-body decays $D^+ \to K^-\pi^+e^+\nu_e$ ($D_{e4}^+$) and $D^0\to \overline{K^0}\pi^-e^+\nu_e$ ($D^0_{e4}$) are studied in a model where the momentum-dependence of the hadronic matrix elements are described in terms of $K^*(892)$ and $D^*(2010)$ pole contributions. From fits to the recent data of the BESIII collaboration we find that the $D^*$-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 $|V_{cs}|$ quark mixing matrix element are discussed.