Systematic analysis of $D_{(s)}$ meson semi-leptonic decays in the covariant light-front quark model

TL;DR

The paper systematically evaluates D_{(s)} meson semi-leptonic decays to pseudoscalar, scalar, vector, and axial-vector final states within the covariant light-front quark model, computing a full set of transition form factors and extrapolating them over $q^2$ to predict branching ratios. By comparing to BESIII and other theoretical approaches, it finds broad agreement for D_{(s)} → P and D_{(s)} → V channels, while significant discrepancies remain for transitions to scalar and axial-vector mesons, reflecting uncertainties in their internal structures. The work also engages meson mixing phenomena, including η–η′ and K1 mixings, to interpret the patterns in form factors and BRs, offering insights into the nature of scalar and axial-vector states. Overall, the study provides a comprehensive CLFQM-based reference for charm semileptonic decays that can guide future experimental tests and help constrain hadronic structures in non-perturbative QCD.

Abstract

The weak decays of the $D_{(s)}$ meson provide a pivotal platform to advance our understanding of the Standard Model (SM) and to explore New Physics (NP). In recent years, experiments have collected a significant amount of data on the $D_{(s)}$ meson decays, particularly from BESIII, which provides substantial support for theoretical research. In this work, we systematically investigate the semi-leptonic decays of $D_{(s)}$ meson to pseudoscalar (P), scalar (S), vector (V), and axial-vector (A) mesons within the framework of the covariant light-front quark model (CLFQM). We calculate the form factors of the transitions $D_{(s)}\to P,S,V,A$ and the branching ratios of the corresponding semi-leptonic decays, then compare them with experimental data and results from other theoretical models. The form factor values of the transitions $D_{(s)}\to P, V$ obtained from the CLFQM are consistent with those of other theoretical models and available data in most cases. However, significant discrepancies are found in some specific $D_{(s)}\to S,A$ transitions, such as $D\to a_0(980), a_0(1450)$ and $D_{(s)} \to K_{1B}$, compared to other theoretical calculations. The predicted branching ratios for the semi-leptonic decays $D\to P(V)\ellν_\ell$ with $\ell=e,μ$ agree well with experimental data and other theoretical results in most decay channels, validating the reliability of the model. However, for some $D\to S(V)\ellν_\ell$ decays, tension exists among different theoretical predictions and experimental results. Further clarification of such differences is necessary. Our study provides important insights into the internal structures for some scalar and axial-vector mesons and serves as a theoretical reference for future experiments.

Figures (1)

• Figure 1: Feynman diagrams for $D_{(s)}$ decay (left) and transition (right) amplitudes, where $P^{\prime(\prime\prime)}$ is the incoming (outgoing) meson momentum, X denotes the vector or axial-vector transition vertex.