Systematic analysis of D₍ₛ₎ meson semi-leptonic decays in the covariant light-front quark model

The weak decays of the D₍ₛ₎ 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₎ 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₎ 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₎→ P,S,V,A D ( s ) → 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₎→ P, V D ( s ) → 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₎→ S,A D ( s ) → S , A transitions, such as D→ a₀(980), a₀(1450) D → a 0 ( 980 ) , a 0 ( 1450 ) and D₍ₛ₎ → K1B D ( s ) → K 1 B , compared to other theoretical calculations. The predicted branching ratios for the semi-leptonic decays D→ P(V) ν _ D → P ( V ) ℓ ν</m