Eur. Phys. J. C (2024) 84: 1110
https://doi.org/10.1140/epjc/s10052-024-13387-0

Regular Article - Theoretical Physics

Study of the axial-vector and tensor resonant contributions to the $D\to VP{\ell }^{+}{\nu }_{\ell }$ decays based on SU(3) flavor analysis

College of Physics and Communication Electronics, Jiangxi Normal University, 330022, Nanchang, Jiangxi, China

^d ruminwang@sina.com

Received: 25 August 2024
Accepted: 16 September 2024
Published online: 25 October 2024

Abstract

Semileptonic three-body $D\to M{\ell }^{+}{\nu }_{\ell }$ decays, non-leptonic $M\to VP$ decays, and semileptonic four-body $D\to M(M\to VP){\ell }^{+}{\nu }_{\ell }$ decays are analyzed using the SU(3) flavor symmetry/breaking approach, where $\ell =e/\mu$, $M=A/T$, and A/T/V/P denote the axial-vector/tensor/vector/pseudoscalar mesons, respectively. In terms of SU(3) flavor symmetry/breaking, the decay amplitudes of the $D\to M{\ell }^{+}{\nu }_{\ell }$ decays and the vertex coefficients of the $M\to VP$ decays are related. The relevant non-perturbative parameters of the $D\to A{\ell }^{+}{\nu }_{\ell }$, $A\to VP$, and $T\to VP$ decays are constrained by the present experimental data, and the non-perturbative parameters of $D\to T{\ell }^{+}{\nu }_{\ell }$ decays are taken from the results in the light-front quark model since no experimental data are available at present. The branching ratios of the $D\to M{\ell }^{+}{\nu }_{\ell }$, $M\to VP$, and $D\to M(M\to VP){\ell }^{+}{\nu }_{\ell }$ decays are then predicted. We find that some processes receive both tensor and axial-vector resonant contributions, while other processes receive only axial-vector resonant contributions. In cases where both kinds of resonant contributions exist, the axial-vector contributions are dominant. Some branching ratios with axial-vector resonance states are large, and they may be measured experimentally in the near future. In addition, the sensitivities of the branching ratios of $D\to A{\ell }^{+}{\nu }_{\ell }$ and $A\to VP$ decays to the parameters are also investigated, and some decay branching ratios are found to be sensitive to the non-perturbative parameters.