Study of the axial-vector and tensor resonant contributions to the $$D \rightarrow VP\ell ^+\nu _\ell $$ D → V P ℓ + ν ℓ decays based on SU(3) flavor analysis

Abstract Semileptonic three-body $$D \rightarrow M\ell ^+\nu _\ell $$ D → M ℓ + ν ℓ decays, non-leptonic $$M \rightarrow VP$$ M → V P decays, and semileptonic four-body $$D \rightarrow M(M \rightarrow VP)\ell ^+\nu _\ell $$ D → M ( M → V P ) ℓ + ν ℓ decays are analyzed using the SU(3) flavor symmetry/breaking approach, where $$\ell =e/\mu $$ ℓ = e / μ , $$M=A/T$$ 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 $$D \rightarrow M \ell ^+ \nu _\ell $$ D → M ℓ + ν ℓ decays and the vertex coefficients of the $$M \rightarrow VP$$ M → V P decays are related. The relevant non-perturbative parameters of the $$D \rightarrow A\ell ^+\nu _\ell $$ D → A ℓ + ν ℓ , $$A \rightarrow VP$$ A → V P , and $$T \rightarrow VP$$ T → V P decays are constrained by the present experimental data, and the non-perturbative parameters of $$D \rightarrow T\ell ^+\nu _\ell $$ D → T ℓ + ν ℓ 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 $$D \rightarrow M \ell ^+ \nu _\ell $$ D → M ℓ + ν ℓ , $$M \rightarrow VP$$ M → V P , and $$D\rightarrow M(M\rightarrow VP)\ell ^+\nu _\ell $$ D → M ( M → V P ) ℓ + ν ℓ 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 $$D \rightarrow A \ell ^+ \nu _\ell $$ D → A ℓ + ν ℓ and $$A \rightarrow VP$$ A → V P decays to the parameters are also investigated, and some decay branching ratios are found to be sensitive to the non-perturbative parameters.