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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.

Abstract Motivated by the persistent anomalies reported in the $$b\rightarrow c \tau \bar{\nu }$$ b → c τ ν ¯ data, we investigate the semileptonic decays $$\bar{B}^* \rightarrow V \tau ^-\bar{\nu }_{\tau } (V=D^*_{u,d,s},J/\psi )$$ B ¯ ∗ → V τ - ν ¯ τ ( V = D u , d , s ∗ , J / ψ ) , within the Standard Model and beyond. The relevant transition form factors, being calculated in the covariant light-front quark model, is the main source of theoretical uncertainties. Using various best-fit solutions for the new operator Wilson coefficients, we report numerical results on various observables related to the processes $$\bar{B}^* \rightarrow V \tau ^-\bar{\nu }_{\tau }$$ B ¯ ∗ → V τ - ν ¯ τ , such as the branching ratios, the ratio of branching fractions, the hadron and lepton polarization asymmetries, the forward–backward asymmetries and the convexity parameter. We also predict the $$q^2$$ q 2 distribution of these observables both within the Standard Model and in various new physics scenarios. The accessible observables are studied in order to assess their sensitivity to the different new physics scenarios. We can find that some of the new physics scenarios can be differentiated from each other by using these observables and their correlations. We also find that some observables of these decay modes are sizeable and deviate significantly (for new physics coupling parameter $$S_R$$ S R especially) from their corresponding standard model values, which are expected to be within the reach of Run III of Large Hadron Collider experiment. And experimental information on these distributions which will be testified in the future can help to disentangle the dynamical origin of the current anomalies.