Study of Semileptonic <i>B</i> ⟶DP <i>ℓ</i> ⁺ <i>ν</i> _<i>ℓ</i> Decays Based on the SU(3) Flavor Symmetry

Decays B ⟶DP ℓ + ν ℓ ( ℓ = e , μ , τ ) with the nonresonance, the charmed vector resonances, the charmed scalar resonances, and the charmed tensor resonances are explored by using the SU(3) flavor symmetry approach. Firstly, the decay amplitudes of different modes are related by the SU(3) flavor symmetry. Then, relevant experimental data are used to constrain nonperturbative coefficients in the nonresonant and various resonant B ⟶ D P ℓ + ν ℓ decays. Finally, using the constrained nonperturbative coefficients, the branching ratios of not‐yet‐measured B ⟶DP ℓ + ν ℓ decays with the nonresonant and various charmed resonant contributions are predicted. Many branching ratios are predicted for the first time. We find that B ⟶ D η ′ ℓ + ν ℓ , B s ⟶ D s η ′ ℓ + ν ℓ decays only receive the nonresonant contributions; B ⟶ D s K ℓ + ν ℓ , B s ⟶DK ℓ + ν ℓ , B ⟶ D η ℓ + ν ℓ , and B s ⟶ D s η ℓ + ν ℓ decays receive both the nonresonant and the tensor resonant contributions; B + ⟶ D − π + ℓ + ν ℓ decays receive the nonresonant, the scalar resonant, and the tensor resonant contributions; and other B ⟶ D π ℓ + ν ℓ decays receive all kinds of contributions. These results can be used to test the SU(3) flavor symmetry approach in the four‐body semileptonic B decays in future experiments at LHCb and Belle‐II.