Systematic analysis of the transition form factors of Bc to D-wave charmonia and corresponding semileptonic decays

In this article, the vector, axial vector and tensor form factors of Bc to D-wave charmonia ψJ ($J=1,2,3$) and ηc2 are analyzed within the framework of three-point QCD sum rules. With the estimated vector and axial vector form factors, we study the decay widths and branching ratios of semileptonic decays Bc→ψJlνₗ̄ and Bc→ηc2lνₗ̄. Our results indicate that the semileptonic decay branching ratios of Bc to D-wave charmonia decreases as the total angler momentum of the final state D-wave charmonia increases. For decay processes Bc→ ψ₁lνₗ, Bc→ ψ₂[ηc2]lνₗ and Bc→ ψ₃lνₗ, the branching ratios can reach the order 10⁻³, 10⁻⁴ and 10⁻⁵, respectively, which can provide a valuable reference for future experimental measurements for Bc meson by LHCb collaboration. Furthermore, these results also can provide useful information to study the properties of Bc meson and D-wave charmonia.