Study of Bc → χcJ\ (P, V) decays in the improved perturbative QCD formalism

Motivated by the recent LHCb measurements of the ratios between the branching ratios (BRs), R_χc2/J/ψ ≡ BR(Bc⁺ → χc2 π⁺)/ BR(Bc⁺ → J/ψπ⁺) and R_χc1/χc2 ≡ BR(Bc⁺ → χc1 π⁺)/ BR(Bc⁺ → χc2 π⁺), we analyze the decays Bc⁺ → χcJ (P, V)⁺ in the improved perturbative QCD (iPQCD) formalism, where χcJ denotes the p-wave charmonia with $J=0, 1, 2$, and $P (V)$ denotes the pseudoscalars $π$ and K (the vectors $ρ$ and K^*). Our results R_χc2/J/ψ = 0.32 ± 0.05 and R_χc1/χc2= 0.11 ± 0.01 at leading order in the strong coupling αₛ agree well with the data within uncertainties. The result R_χc0/J/ψ ≡ BR(Bc⁺ → χc0 π⁺)/ BR(Bc⁺ → J/ψπ⁺) = 0.17 ± 0.02 is lower than 1.41+0.50-0.45 inferred by the Bc⁺ → χc0 π⁺ measurement. The large longitudinal polarization fractions imply that these components dominate the Bc⁺ → χc1,c2 ρ⁺ BRs. A peculiar constructive (destructive) interference between the twist-2 and twist-3 contributions is identified in the Bc⁺→ χc1 ρ⁺ (Bc⁺→ χc1 π⁺) mode, but not in the corresponding ones with χc0,c2 mesons. Inputting the BRs of the strong decays χc0,c2 → π⁺ π⁻ / K⁺ K⁻ and χcJ → π⁺π⁻(π⁺ π⁻/K⁺K⁻) reported by the BESIII Collaboration, we obtain those of Bc⁺ → χcJ (ρ, π)⁺ followed by secondary decay chains under the narrow-width approximation. All the above iPQCD predictions can be confronted by more precise experiments in the future to deepen our understanding of QCD dynamics in Bc→χcJ transitions.