Motivated by the recent LHCb measurements of the ratios between the branching ratios (BRs), Rχc2/J/ψ≡BR(Bc+→χc2π+)/BR(Bc+→J/ψπ+) and Rχc1/χc2≡BR(Bc+→χc1π+)/BR(Bc+→χc2π+), 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 Rχc2/J/ψ=0.32±0.05 and Rχc1/χc2=0.11±0.01 at leading order in the strong coupling αs agree well with the data within uncertainties. The result Rχc0/J/ψ≡BR(Bc+→χc0π+)/BR(Bc+→J/ψπ+)=0.17±0.02 is lower than 1.41−0.45+0.50 inferred by the Bc+→χc0π+ measurement. The large longitudinal polarization fractions imply that these components dominate the Bc+→χc1,c2ρ+ BRs. A peculiar constructive (destructive) interference between the twist-2 and twist-3 contributions is identified in the Bc+→χc1ρ+ (Bc+→χc1π+) 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.
Liu et al. (Mon,) studied this question.