Study of Bc χ₂₉\ (P, V) decays in the improved perturbative QCD formalism

Motivated by the recent LHCb measurements of the ratios between the branching ratios (BRs), R⏦_₂₂/J/ψ BR (Bc^+ χ₂₂ π^+) / BR (Bc^+ J/ψπ^+) and R⏦_₂₁/χ₂₂ BR (Bc^+ χ₂₁ π^+) / BR (Bc^+ χ₂₂ π^+), we analyze the decays Bc^+ χ₂₉ (P, V) ^+ in the improved perturbative QCD (iPQCD) formalism, where χ₂₉ 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⏦_₂₂/J/ψ = 0. 32 0. 05 and R⏦_₂₁/χ₂₂= 0. 11 0. 01 at leading order in the strong coupling αₛ agree well with the data within uncertainties. The result R⏦_₂₀/J/ψ BR (Bc^+ χ₂₀ π^+) / BR (Bc^+ J/ψπ^+) = 0. 17 0. 02 is lower than 1. 41^+0. 50-₀. ₄₅ inferred by the Bc^+ χ₂₀ π^+ measurement. The large longitudinal polarization fractions imply that these components dominate the Bc^+ χ₂₁, ₂₂ ρ^+ BRs. A peculiar constructive (destructive) interference between the twist-2 and twist-3 contributions is identified in the Bc^+ χ₂₁ ρ^+ (Bc^+ χ₂₁ π^+) mode, but not in the corresponding ones with χ₂₀, ₂₂ mesons. Inputting the BRs of the strong decays χ₂₀, ₂₂ π^+ π^- / K^+ K^- and χ₂₉ π^+π^- (π^+ π^-/K^+K^-) reported by the BESIII Collaboration, we obtain those of Bc^+ χ₂₉ (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 Bcχ₂₉ transitions.