Study of $B_{c} \to J/ψ(a_1(1260), b_1(1235),a_2(1320), K_2^*(1430))$ in the perturbative QCD approach

Motivated by systematic observations of $B_c$ decays at LHCb, we analyze $B_c^+ \to J/ψ(A, T)$ decays (where $A$ denotes axial-vector mesons $a_1(1260)^+, b_1(1235)^+$, and $T$ denotes tensor mesons $a_2(1320)^+, K_2^*(1430)^+$) within the perturbative QCD (pQCD) factorization framework. Nonperturbative dynamics are regulated by light-cone distribution amplitudes (LCDAs), with endpoint divergences controlled via Sudakov suppression. Predictions yield branching ratios ranging from $10^{-3}$ to $10^{-2}$ for $B_c^{+} \to J/ψA$ and at the level of $10^{-6}$ for $B_c^{+} \to J/ψT$, which seem to be in the reach of future experiments. We also provide predictions for the polarization fractions of $B_c^+ \to J/ψ(A, T)$, according to quark helicity analysis, the longitudinal polarization amplitudes are expected to dominate the branching ratios.