Study of $B_{c} \to J/\psi (a_1(1260)$, $b_1(1235)$, $a_2(1320)$, $K_2^*(1430)) $ decay with a perturbative QCD approach

Abstract

Motivated by systematic observations of $ B_c $ decays at LHCb, we analyze $B_c^+ \to J/\psi (A, T)$ 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. The framework employs light-cone distribution amplitudes (LCDAs) to regulate nonperturbative dynamics, utilizing Sudakov suppression to control endpoint divergences. Our predictions indicate branching ratios of $10^{-3}\sim 10^{-2}$ for $B_c^{+} \to J/\psi A$ and $10^{-5}\sim 10^{-4}$ for $B_c^{+} \to J/\psi T$ decays, which seem to be in the reach of future experiments. We also provide predictions for the polarization fractions of these decays. Based on quark helicity analysis, the longitudinal polarization amplitudes are expected to dominate the branching ratios.