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In this paper we calculate the branching ratios (BRs) of the 32 charmlesshadronic $B_c \to A P$ decays ($A=a_1(1260),b_1(1235),K_1(1270),K_1(1400),f_1(1285),f_1(1420),h_1(1170),h_1(1380)$) by employing the perturbativeQCD(pQCD) factorization approach. These considered decay channels can onlyoccur via annihilation type diagrams in the standard model. From the numericalcalculations and phenomenological analysis, we found the following results: (a)the pQCD predictions for the BRs of the considered $B_c$ decays are in therange of $10^{-6}$ to $10^{-8}$, while the CP-violating asymmetries are absentbecause only one type tree operator is involved here; (b) the BRs of $\Delta S=0$ processes are generally much larger than those of $\Delta S =1$ ones due tothe large CKM factor of $|V_{ud}/V_{us}|^2\sim 19$; (c) since the behavior for$^1P_1$ meson is much different from that of $^3P_1$ meson, the BRs of $B_c \toA(^1P_1) P$ decays are generally larger than that of $B_c \to A(^3P_1) P$decays; (d) the pQCD predictions for the BRs of $B_c \to (K_1(1270), K_1(1400))\etap $ and $(K_1(1270), K_1(1400)) K$ decays are rather sensitive to the valueof the mixing angle $\theta_K$.

Branching ratios of $B_c \to A P $ decays in the perturbative QCD approach