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Charmless hadronic $B_c \to VA, AA$ decays in the perturbative QCD approach

In this work, we calculate the branching ratios (BRs) and the polarization fractions of sixty two charmless two-body $B_c$ meson decays into final states involving one vector and one axial-vector meson ($VA$) or two axial-vector mesons($AA$) within the framework of perturbative QCD (pQCD) approach systematically, where $A$ is either a $^3P_1$ or $^1P_1$ axial-vector meson. All considered decay channels can only occur through the annihilation topologies in the standard model. Based on the perturbative calculations and phenomenological analysis, we find the following results: (i) the CP-averaged BRs of the considered sixty two $B_c$ decays are in the range of $10^{-5}$ to $10^{-9}$; (ii) since the behavior for $^1P_1$ meson is much different from that of $^3P_1$ meson, the BRs of $B_c \to A(^1P_1) (V, A(^1P_1))$ decays are generally larger than that of $B_c \to A(^3P_1) (V, A(^3P_1))$ decays in the pQCD approach; (iii) many considered decays modes, such as $B_c\to a_1(1260)^+ ω$, $b_1(1235) ρ$, etc, have sizable BRs within the reach of the LHCb experiments; (iv) the longitudinal polarization fractions of most considered decays are large and play the dominant role; (v) the pQCD predictions for several decays involving mixtures of $^3P_1$ and/or $^1P_1$ mesons are highly sensitive to the values of the mixing angles, which will be tested by the ongoing LHC and forthcoming Super-B experiments; (vi) the CP-violating asymmetries of these considered $B_c$ decays are absent in the standard model because only one type tree operator is involved.