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

TL;DR

This paper systematically calculates branching ratios and polarization fractions for 62 charmless $B_c$ meson decays into $VA$ and $AA$ final states using perturbative QCD, revealing sizable decay modes and sensitivity to mixing angles.

Contribution

It provides the first comprehensive pQCD analysis of charmless $B_c o VA, AA$ decays, including polarization and CP asymmetry predictions, highlighting differences between $^1P_1$ and $^3P_1$ mesons.

Findings

Branching ratios range from 10^{-5} to 10^{-9}.

Decays involving $^1P_1$ mesons generally have larger BRs.

Many decay modes are within LHCb detection capabilities.

Abstract

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 $B_c\to a_1(1260)^+ \omega$, $b_1(1235) \rho$, 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.