The pure annihilation type B_c to M_2 M_3 decays in the perturbative QCD approach

Abstract

In the standard model the two-body charmless hadronic $B_c$ meson decays can occur via annihilation diagrams only. In this work, we studied the $B_c\to PP,PV/VP,VV$ decays by employing the perturbative QCD (pQCD) factorization approach. From our calculations, we find that (a) the pQCD predictions for the branching ratios of the considered $B_c$ decays are in the range of $10^{-6}$ to $10^{-8}$; (b) for $B_c\to PV/VP,VV$ decays, the branching ratios of $\Delta S=0$ decays are much larger than those of $\Delta S=1$ ones because the different Cabibbo-Kobayashi-Maskawa(CKM) factors are involved; (c) analogous to $B\to K{\eta }^{(\prime )}$ decays, we find $Br(B_c\to K^{+}{\eta }^{\prime })\sim 10\times Br(B_c\to K^{+}\eta )$, which can be understood by the destructive and constructive interference between the ${\eta }_q$ and ${\eta }_s$ contribution to the $B_c\to K^{+}\eta$ and $B_c\to K^{+}{\eta }^{\prime }$ decay; (d) the longitudinal polarization fractions of $B_c\to VV$ decays are in the range of $86$ and play the dominant role; and (e) there is no CP-violating asymmetries for the considered $B_c$ decays because only one type tree operators involved.

Comments: 22 pages, 1 figure