Improved estimates of the $B_{(s)}\to VV$ decays in perturbative QCD approach

We reexamine the branching fractions, $CP$ asymmetries, and other observables in a large number of $B_q\to VV(q=u,d,s)$ decays in the perturbative QCD approach, where $V$ denotes a light vector meson $(\rho ,K^{*},\omega ,\varphi )$. The essential difference between this work and earlier similar works is of parametric origin and in the estimates of the power corrections related to the ratio $r_i^2=m_{V_i}^2/m_B^2(i=2,3)$ ($m_V$ and $m_B$ denote the masses of the vector and $B$ meson, respectively). In particular, we use up-to-date distribution amplitudes for the final state mesons and keep the terms proportional to the ratio $r_i^2$ in our calculations. Our updated calculations are in agreement with the experimental data, except for a limited number of decays which we discuss. We emphasize that the penguin annihilation and the hard-scattering emission contributions are essential to understanding the polarization anomaly, such as in the $B\to \varphi K^{*}$ and $B_s\to \varphi \varphi$ decay modes. We also compare our results with those obtained in the QCD factorization approach and comment on the similarities and differences, which can be used to discriminate between these approaches in future experiments.

Figure 1

Leading order Feynman diagrams contributing to the $B_{(s)}\to VV$ decays in PQCD.