Polarization, CP Asymmetry and Branching ratios in B \to K^* K^* with Perturbative QCD approach

Abstract

We study the charmless rare decays $B\to K^{\ast }{K}^{\ast }$ within the Perturbative QCD picture. We calculate not only factorizable and non-factorizable diagrams, but also annihilation ones. Our predictions are the following: The longitudinal polarization fraction vary from 75% to 99% depending on channels, the branching ratios are of order $10^{-7}$ for $B^0({\bar{B}}^0)\to K^{\ast 0}{\bar{K}}^{\ast 0}$ and $B^{\pm }\to K^{\ast \pm }{\bar{K}}^{\ast 0}(K^{\ast 0})$, much bigger than that for $B^0({\bar{B}}^0)\to K^{\ast +}{K}^{\ast -}$($10^{-8}$). The direct CP asymmetry in $B^{\pm }\to K^{\ast \pm }{\bar{K}}^{\ast 0}(K^{\ast 0})$ and $B^0({\bar{B}}^0)\to K^{\ast +}{K}^{\ast -}$ is about -15% and -65% if we choose $\alpha ({\varphi }_2)$ as $95^{\circ }$. There's no direct CPV in $B^0({\bar{B}}^0)\to K^{\ast 0}{\bar{K}}^{\ast 0}$ decays because of the pure $b\to d$ penguin topology. Our predictions will be tested in the future B experiments.

32 pages, 8 figures