Polarization,CPasymmetry, and branching ratios inB→K*K*with the perturbative QCD approach

Abstract

We study the charmless rare decays $B\ensuremath{\rightarrow}{K}^{*}{K}^{*}$ within the perturbative QCD picture. We calculate not only factorizable and nonfactorizable 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 ${10}^{\ensuremath{-}7}$ for ${B}^{0}({\overline{B}}^{0})\ensuremath{\rightarrow}{K}^{*0}{\overline{K}}^{*0}$ and ${B}^{\ifmmode\pm\else\textpm\fi{}}\ensuremath{\rightarrow}{K}^{*\ifmmode\pm\else\textpm\fi{}}{\overline{K}}^{*0}({K}^{*0})$, much bigger than that for ${B}^{0}({\overline{B}}^{0})\ensuremath{\rightarrow}{K}^{*+}{K}^{*\ensuremath{-}}$(${10}^{\ensuremath{-}8}$). The direct $\mathrm{CP}$ asymmetry in ${B}^{\ifmmode\pm\else\textpm\fi{}}\ensuremath{\rightarrow}{K}^{*\ifmmode\pm\else\textpm\fi{}}{\overline{K}}^{*0}({K}^{*0})$ and ${B}^{0}({\overline{B}}^{0})\ensuremath{\rightarrow}{K}^{*+}{K}^{*\ensuremath{-}}$ is about $\ensuremath{-}15%$ and $\ensuremath{-}65%$ if we choose $\ensuremath{\alpha}({\ensuremath{\varphi}}_{2})$ as $95\ifmmode^\circ\else\textdegree\fi{}$. The direct $\mathrm{CP}$ violation in ${B}^{0}({\overline{B}}^{0})\ensuremath{\rightarrow}{K}^{*0}{\overline{K}}^{*0}$ decays is negligible if there is not strong final state interactions. Our predictions will be tested in the future $B$ experiments.