Final state interaction and $B\to KK$ decays in perturbative QCD

Abstract

We predict branching ratios and CP asymmetries of the $B\to KK$ decays using perturbative QCD factorization theorem, in which tree, penguin, and annihilation contributions, including both factorizable and nonfactorizable ones, are expressed as convolutions of hard six-quark amplitudes with universal meson wave functions. The unitarity angle $\phi_3= 90^o$ and the $B$ and $K$ meson wave functions extracted from experimental data of the $B\to K\pi$ and $\pi\pi$ decays are employed. Since the $B\to KK$ decays are sensitive to final-state-interaction effects, the comparision of our predictions with future data can test the neglect of these effects in the above formalism. The CP asymmetry in the $B^\pm\to K^\pm K^0$ modes and the $B_d^0\to K^\pm K^\mp$ branching ratios depend on annihilation and nonfactorizable amplitudes. The $B\to KK$ data can also verify the evaluation of these contributions.