Analysis of B-> ϕK Decays in QCD Factorization

Abstract

We analyze the decay $B\to ϕK$ within the framework of QCD-improved factorization. We found that although the twist-3 kaon distribution amplitude dominates the spectator interactions, it will suppress the decay rates slightly. The weak annihilation diagrams induced by $(S-P)(S+P)$ penguin operators, which are formally power-suppressed by order $(Λ/m_b)^2$, are chirally and logarithmically enhanced. Therefore, these annihilation contributions are not subject to helicity suppression and can be sizable. The predicted branching ratio of $B^-\toϕK^-$ is $(3.8\pm0.6)\times 10^{-6}$ in the absence of annihilation contributions and it becomes $(4.3^{+3.0}_{-1.4})\times 10^{-6}$ when annihilation effects are taken into account. The prediction is consistent with CLEO and BaBar data but smaller than the BELLE result.