Analysis of B-> φK Decays in QCD Factorization

We analyze the decay $B\to \phi K$ 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 (V-A)(V+A) penguin operators, which are formally power-suppressed by order $(\Lambda_{QCD}/m_b)^2$, are chirally and in particular logarithmically enhanced. Therefore, these annihilation contributions are not subject to helicity suppression and can be sizable. The predicted branching ratio of $B\to\phi K$ is of order $(0.7\sim 1.1)\times 10^{-5}$ if the phase of the annihilation amplitude lies in the range $45^\circ<\theta< 90^\circ$. The corresponding absolute ratio of annihilation to penguin amplitudes is about $0.4\sim 0.5$.