Analysis of B-> \phi K Decays in QCD Factorization

Abstract

We analyze the decay $B\to \varphi K$ 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 $(S-P)(S+P)$ penguin operators, which are formally power-suppressed by order $(\Lambda /m_b{)}^2$, are chirally and logarithmically enhanced. Therefore, these annihilation contributions are not subject to helicity suppression and can be sizable. The predicted branching ratio of $B^{-}\to \varphi K^{-}$ is $(3.8\pm 0.6)\times 10^{-6}$ in the absence of annihilation contributions and it becomes $(4.3_{-1.4}^{+3.0})\times 10^{-6}$ when annihilation effects are taken into account. The prediction is consistent with CLEO and BaBar data but smaller than the BELLE result.

Comments: 13 pages, 3 figures. A major change for the presentation of branching-ratio predictions. Experimental data are updated