Analysis ofB→φKdecays in QCD factorization

We analyze the decay $\overrightarrow{B}\phi K$ within the framework of QCD-improved factorization. We find 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 $\left(S-P\right)(S+P)\mathrm{}$ penguin operators, which are formally power suppressed by order $({\Lambda }_{\mathrm{QCD}}{/m}_b{)}^2,$ are chirally and logarithmically enhanced. Therefore, these annihilation contributions are not subject to helicity suppression and can be sizable. The predicted branching ratio of $B^{-}\to \phi K^{-}$ is $(3.8\mathrm{}\pm 0.6)\times {10}^{-6}$ in the absence of annihilation contributions, and it becomes ${(4.3\mathrm{}}_{-1.4}^{+3.0\mathrm{}})\times {10}^{-6}$ when annihilation effects are taken into account. The prediction is consistent with the experimental data.