Perturbative QCD analysis of $B \to \phi K$ decays and Power counting

Abstract

We investigate exclusive nonleptonic $B$ meson decays $B\to\phi K$ in perturbative QCD formalism. It is shown that the end-point (logarithmic and linear) singularities in decay amplitudes do not exist, after $k_T$ and threshold resummations are included. Power counting for emission and annihilation topologies of diagrams, including both factorizable and nonfactorizable ones, is discussed with Sudakov effects taken into account. Our predictions for the branching ratios $B(B\to\phi K)\sim 10 \times 10^{-6}$ are larger than those ($\sim 4 \times 10^{-6}$) from the factorization approach because of dynamical enhancement of penguin contributions. Whether this enhancement is essential for penguin-dominated modes can be justified by experimental data.