Perturbative QCD analysis ofB→φKdecays and power counting

Abstract

We investigate the exclusive nonleptonic B meson decays $\stackrel{\ensuremath{\rightarrow}}{B}\ensuremath{\varphi}K$ in the perturbative QCD formalism. It is shown that the end-point (logarithmic and linear) singularities in the 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 $B(\stackrel{\ensuremath{\rightarrow}}{B}\ensuremath{\varphi}K)\ensuremath{\sim}10\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}6}$ are larger than those $(<~4\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}6})$ 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.