Fat penguins and imaginary penguins in perturbative QCD
  We evaluate $B\to K\pi$ decay amplitudes in perturbative QCD picture. It is found that penguin contributions are dynamically enhanced by nearly 50% compared to those assumed in the factorization approximation. It is also shown that annihilation diagrams are not negligible, and give large strong phases. Our results for branching ratios of $B\to K\pi$ decays for a representative parameter set are consistent with data. We evaluate $B\to K\pi$ decay amplitudes in perturbative QCD picture. It is found that penguin contributions are dynamically enhanced by nearly 50% compared to those assumed in the factorization approximation. It is also shown that annihilation diagrams are not negligible, and give large strong phases. Our results for branching ratios of $B\to K\pi$ decays for a representative parameter set are consistent with data. 
Yong-Yeon Keum, Hsiang-nan Li and A.I. Sanda