Penguin Enhancement and $B\to K\pi$ decays in perturbative QCD

Abstract

We compute branching ratios of $B\to K\pi$ decays in the framework of perturbative QCD factorization theorem. Decay amplitudes are classified into the topologies of tree, penguin and annihilation, all of which contain both factorizable and nonfactorizable contributions. These contributions are expressed as the convolutions of hard $b$ quark decay amplitudes with universal meson wave functions. It is shown that (1) matrix elements of penguin operators are dynamically enhanced compared to those employed in the factorization assumption; (2) annihilation diagrams are not negligible, contrary to common belief; (3) annihilation diagrams contribute large strong phases; (4) the uncertainty of current data of the ratio $R={\cal B}(B_d^0\to K^\pm\pi^\mp)/{\cal B}(B^\pm\to K^0\pi^\pm)$ and of CP asymmetries is too large to give a constraint of $\phi_3$. Assuming $\phi_3=90^o$ which is extracted from the best fit to the data of $R$, predictions for the branching ratios of the four $B\to K\pi$ modes are consistent with data.