Penguin enhancement and<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:mrow><mml:mover><mml:mrow><mml:mi>B</mml:mi></mml:mrow><mml:mrow><mml:mo>→</mml:mo></mml:mrow></mml:mover></mml:mrow></mml:mrow><mml:mi>K</mml:mi><mml:mi>π</mml:mi></mml:math>decays in perturbative QCD

Abstract

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