Penguin Enhancement and $B\to Kπ$ decays in perturbative QCD

TL;DR

The paper addresses the challenge of calculating exclusive charmless B decays by applying perturbative QCD factorization, which separates short-distance hard amplitudes from universal meson wave functions. It demonstrates that, with a dynamically determined hard scale, penguin contributions are dynamically enhanced and annihilation diagrams provide sizable strong phases, enabling predictions for B→Kπ branching ratios and CP asymmetries that align with data for a CKM angle φ_3 ≈ 90°. The analysis emphasizes the negligible role of soft final-state interactions and argues that the PQCD framework, including Sudakov suppression and k_T effects, yields a predictive, model-independent treatment of these decays. Overall, the work identifies penguin enhancement and annihilation-driven strong phases as key mechanisms for reconciling theory with experiment in B→Kπ and related modes. The results also suggest that the ratio R is a robust observable for constraining φ_3 with improved data.

Abstract

We compute branching ratios of $B\to Kπ$ 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 $R={\cal B}(B_d^0\to K^\pmπ^\mp)/{\cal B}(B^\pm\to K^0π^\pm)$ and of CP asymmetries is too large to give a constraint of $φ_3$. Assuming $φ_3=90^o$ which is extracted from the best fit to the data of $R$, predictions for the branching ratios of the four $B\to Kπ$ modes are consistent with data.