ar X iv : h ep - p h / 05 08 07 9 v 2 1 1 O ct 2 00 5 Revisiting B → ππ , πK Decays in QCD Factorization Approach

Motivated by the recent experimental data, we have revisited the B → πK, ππ decays in the framework of QCD factorization, with inclusion of the important strong penguin corrections of order αs induced by b → Dg∗g∗ (D = d or s and g∗ denotes an off-shell gluon) transitions. We find that these higher order strong penguin contributions can provide ∼ 30% enhancement to the penguin-dominated B → πK decay rates, and such an enhancement can improve the consistency between the theoretical predictions and the experimental data significantly, while for the tree-dominated B → ππ decays, these higher order contributions play only a minor role. When these strong penguin contributions are summed, only a small strong phase remains and the direct CP asymmetries get small corrections. We also find patterns of the ratios between the CP -averaged branching fractions remain nearly unaffected even after including these higher order corrections and the πK puzzle still persists. Our results may indicate that to resolve the puzzle one would have to resort to new physics contributions in the electroweak penguin sector as found by Buras et al. PACS Numbers: 13.25Hw,12.15Mm, 12.38Bx ∗Corresponding author. E-mail address: [email protected] 1