Direct CP violation, branching ratios and form factors B→π,B→K in B decays

The B --> pi and B --> K transitions involved in hadronic B decays are investigated in a phenomenological way through the framework of QCD factorization. By comparing our results with experimental branching ratios from the BELLE, BABAR and CLEO collaborations for all the B decays including either a pion or a kaon, we propose boundaries for the transition form factors B --> pi and B --> K depending on the CKM matrix element parameters p and eta. From this analysis, the form factors required to reproduce the experimental data for branching ratios are FB-->pi = 0.31 +/- 0.12 and FB-->K = 0.37 +/- 0.13. We calculate the direct CP violating asymmetry parameter, acp, for B --> pi(+)pi(-)pi and B --> pi(+)pi(-)K decays, in the case where p-w mixing effects are taken into account. Based on these results, we find that the direct CP asymmetry for B- --> pi(+)pi(-)pi(-), (B) over bar (0) --> pi(+)pi(-)pi(0), B- --> pi(+)pi(-)K(-) and (B) over bar (0) --> pi(+)pi(-)(K) over bar (0), reaches its maximum when the invariant mass pi(+)pi(-) is in the vicinity of the w meson mass. The inclusion of p-w mixing provides an opportunity to erase, without ambiguity, the phase uncertainty mod(pi) in the determination of the CKM angles alpha in the case of b --> u and gamma in the case of b --> s.