DirectCPviolation, branching ratios and form factorsB→ π,B→KinBdecays

The B → π 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 → π and B → K depending on the CKM matrix element parameters ρ and η. From this analysis, the form factors required to reproduce the experimental data for branching ratios are F B →π = 0.31 ± 0.12 and F B → K = 0.37 ± 0.13. We calculate the direct CP violating asymmetry parameter, a CP , for B → π + π − π and B → π + π − K decays, in the case where ρ–ω mixing effects are taken into account. Based on these results, we find that the direct CP asymmetry for B − → π + π − π − , and , reaches its maximum when the invariant mass π + π − is in the vicinity of the ω meson mass. The inclusion of ρ–ω mixing provides an opportunity to erase, without ambiguity, the phase uncertainty mod(π) in the determination of the CKM angles α in the case of b → u and γ in the case of b → s .