Direct CP violation in B→π+π−π : determination of α without discrete ambiguity

Abstract

Direct CP violation in the hadronic decays B̄0 → π+π-π0 is investigated near the peak of the ρ0, taking into account the effect of ρ-ω mixing. The branching ratios for the processes B±,0 → ρ±,0π±,0 and B- → ωπ- are calculated as well. We find that the CP violating asymmetry is strongly dependent on the CKM matrix elements. For a fixed N Ceff, the CP violating asymmetry, aCP, has a maximum of order -40% to -70% for B̄0 → ρ 0(ω)π0 when the invariant mass of the π +π- pair is in the vicinity of the w resonance. The sensitivity of the asymmetry to NCeff is small in that case. Moreover, we find that in the range of NCeff which is allowed by the most recent experimental branching ratios from the BABAR, BELLE and CLEO Collaborations, the sign of sin δ is always positive. Thus, a measurement of direct CP violation in the decays B̄0 → π+π-π0 would remove the mod (π) ambiguity in the determination of the CP violating phase angle α.