Direct CP Violation in B \to π^{+} π^{-} π: Determination of α without discrete ambiguity
Abstract
Direct CP violation in the hadronic decays \Bar{B}^{0} \to \pi^{+}\pi^{-} \pi^{0} is investigated near the peak of the \rho^{0} taking into account the effect of \rho - \omega mixing. Branching ratios for processes B^{\pm,0} \to \rho^{\pm,0}\pi^{\pm,0} and B^{-} \to \omega \pi^{-} are calculated as well. We find that the CP violating asymmetry is strongly dependent on the CKM matrix elements. For a fixed N_{c}^{eff}, the CP violating asymmetry, a, has a maximum of order -40% to -70% for \Bar{B}^{0} \to \rho^{0}(\omega) \pi^{0} when the invariant mass of the \pi^{+}\pi^{-} pair is in the vicinity of the \omega resonance.
The sensitivity of the asymmetry to N_{c}^{eff} is small in that case. Moreover, we find that in the range of N_{c}^{eff} which is allowed by the most recent experimental branching ratios from the BABAR, BELLE and CLEO Collaborations, the sign of \sin \delta is always positive. Thus, a measurement of direct CP violation in decays \Bar{B}^{0} \to \pi^{+}\pi^{-} \pi^{0} would remove the mod(\pi) ambiguity in the determination of the CP violating phase angle \alpha.