DirectCPviolation in [equation] : determination of [equation] without discrete ambiguity

摘要

Direct CP violation in the hadronic decays (Bar{B}^{0} ightarrow pi^{ + }pi^{-} pi^{0}) is investigated near the peak of the ( ho^{0}), taking into account the effect of ( ho )-( omega) mixing. The branching ratios for the processes (B^{pm,0} ightarrow ho^{pm,0}pi^{pm,0}) and (B^{-} ightarrow omega pi^{-}) are calculated as well. We find that the CP violating asymmetry is strongly dependent on the CKM matrix elements. For a fixed Nceff, the CP violating asymmetry, aCP, has a maximum of order (-40%) to (- 70%) for (Bar{B}^{0} ightarrow ho^{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 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 delta) is always positive. Thus, a measurement of direct CP violation in the decays (Bar{B}^{0} ightarrow pi^{ + }pi^{-} pi^{0}) would remove the (mod(pi)) ambiguity in the determination of the CP violating phase angle (alpha).