Rho-Omega Mixing and Direct CP Violation in Hadronic B-Decays

We study direct CP violation in hadronic B-decays in the $\rho^0 - \omega$ interference region, and focus specifically on the rate asymmetry in $B^{\pm} \to \rho^{\pm}\rho^0(\omega) \to \rho^{\pm}\pi^+\pi^-$. In this channel, the strong phase is dominated by isospin violation, so that it can be essentially determined by $e^+e^- \to \pi^+ \pi^-$ data in the $\rho^0$-$\omega$ interference region. We find that the asymmetry in the $\rho^{\pm} \pi^+\pi^-$ channel is of order of 20% at the $\omega$ invariant mass. Moreover, the sign and magnitude of the asymmetry are robust with respect to the estimable uncertainties in the strong phase.