Direct CP violation in B \to \rho^0(\omega) PS

We calculate the direct CP violating asymmetry parameter, $a_{CP}$, for $B \to \pi^{+} \pi^{-} \pi$and$B \to \pi^{+} \pi^{-} K$ decays, in the case where ${\rho }^0-\omega$ mixing effects are taken into account. We find that the direct CP asymmetry for $B^{-}\to {\pi }^{+}{\pi }^{-}{\pi }^{-}$, $\bar{B}^{0} \to \pi^{+} \pi^{-}\pi^{0}$,$B^{-} \to \pi^{+} \pi^{-} K^{-}$and$\bar{B}^{0} \to \pi^{+} \pi^{-}\bar{K}^{0}$,reachesitsmaximumwhentheinvariantmass$\pi^{+} \pi^{-}$isinthevicinityofthe$\omega$ meson mass. The inclusion of ${\rho }^0-\omega$ mixing provides an opportunity to erase, without ambiguity, the phase uncertainty mod$(\pi )$ in the determination of the CKM angles $\alpha$ in case of $b\to u$ and $\gamma$ in case of $b\to s$.