Direct CP violation in B → ρ⁰(ω) PS

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We calculate the direct CP violating asymmetry parameter, aCP, for B → π⁺ π⁻ π and B → π⁺ π⁻ K decays, in the case where ρ⁰-ω mixing effects are taken into account. We find that the direct CP asymmetry for B⁻ → π⁺ π⁻ π⁻, B⁰ → π⁺ π⁻π⁰, B⁻ → π⁺ π⁻ K⁻ and B⁰ → π⁺ π⁻K⁰, reaches its maximum when the invariant mass π⁺ π⁻ is in the vicinity of the ω meson mass. The inclusion of ρ⁰-ω mixing provides an opportunity to erase, without ambiguity, the phase uncertainty mod(π) in the determination of the CKM angles α in case of b→ u and γ in case of b → s.