CP Asymmetry Relations between bar B0→ππ and bar B0→πK Rates

We prove that the CP violating rate difference Δ(π+π-)=Γ(bar B0→π+π-)-Γ(B0→π-π+) is related to Δ(π+K-)=Γ(π+K-)-Γ(B0→π-K+) in the three generation standard model. Neglecting small annihilation diagrams, and in the SU(3) symmetry limit, we show that Δ(π+π-)=-Δ(π+K-). The SU(3) breaking effects are estimated using the factorization approximation, and yield Δ(π+π-)∼-(fπ/fK)2Δ(π+K-). The usefulness of this relation for determining phases in the CKM unitarity triangle is discussed