CP ASYMMETRY RELATIONS BETWEEN (B)OVER-BAR(O)-]PI-PI AND (B)OVER-BAR(O)-]PI K-RATES

We prove that the CP violating rate difference Delta(pi(+)pi(-)) = Gamma((B) over bar(0) --> pi(+)pi(-)) - Gamma(B-0 --> pi(-)pi(+)) is related to Delta(pi(+)K(-)) = Gamma(pi(+)K(-)) - Gamma(B-0 --> pi(-)K(+)) in the three generation standard model. Neglecting small annihilation diagrams, and in the SU(3) symmetry limit, we show that Delta(pi(+)pi(-)) = -Delta(pi(+)K(-)). The su(3) breaking effects are estimated using the factorization approximation, and yield Delta(pi(+)pi(-)) approximate to -(f(pi)/f(K))(2) Delta(pi(+)K(-)). The usefulness of this relation for determining phases in the CKM unitarity triangle is discussed.