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We prove that CP violating rate difference $\Delta (\bar B^0 \rightarrow\pi^+\pi^-) = \Gamma (\bar B^0 \rightarrow \pi^+\pi^-) - \Gamma ( B^0\rightarrow \pi^-\pi^+)$ is related to $\Delta (\bar B^0 \rightarrow \pi^+ K^-)= \Gamma (\bar B^0 \rightarrow \pi^+K^-) - \Gamma (B^0 \rightarrow \pi^-K^+)$in the three generation Standard Model. Neglecting small annihilation diagrams,and in the SU(3) symmetry limit, we show $\Delta (\bar B^0 \rightarrow\pi^+\pi^-) = - \Delta (\bar B^0 \rightarrow \pi^+ K^-)$. The SU(3) breakingeffects are estimated using factorization approximation, and yield $\Delta(\bar B^0\rightarrow \pi^+\pi^-) \approx -(f_\pi/f_K)^2\Delta (\bar B^0\rightarrow \pi^+K^-)$. Usefulness of this remarkable relation for determiningphases in the CKM unitarity triangle is discussed.Comment: 9 pages, Revte

physical review letters

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