%0 Journal Article
%T CP asymmetry Relations Between $\bar B^0\rightarrow ¦Ð¦Ð$ and $\bar B^0\rightarrow ¦ÐK$ Rates
%A N. G. Deshpande
%A Xiao-Gang He
%J Physics
%D 1994
%I arXiv
%R 10.1103/PhysRevLett.75.1703
%X 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) breaking effects 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 determining phases in the CKM unitarity triangle is discussed.
%U http://arxiv.org/abs/hep-ph/9412393v1