CP asymmetry Relations Between $\bar B^0\rightarrow ππ$ and $\bar B^0\rightarrow πK$ Rates

Details CP asymmetry Relations Between $\bar B^0\rightarrow ππ$ and $\bar B^0\rightarrow πK$ Rates CP asymmetry Relations Between $\bar B^0\rightarrow ππ$ and $\bar B^0\rightarrow πK$ Rates

1994-12-30

arxiv.org/abs/hep-ph/9412393v1

Phys.Rev.Lett.75:1703-1706,1995

Physics

High Energy Physics

High Energy Physics - Phenomenology

9 pages, Revtex

Scientific paper

10.1103/PhysRevLett.75.1703

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.

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