CP asymmetry Relations Between ${\bar{B}}^0\to \pi \pi$ and ${\bar{B}}^0\to \pi K$ Rates

Abstract

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

9 pages, Revtex

References in corpus (10)

• The $\Delta S=1$ Effective Hamiltonian Including Next-to-Leading Order QCD and QED Corrections
• Decays of $B$ Mesons to Two Light Pseudoscalars
• The Two-Loop Anomalous Dimension Matrix for $\Delta S=1$ Weak Non-Leptonic Decays I: $\mathcal{O}({\alpha }_s^2)$
• Two--Loop Anomalous Dimension Matrix for $\Delta S=1$ Weak Non-Leptonic Decays II: $\mathcal{O}({\alpha }_e{\alpha }_s)$
• Weak Coupling Phase from Decays of Charged B Mesons to $\pi K$ and $\pi \pi$
• Isospin Structure of Penguins And Their Consequences in $B$ Physics
• Hadronic Penguin B Decays In The Standard And The Two-Higgs-Doublet Models
• Limitations in Measuring the Angle $\beta$ by Using $SU(3)$ Relations for $B$-Meson Decay-Amplitudes
• Penguin contributions to rates and CP asymmetries in non-leptonic B-decays. Possible experimental procedures and estimates
• Penguin Effects on K Pi and PiPi Decays of the $B$ Meson

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