Direct CP Violation in $K_L\to\pi^+\pi^-\gamma$

Abstract

CP violation due to interference between $K_L$ and $K_S$ decays into $\pi ^+\pi^-\gamma$ is analyzed in the Standard Model. The CP-violating parameter $\epsilon'_{+- \gamma}$, which is the difference between $\eta_{+-\gamma}$ and $\eta_{+-}$, receives dominant contributions from $K^0-\bar{K}^0$ mixing and the gluon penguin diagram; its magnitude is calculated to be $10^{-2}\epsilon$ at a typical region of the Dalitz plot. Genuine direct CP violation in $K_L\to\pi^+ \pi^-\gamma$ decay originating from the electromagnetic penguin diagram is of order $10^{-4}\epsilon$.