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 ${ϵ}_{+-\gamma }^{\prime }$, 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 $10^{-2}ϵ$ 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 $10^{-4}ϵ$.

Comments: Latex, 14 pages, ITP-SB-93-32, IP-ASTP-20-93