CP violation in $K^{\pm }\to {\pi }^0{\pi }^0{\pi }^{\pm }$ decay

Abstract

CP violation leads to a difference between the parameters $g^{+}$ and $g^{-}$ describing the energy distributions of the charged pions produced in the $K^{+}\to {\pi }^0{\pi }^0{\pi }^{+}$ and $K^{-}\to {\pi }^0{\pi }^0{\pi }^{-}$ decays. We study the difference $(g^{+}-g^{-})$ as a function of the relative contributions from the QCD-penguin and the electroweak-penguin diagrams. We find that the combination of these contributions in $(g^{+}-g^{-})$ is very similar to the corresponding one defining the parameter ${\epsilon }^{\prime }$ in the $K_L\to 2\pi$ decays. This observation allows a determination of the value of $(g^{+}-g^{-})$, using data on ${\epsilon }^{\prime }$.