CP-violation and $ππ$-interaction in the radiative decays of $K_L$ and $K_S$

Abstract

The phases of terms of amplitude that arise from the $ππ$ interaction are obtained by using a simple realistic model of $ππ$ interaction via virtual $ρ$-meson, instead of the ChPT. It is shown that the standard ChPT approach cannot reproduce the contribution of the $ρ$-meson to the $ππ$ interaction. It is shown that the interference between the terms of amplitude with different CP-parity appears only when the photon is polarized (linearly or circularly). Instead of measuring the linear polarization, the angular correlation between the $π^{+}π^{-}$ and $e^{+}e^{-}$ planes in $K_{S,L}\toπ^{+}π^{-}e^{+}e^{-}$ decay can be studied.