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

The phases of terms of amplitude that arise from the $\pi \pi$ interaction are obtained by using a simple realistic model of $\pi \pi$ interaction via virtual $\rho$-meson, instead of the ChPT. It is shown that the standard ChPT approach cannot reproduce the contribution of the $\rho$-meson to the $\pi \pi$ 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 ${\pi }^{+}{\pi }^{-}$ and $e^{+}{e}^{-}$ planes in $K_{S,L}\to {\pi }^{+}{\pi }^{-}{e}^{+}{e}^{-}$ decay can be studied.