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

Abstract

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.