CP-violation in K_{S,L}->\pi^{+}\pi^{-}\gamma and K_{S,L}->\pi^{+}\pi^{-}e^{+}e^{-} decays

Abstract

The dependence of K_{S,L}->\pi^{+}\pi^{-}\gamma decay probabilities on photon polarization is calculated. The phases of terms of amplitude that arise from the pion-pion interaction are obtained by using a simple realistic model of pion-pion interaction via virtual \rho-meson, instead of the ChPT. The results are compared with those of other authors and the origin of slight discrepancies is explained. It is shown that the standard ChPT approach for K_{S,L}-> \pi^{+}\pi^{-}\gamma decays cannot reproduce the contribution of the \rho-meson to the P-wave \pi\pi interaction. The departure of the photon spectrum from pure bremsstrahlung due to the pion loop contribution to the direct emission amplitude is calculated. 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}->\pi^{+}\pi^{-}e^{+}e^{-} decay can be studied.