Semi-Phenomenological Approach to the Estimate of CP Effects in $K^{\pm} \to 3 \pi $ Decays

Abstract

The amplitudes of the $K^{\pm} \to 3\pi$ and $K \to 2\pi$ decays are expressed in terms of different combinations of one and the same set of CP-conserving and CP-odd parameters. Extracting the magnitudes of these parameters from the data on $K \to 2\pi$ dacays, we estimate an expected CP-odd difference between the values of the slope parameters $g^+$ and $g^-$ of the energy distributions of "odd" pions in $K^+ \to \pi^+\pi^+ \pi^-$ and $K^- \to \pi^-\pi^-\pi^+$ decays.