Phenomenological Analysis ofK→ππ(I=2)Amplitudes and Violation ofCPInvariance

Abstract

A phenomenological analysis of the $K\to \pi \pi \mathrm{}(I=2\mathrm{})\mathrm{}$ amplitudes, $K^0\to \pi \pi \mathrm{}(I=2\mathrm{})\mathrm{}$, ${\overline{K}}^0\to \pi \pi \mathrm{}(I=2\mathrm{})\mathrm{}$, and $K^{\pm }\to {\pi }^{+}{\pi }^0$, in terms of their irreducible isospin amplitudes corresponding to the $\Delta I=\frac{3}{2}$ and $\Delta I=\frac{5}{2}$ transitions, is given with reference to the observed violation of $\mathrm{CP}$ invariance. The unitarity condition for the $K^0-{\overline{K}}^0$ system is also discussed, and an evaluation of the parameters describing the $2\pi$ decay modes made. Terms in the unitarity condition referring to the modes $\pi \pi \mathrm{}(I=0\mathrm{})\mathrm{}$, $\pi \pi \mathrm{}(I=2\mathrm{})\mathrm{}$, $3\pi$, and semileptonic are explicitly taken into account.