Possible Effects ofCPViolation inK±→3πDecay

The effects of $\mathrm{CP}$ violation in $K\to 3\pi$ decay have been investigated. In a linear energy approximation for the decay matrix elements, one can prove, using the $\mathrm{TCP}$ theorem alone, that the partial decay rate of the $\tau$ (or ${\tau }^{\prime }$) mode (and also $\theta$ modes) for the $K^{+}$ meson is nearly equal to that for the $K^{-}$ meson, provided that one can neglect contributions from the final $I=3\mathrm{}$ pion configuration. Also, effects of final pion-pion interactions have been computed by extending the dispersion-theoretical treatment of Khuri and Treiman.