CP violation in K-->3 pi.

Abstract

For the weak nonleptonic decay K\ensuremath{\rightarrow}3\ensuremath{\pi}, we analyze the amount of CP violation expected to arise in the Kobayashi-Maskawa model using two recently uncovered aspects: (1) quadratic terms in the K\ensuremath{\rightarrow}3\ensuremath{\pi} amplitude (found in the CP-conserving data) and (2) electromagnetic and isospin-breaking effects in the relation of the CP-violating parameters of K\ensuremath{\rightarrow}2\ensuremath{\pi} and K\ensuremath{\rightarrow}3\ensuremath{\pi}. Previous to the inclusion of these effects the non-\ensuremath{\epsilon} signal in ${\ensuremath{\eta}}_{+\mathrm{\ensuremath{-}}0}$ (${\ensuremath{\eta}}_{+\mathrm{\ensuremath{-}}0}$=\ensuremath{\epsilon}+${\ensuremath{\epsilon}}_{+\mathrm{\ensuremath{-}}0}^{\mathcal{'}}$) required interference with the highly suppressed \ensuremath{\Delta}I=(3/2 amplitude; however in the present analysis the ${\ensuremath{\epsilon}}_{+\mathrm{\ensuremath{-}}0}^{\mathcal{'}}$ signal is not suppressed. We estimate values for ${\ensuremath{\epsilon}}_{+\mathrm{\ensuremath{-}}0}^{\mathcal{'}}$ about an order of magnitude larger than previously anticipated, although still smaller than \ensuremath{\epsilon}.