Direct CP violation in K-->3 pi decay: Addendum on CP-violating effects in charged-K decay.

Abstract

Contrary to a recent claim that CP asymmetry in the slope parameter of ${\mathit{K}}^{\ifmmode\pm\else\textpm\fi{}}$\ensuremath{\rightarrow}${\mathrm{\ensuremath{\pi}}}^{\ifmmode\pm\else\textpm\fi{}}$${\mathrm{\ensuremath{\pi}}}^{+}$${\mathrm{\ensuremath{\pi}}}^{\mathrm{\ensuremath{-}}}$ is as large as of order ${10}^{\mathrm{\ensuremath{-}}3}$, our calculation shows that, within the framework of the 1/${\mathit{N}}_{\mathit{c}}$ approach, its magnitude is not likely to exceed the level of ${10}^{\mathrm{\ensuremath{-}}5}$ even after including the effects of ${\mathit{Z}}^{0}$ penguin diagrams, isospin breaking, and higher-order weak chiral Lagrangians. Our result suggests that it is a formidable task to observe direct CP violation in charged K\ensuremath{\rightarrow}3\ensuremath{\pi} decay.