DirectCPviolation inK→3π decay: Addendum onCP-violating effects in charged-Kdecay

Contrary to a recent claim that CP asymmetry in the slope parameter of ${\mathit{K}}^{\pm }$→${\mathrm{\pi }}^{\pm }$ ${\mathrm{\pi }}^{+}$ ${\mathrm{\pi }}^{\mathrm{-}}$ is as large as of order ${10}^{\mathrm{-}3}$, 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 ${10}^{\mathrm{-}5}$ 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→3π decay.