  We give the first full next-to-leading order analytical results in Chiral
Perturbation Theory for the charged Kaon K \to 3 pi slope g and decay rates
CP-violating asymmetries. We have included the dominant Final State
Interactions at NLO analytically and discussed the importance of the unknown
counterterms. We find that the uncertainty due to them is reasonable just for
\Delta g_C, i.e. the asymmetry in the K^+ \to pi^+ pi^+ pi^- slope g; we get
\Delta g_C = -(2.4 +- 1.2) 10^{-5}. The rest of the asymmetries are very
sensitive to the unknown counterterms. In particular, the decay rate
asymmetries can change even sign. One can use this large sentivity to get
valuable information on those counterterms and on Im(G_8) coupling --very
important for the CP-violating parameter epsilon'_K-- from the eventual
measurement of these asymmetries. We also provide the one-loop O(e^2 p^2)
electroweak octet contributions for the neutral and charged Kaon K \to 3 pi
decays.

High Energy Physics - Phenomenology;High Energy Physics - Experiment