Obtaining K → ππ from Off - Shell K → π Amplitudes

We properly define off-shell K → π transition amplitudes and use them to extract information for on-shell K → ππ amplitudes within Chiral Perturbation Theory. At order p2 in the chiral expansion all three parameters of weak interaction can be determined. At order p4 we are able to fix eleven additional constants out of thirteen contributing to off-shell K → π transitions, which leaves four undetermined constants in the onshell K → ππ amplitudes. All O(p4) contributions have been exactly derived with mπ 6= 0. We finally discuss the weak mass term issue and find contributions to on-shell ∆S = ±1 Kaon decays, in particular to transitions like KL → γγ, KL → μ+μ− and KS → π0γγ at the lowest non-zero order. PACS numbers: 11.30.Rd, 13.25.Es, 12.38.Gc, 12.39.Fe January 1998