Obtaining Κ→ππ from off-shell Κ→π amplitudes

We properly define off-shell K --> pi transition amplitudes and use them to extract information for on-shell K --> pi pi amplitudes within Chiral Perturbation Theory. At order p(2) in the chiral expansion all three parameters of weak interaction can be determined. At order p(4) we are able to fix eleven additional constants out of thirteen contributing to off-shell K --> pi transitions, which leaves four undetermined constants in the on-shell K --> pi pi amplitudes. All O (p(4)) contributions have been exactly derived with m(pi)(2) not equal 0. We finally discuss the weak mass term issue and find contributions to on-shell Delta S = +/- 1 kaon decays, in particular to transitions like K-L --> gamma gamma, K-L --> mu(+) mu(-) and K-S --> pi(0)gamma gamma at the lowest non-zero order. (C) 1998 Elsevier Science B.V.