Dispersion relations and soft pion theorems for K -> pi pi

We propose a new method to obtain the K --> pi pi amplitude from K --> pi p i which allows one to fully account for the effects of final state interact ions. The method is based on a set of dispersion relations for the K --> pi amplitude in which the weak Hamiltonian carries momentum. The soft pion th eorem, which relates this amplitude to the K --> pi amplitude, can be used to determine one of the two subtraction constants-the second constant is at present known only to leading order in chiral perturbation theory. We solv e the dispersion relations numerically and express the result in terms of t he unknown higher order corrections to this subtraction constant. (C) 2001 Elsevier Science B.V. All rights reserved.