ar X iv : h ep - l at / 0 21 00 03 v 1 3 O ct 2 00 2 1 K → ππ decay amplitudes from the lattice ∗

The techniques of lattice gauge theory offer the possibility of accurate, non-perturbative calculation of the masses and matrix elements predicted by low-energy QCD. Of particular interest are the properties of the K-meson system and the lowenergy, weak matrix elements that are required to understand Kaon decays, especially those which enter the K → ππ amplitudes which violate CP symmetry. Presently well-developed methods permit the calculation of K to vacuum and K to π weak matrix elements. When combined with chiral perturbation theory and the accurate chiral symmetry of the domain wall fermion formulation, lattice methods can be used to evaluate all the matrix elements that contribute to the weak K → ππ amplitudes in the chiral limit[1,2]. In this paper we describe a method which may provide a practical approach to the direct lattice calculation of the desired, on-shell, K → ππ amplitudes without the use of chiral perturbation theory.