Chiral perturbation theory and the delta I = 1/2 rule

Abstract

Chiral perturbation theory is applied to the decay K π 2π. It is shown that, to quadratic order-in meson masses, the amplitude for K → 2π can be written in terms of the unphysical amplitudes K + π and K + 0, where "0" is the vacuum. One may then hope to calculate these two simpler amplitudes with lattice Monte Carlo techniques, and thereby gain understanding of the ΔI = 1/2 rule in K decay. The reason for the presence of the K → 0 amplitude is explained: it serves to cancel off unwanted renormalization contributions to K + π. We make a rough rest of the practicability of these ideas to Monte Carlo studies. We also describe a method for evaluating meson decay constants which does not require a determination of the quark masses.