Application of chiral perturbation theory toK→2πdecays

Chiral perturbation theory is applied to the decay K{→}2{π}. It is shown that, to quadratic order in meson masses, the amplitude for K{→}2{π} 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 {Δ}I=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 test of the practicability of these ideas in Monte Carlo studies. We also describe a method for evaluating meson decay constants which does not require a determination of the quark masses.