Lattice QCD should allow a derivation of the ΔI=1/2 rule from first principles, but numerical calculations to date have been plagued by a variety of problems. After a brief review of these problems, we present several new methods for calculating K→ππ amplitudes. These are designed for Wilson fermions, though they can be used also with staggered fermions. They all involve a non-perturbative determination of matching coefficients. We show how problems of operator mixing can be greatly reduced by using point-split hadronic currents, and how CP violating parts of the K→ππ amplitudes can be calculated by introducing a fake top quark. Many of the methods can also be applied to the calculation of two body non-leptonic B-meson decays.
@article{arxiv.hep-lat/9707009,
title = {New lattice approaches to the $\Delta I=1/2$ rule},
author = {C. Dawson and G. Martinelli and G. C. Rossi and C. T. Sachrajda and S. Sharpe and M. Talevi and M. Testa},
journal= {arXiv preprint arXiv:hep-lat/9707009},
year = {2009}
}