Lattice QCD, O.P.E. and the Standard Model

Abstract

A number of old and new methods for computing $K\to \pi \pi$ amplitudes on the lattice are reevaluated. They all involve a non-perturbative determination of matching coefficients. I will show how problems related to operator mixing can be greatly reduced by introducing the O.P.E. of hadronic currents directly on the lattice. Applications to the evaluation of CP-symmetric ($\Delta I=1/2$ rule) and CP-violating (${ϵ}^{\prime }/ϵ$) processes are presented.

Comments: 16 pages Latex, talk given at CHIRAL '99, Taipei, Sep. 13-18, 1999