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

A number of old and new methods for computing $K\toππ$ 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 ($ΔI = 1/2$ rule) and CP-violating ($ε'/ε$) processes are presented.