Non - Perturbative Renormalisation of the Lattice ∆ S = 2 Four - Fermion Operator

We compute the renormalised four-fermion operator O ∆S=2 using a non-perturbative method recently introduced for determining the renormalisation constants of generic lattice composite operators. Because of the presence of the Wilson term, O ∆S=2 mixes with operators of different chiralities. A projection method to determine the mixing coefficients is implemented. The numerical results for the renormalisation constants have been obtained from a simulation performed using the SW-Clover quark action, on a 16 3 × 32 lattice, at β = 6.0. We show that the use of the constants determined non-perturbatively improves the chiral behaviour of the lattice kaon matrix element ¯ K 0 |O ∆S=2 |K 0 latt .