Non-perturbative renormalisation of the lattice $\Delta$S = 2 four-fermion operator

We compute the renormalised four-fermion operator O^{\Delta 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^{\Delta 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 \times 32 lattice, at \beta=6.0. We show that the use of the constants determined non-perturbatively improves the chiral behaviour of the lattice kaon matrix element \<\bar K^0| O^{\Delta S=2} | K^0\>_{\latt}.