Non-Perturbative Renormalisation of the Lattice $\Delta s=2$ Four-Fermion Operator

Abstract

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 $\text{<}{\bar{K}}^0|O^{\Delta S=2}|K^0{}_{\text{latt}}$.

Comments: LaTeX, 16 pages, 2 postscript figures