Quenched $B_K$-parameter with the Wilson and Clover actions at ${\hat{I}}^2=6.0$

Abstract

We present results for the Kaon $B$ parameter from a sample of $200$ configurations using the Wilson action and $460$ configurations using the Clover action, on a $18^3\times 64$ lattice at ${\hat{I}}^2=6.0$. A slight improvement of the chiral behaviour of $B_K$ is observed due to the Clover action. We have also compared the results for $B_K$ obtained from two different procedures for the boosting of the coupling constant $g$. We observe a strong dependence of $B_K$ on the prescription adopted for $g$ in the Wilson case, contrary to the results of the Clover case which are almost unaffected by the choice of $g$. Combining some recently obtained non perturbative estimates for the renormalisation constants with our Clover matrix element, we observe a significant improvement in the chiral behaviour of $B_K$.

3 pages, Latex, Postscript file with figures available at ftp://hpteo.roma1.infn.it/pub/preprints/lat94/donini ; to appear in Lattice '94, Nucl. Phys. (Proc.Suppl.)