Chiral behaviour of the lattice $B_K$-parameter with the Wilson and Clover Actions at ${\hat{I}}^2=6.0$

Abstract

We present results for the kaon $B$-parameter $B_K$ from a sample of $200$ configurations using the Wilson action and $460$ configurations using the SW-Clover action, on a $18^3\times 64$ lattice at ${\hat{I}}^2=6.0$. We compare results obtained by renormalizing the relevant operator with different ``boosted" values of the strong coupling constant $\hat{I}{\pm }_s$. In the case of the SW-Clover action, we also use the operator renormalized non-perturbatively. In the Wilson case, we observe a strong dependence of $B_K$ on the prescription adopted for $\hat{I}{\pm }_s$, contrary to the results of the Clover case which are almost unaffected by the choice of the coupling. We also find that the matrix element of the operator renormalized non-perturbatively has a better chiral behaviour. This gives us our best estimate of the renormalization group invariant $B$-parameter, ${\hat{B}}_K=0.86\pm 0.15$.

LaTeX, 17 pages, 3 postscript figures uuencoded