Chiral behaviour of the lattice $B_K$-parameter with the Wilson and Clover Actions at $\beta = 6.0$

TL;DR

This study compares the lattice $B_K$-parameter using Wilson and Clover actions at $eta=6.0$, highlighting the impact of renormalization methods and demonstrating improved chiral behavior with non-perturbative renormalization.

Contribution

It provides a comparative analysis of $B_K$ using different actions and renormalization techniques, emphasizing the advantages of non-perturbative methods for better chiral properties.

Findings

Wilson action results depend strongly on the renormalization prescription.

Clover action results are stable across different renormalization schemes.

Non-perturbative renormalization yields better chiral behavior and a reliable estimate of $oxed{B_K}$.

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 $\beta=6.0$. We compare results obtained by renormalizing the relevant operator with different ``boosted" values of the strong coupling constant $\alpha_s$. 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 $\alpha_s$, 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, $\hat B_K=0.86 \pm 0.15$.