Quenched $B_K$-parameter with the Wilson and Clover actions at $\beta = 6.0$

TL;DR

This study compares the calculation of the Kaon $B$ parameter using Wilson and Clover lattice actions at $eta=6.0$, highlighting the improved chiral behavior with the Clover action and the impact of different coupling boosting procedures.

Contribution

It provides a comparative analysis of $B_K$ calculations with Wilson and Clover actions, emphasizing the benefits of the Clover action and non-perturbative renormalization techniques.

Findings

Clover action shows improved chiral behavior of $B_K$.

Results are less sensitive to coupling boosting in Clover case.

Non-perturbative renormalization enhances $B_K$ results.

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 $\beta=6.0$. 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 $B_K$.