The Kaon $B$-parameter with Wilson Fermions

TL;DR

This paper computes the kaon B-parameter using quenched lattice QCD with Wilson fermions, employing smeared sources to reduce errors and performing non-perturbative subtraction to mitigate lattice artifacts, with results aligning with staggered fermion studies.

Contribution

It introduces the use of smeared sources in Wilson fermion calculations to improve accuracy and demonstrates non-perturbative subtraction methods for lattice artifacts in kaon B-parameter computations.

Findings

Smeared sources significantly reduce calculation errors.

Results agree with staggered fermion calculations.

Preliminary results include dynamical quark effects.

Abstract

We calculate the kaon $B$-parameter in quenched lattice QCD at $\beta=6.0$ using Wilson fermions at $\kappa=0.154$ and $0.155$. We use two kinds of non-local (``smeared'') sources for quark propagators to calculate the matrix elements between states of definite momentum. The use of smeared sources yields results with much smaller errors than obtained in previous calculations with Wilson fermions. By combining results for $\vec p =(0,0,0)$ and $\vec p =(0,0,1)$, we show that one can carry out the non-perturbative subtraction necessary to remove the dominant lattice artifacts induced by the chiral symmetry breaking term in the Wilson action. Our final results are in good agreement with those obtained using staggered fermions. We also present results for $B$-parameters of the $\Delta I = 3/2$ part of the electromagnetic penguin operators, and preliminary results for \bk\ in the presence of two flavors of dynamical quarks.