$B_K$ from improved staggered fermions using SU(3) chiral perturbation theory

TL;DR

This paper reports progress in calculating the kaon B-parameter ($B_K$) using improved staggered fermions and SU(3) chiral perturbation theory, achieving higher statistical precision and better continuum extrapolation.

Contribution

It introduces an improved SU(3) chiral perturbation theory approach for $B_K$ calculation with higher statistics and refined continuum extrapolation methods.

Findings

Updated $oxed{B_K}$ value with reduced statistical error.

Results consistent with SU(2) chiral perturbation theory estimates.

Larger total error compared to previous SU(2) based analysis.

Abstract

We present recent progress in our calculation of $B_K$ with improved staggered fermions using chiral extrapolations based on SU(3) staggered chiral perturbation theory. We have accumulated significantly higher statistics on the coarse, fine, and ultrafine MILC asqtad lattices. This leads to a reduction in statistical error and an improved continuum extrapolation. Our updated result is $\hat{B}_K = B_K(\text{RGI}) = 0.737 \pm 0.003(\text{stat}) \pm 0.046 (\text{sys})$. This is consistent with the result obtained using chiral extrapolations based on SU(2) staggered chiral perturbation theory, although the total error is somewhat larger with the SU(3) analysis.