$B_K$ with improved staggered fermions: analysis using SU(3) staggered chiral perturbation theory

TL;DR

This paper presents updated lattice QCD calculations of the $B_K$ parameter using improved staggered fermions and SU(3) chiral perturbation theory, including a new ultrafine lattice to better control continuum extrapolation.

Contribution

The study introduces an analysis with an ultrafine lattice spacing and provides a comprehensive error budget for $B_K$ using SU(3) staggered chiral perturbation theory.

Findings

Updated $B_K$ value with reduced errors

Inclusion of ultrafine lattice improves continuum extrapolation

SU(3) analysis less precise than SU(2) due to Bayesian priors

Abstract

We report updated results for $B_K$ using HYP-smeared staggered valence quarks on MILC asqtad lattices based on an analysis using SU(3) staggered chiral perturbation theory. The most important new feature of our data sample is the inclusion of a fourth ("ultrafine") lattice spacing. This improves the control over the continuum extrapolation and errors due our use of one-loop perturbative matching. We present a complete updated error budget, which leads to $B_K(\text{NDR}, \mu = 2 \text{GeV}) = 0.5309 \pm 0.0051 \pm 0.0424$ and $\hat{B}_K = B_K(\text{RGI}) = 0.727 \pm 0.07 \pm 0.058$. The results of the SU(3) analysis are inferior to those based on SU(2) staggered chiral perturbation theory, primarily because of the dependence on the Bayesian priors we use in the SU(3) fits.