Determination of $B_K$ using improved staggered fermions (I): SU(3) chiral perturbation theory fit

TL;DR

This paper reports a lattice QCD calculation of the parameter $B_K$ using improved staggered fermions across multiple lattice spacings, fitting data with SU(3) chiral perturbation theory, and providing a preliminary value with quantified uncertainties.

Contribution

It introduces a novel calculation of $B_K$ employing HYP-smeared staggered fermions and SU(3) chiral perturbation theory fits on multiple lattice ensembles.

Findings

Preliminary $B_K$ value: 0.528 with errors.

Analysis shows larger errors compared to SU(2) chiral perturbation theory.

Results are based on 8 lattice ensembles with three different spacings.

Abstract

We present the results for $B_K$ calculated using HYP-smeared staggered fermions using lattices generated by the MILC collaboration using the asqtad staggered action. We have done the calculation on 8 ensembles of these lattices, including three different lattice spacings ($a=0.12, 0.09, 0.06$ fm). We fit the data to forms based on those predicted by SU(3) mixed-action partially-quenched staggered chiral perturbation theory. Our preliminary result is $ B_K(\text{NDR},\mu=2\text{GeV}) = 0.528 \pm 0.011 \pm 0.048 $, where the first error is statistical and the second systematic. The error turns out to be larger than that from an analysis using SU(2) chiral perturbation theory.