Determination of $B_K$ using improved staggered fermions (II) SU(2) chiral perturbation theory fit

TL;DR

This paper reports on calculating the $B_K$ parameter using improved staggered fermions and SU(2) chiral perturbation theory, providing more precise results and analyzing systematic errors and dependencies.

Contribution

It introduces a novel SU(2) SChPT fit to $B_K$ data with improved staggered fermions, enhancing accuracy over previous SU(3) analyses.

Findings

Preliminary $B_K$ result: 0.512 ± 0.014 ± 0.034

RGI $ ext{hat} B_K$ value: 0.701 ± 0.019 ± 0.047

Results are consistent with domain-wall fermion calculations

Abstract

We present results for $B_K$ calculated using HYP-smeared improved staggered fermions on the MILC asqtad lattices. In this report, the data is analyzed using the results of SU(2) staggered chiral perturbation theory (SChPT). We outline the derivation of the NLO SU(2) SChPT result, explain our fitting procedure, and outline how we estimate systematic errors. We also show the light sea-quark mass and lattice spacing dependence for both SU(2) and SU(3)-based analyses. Our preliminary result from the SU(2) analysis is $B_K(\text{NDR}, \mu = 2 \text{GeV}) = 0.512 \pm 0.014 \pm 0.034$ and $\hat{B}_K = B_K(\text{RGI})= 0.701 \pm 0.019 \pm 0.047$. This is somewhat more accurate than our result from the SU(3) analysis. It is consistent with results obtained using valence domain-wall fermions