First results for $B_K$ on the ultrafine ($a=0.045$ fm) ensemble

TL;DR

This paper reports preliminary lattice QCD results for the parameter $B_K$ on ultrafine lattices, demonstrating consistency between different chiral perturbation theory analyses and contributing to improved continuum extrapolation control.

Contribution

First preliminary $B_K$ results on ultrafine lattices using HYP-smeared staggered quarks and multiple chiral fits, advancing lattice QCD precision.

Findings

SU(2) and SU(3) analyses yield consistent $B_K$ values

NLO and partial NNLO fits agree within uncertainties

Results aid in better continuum extrapolation

Abstract

We present preliminary results for $B_K$ from the MILC ultrafine lattices, based on a partial ensemble of 305 configurations. We use HYP-smeared improved staggered valence quarks. The analysis is done using fitting forms based on both SU(2) and SU(3) staggered chiral perturbation thery. For the SU(2) analysis, we find that the result using the NLO fit function is consistent with that from a partial NNLO fit. For the SU(3) analysis, where we have to use partially constrained fits due to the number of fit parameters, we find that our two preferred fits ("N-BB1" and "N-BB2") are also consistent, both with each other and with the results of the SU(2) fits. These results are used in companion proceedings to improve the control over the continuum extrapolation.