Recent progress in calculation of $B_K$ using staggered fermions

TL;DR

This paper reports recent progress in calculating $B_K$ using improved staggered fermions on various lattice spacings, highlighting the dependence on sea quark mass and methods for extrapolation.

Contribution

It introduces new measurements on finer lattices and discusses improved methods for chiral and continuum extrapolations in $B_K$ calculations.

Findings

Stronger sea quark mass dependence on fine lattices

Enhanced data on superfine and coarse lattices

Discussion of extrapolation methods

Abstract

We report on recent progress in the calculation of $B_K$ using HYP-smeared improved staggered fermions on the MILC asqtad lattices. We have added measurements on fine ($a\sim 0.09 $fm) and superfine ($a\sim 0.06 $fm) ensembles at different values of the light sea quark mass ($a m_\ell$), as well as increased the statistics on some other ensembles. We find that the results on the fine lattices show a significantly stronger $am_\ell$ dependence than those on the superfine and coarse ($a\sim 0.12 $fm) lattices. We discuss different methods for accounting for these new results when doing the $a m_\ell$ and continuum extrapolations.