Update on $B_K$ and $\varepsilon_K$ with staggered quarks

TL;DR

This paper updates the calculation of the $B_K$ parameter using improved staggered quark techniques on MILC lattices, achieving reduced systematic errors and providing a more precise value relevant for understanding CP violation.

Contribution

The study introduces additional measurements on finer lattices, enabling a combined extrapolation that significantly reduces systematic uncertainties in $B_K$ determination.

Findings

Updated $oxed{B_K}$ value: 0.738 with improved precision.

Reduced systematic errors through combined extrapolation.

Enhanced understanding of CP violation parameters.

Abstract

We update our results for $B_K$ obtained using HYP-smeared staggered valence quarks on the MILC asqtad lattices. In the last year, we have added 5 new measurments on the fine ($a\approx 0.09\;$fm) ensembles, and 2 new measurements on the superfine ($a\approx 0.06\;$fm) ensembles. These allow a simultaneous extrapolation in $a^2$ and sea quark masses, reducing the corresponding systematic error significantly. Our updated result is $\hat{B}_K = 0.738 \pm 0.005 (\text{stat}) \pm 0.034 (\text{sys})$.