$B_K$ with improved staggered fermions: analysis using SU(3) staggered chiral perturbation theory

Understand

We report updated results for $B_K$ using HYP-smeared staggered valence quarks on MILC asqtad lattices based on an analysis using SU(3) staggered chiral perturbation theory.

• The most important new feature of our data sample is the inclusion of a fourth ("ultrafine") lattice spacing.
• This improves the control over the continuum extrapolation and errors due our use of one-loop perturbative matching.
• We present a complete updated error budget, which leads to $B_K(\text{NDR}, \mu = 2 \text{GeV}) = 0.5309 \pm 0.0051 \pm 0.0424$ and $\hat{B}_K = B_K(\text{RGI}) = 0.727 \pm 0.07 \pm 0.058$.