$B_K$ with improved staggered fermions: analysis using SU(2) staggered chiral perturbation theory

We report updated results for $B_K$ calculated using HYP-smeared staggered fermions on the MILC asqtad 2+1 flavor lattices. We use four different lattice spacings ($a \approx$ 0.12, 0.09, 0.06 and 0.045 fm) to control the continuum extrapolation. We use SU(2) staggered chiral perturbation theory to do the data analysis. We find that $B_K(\text{NDR}, \mu=2 \text{GeV}) = 0.526 \pm 0.007 \pm 0.024$ and $\hat{B}_K = B_K(\text{RGI}) = 0.720 \pm 0.010 \pm 0.033$. Here the first error is statistical and the second systematic. The dominant source of error is that due to our use of a truncated (one-loop) matching factor.