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

Abstract

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.

Comments: 7 pages, 7 figures, Lattice 2010 proceeding, references updated