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We report updated results for $B_K$ using HYP-smeared staggered valencequarks on MILC asqtad lattices based on an analysis using SU(3) staggeredchiral perturbation theory. The most important new feature of our data sampleis the inclusion of a fourth ("ultrafine") lattice spacing. This improves thecontrol over the continuum extrapolation and errors due our use of one-loopperturbative matching. We present a complete updated error budget, which leadsto $B_K(\text{NDR}, \mu = 2 \text{GeV}) = 0.5309 \pm 0.0051 \pm 0.0424$ and$\hat{B}_K = B_K(\text{RGI}) = 0.727 \pm 0.07 \pm 0.058$. The results of theSU(3) analysis are inferior to those based on SU(2) staggered chiralperturbation theory, primarily because of the dependence on the Bayesian priorswe use in the SU(3) fits.

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