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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. 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Sharpe, Taegil Bae, Weonjong Lee, Yong-Chull Jang","submitted_at":"2010-10-22T19:16:47Z","abstract_excerpt":"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. 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