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We present a calculation of the kaon $B$-parameter, $B_K$, using lattice QCD.We use improved staggered valence and sea fermions, the latter generated by theMILC collaboration with $N_f=2+1$ light flavors. To control discretizationerrors, we use four different lattice spacings ranging down to $a\approx0.045\;$fm. The chiral and continuum extrapolations are done using SU(2)staggered chiral perturbation theory. Our final result is $\hat{B}_K = 0.727\pm 0.004 (\text{stat}) \pm 0.038 (\text{sys})$, where the dominant systematicerror is from our use of truncated (one-loop) matching factors.

Kaon $B$-parameter from improved staggered fermions in $N_f=2+1$ QCD