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

Abstract

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 the MILC collaboration with $N_f=2+1$ light flavors. To control discretization errors, we use four different lattice spacings ranging down to $a\approx 0.045$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 systematic error is from our use of truncated (one-loop) matching factors.

Comments: 4 pages, 4 figures, 2 tables, updated references, updated grant numbers