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

TL;DR

This paper calculates the kaon B-parameter using improved staggered fermions in lattice QCD with multiple lattice spacings to control errors, providing a precise value for $ ext{B}_K$.

Contribution

It presents a new lattice QCD calculation of $ ext{B}_K$ with improved staggered fermions and multiple lattice spacings, including systematic error analysis.

Findings

Final result: $ ext{B}_K = 0.727 \\pm 0.004$ (stat) \\pm 0.038$ (sys)

Controlled discretization errors with four lattice spacings down to 0.045 fm

Systematic error dominated by one-loop matching factors

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.