We present results of a large-scale simulation for the kaon $B$ parameter $B_K$ in quenched lattice QCD with the Kogut-Susskind quark action. Calculating $B_K$ at 1% statistical accuracy for seven values of lattice spacing in the range $a\approx 0.24–0.04\mathrm{fm}$ on lattices up to ${56}^3\times 96$, we verify the theoretically predicted quadratic $a$ dependence. Strong indications are found that, with our level of accuracy, ${\alpha }_{\overline{\mathrm{MS}}}(1/a{)}^2$ terms arising from our one-loop matching procedure have to be included in the continuum extrapolation. We present $B_K(\mathrm{NDR},2\mathrm{GeV})=0.628\mathrm{}\left(42\right)$ as our final value, where NDR indicates naive dimensional regularization.

• Received 22 October 1997

DOI:https://doi.org/10.1103/PhysRevLett.80.5271