Kaon B parameter from quenched Lattice QCD

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 $a\approx 0.24-0.04$ fm on lattices up to ${56}^3\times 96$, we verify a quadratic $a$ dependence of $B_K$ theoretically predicted. Strong indications are found that, with our level of accuracy, ${\alpha }_{\overline{MS}}(1\mathrm{/}a{)}^2$ terms arising from our one-loop matching procedure have to be included in the continuum extrapolation. We present $B_K$(NDR, 2 GeV)=0.628(42) as our final value, as obtained by a fit including the ${\alpha }_{\overline{MS}}(1\mathrm{/}a{)}^2$ term.