Results for Quenched $B_K$ from JLQCD

A report is presented on our continued effort to elucidate the continuum limit of $B_K$ using the quenched Kogut-Susskind quark action. By adding to our previous simulations one more point at $\beta =6.65$ employing a $56^3\times 96$lattice,wenowconfirmtheexpected$O(a^2)$behaviorof$B_K$ with the Kogut-Susskind action. A simple continuum extrapolation quadratic in $a$ leads to $B_K$(NDR, 2 GeV) = 0.598(5). As our final value of $B_K$ in the continuum we present $B_K$(NDR, 2 GeV)=0.628(42), as obtained by a fit including an ${\alpha }_{\overline{MS}}(1\mathrm{/}a{)}^2$ term arising from the lattice-continuum matching with the one-loop renormalization.