Toward the Continuum Limit of $B_K$ with the Quenched Kogut-Susskind Quark Action

Abstract

We present new results of our ongoing project toward a precision determination of the kaon $B$ parameter with the Kogut-Susskind quark action in quenched QCD. New results taken at ${\hat{I}}^2$=6.4 and ${\hat{I}}^2=5.7$ suggest that an apparently linear $a$ dependence of $B_K$ previously observed for ${\hat{I}}^2=5.85-6.2$ arises from a change of curvature from convex to concave as the lattice spacing is reduced. Fitting data for ${\hat{I}}^2\ge 5.93$ with an $O(a^2)$ form yields $B_K$(NDR,2 GeV)=0.587(7)(17) in the continuum limit. We also describe a finite-size study of $B_K$ at ${\hat{I}}^2=$ 6.0 and 6.4, and a reanalysis of the theoretical argument for $O(a^2)$ behavior.

4 pages incl. 2 figures, Latex+espcrc2+epsf, Talk presented at LATTICE96(poster) by S. Aoki