arXiv:hep-lat/9608134·v1·High Energy Physics — Lattice

Toward the Continuum Limit of $B_{K}$ with the Quenched Kogut-Susskind Quark Action

JLQCD Collaboration: S. Aoki🇯🇵 · M. Fukugita🇯🇵 · S. Hashimoto🇯🇵 · N. Ishizuka🇯🇵 · Y. Iwasaki🇯🇵 · K. Kanaya🇯🇵 · Y. Kuramashi🇯🇵 · H. Mino🇯🇵 · M. Okawa🇯🇵 · A. Ukawa🇯🇵 · T. Yoshie🇯🇵

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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 $β$ =6.4 and $β = 5.7$ suggest that an apparently linear $a$ dependence of $B_{K}$ previously observed for $β = 5.85 - 6.2$ arises from a change of curvature from convex to concave as the lattice spacing is reduced. Fitting data for $β \geq 5.93$ 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 $β =$ 6.0 and 6.4, and a reanalysis of the theoretical argument for $O (a^{2})$ behavior.