Lattice QCD Calculation of the KaonBParameter with the Wilson Quark Action

Abstract

The kaon $B$ parameter is calculated in quenched lattice QCD with the Wilson quark action. The mixing problem of the $\Delta s=2\mathrm{}$ four-quark operators is solved nonperturbatively with full use of chiral Ward identities, and this method enables us to construct the weak four-quark operators exhibiting good chiral behavior. We find $B_K(\mathrm{NDR},2\mathrm{GeV})=0.69\mathrm{}\left(7\right)$ (where NDR denotes naive dimensional regularization) at the lattice cutoff scale of $a^{-1\mathrm{}}=2.7\mathrm{}–4.3\mathrm{GeV}$.