The Kaon B-parameter with the Wilson Quark Action using Chiral Ward Identities

We present a detailed description of the method and results of our calculation of the kaon B parameter using the Wilson quark action in quenched QCD at $\beta =5.9-6.5$. The mixing problem of the $\mathrm{\Delta }s=2$ four-quark operators is solved non-perturbatively with full use of chiral Ward identities. We find $B_K(NDR,2GeV)=0.562(64)$ in the continuum limit, which agrees with the value obtained with the Kogut-Susskind quark action.