Kaon B parameter from quenched domain-wall QCD

Abstract

We report on a calculation of $B_K$ with domain wall fermion action in quenched QCD. Simulations are made with a renormalization group improved gauge action at $\beta =2.6$ and 2.9 corresponding to $a^{-1}\approx 2$GeV and 3GeV. Effects due to finite fifth dimensional size $N_5$ and finite spatial size $N_{\sigma }$ are examined in detail. Matching to the continuum operator is made perturbatively at one loop order. We obtain $B_K(\mu =2GeV)=0.5746(61)(191)$, where the first error is statistical and the second error represents an estimate of scaling violation and $\mathcal{O}({\alpha }^2)$ errors in the renormalization factor added in quadrature, as an estimate of the continuum value in the $\msbar$ scheme with naive dimensional regularization. This value is consistent, albeit somewhat small, with $B_K(\mu =2GeV)=0.628(42)$ obtained by the JLQCD Collaboration using the Kogut-Susskind quark action. Results for light quark masses are also reported.

35 pages, 18 eps figures

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