Kaon<i>B</i>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 $\ensuremath{\beta}=2.6$ and $2.9$ corresponding to ${a}^{\ensuremath{-}1}\ensuremath{\approx}2$ and 3 GeV. Effects due to finite fifth dimensional size ${N}_{5}$ and finite spatial size ${N}_{\ensuremath{\sigma}}$ are examined in detail. Matching to the continuum operator is made perturbatively at one loop order. We obtain ${B}_{K}(\ensuremath{\mu}=2 \mathrm{GeV})=0.5746(61)(191),$ where the first error is statistical and the second error represents an estimate of scaling violation and $\mathcal{O}({\ensuremath{\alpha}}^{2})$ errors in the renormalization factor added in quadrature, as an estimate of the continuum value in the modified minimal subtraction $(\overline{\mathrm{MS}})$ scheme with naive dimensional regularization. This value is consistent, albeit somewhat small, with ${B}_{K}(\ensuremath{\mu}=2 \mathrm{GeV})=0.628(42)$ obtained by the JLQCD Collaboration using the Kogut-Susskind quark action. Results for light quark masses are also reported.