KaonB-parameter from quenched domain-wall QCD

We present numerical results for the kaon $B$-parameter, $B_K$, determined in the quenched approximation of lattice QCD. Our simulations are performed using domain-wall fermions and the renormalization group improved, DBW2 gauge action which combine to give quarks with good chiral symmetry at finite lattice spacing. Operators are renormalized nonperturbatively using the RI/MOM scheme. We study scaling by performing the simulation on two different lattices with $a^{-1}=1.982(30)$ and 2.914(54) GeV. We combine this quenched scaling study with an earlier calculation of $B_K$ using two flavors of dynamical, domain-wall quarks at a single lattice spacing to obtain $B_K^{\overline{\mathrm{MS}}\mathrm{NDR}}(\mu =2\mathrm{GeV})=0.563(21)(39)(30)$, were the first error is statistical, the second systematic (without quenching errors) and the third estimates the error due to quenching.