B_K with two flavors of dynamical overlap fermions

Abstract

We present a two-flavor QCD calculation of $B_K$ on a $16^3\times 32$ lattice at $a\sim 0.12$ fm (or equivalently $a^{-1}\sim$1.67 GeV). Both valence and sea quarks are described by the overlap fermion formulation. The matching factor is calculated non-perturbatively with the so-called RI/MOM scheme. We find that the lattice data are well described by the next-to-leading order (NLO) partially quenched chiral perturbation theory (PQChPT) up to around a half of the strange quark mass ($m_s^{\mathrm{phys}}/2$). The data at quark masses heavier than $m_s^{\mathrm{phys}}/2$ are fitted including a part of next-to-next-to-leading order terms. We obtain $B_K^{\overline{\mathrm{MS}}}(2\mathrm{GeV})=0.537(4)(40)$, where the first error is statistical and the second is an estimate of systematic uncertainties from finite volume, fixing topology, the matching factor, and the scale setting.

Comments: 36 pages, 14 figures, comments and references added, analysis and systematic error revised, minor change in the final result. version to appear in PRD, reference corrected