BKwith two flavors of dynamical overlap fermions

Abstract

We present a two-flavor QCD calculation of ${B}_{K}$ on a ${16}^{3}\ifmmode\times\else\texttimes\fi{}32$ lattice at $a\ensuremath{\sim}0.12\text{ }\text{ }\mathrm{fm}$ (or equivalently ${a}^{\ensuremath{-}1}=1.67\text{ }\text{ }\mathrm{GeV}$). Both valence and sea quarks are described by the overlap fermion formulation. The matching factor is calculated nonperturbatively 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 ${B}_{K}^{\overline{\mathrm{MS}}}(2\text{ }\text{ }\mathrm{GeV})=0.537(4)(40)$, 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.