B_K with two flavors of dynamical overlap fermions

TL;DR

This paper reports a lattice QCD calculation of the $B_K$ parameter using two-flavor overlap fermions, achieving a precise result with systematic uncertainties estimated, and demonstrating the applicability of NLO PQChPT up to half the strange quark mass.

Contribution

The study introduces a two-flavor QCD calculation of $B_K$ with overlap fermions, including non-perturbative matching and analysis up to NLO and NNLO chiral perturbation theory.

Findings

$B_K^{ar{ m MS}}(2 { m GeV})= 0.537(4)(40)$

Lattice data well described by NLO PQChPT up to $m_s^{ m phys}/2$

Systematic uncertainties estimated from multiple sources

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^{\rm phys}/2$). The data at quark masses heavier than $m_s^{\rm phys}/2$ are fitted including a part of next-to-next-to-leading order terms. We obtain $B_K^{\bar{\rm MS}}(2 {\rm GeV})= 0.537(4)(40)$, 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.