Physics – High Energy Physics – High Energy Physics - Lattice
Scientific paper
2008-01-28
Phys.Rev.D77:094503,2008
Physics
High Energy Physics
High Energy Physics - Lattice
36 pages, 14 figures, comments and references added, analysis and systematic error revised, minor change in the final result.
Scientific paper
10.1103/PhysRevD.77.094503
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.
Aoki Sadao
for the JLQCD Collaboration
Fukaya Hidenori
Hashimoto Shigehira
Kaneko Tak
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