Stochastic calculation of the Dirac spectrum on the lattice and a determination of chiral condensate in 2+1-flavor QCD

TL;DR

This paper calculates the chiral condensate in 2+1-flavor QCD using a stochastic method to analyze the Dirac spectrum on the lattice, confirming theoretical expectations and controlling systematic errors.

Contribution

It introduces a stochastic eigenvalue filtering technique applied to lattice QCD configurations to determine the chiral condensate with high precision.

Findings

Chiral condensate value: 270.0(4.9) MeV at 2 GeV

Spectrum shape matches one-loop chiral perturbation theory

Finite volume effects are well-controlled

Abstract

We compute the chiral condensate in 2+1-flavor QCD through the spectrum of low-lying eigenmodes of Dirac operator. The number of eigenvalues of the Dirac operator is evaluated using a stochastic method with an eigenvalue filtering technique on the background gauge configurations generated by lattice QCD simulations including the effects of dynamical up, down and strange quarks described by the Mobius domain-wall fermion formulation. The low-lying spectrum is related to the chiral condensate, which is one of the leading order low-energy constants in chiral effective theory, as dictated by the Banks-Casher relation. The spectrum shape and its dependence on the sea quark masses calculated in numerical simulations are consistent with the expectation from one-loop chiral perturbation theory. After taking the chiral limit as well as the continuum limit using the data at three lattice spacings ranging 0.080-0.045 fm, we obtain $\Sigma^{1/3}$(2 GeV) = 270.0(4.9) MeV, with the error combining those from statistical and from various sources of systematic errors. Finite volume effect is confirmed to be under control by a direct comparison of the results from two different volumes at the lightest available sea quarks corresponding to 230 MeV pions.