Abstract
The eigenvalue spectrum $\rho(\lambda)$ of the Dirac operator is numerically calculated in lattice QCD with 2+1 flavors of dynamical domain-wall fermions. In the high-energy regime, the discretization effects become significant. We subtract them at the leading order and then take the continuum limit with lattice data at three lattice spacings. Lattice results for the exponent $\partial\ln\rho/\partial\ln\lambda$ are matched to continuum perturbation theory, which is known up to $O(\alpha_s^4)$, to extract the strong coupling constant $\alpha_s$.
Highlights
The Dirac operator D is a fundamental building block of gauge theories such as quantum chromodynamics (QCD), the underlying theory of strong interaction
Any observable consisting of quarks in QCD can be written in terms of its eigenmodes, i.e., eigenvalues and their associated eigenfunctions, after an average over background gauge configurations with a weight determined by the path-integral formulation
The best-known example is the Banks-Casher relation [1], which relates the near-zero eigenvalue density to the chiral condensate hψψi, the order parameter of spontaneous chiral symmetry breaking in QCD
Summary
The Dirac operator D is a fundamental building block of gauge theories such as quantum chromodynamics (QCD), the underlying theory of strong interaction. This paper presents a lattice calculation of the Dirac spectral density in the perturbative regime. We calculate the eigenvalue density in the whole energy range from zero up to the lattice cutoff with the domain-wall fermion formulation using a stochastic technique to evaluate the average number of eigenvalues in small intervals. Our construction corresponds to a slightly different prescription to cancel the bulk effects of the five-dimensional fermion modes leaving the physical modes on the four-dimensional surface Using this scheme, the remaining discretization effects are made small, so that we are able to extrapolate the lattice data to the continuum limit with a linear ansatz in a2. A preliminary version of this work was presented in [15]
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