Lattice computation of the Dirac eigenvalue density in the perturbative regime of QCD

TL;DR

This paper computes the Dirac eigenvalue density in lattice QCD, carefully subtracts discretization effects, and matches results to perturbation theory to extract the strong coupling constant with high precision.

Contribution

It introduces a lattice computation method for the Dirac eigenvalue density in the perturbative regime of QCD and extracts the strong coupling constant by matching to high-order perturbation theory.

Findings

Lattice results agree with continuum perturbation theory at high energies.

Discretization effects are effectively subtracted at leading order.

The strong coupling constant $oldsymbol{ extalpha_s}$ is extracted with improved accuracy.

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 $\alpha_s$.