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

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 $\mathrm{\partial }\ln \rho \mathrm{/}\mathrm{\partial }\ln \lambda$ are matched to continuum perturbation theory, which is known up to $O({\alpha }_s^4)$, to extract the strong coupling constant ${\alpha }_s$.