The Wilson Dirac Spectrum for QCD with Dynamical Quarks

TL;DR

This paper computes the microscopic correlation functions of the Hermitian Wilson Dirac operator spectrum in QCD with dynamical quarks, including effects of discretization errors, using chiral Lagrangians.

Contribution

It provides explicit formulas for the spectral density with two light quark flavors, incorporating discretization effects and fixed operator index, derived from chiral Lagrangian methods.

Findings

Explicit spectral density for two light flavors

Inclusion of leading discretization error effects

Results for fixed Wilson Dirac operator index

Abstract

All microscopic correlation functions of the spectrum of the Hermitian Wilson Dirac operator with any number of flavors with equal masses are computed. In particular, we give explicit results for the spectral density in the physical case with two light quark flavors. The results include the leading effect in the discretization error and are given for fixed index of the Wilson Dirac operator. They have been obtained starting from chiral Lagrangians for the generating function of the Dirac spectrum. Microscopic correlation functions of the real eigenvalues of the Wilson Dirac operator are computed following the same approach.