The microscopic spectrum of the QCD Dirac operator with finite quark masses

TL;DR

This paper calculates the detailed microscopic spectral properties of the QCD Dirac operator with finite quark masses using random-matrix theory, covering various flavor numbers, masses, and topological charges.

Contribution

It provides a comprehensive analytical framework for the microscopic spectrum of the QCD Dirac operator with finite masses, extending previous models to include arbitrary flavors and topologies.

Findings

Derived microscopic spectral correlators and density functions.

Obtained distributions for the smallest eigenvalue across different parameters.

Extended the random-matrix theory approach to more realistic QCD scenarios.

Abstract

We compute the microscopic spectrum of the QCD Dirac operator in the presence of dynamical fermions in the framework of random-matrix theory for the chiral Gaussian unitary ensemble. We obtain results for the microscopic spectral correlators, the microscopic spectral density, and the distribution of the smallest eigenvalue for an arbitrary number of flavors, arbitrary quark masses, and arbitrary topological charge.