Spectral density of the Dirac operator in two-flavour QCD

TL;DR

This study calculates the spectral density of the Hermitean Dirac operator in two-flavor QCD near zero eigenvalues, confirming the Banks-Casher mechanism and matching theoretical predictions with lattice data.

Contribution

It provides the first lattice-based computation of the spectral density near zero in two-flavor QCD with controlled chiral and continuum extrapolations.

Findings

Spectral density at the origin is non-zero, indicating chiral symmetry breaking.

Spectral density remains approximately constant up to eigenvalues of 80 MeV.

The measured spectral density agrees with the value from the Gell-Mann-Oakes-Renner relation.

Abstract

We compute the spectral density of the (Hermitean) Dirac operator in Quantum Chromodynamics with two light degenerate quarks near the origin. We use CLS/ALPHA lattices generated with two flavours of O(a)-improved Wilson fermions corresponding to pseudoscalar meson masses down to 190 MeV, and with spacings in the range 0.05-0.08 fm. Thanks to the coverage of parameter space, we can extrapolate our data to the chiral and continuum limits with confidence. The results show that the spectral density at the origin is non-zero because the low modes of the Dirac operator do condense as expected in the Banks-Casher mechanism. Within errors, the spectral density turns out to be a constant function up to eigenvalues of approximately 80 MeV. Its value agrees with the one extracted from the Gell-Mann-Oakes-Renner relation.