Chiral symmetry restoration and eigenvalue density of Dirac operator

TL;DR

This paper investigates the eigenvalue density of the Dirac operator in 2-flavor QCD at finite temperature, showing that it and its derivatives vanish at the origin, implying chiral symmetry restoration and the disappearance of the U(1) anomaly.

Contribution

It provides new constraints on the eigenvalue density and its derivatives in the chiral symmetric phase using overlap Dirac operator, improving previous results.

Findings

Eigenvalue density and its first two derivatives vanish at the origin.

Axial U(1) anomaly effects become unobservable in meson susceptibilities.

Stronger constraints on eigenvalue density than previous studies.

Abstract

We reinvestigate constraints on the eigenvalue density of the Dirac operator in the chiral symmetric phase of 2 flavor QCD at finite temperature, employing the overlap Dirac operator with the exact chiral symmetry at finite lattice spacings to avoid possible ultra-violet(UV) divergences. Studying multi-point correlation functions in various channels in the thermodynamical limit, we obtain stronger constraints than those found in the previous studies that not only the eigenvalue density at the origin but also its first and second derivatives vanish in the chiral limit of 2 flavor QCD. In addition we show that the axial U(1) anomaly becomes invisible in susceptibilities of scalar and pseudo scalar mesons.