Chiral symmetry restoration, eigenvalue density of Dirac operator and axial U(1) anomaly at finite temperature

TL;DR

This study uses lattice QCD with overlap Dirac operator to show that eigenvalue density and its derivatives vanish at the origin in 2-flavor QCD at finite temperature, impacting the understanding of chiral symmetry restoration.

Contribution

It provides stronger constraints on eigenvalue density and its derivatives at the origin, indicating the axial U(1) anomaly's irrelevance at the chiral transition in 2-flavor QCD.

Findings

Eigenvalue density at the origin vanishes in the chiral limit.

The axial U(1) anomaly becomes invisible in scalar and pseudo-scalar susceptibilities.

Second order chiral phase transition with O(4) scaling is unlikely.

Abstract

We reconsider constraints on the eigenvalue density of the Dirac operator in the chiral symmetric phase of 2 flavor QCD at finite temperature. To avoid possible ultra-violet(UV) divergences, we work on a lattice, employing the overlap Dirac operator, which ensures the exact "chiral" symmetry at finite lattice spacings. Studying multi-point correlation functions in various channels and taking their thermodynamical limit (and then taking the chiral limit), we obtain stronger constraints than those found in the previous studies: both the eigenvalue density at the origin and 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, suggesting that the 2nd order chiral phase transition with the O(4) scaling is not realized in 2 flavor QCD. Possible lattice artifacts when non-chiral lattice Dirac operator is employed are briefly discussed.