Microscopic Origin of \boldmath{$U_A(1)$} Symmetry Violation in the High Temperature Phase of QCD

TL;DR

This study examines the origin of $U_A(1)$ symmetry violation in high-temperature QCD by analyzing eigenmodes of the Dirac operator, finding persistent near-zero modes linked to instantons even above the chiral crossover temperature.

Contribution

It provides new insights into the microscopic mechanisms behind $U_A(1)$ symmetry breaking at high temperatures using lattice QCD with overlap fermions.

Findings

No gap in eigenvalue spectrum at 1.5 T_c

Near-zero eigenmodes remain localized at high temperature

Instanton size and density measured at 1.5 T_c

Abstract

We investigate the low-lying eigenmodes of the Dirac matrix with the aim to gain more insight into the temperature dependence of the anomalous $U_A(1)$ symmetry. We use the overlap operator to probe dynamical QCD configurations generated with (2+1)-flavors of highly improved staggered quarks. We find no evidence of a gap opening up in the infrared region of the eigenvalue spectrum even at $1.5\,T_c$, $T_c$ being the chiral crossover temperature. Instead, we observe an accumulation of near-zero eigenmodes. We argue that these near-zero eigenmodes are primarily responsible for the anomalous breaking of the axial symmetry still being effective. At $1.5\,T_c$, these near-zero eigenmodes remain localized and their distribution is consistent with the dilute instanton gas picture. At this temperature, the average size of the instantons is $0.223(8)\,\text{fm}$ and their density is $0.147(7)\,\text{fm}^{-4}$.