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

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 $1.5T_c$, $T_c$ 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 $1.5T_c$, 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 $0.147(7){\text{fm}}^{-4}$.

15 pages, 19 figures

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Cited by in corpus (25)

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• The chiral phase transition and the axial anomaly
• Localization of Dirac Fermions in Finite-Temperature Gauge Theory
• Second order chiral phase transition in three flavor quantum chromodynamics?
• Chiral spin symmetry and hot/dense QCD
• Eigenvalues of the QCD Dirac matrix with improved staggered quarks in the continuum limit
• Constraining the QCD phase diagram at finite temperature and density
• Localization of Dirac modes in finite-temperature ${\mathbb{Z}}_2$ gauge theory on the lattice
• Deconfinement transition and localization of Dirac modes in finite-temperature ${\mathbb{Z}}_3$ gauge theory on the lattice
• Localisation of Dirac modes in gauge theories and Goldstone's theorem at finite temperature
• Thermal behavior of effective U_A(1) anomaly couplings in reflection of higher topological sectors
• QCD Anderson transition with overlap valence quarks on a twisted-mass sea
• The pion-kaon scattering amplitude and the $K^0(700)$ and $K^{\ast }(892)$ resonances at finite temperature
• Statistical tweaks and flow scale from masses
• Understanding the approach to thermalization from the eigenspectrum of non-Abelian gauge theories
• Symmetry of screening masses of mesons in two-flavor lattice QCD at high temperatures
• Axial U(1) symmetry and mesonic correlators at high temperature in $N_f=2$ lattice QCD
• Testing the strength of the ${\text{U}}_A(1)$ anomaly at the chiral phase transition in two-flavour QCD
• QCD at high temperature and density: selected highlights
• Free caloron gas in high temperature quenched QCD
• Dirac Eigenvalue spectrum of $N_f$=2+1 QCD towards the chiral limit using HISQ fermions
• Imprints of $U_A(1)$ chiral anomaly and disorder in the Dirac eigenspectrum of QCD at finite temperature
• Backreaction of mesonic fluctuations on the axial anomaly at finite temperature