Correlated Dirac Eigenvalues and Axial Anomaly in Chiral Symmetric QCD

Abstract

We introduce novel relations between the derivatives [${\partial }^n\rho (\lambda ,m_l)/\partial m_l^n$] of the Dirac eigenvalue spectrum [$\rho (\lambda ,m_l)$] with respect to the light sea quark mass ($m_l$) and the $(n+1)$-point correlations among the eigenvalues ($\lambda$) of the massless Dirac operator. Using these relations we present lattice QCD results for ${\partial }^n\rho (\lambda ,m_l)/\partial m_l^n$ ($n=1,2,3$) for $m_l$ corresponding to pion masses $m_{\pi }=160-55$ MeV, and at a temperature of about 1.6 times the chiral phase transition temperature. Calculations were carried out using (2+1) flavors of highly improved staggered quarks with the physical value of strange quark mass, three lattice spacings $a=0.12,0.08,0.06$ fm, and lattices having aspect ratios $4-9$. We find that $\rho (\lambda \to 0,m_l)$ develops a peaked structure. This peaked structure arises due to non-Poisson correlations within the infrared part of the Dirac eigenvalue spectrum, becomes sharper as $a\to 0$, and its amplitude is proportional to $m_l^2$. We demonstrate that this $\rho (\lambda \to 0,m_l)$ is responsible for the manifestations of axial anomaly in two-point correlation functions of light scalar and pseudoscalar mesons. After continuum and chiral extrapolations we find that axial anomaly remains manifested in two-point correlation functions of scalar and pseudoscalar mesons in the chiral limit.

17 pages, 18 figures, minor updates to match the published version in PRL

References in corpus (44)

• The equation of state in (2+1)-flavor QCD
• The chiral and deconfinement aspects of the QCD transition
• The QCD transition temperature: results with physical masses in the continuum limit II.
• Chiral crossover in QCD at zero and non-zero chemical potentials
• The QCD Equation of State to $\mathcal{O}({\mu }_B^6)$ from Lattice QCD
• The QCD phase transition with physical-mass, chiral quarks
• The QCD crossover at finite chemical potential from lattice simulations
• Fluctuations and Correlations of net baryon number, electric charge, and strangeness: A comparison of lattice QCD results with the hadron resonance gas model
• Chiral phase transition temperature in (2+1)-Flavor QCD
• Scaling studies of QCD with the dynamical HISQ action
• Curvature of the chiral pseudo-critical line in QCD: continuum extrapolated results
• Relevance of the axial anomaly at the finite-temperature chiral transition in QCD
• Chiral symmetry breaking and the Banks--Casher relation in lattice QCD with Wilson quarks
• The QCD chiral transition, $\ua$ symmetry and the Dirac spectrum using domain wall fermions
• The chiral transition and U(1)_A symmetry restoration from lattice QCD using Domain Wall Fermions
• Chiral symmetry restoration, eigenvalue density of Dirac operator and axial U(1) anomaly at finite temperature
• Finite temperature study of the axial U(1) symmetry on the lattice with overlap fermion formulation
• Meson screening masses from lattice QCD with two light and the strange quark
• Exact 2+1 flavour RHMC simulations
• Meson Screening Masses in (2+1)-Flavor QCD
• Microscopic Origin of \boldmath{$U_A(1)$} Symmetry Violation in the High Temperature Phase of QCD
• Evidence of effective axial U(1) symmetry restoration at high temperature QCD
• Symanzik improvement of the gradient flow in lattice gauge theories
• On the nature of the finite-temperature transition in QCD
• Scale-dependent mass anomalous dimension from Dirac eigenmodes
• Chiral properties of (2+1)-flavor QCD in strong magnetic fields at zero temperature
• A precise determination of the psibar-psi anomalous dimension in conformal gauge theories
• On the strength of the $U_A(1)$ anomaly at the chiral phase transition in $N_f=2$ QCD
• Thouless Energy and Correlations of QCD Dirac Eigenvalues
• Comment on "Chiral anomalies and rooted staggered fermions"
• Possible New Phase of Thermal QCD
• Topology and axions in QCD
• Order of the Chiral and Continuum Limits in Staggered Chiral Perturbation Theory
• Statistical properties of the spectrum of the QCD Dirac operator at low energy
• U(1) axial symmetry and Dirac spectra in QCD at high temperature
• Phases of SU(3) Gauge Theories with Fundamental Quarks via Dirac Spectral Density
• U(2)xU(2)-symmetric fixed point from the Functional Renormalization Group
• Lattice computation of the Dirac eigenvalue density in the perturbative regime of QCD
• GMOR-like relation in IR-conformal gauge theories
• Quasi-instantons in QCD with chiral symmetry restoration
• QED${}_3$-inspired three-dimensional conformal lattice gauge theory without fine-tuning
• Quark mass anomalous dimension and ${\Lambda }_{\overline{\text{MS}}}$ from the twisted mass Dirac operator spectrum
• Alternatives to the stochastic "noise vector" approach
• The gradient flow of the Dirac spectrum

Cited by in corpus (40)

• 50 Years of Quantum Chromodynamics
• QCD at finite temperature and density within the fRG approach: An overview
• Study of the axial U(1) anomaly at high temperature with lattice chiral fermions
• Eigenvalue spectra of QCD and the fate of $U_A(1)$ breaking towards the chiral limit
• Chiral condensates and screening masses of neutral pseudoscalar mesons in thermomagnetic QCD medium
• Quantum Simulation of Chiral Phase Transitions
• Unusual Features of QCD Low-Energy Modes in IR Phase
• QCD phase transitions in the light quark chiral limit
• The chiral phase transition and the axial anomaly
• Curvature of the chiral phase transition line from the magnetic equation of state of (2+1)-flavor QCD
• Localization of Dirac Fermions in Finite-Temperature Gauge Theory
• Second order chiral phase transition in three flavor quantum chromodynamics?
• Eigenvalues of the QCD Dirac matrix with improved staggered quarks in the continuum limit
• Anderson Metal-to-Critical Transition in QCD
• Critical behaviors of the $O(4)$ and $Z(2)$ symmetries in the QCD phase diagram
• Localization of Dirac modes in finite-temperature ${\mathbb{Z}}_2$ gauge theory on the lattice
• Microscopic Encoding of Macroscopic Universality: Scaling Properties of Dirac Eigenspectra near QCD Chiral Phase Transition
• Gravitational waves and primordial black holes from chirality imbalanced QCD first-order phase transition with $\mathcal{P}$ and $\mathcal{C}\mathcal{P}$ violation
• Overview of the QCD phase diagram -- Recent progress from 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
• Detecting scale anomaly in chiral phase transition of QCD: new critical endpoint pinned down
• New aspect of chiral and axial breaking in QCD
• Correlated Dirac eigenvalues around the transition temperature on $N_{\tau }=8$ lattices
• Critical behavior towards the chiral limit at vanishing and non-vanishing chemical potentials
• $U_A(1)$ symmetry restoration at high baryon density
• $U_A(1)$ symmetry breaking quark interactions from vacuum polarization
• Axial inverse magnetic catalysis
• QCD transition at the physical point, and its scaling window from twisted mass Wilson fermions
• Study of some local and global $U(1)$ axial condensates in QCD at finite temperature
• Understanding the approach to thermalization from the eigenspectrum of non-Abelian gauge theories
• Dirac Equation Solution with Generalized tanh-Shaped Hyperbolic Potential: Application to Charmonium and Bottomonium Mass Spectra
• QCD at high temperature and density: selected highlights
• Imprints of $U_A(1)$ chiral anomaly and disorder in the Dirac eigenspectrum of QCD at finite temperature
• Microscopic Encoding of Macroscopic Universality in QCD Chiral Phase Transition
• Backreaction of mesonic fluctuations on the axial anomaly at finite temperature
• Gap in the Dirac spectrum and quark propagator symmetries in lattice QCD
• Chiral Symmetry Breaking and Confinement from an Interacting Ensemble of Instanton-dyons in Two-flavor Massless QCD