The U_A(1) Problem on the Lattice with Ginsparg-Wilson Fermions

Abstract

We show how it is possible to give a precise and unambiguous implementation of the Witten--Veneziano formula for the eta' mass on the lattice, which looks like the formal continuum one, if the expression of the topological charge density operator, suggested by fermions obeying the Ginsparg--Wilson relation, is employed. By using recent numerical results from simulations with overlap fermions in 2 (abelian Schwinger model) and 4 (QCD) dimensions, one obtains values for the mass of the lightest pseudo-scalar flavour-singlet state that agree within errors with theoretical expectations and experimental data, respectively.

arXiv commentExpanded discussion in section three and in the conclusions

References in corpus (42)

• Exactly massless quarks on the lattice
• Exact chiral symmetry on the lattice and the Ginsparg-Wilson relation
• A construction of lattice chiral gauge theories
• More about exactly massless quarks on the lattice
• The index theorem in QCD with a finite cut-off
• Locality properties of Neuberger's lattice Dirac operator
• Chiral Fermions on the Lattice
• Lattice QCD without tuning, mixing and current renormalization
• Abelian chiral gauge theories on the lattice with exact gauge invariance
• Exact chiral symmetry, topological charge and related topics
• Topological susceptibility at zero and finite $T$ in SU(3) Yang-Mills theory
• Accurate Scale Determinations for the Wilson Gauge Action
• Topology of the SU(2) vacuum: a lattice study using improved cooling
• A study of chiral symmetry in quenched QCD using the Overlap-Dirac operator
• On the low fermionic eigenmode dominance in QCD on the lattice
• Spectral flow, condensate and topology in lattice QCD
• Instantons, the QCD Vacuum, and Hadronic Physics
• Instanton Content of the SU(3) Vacuum
• Target Independence of the Emc-SMC Effect
• Dynamical Quark Effects on Light Quark Masses
• Some more remarks on the Witten-Veneziano formula for the ${\eta }^{\prime }$ mass
• Geometrical aspects of chiral anomalies in the overlap
• Soft QCD Dynamics of Elastic Scattering in Impact Parameter Representation
• Renormalization and topological susceptibility on the lattice: SU(2) Yang-Mills theory
• Towards N=1 Super-Yang-Mills on the Lattice
• The eta and eta' mesons in QCD
• Approach to the Continuum Limit of the Quenched Hermitian Wilson-Dirac Operator
• Improved lattice operators: the case of the topological charge density
• Topological Charge Screening and the `Proton Spin' Beyond the Chiral Limit
• Anomalous Chiral Behavior in Quenched Lattice QCD
• Some Observations on Broken Symmetries
• On the continuum limit of fermionic topological charge in lattice gauge theory
• On the Nf and a Dependence of BK
• Unquenched QCD simulation results
• Flavour singlet pseudoscalar masses in N_f = 2 QCD
• Eta meson mass and topology in QCD with two light flavors
• Gluinos on the lattice: quenched calculations
• Schwinger Model with the Overlap-Dirac Operator: exact results versus a physics motivated approximation
• The Index of a Ginsparg-Wilson Dirac operator
• Effects of non-perturbatively improved dynamical fermions in UKQCD simulations
• The Eta-prime and Cooling with Staggered Fermions
• Chiral Effects of Quenched Eta-Prime Loops

Cited by in corpus (61)

• Properties and uses of the Wilson flow in lattice QCD
• Exploring improved holographic theories for QCD: Part II
• Theta dependence of SU(N) gauge theories in the presence of a topological term
• Theta dependence of SU(N) gauge theories
• Topological susceptibility in the SU(3) gauge theory
• Low-Dimensional Long-Range Topological Charge Structure in the QCD Vacuum
• Topological effects in QCD and the problem of short-distance singularities
• Universality of the topological susceptibility in the SU(3) gauge theory
• Non-Gaussianities in the topological charge distribution of the SU(3) Yang--Mills theory
• Calculation of the neutron electric dipole moment with two dynamical flavors of domain wall fermions
• Light quark masses, chiral condensate and quark-gluon condensate in quenched lattice QCD with exact chiral symmetry
• Masses and decay constants of the $\eta$ and ${\eta }^{\prime }$ mesons from lattice QCD
• Topological susceptibility in full QCD with Ginsparg-Wilson fermions
• Topological susceptibility and the sampling of field space in $N_f=2$ lattice QCD simulations
• An Introduction to Chiral Symmetry on the Lattice
• Theta dependence of the vacuum energy in the SU(3) gauge theory from the lattice
• The Negativity of the Overlap-Based Topological Charge Density Correlator in Pure-Glue QCD and the Non-Integrable Nature of its Contact Part
• U_A(1) anomaly and eta' mass from an infrared singular quark-gluon vertex
• The topological susceptibility in the large-N limit of SU(N) Yang-Mills theory
• Topological Lattice Actions
• Inherently Global Nature of Topological Charge Fluctuations in QCD
• Spontaneous $CP$ breaking in QCD and the axion potential: an effective Lagrangian approach
• Accelerated Overlap Fermions
• Topological susceptibility with the asqtad action
• Witten-Veneziano Relation, Quenched QCD, and Overlap Fermions
• Low-energy couplings of QCD from topological zero-mode wave functions
• Flow-based sampling in the lattice Schwinger model at criticality
• Topological susceptibility from the overlap
• Non-perturbative Test of the Witten-Veneziano Formula from Lattice QCD
• Topological susceptibility at $T>T_{\mathrm{c}}$ from master-field simulations of the SU(3) gauge theory
• Chiral Effective Lagrangian and Quark Masses
• The role of the chiral anomaly in polarized deeply inelastic scattering II: Topological screening and transitions from emergent axion-like dynamics
• Topological susceptibility from twisted mass fermions using spectral projectors and the gradient flow
• Topological sampling through windings
• Axial anomaly with the overlap-Dirac operator in arbitrary dimensions
• OPE of the pseudoscalar gluonium correlator in massless QCD to three-loop order
• The Reality of the Fundamental Topological Structure in the QCD Vacuum
• Spontaneous chiral symmetry breaking in QCD:a finite-size scaling study on the lattice
• The Large $N_c$ limit of QCD on the lattice
• Exact Chiral Symmetry on the Lattice: QCD Applications
• QCD with two dynamical flavors of chirally improved quarks
• Topological susceptibility from the twisted mass Dirac operator spectrum
• Analyticity in theta on the lattice and the large volume limit of the topological susceptibility
• Reviewing the problem of the U(1) axial symmetry and the chiral transition in QCD
• Computing the eta and eta' Mesons in Lattice QCD
• Quenched chiral logarithms in lattice QCD with exact chiral symmetry
• The clash of positivities in topological density correlators
• Topological charge density correlator in Lattice QCD with two flavours of unimproved Wilson fermions
• Topological Susceptibility in a Uniform Magnetic Field
• A Study of the 't Hooft Model with the Overlap Dirac Operator
• $U(1{)}_A$ axial anomaly, ${\eta }^{\prime }$, and topological susceptibility in the holographic soft-wall model
• Discretisation effects in the topological susceptibility in lattice QCD
• Topological susceptibility for the SU(3) Yang--Mills theory
• An upper limit to the electric dipole moment of the neutron from lattice QCD
• Chiral symmetry on the lattice
• On the YM and QCD spectra from five dimensional strings
• Chiral and isospin breaking in the two-flavor Schwinger Model
• On the chiral anomaly and the Yang-Mills gradient flow
• The problem of the U(1) axial symmetry and the chiral transition in QCD
• Monopole and instanton effects on connected and disconnected correlations for scalar density
• Monopoles, spectra of overlap fermions, and eta-prime meson in external magnetic fields