The quark-gluon vertex in Landau gauge QCD: Its role in dynamical chiral symmetry breaking and quark confinement

Abstract

The infrared behavior of the quark-gluon vertex of quenched Landau gauge QCD is studied by analyzing its Dyson-Schwinger equation. Building on previously obtained results for Green functions in the Yang-Mills sector we analytically derive the existence of power-law infrared singularities for this vertex. We establish that dynamical chiral symmetry breaking leads to the self-consistent generation of components of the quark-gluon vertex forbidden when chiral symmetry is forced to stay in the Wigner-Weyl mode. In the latter case the running strong coupling assumes an infrared fixed point. If chiral symmetry is broken, either dynamically or explicitely, the running coupling is infrared divergent. Based on a truncation for the quark-gluon vertex Dyson-Schwinger equation which respects the analytically determined infrared behavior numerical results for the coupled system of the quark propagator and vertex Dyson-Schwinger equation are presented. The resulting quark mass function as well as the vertex function show only a very weak dependence on the current quark mass in the deep infrared. From this we infer by an analysis of the quark-quark scattering kernel a linearly rising quark potential with an almost mass independent string tension in the case of broken chiral symmetry. Enforcing chiral symmetry does lead to a Coulomb type potential. Therefore we conclude that chiral symmetry breaking and confinement are closely related. Furthermore we discuss aspects of confinement as the absence of long-range van-der-Waals forces and Casimir scaling. An examination of experimental data for quarkonia provides further evidence for the viability of the presented mechanism for quark confinement in the Landau gauge.

arXiv comment64 pages, 31 figures

References in corpus (64)

• Big-Bang nucleosynthesis (Particle Data Group mini-review)
• The Cosmological Parameters 2006
• Dyson-Schwinger Equations and the Application to Hadronic Physics
• The Infrared Behavior of QCD Green's Functions - Confinement, Dynamical Symmetry Breaking, and Hadrons as Relativistic Bound States
• Aspects of the Functional Renormalisation Group
• Observation of a Broad Structure in the ${\pi }^{+}{\pi }^{-}J/\psi$ Mass Spectrum around 4.26 GeV/$c^2$
• Effective field theories for heavy quarkonium
• Dyson-Schwinger equations: a tool for hadron physics
• Infrared Properties of QCD from Dyson-Schwinger equations
• The Infrared Behavior of Gluon and Ghost Propagators in Landau Gauge QCD
• Goldstone Theorem and Diquark Confinement Beyond Rainbow-Ladder Approximation
• On the Infrared Exponent for Gluon and Ghost Propagation in Landau Gauge QCD
• A Solution to Coupled Dyson-Schwinger Equations for Gluons and Ghosts in Landau Gauge
• Non-perturbative Propagators, Running Coupling and Dynamical Quark Mass of Landau gauge QCD
• Non-perturbative Landau gauge and infrared critical exponents in QCD
• Coulomb Gauge QCD, Confinement, and the Constituent Representation
• Casimir scaling of SU(3) static potentials
• Analytic properties of the Landau gauge gluon and quark propagators
• Infrared behaviour and fixed points in Landau gauge QCD
• Dynamical Chiral Symmetry Breaking, Goldstone's Theorem and the Consistency of the Schwinger--Dyson and Bethe--Salpeter Equations
• The $\pi$, $K^{+}$, and $K^0$ electromagnetic form factors
• Unquenched quark propagator in Landau gauge
• Confirmation of the Y(4260) Resonance Production in ISR
• Complete O(v^2) corrections to the static interquark potential from SU(3) gauge theory
• Infrared Exponents and Running Coupling of SU(N) Yang-Mills Theories
• Vertex functions and infrared fixed point in Landau gauge SU(N) Yang-Mills theory
• Aspects and consequences of a dressed-quark-gluon vertex
• n-Particle irreducible effective action techniques for gauge theories
• Bethe-Salpeter equation and a nonperturbative quark-gluon vertex
• Uniqueness of infrared asymptotics in Landau gauge Yang-Mills theory
• Renormalization flow of Yang-Mills propagators
• Nonperturbative structure of the quark-gluon vertex
• Electromagnetic properties of ground and excited state pseudoscalar mesons
• QCD modeling of hadron physics
• Detailed Analysis of the Tetraquark Potential and Flip-Flop in SU(3) Lattice QCD
• Quark-gluon vertex in arbitrary gauge and dimension
• Meson Structure in a Relativistic Many-Body Approach
• Scalar One-Loop Integrals using the Negative-Dimension Approach
• Nucleon Properties in the Covariant Quark-Diquark Model
• Verifying the Kugo-Ojima Confinement Criterion in Landau Gauge Yang-Mills Theory
• Quark-gluon vertex model and lattice-QCD data
• Quark-gluon vertex from lattice QCD
• Hadron Spectroscopy and Structure from AdS/CFT
• A Systematic Extended Iterative Solution for QCD
• Quark Confinement: The Hard Problem of Hadron Physics
• Quark-gluon vertex in general kinematics
• Quark-gluon vertex dressing and meson masses beyond ladder-rainbow truncation
• Analytic Structure of Amplitudes in Gauge Theories with Confinement
• On the Dirac Structure of Confinement
• Relativistic Many-Body Hamiltonian Approach to Mesons
• Aspects of the confinement mechanism in Coulomb-gauge QCD
• QCD Coulomb gauge approach to hybrid mesons
• Hadron Spectroscopy: Theory and Experiment
• QCD Glueball Regge Trajectories and the Pomeron
• Analytic structure of the gluon and quark propagators in Landau gauge QCD
• Dynamically induced scalar quark confinement
• Quark-gluon vertex with an off-shell O(a)-improved chiral fermion action
• The analytic structure of heavy quark propagators
• Dynamical Mass Generation in Landau gauge QCD
• Low Energy Dynamics in Ultradegenerate QCD Matter
• QCD string and the Lorentz nature of confinement
• Chiral Symmetry Breaking with Scalar Confinement
• Relativistic corrections for two- and three-body flux tube model
• The effect of the ultraviolet part of the gluon propagator on the heavy quark propagator

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• Polyakov loop, gluon mass, gluon condensate and its asymmetry near deconfinement
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• Confinement, the gluon propagator and the interquark potential for heavy mesons
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