A Solution to Coupled Dyson-Schwinger Equations for Gluons and Ghosts in Landau Gauge

Abstract

A truncation scheme for the Dyson-Schwinger equations of QCD in Landau gauge is presented which implements the Slavnov-Taylor identities for the 3-point vertex functions. Neglecting contributions from 4-point correlations such as the 4-gluon vertex function and irreducible scattering kernels, a closed system of equations for the propagators is obtained. For the pure gauge theory without quarks this system of equations for the propagators of gluons and ghosts is solved in an approximation which allows for an analytic discussion of its solutions in the infrared: The gluon propagator is shown to vanish for small spacelike momenta whereas the ghost propagator is found to be infrared enhanced. The running coupling of the non-perturbative subtraction scheme approaches an infrared stable fixed point at a critical value of the coupling alpha_c of approx. 9.5. The gluon propagator is shown to have no Lehmann representation. The results for the propagators obtained here compare favorably with recent lattice calculations.

60 pages, LaTeX209, 17 figures (epsfig.sty), to appear in Ann. Phys., some typos corrected. In particular, in Eqs. (83), (85) and (90) a factor 1/(4 kappa) that was erroneously inserted in the original typing process had to be removed. We are indebted to A. Cucchieri for helping us become aware of this typo

References in corpus (4)

• The Infrared Behavior of Gluon and Ghost Propagators in Landau Gauge QCD
• Hadron Physics from the Global Color Model of QCD
• Gribov Copies in the Minimal Landau Gauge: the Influence on Gluon and Ghost Propagators
• Nucleon Form Factors in a Covariant Diquark-Quark Model

Cited by in corpus (246)

• Aspects of the Functional Renormalisation Group
• Dyson-Schwinger Equations: Density, Temperature and Continuum Strong QCD
• Infrared Properties of QCD from Dyson-Schwinger equations
• Lattice gluodynamics computation of Landau-gauge Green's functions in the deep infrared
• Bethe-Salpeter Study of Vector Meson Masses and Decay Constants
• Baryons as relativistic three-quark bound states
• On the infrared behavior of Landau gauge Yang-Mills theory
• Constraints on the IR behavior of the gluon propagator in Yang-Mills theories
• On the Infrared Exponent for Gluon and Ghost Propagation in Landau Gauge QCD
• Non-perturbative Propagators, Running Coupling and Dynamical Quark Mass of Landau gauge QCD
• QCD at finite temperature and chemical potential from Dyson-Schwinger equations
• Non-perturbative Landau gauge and infrared critical exponents in QCD
• The QCD Running Coupling
• Fermion Interactions and Universal Behavior in Strongly Interacting Theories
• Analytic properties of the Landau gauge gluon and quark propagators
• Infrared behaviour and fixed points in Landau gauge QCD
• Non-perturbative quark, gluon and meson correlators of unquenched QCD
• Gauge bosons at zero and finite temperature
• Non-perturbative Faddeev-Popov formula and infrared limit of QCD
• Hadron Properties and Dyson-Schwinger Equations
• Non-perturbative comparison of QCD effective charges
• Analysis of a quenched lattice-QCD dressed-quark propagator
• The Infrared Behaviour of the Pure Yang-Mills Green Functions
• 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
• The quark-gluon vertex in Landau gauge QCD: Its role in dynamical chiral symmetry breaking and quark confinement
• Scaling behavior and positivity violation of the gluon propagator in full QCD
• Aspects and consequences of a dressed-quark-gluon vertex
• Asymptotic Scaling and Infrared Behavior of the Gluon Propagator
• Landau-gauge propagators in Yang-Mills theories at beta = 0: massive solution versus conformal scaling
• A dynamical gluon mass solution in a coupled system of the Schwinger-Dyson equations
• The three-gluon vertex in Landau gauge
• The Elusiveness of Infrared Critical Exponents in Landau Gauge Yang--Mills Theories
• Gluonic three-point correlations in pure Landau gauge QCD
• Mesons in a Poincare Covariant Bethe-Salpeter Approach
• The strong coupling and its running to four loops in a minimal MOM scheme
• Confinement from Correlation Functions
• Running coupling in Yang-Mills theory - a flow equation study -
• Uniqueness of infrared asymptotics in Landau gauge Yang-Mills theory II
• IR finiteness of the ghost dressing function from numerical resolution of the ghost SD equation
• Gluon propagators and quark confinement
• Dynamical Chiral Symmetry Breaking in Unquenched ${QED}_3$
• Bethe-Salpeter equation and a nonperturbative quark-gluon vertex
• Universality of spontaneous chiral symmetry breaking in gauge theories
• The Gribov parameter and the dimension two gluon condensate in Euclidean Yang-Mills theories in the Landau gauge
• Towards the infrared limit in SU(3) Landau gauge lattice gluodynamics
• Exploratory study of three-point Green's functions in Landau-gauge Yang-Mills theory
• Renormalization flow of Yang-Mills propagators
• Nonperturbative structure of the quark-gluon vertex
• Propagators and running coupling from SU(2) lattice gauge theory
• Two- and three-point Green's functions in two-dimensional Landau-gauge Yang-Mills theory
• Numerical Study of the Ghost-Gluon Vertex in Landau gauge
• Relating a gluon mass scale to an infrared fixed point in pure gauge QCD
• QCD modeling of hadron physics
• Infrared behaviour of the ghost-gluon vertex in Landau gauge Yang-Mills theory
• Infrared properties of propagators in Landau-gauge pure Yang-Mills theory at finite temperature
• Probing Unquenching Effects in the Gluon Polarisation in Light Mesons
• SU(2) lattice gluon propagator: continuum limit, finite-volume effects and infrared mass scale m_IR
• Gribov Copies in the Minimal Landau Gauge: the Influence on Gluon and Ghost Propagators
• Freezing of the QCD coupling constant and solutions of Schwinger-Dyson equations
• Running Coupling in Non-Perturbative QCD - I. Bare Vertices and y-max Approximation
• The QCD Phase Boundary from Quark-Gluon Dynamics
• More on Gribov copies and propagators in Landau-gauge Yang-Mills theory
• Infrared singularities in Landau gauge Yang-Mills theory
• Verifying the Kugo-Ojima Confinement Criterion in Landau Gauge Yang-Mills Theory
• On the influence of three-point functions on the propagators of Landau gauge Yang-Mills theory
• Correlation functions of Landau gauge Yang-Mills theory
• A Dyson-Schwinger study of the four-gluon vertex
• Propagators and Dimensional Reduction of Hot SU(2) Gauge Theory
• Quark-gluon vertex from lattice QCD
• Landau gauge gluon and ghost propagators at finite temperature from quenched lattice QCD
• Gauge Sector Dynamics in QCD
• Time-independant stochastic quantization, DS equations, and infrared critical exponents in QCD
• Equation of State of Gluon Plasma from Fundamental Modular Region
• Gribov horizon and i-particles: about a toy model and the construction of physical operators
• Improved Landau gauge fixing and the suppression of finite-volume effects of the lattice gluon propagator
• Propagators in Coulomb gauge from SU(2) lattice gauge theory
• On gluon and ghost propagators in linear covariant gauges
• Algorithmic derivation of functional renormalization group equations and Dyson-Schwinger equations
• Multiplicative renormalizability and quark propagator
• Magnetic Screening in Hot Non-Abelian Gauge Theory
• QCD Running Couplings and Effective Charges
• High-Temperature Limit of Landau-Gauge Yang-Mills Theory
• Beyond Miransky Scaling
• Just how different are SU(2) and SU(3) Landau-gauge propagators in the IR regime?
• Infrared Features of the Landau Gauge QCD
• Infrared behavior and Gribov ambiguity in SU(2) lattice gauge theory
• Signals of confinement in Green functions of SU(2) Yang-Mills theory
• Landau gauge Yang-Mills propagators in the complex momentum plane
• Two- and three-point functions in two-dimensional Landau-gauge Yang-Mills theory: Continuum results
• The Gluon Propagator without lattice Gribov copies
• Infrared Behaviour of Propagators and Vertices
• What's up with IR gluon and ghost propagators in Landau gauge? A puzzling answer from huge lattices
• Unqueched Kogut-Susskind quark propagator in Lattice Landau Gauge QCD
• Infrared behavior of the gluon propagator in lattice Landau gauge: the three-dimensional case
• The High-Temperature Phase of Landau-Gauge Yang-Mills Theory
• Equation of State of Gluon Plasma from Local Action
• On mass generation in Landau-gauge Yang-Mills theory
• Correlation functions of three-dimensional Yang-Mills theory from Dyson-Schwinger equations
• Propagator Dyson-Schwinger Equations of Coulomb Gauge Yang-Mills Theory Within the First Order Formalism
• The Gluon Propagator without lattice Gribov copies on a finer lattice
• Large volume behaviour of Yang-Mills propagators
• The Coulomb gauge ghost Dyson-Schwinger equation
• One loop gluon form factor and freezing of alpha_s in the Gribov-Zwanziger QCD Lagrangian
• What the Gribov copy tells on the confinment and the theory of dynamical chiral symmetry breaking
• High statistics determination of the strong coupling constant in Taylor scheme and its OPE Wilson coefficient from lattice QCD with a dynamical charm
• Progress in vacuum susceptibilities and their applications to the chiral phase transition of QCD
• A study of the gauge invariant, nonlocal mass operator $Tr\int d^{4}x{F}_{\mu \nu }(D^2{)}^{-1}{F}_{\mu \nu }$ in Yang-Mills theories
• Nonperturbative structure of the ghost-gluon kernel
• Strong-coupling study of the Gribov ambiguity in lattice Landau gauge
• Infrared Behavior of Three-Point Functions in Landau Gauge Yang-Mills Theory
• Analytic calculation of color-Coulomb potential and color confinement
• Fit to Gluon Propagator and Gribov Formula
• Polyakov loop and QCD thermodynamics from the gluon and ghost propagators
• On the analytic structure of scalar glueball operators at Born level
• Gluon confinement, i-particles and BRST soft breaking
• On practical problems to compute the ghost propagator in SU(2) lattice gauge theory
• On the infrared behaviour of Gluons and Ghosts in Ghost-Antighost symmetric gauges
• Describing a1 and b1 decays
• Are the Dressed Gluon and Ghost Propagators in the Landau Gauge presently determined in the confinement regime of QCD?
• Quantum Yang-Mills field theory
• Decontracted double BRST on the lattice
• Spin Zero Glueballs in the Bethe-Salpeter Formalism
• Infrared analysis of Dyson-Schwinger equations taking into account the Gribov horizon in Landau gauge
• Landau gauge gluon and ghost propagators from lattice QCD with Nf=2 twisted mass fermions at finite temperature
• Current Conservation in the Covariant Quark-Diquark Model of the Nucleon
• Analytic structure of the gluon and quark propagators in Landau gauge QCD
• On non-primitively divergent vertices of Yang-Mills theory
• Accessing directly the properties of fundamental scalars in the confinement and Higgs phase
• Coulomb-gauge ghost and gluon propagators in SU(3) lattice Yang-Mills theory
• CrasyDSE: A framework for solving Dyson-Schwinger equations
• Infrared Behaviour and Running Couplings in Interpolating Gauges in QCD
• Finite-density gauge correlation functions in QC2D
• Analytic Approach to Perturbative QCD
• A study of the maximal Abelian gauge in SU(2) Euclidean Yang-Mills theory in the presence of the Gribov horizon
• Two- and three-point functions in Landau gauge Yang-Mills-Higgs theory
• On the infrared scaling solution of SU(N) Yang-Mills theories in the maximally Abelian gauge
• Multiplicative renormalizability of gluon and ghost propagators in QCD
• Modified instanton profile effects from lattice Green functions
• Infrared exponents and the strong-coupling limit in lattice Landau gauge
• Gluon propagator in two-color dense QCD: Massive Yang-Mills approach at one-loop
• Gluon condensation and scaling exponents for the propagators in Yang-Mills theory
• On the spectrum of the Faddeev-Popov operator in topological background fields
• Epsilon expansion for infrared Yang-Mills theory in Landau gauge
• Gribov horizon in the presence of dynamical mass generation in Euclidean Yang-Mills theories in the Landau gauge
• Infrared features of KS fermion and Wilson fermion in Lattice Landau Gauge QCD
• Synthetic Running Coupling of QCD
• Solving a Coupled Set of Truncated QCD Dyson-Schwinger Equations
• The No-Pole Condition in Landau gauge: Properties of the Gribov Ghost Form-Factor and a Constraint on the 2d Gluon Propagator
• On the Infrared Behavior of Landau Gauge Yang-Mills Theory with a Fundamentally Charged Scalar Field
• Spurious divergences in Dyson-Schwinger equations
• Modeling the Landau-Gauge Ghost Propagator in 2, 3 and 4 Space-Time Dimensions
• Dense two-color QCD from Dyson-Schwinger equations
• A first look at Landau-gauge propagators in G2 Yang-Mills theory
• Temperature Dependence of Gluon and Ghost Propagators in Landau-Gauge Yang-Mills Theory below the Phase Transition
• Running coupling constant and propagators in SU(2) Landau gauge
• Solving coupled Dyson--Schwinger equations on a compact manifold
• The Gluon Propagator with Two-loop Schwinger-Dyson Equations
• Yang-Mills propagators in linear covariant gauges from Nielsen identities
• Some more details of minimal-Landau-gauge Yang-Mills propagators
• A model for QCD ground state with magnetic disorder
• The spectrum of an SU(3) gauge theory with a fundamental Higgs field
• Non-perturbative Propagators, Running Coupling and Dynamical Mass Generation in Ghost-Antighost Symmetric Gauges in QCD
• Landau gauge ghost and gluon propagators and the Faddeev-Popov operator spectrum
• Two infrared Yang-Mills solutions in stochastic quantization and in an effective action formalism
• Slavnov-Taylor identities in Coulomb gauge Yang-Mills theory
• Thermal quarks and gluon propagators in two-color dense QCD
• Ghost sector and geometry in minimal Landau gauge: further constraining the infinite-volume limit
• On the gauge-algebra dependence of Landau-gauge Yang-Mills propagators
• Infrared features of unquenched finite temperature lattice Landau gauge QCD
• Infrared-suppressed gluon propagator in 4d Yang-Mills theory in a Landau-like gauge
• Dependence of the propagators on the sampling of Gribov copies inside the first Gribov region of Landau gauge
• A non-perturbative study of matter field propagators in Euclidean Yang-Mills theory in linear covariant, Curci-Ferrari and maximal Abelian gauges
• Planar degeneracy of the three-gluon vertex
• Lattice Landau gauge with stochastic quantisation
• Solving a Set of Truncated Dyson-Schwinger Equations with a Globally Converging Method
• Calculation of the non-perturbative strong coupling from first principles
• 3-loop 3PI effective action for 3D SU(3) QCD
• Linear Covariant Gauges on the Lattice
• Mass spectrum of pseudo-scalar glueballs from a Bethe-Salpeter approach with the rainbow-ladder truncation
• Non-perturbative finite $T$ broadening of the $\rho$ meson and dilepton emission in heavy ion-collisions
• Two-point functions of quenched lattice QCD in Numerical Stochastic Perturbation Theory. (II) The gluon propagator in Landau gauge
• The Wilson loop from a Dyson equation
• Continuum Strong QCD: Confinement and Dynamical Chiral Symmetry Breaking
• Fluctuations of order parameter in an $SU(N_c)$ effective model
• The Gribov-Zwanziger action in the presence of the gauge invariant, nonlocal mass operator $Tr\int d^{4}x{F}_{\mu \nu }(D^2{)}^{-1}{F}_{\mu \nu }$ in the Landau gauge
• SU(2) Running Coupling Constant and Confinement in Minimal Coulomb and Landau Gauges
• A study of the influence of the gauge group on the Dyson-Schwinger equations for scalar-Yang-Mills systems
• Spectral dimension as a tool for analyzing non-perturbative propagators
• Dpes massless QCD have vacuum energy?
• Gluon mass scale through the Schwinger mechanism
• On the dynamical mass generation in confining Yang-Mills theories
• The Gribov horizon and the one-loop color-Coulomb potential
• Goldstone Boson's Valence-Quark Distribution
• Dyson-Schwinger approach to strongly coupled theories
• Numerical Study of Lattice Landau Gauge QCD and the Gribov Copy Problem
• Faddeev-Popov spectra at the Gribov horizon
• Counting Gribov copies
• Determination of the quantum part of the truly nonperturbative Yang-Mills vacuum energy density in the covariant gauge QCD
• Lattice Gluon Propagator in the Landau Gauge: A Study Using Anisotropic Lattices
• The ice-limit of Coulomb gauge Yang-Mills theory
• Gluon confinement criterion in QCD
• Kugo-Ojima confinement and QCD Green's functions in covariant gauges
• Solving the Ghost-Gluon System of Yang-Mills Theory on GPUs
• Dynamical symmetry breaking, confinement with flat-bottom potential
• Perturbative aspects of the deconfinement transition -- Physics beyond the Faddeev-Popov model
• On the gauge boson's properties in a candidate technicolor theory
• Propagation of Gluons From a Non-Perturbative Evolution Equation in Axial Gauges
• Infrared and ultraviolet asymptotic solutions to gluon and ghost propagators in Yang-Mills theory
• Gribov copies and anomalous scaling
• An exploratory study of Yang-Mills three-point functions at non-zero temperature
• What the Infrared Behaviour of QCD Vertex Functions in Landau gauge can tell us about Confinement
• Meson Form Factors and Non-Perturbative Gluon Propagators
• Infrared Exponents and the Running Coupling of Landau gauge QCD and their Relation to Confinement
• Dispersive approach to QCD and hadronic contributions to electroweak observables
• Test of the Kugo-Ojima Confinement Criterion in the Lattice Landau Gauge
• The Kugo-Ojima confinement criterion and the Infrared Behavior of Landau gauge QCD
• Propagators and topology
• Confinement & Chiral Symmetry Breaking: The fundamental problems of hadron physics
• Confinement and Green functions in Landau-gauge QCD
• Structure and decay constant of the ρmeson with Bethe-Salpeter equation
• Infrared scaling solutions beyond the Landau gauge: The maximally Abelian gauge and Abelian infrared dominance
• Gluon bound state and asymptotic freedom derived from the Bethe--Salpeter equation
• The hybrid meson: new results from the updated mg and alpha_s parameters
• Consistent power corrections to ultraviolet asymptotic solutions in Yang-Mills theory
• Exploring the Tan contact term in Yang-Mills theory
• Schwinger-Dyson equations and disorder
• The Confinement Property in SU(3) Gauge Theory
• Numerical Study of the Gluon Propagator in Lattice Landau Gauge: the Three-Dimensional Case
• Solving the Schwinger-Dyson Equations for Gluodynamics in the Maximal Abelian Gauge
• Quark sector of Coulomb gauge Quantum Chromodynamics
• Roles of the color antisymmetric ghost propagator in the infrared QCD
• The production of charged-kaon pairs in proton-antiproton collisions: The role of higher-twist mechanism
• Quark-Gluon Coupling in the Global Colour Model of QCD
• Study of the nonlocal gauge invariant mass operator $\mathrm{Tr}\int d^{4}x{F}_{\mu \nu }(D^2{)}^{-1}{F}_{\mu \nu }$ in the maximal Abelian gauge
• Dyson-Schwinger equations and $\mathcal{N}=4$ SYM in Landau gauge
• Non-perturbative aspects of Yang-Mills theories
• A Numerical Approach to Coulomb Gauge QCD
• Local renormalizable gauge theories from nonlocal operators
• Short Strings and Gluon Propagator in the Infrared Region
• The inclusive production of charged pion pairs in proton-antiproton collisions
• Quantum fields in the non-perturbative regime - Yang-Mills theory and gravity
• Non-perturbative study of QCD correlators
• Higher-twist mechanism and inclusive gluon production in pion-proton collisions
• Dynamically induced scalar quark confinement: A link between chiral symmetry breaking and confinement
• Confinement encoded in Landau gauge gluon and ghost propagators