Constraints on the IR behavior of the ghost propagator in Yang-Mills theories

Abstract

We present rigorous upper and lower bounds for the momentum-space ghost propagator G(p) of Yang-Mills theories in terms of the smallest nonzero eigenvalue (and of the corresponding eigenvector) of the Faddeev-Popov matrix. We apply our analysis to data from simulations of SU(2) lattice gauge theory in Landau gauge, using the largest lattice sizes to date. Our results suggest that, in three and in four space-time dimensions, the Landau-gauge ghost propagator is not enhanced as compared to its tree-level behavior. This is also seen in plots and fits of the ghost dressing function. In the two dimensional case, on the other hand, we find that G(p) diverges as p^{-2-2 kappa} with kappa \approx 0.15, in agreement with Ref. [1]. We note that our discussion is general, although we make an application only to pure gauge theory in Landau gauge. Most of our simulations have been performed on the IBM supercomputer at the University of Sao Paulo.

6 pages, 5 tables, 2 figures (6 plots); added plots and fits of the ghost dressing function

References in corpus (12)

• A refinement of the Gribov-Zwanziger approach in the Landau gauge: infrared propagators in harmony with the lattice results
• Constraints on the IR behavior of the gluon propagator in Yang-Mills theories
• New features of the gluon and ghost propagator in the infrared region from the Gribov-Zwanziger approach
• Scaling behavior and positivity violation of the gluon propagator in full QCD
• Exploratory study of three-point Green's functions in Landau-gauge Yang-Mills theory
• Two- and three-point Green's functions in two-dimensional Landau-gauge Yang-Mills theory
• Quark Confinement: The Hard Problem of Hadron Physics
• Just how different are SU(2) and SU(3) Landau-gauge propagators in the IR regime?
• A first look at Landau-gauge propagators in G2 Yang-Mills theory
• Effects of the quark field on the ghost propagator of Lattice Landau Gauge QCD
• Infrared Maximally Abelian Gauge
• Lattice Results in Coulomb Gauge

Cited by in corpus (69)

• Lattice gluodynamics computation of Landau-gauge Green's functions in the deep infrared
• Baryons as relativistic three-quark bound states
• Infrared propagators of Yang-Mills theory from perturbation theory
• Gribov no-pole condition, Zwanziger horizon function, Kugo-Ojima confinement criterion, boundary conditions, BRST breaking and all that
• More on Gribov copies and propagators in Landau-gauge Yang-Mills theory
• A Dyson-Schwinger study of the four-gluon vertex
• Correlation functions of Landau gauge Yang-Mills theory
• The Landau gauge gluon and ghost propagator in the refined Gribov-Zwanziger framework in 3 dimensions
• Gauge Sector Dynamics in QCD
• Covariant gauge on the lattice: a new implementation
• Gribov horizon and BRST symmetry: a few remarks
• Infrared behavior and Gribov ambiguity in SU(2) lattice gauge theory
• An all-order proof of the equivalence between Gribov's no-pole and Zwanziger's horizon conditions
• Chemical potential and the gap equation
• A remark on the BRST symmetry in the Gribov-Zwanziger theory
• Alternative refined Gribov-Zwanziger Lagrangian
• The Coulomb gauge ghost Dyson-Schwinger equation
• Ghost dynamics in the soft gluon limit
• Properties of the Faddeev-Popov operator in the Landau gauge, matter confinement and soft BRST breaking
• BRST-Symmetry Breaking and Bose-Ghost Propagator in Lattice Minimal Landau Gauge
• On non-primitively divergent vertices of Yang-Mills theory
• Kugo-Ojima color confinement criterion and Gribov-Zwanziger horizon condition
• Accessing directly the properties of fundamental scalars in the confinement and Higgs phase
• The effects of Gribov copies in 2D gauge theories
• Rho-meson, Bethe-Salpeter equation, and the far infrared
• Study of the properties of the Gribov region in SU(N) Euclidean Yang-Mills theories in the maximal Abelian gauge
• Study of the Gribov region in Euclidean Yang-Mills theories in the maximal Abelian gauge
• On the Infrared Behavior of Landau Gauge Yang-Mills Theory with a Fundamentally Charged Scalar Field
• SU(3) Landau gauge gluon and ghost propagators using the logarithmic lattice gluon field definition
• Off-shell two loop QCD vertices
• Yang-Mills propagators in linear covariant gauges from Nielsen identities
• Symmetric point quartic gluon vertex and momentum subtraction
• A model for QCD ground state with magnetic disorder
• Renormalizability of the linearly broken formulation of the BRST symmetry in presence of the Gribov horizon in Landau gauge Euclidean Yang-Mills theories
• Phase structure and propagators at nonvanishing temperature for QCD and QCD-like theories
• On bounds and boundary conditions in the continuum Landau gauge
• Vertex functions of Coulomb gauge Yang--Mills theory
• A renormalization group invariant scalar glueball operator in the (Refined) Gribov-Zwanziger framework
• Two-loop corrections to the QCD propagators within the Curci-Ferrari model
• One-loop RG improvement of the screened massive expansion in the Landau gauge
• Novel sum rules for the three-point sector of QCD
• Gluon mass scale through the Schwinger mechanism
• Universal scaling of gluon and ghost propagators in the infrared
• Loop calculations in the three dimensional Gribov-Zwanziger Lagrangian
• Probing the singularities of the Landau-gauge gluon and ghost propagators with rational approximants
• Remarks on the effects of the Gribov copies on the infrared behavior of higher dimensional Yang-Mills theory
• Four-gluon vertex from the Curci-Ferrari model at one-loop order
• Thermal extension of the screened massive expansion in the Landau gauge
• The Generalised LKF Transformations for Arbitrary $N$-point Fermion Correlators
• The Nielsen identities in screened theories
• Low momentum propagators at two loops in gluon mass model
• Dynamically massive linear covariant gauges: setup and first results
• Polyakov loop, gluon mass, gluon condensate and its asymmetry near deconfinement
• Study of the all orders multiplicative renormalizability of a local confining quark action in the Landau gauge
• Schwinger-Dyson truncations in the all-soft limit: a case study
• Analytic continuation and physical content of the gluon propagator
• Effects of a quark chemical potential on the analytic structure of the gluon propagator
• Natural solution in the refined Gribov-Zwanziger theory
• Screened massive expansion of Schwinger-Dyson equations
• pQCD running couplings finite and monotonic in the infrared: when do they reflect the holomorphic properties of spacelike observables?
• A window on infrared QCD with small expansion parameters
• The gap equations of background field invariant Refined Gribov-Zwanziger action proposals and the deconfinement transition
• Spinning Pairs: Supporting ${}^3{P}_0$ Quark-Pair Creation from Landau Gauge Green's Functions
• Infrared propagators of Yang-Mills-Chern-Simons theories in linear covariant gauges
• Three loop effective potential for $⟨\frac{1}{2}{A_{\mu }^a}^2⟩$ in the Landau gauge in QCD
• Gribov Propagator and Symmetry Breaking
• Non-perturbative BRST symmetry and the spectral structure of the ghost propagator
• Ground state pseudoscalar mesons on the light front: from the light to heavy sector
• Screened massive expansion of the quark propagator in the Landau gauge