Roles of the color antisymmetric ghost propagator in the infrared QCD

The results of Coulomb gauge and Landau gauge lattice QCD simulation do not agree completely with continuum theory. There are indications that the ghost propagator in the infrared region is not purely color diagonal as in high energy region. After presenting lattice simulation of configurations produced with Kogut-Susskind fermion (MILC collaboration) and those with domain wall fermion (RBC/UKQCD collaboration), I investigate in triple gluon vertex and the ghost-gluon-ghost vertex how the square of the color antisymmetric ghost contributes. Then the effect of the vertex correction to the gluon propagator and the ghost propagator is investigated. Recent Dyson-Schwinger equation analysis suggests the ghost dressing function $G(0)=$ finite and no infrared enhancement or $\alpha_G=0$. But the ghost propagator renormalized by the loop containing a product of color antisymmetric ghost is expected to behave as $_r =-\frac{G(q^2)}{q^2}$ with $G(q^2)\propto q^{-2(1+\alpha_G)}$ with $\alpha_G = 0.5$, if the fixed point scenario is valid. I interpret the $\alpha_G=0$ solution should contain a vertex correction. The infrared exponent of our lattice Landau gauge gluon propagator of the RBC/UKQCD is $\kappa=\alpha_G=-0.5$ and that of MILC is about -0.7. The implication for the Kugo-Ojima color confinement criterion, QCD effective coupling and the Slavnov identity are given.Comment: 13 pages 10 figures, references added and revised. version to be published in Few-Body System

Studying unquenching effects in QCD with Dyson-Schwinger equations

We summarise recent results on the properties of gluons, quarks and light mesons from the Green's functions approach to QCD. We discuss a self-consistent, infrared power law solution for the Schwinger-Dyson equations of the 1PI-Greens functions of Yang-Mills theory. The corresponding running coupling has a universal fixed point at zero momentum. Based on these analytical results a truncation scheme for the coupled system of Schwinger-Dyson equations for the propagators of QCD and the Bethe-Salpeter equation for light mesons has been formulated. We compare numerical results for charge eigenstate vector and pseudoscalar meson observables with corresponding lattice data. The effects of unquenching the system are found to be small but not negligible.Comment: 8 pages, 8 figures. Invited talk given by C.S.F. at the 'Workshop on computational hadron physics', Sept. 13 - 17, Nikosia, Cypru

Large volume behavior of Yang-Mills propagators

We summarize results on finite-volume effects in the propagators of Landau gauge Yang-Mills theory using Dyson-Schwinger equations on a 4-dimensional torus. We demonstrate explicitly how the solutions for the gluon and the ghost propagator tend towards their respective infinite volume forms in the corresponding limit. We discuss the relation of our solutions with results from lattice Monte-Carlo simulations.Comment: 7 pages, 2 figures, Presented by CF at the XXV International Symposium on Lattice Field Theory, July 30 - August 4 2007, Regensburg, German

Infrared Properties of QCD from Dyson-Schwinger equations

I review recent results on the infrared properties of QCD from Dyson-Schwinger equations. The topics include infrared exponents of one-particle irreducible Green's functions, the fixed point behaviour of the running coupling at zero momentum, the pattern of dynamical quark mass generation and properties of light mesons.Comment: 47 pages, 19 figures, Topical Review to be published in J.Phys.G, v2: typos corrected and some references adde

Slavnov-Taylor identities in Coulomb gauge Yang-Mills theory

The Slavnov-Taylor identities of Coulomb gauge Yang-Mills theory are derived from the (standard, second order) functional formalism. It is shown how these identities form closed sets from which one can in principle fully determine the Green's functions involving the temporal component of the gauge field without approximation, given appropriate input.Comment: 20 pages, no figure

Two- and three-point functions in two-dimensional Landau-gauge Yang-Mills theory: Continuum results

We investigate the Dyson-Schwinger equations for the gluon and ghost propagators and the ghost-gluon vertex of Landau-gauge gluodynamics in two dimensions. While this simplifies some aspects of the calculations as compared to three and four dimensions, new complications arise due to a mixing of different momentum regimes. As a result, the solutions for the propagators are more sensitive to changes in the three-point functions and the ansaetze used for them at the leading order in a vertex a expansion. Here, we therefore go beyond this common truncation by including the ghost-gluon vertex self-consistently for the first time, while using a model for the three-gluon vertex which reproduces the known infrared asymptotics and the zeros at intermediate momenta as observed on the lattice. A separate computation of the three-gluon vertex from the results is used to confirm the stability of this behavior a posteriori. We also present further arguments for the absence of the decoupling solution in two dimensions. Finally, we show how in general the infrared exponent kappa of the scaling solutions in two, three and four dimensions can be changed by allowing an angle dependence and thus an essential singularity of the ghost-gluon vertex in the infrared.Comment: 24 pages; added references, improved choices of parameters for vertex models; identical to version published in JHE

The Infrared Behaviour of the Pure Yang-Mills Green Functions

We review the infrared properties of the pure Yang-Mills correlators and discuss recent results concerning the two classes of low-momentum solutions for them reported in literature; i.e. decoupling and scaling solutions. We will mainly focuss on the Landau gauge and pay special attention to the results inferred from the analysis of the Dyson-Schwinger equations of the theory and from "{\it quenched}" lattice QCD. The results obtained from properly interplaying both approaches are strongly emphasized.Comment: Final version to be published in FBS (54 pgs., 11 figs., 4 tabs

On the infrared scaling solution of SU(N) Yang-Mills theories in the maximally Abelian gauge

An improved method for extracting infrared exponents from functional equations is presented. The generalizations introduced allow for an analysis of quite complicated systems such as Yang-Mills theory in the maximally Abelian gauge. Assuming the absence of cancellations in the appropriately renormalized integrals the only consistent scaling solution yields an infrared enhanced diagonal gluon propagator in support of the Abelian dominance hypothesis. This is explicitly shown for SU(2) and subsequently verified for SU(N), where additional interactions exist. We also derive the most infrared divergent scaling solution possible for vertex functions in terms of the propagators' infrared exponents. We provide general conditions for the existence of a scaling solution for a given system and comment on the cases of linear covariant gauges and ghost anti-ghost symmetric gauges.Comment: 23 pages, 10 figures; version coincides with version published in EPJ

Infrared Behavior of Three-Point Functions in Landau Gauge Yang-Mills Theory

Analytic solutions for the three-gluon and ghost-gluon vertices in Landau gauge Yang-Mills theory at low momenta are presented in terms of hypergeometric series. They do not only show the expected scaling behavior but also additional kinematic divergences when only one momentum goes to zero. These singularities, which have also been proposed previously, induce a strong dependence on the kinematics in many dressing functions. The results are generalized to two and three dimensions and a range of values for the ghost propagator's infrared exponent kappa.Comment: 21 pages, 29 figures; numerical data of the infrared dressing functions can be obtained from the authors v2: a few minor changes, corresponds to version appearing in EPJ

On the gauge boson's properties in a candidate technicolor theory

The technicolor scenario replaces the Higgs sector of the standard model with a strongly interacting sector. One candidate for a realization of such a sector is two-technicolor Yang-Mills theory coupled to two degenerate flavors of adjoint, massless techniquarks. Using lattice gauge theory the properties of the technigluons in this scenario are investigated as a function of the techniquark mass towards the massless limit. For that purpose the minimal Landau gauge two-point and three-point correlation functions are determined, including a detailed systematic error analysis. The results are, within the relatively large systematic uncertainties, compatible with a behavior very similar to QCD at finite techniquark mass. However, the limit of massless techniquarks exhibits features which could be compatible with a (quasi-)conformal behavior.Comment: 27 pages, 17 figures, 1 table; v2: persistent notational error corrected, some minor modification