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Title: 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 explicitly, 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 typemore » 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.« less

Authors:
 [1];  [2];  [1]
  1. Institut fuer Physik der Karl-Franzens Universitaet Graz, A-8010 Graz (Austria)
  2. Departamento de Fisica Teorica I de la Universidad Complutense, 28040 Madrid (Spain)
Publication Date:
OSTI Identifier:
21167701
Resource Type:
Journal Article
Journal Name:
Annals of Physics (New York)
Additional Journal Information:
Journal Volume: 324; Journal Issue: 1; Other Information: DOI: 10.1016/j.aop.2008.07.001; PII: S0003-4916(08)00105-X; Copyright (c) 2008 Elsevier Science B.V., Amsterdam, The Netherlands, All rights reserved; Country of input: International Atomic Energy Agency (IAEA); Journal ID: ISSN 0003-4916
Country of Publication:
United States
Language:
English
Subject:
72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS; BAG MODEL; CHIRAL SYMMETRY; CONFINEMENT; EQUATIONS; GLUONS; GREEN FUNCTION; POTENTIALS; PROPAGATOR; QUANTUM CHROMODYNAMICS; QUARK-QUARK INTERACTIONS; QUARKONIUM; QUARKS; SINGULARITY; STRONG-COUPLING MODEL; SYMMETRY BREAKING; VAN DER WAALS FORCES; VERTEX FUNCTIONS; YANG-MILLS THEORY

Citation Formats

Alkofer, Reinhard, Fischer, Christian S., Llanes-Estrada, Felipe J, and Schwenzer, Kai. The quark-gluon vertex in Landau gauge QCD: Its role in dynamical chiral symmetry breaking and quark confinement. United States: N. p., 2009. Web. doi:10.1016/j.aop.2008.07.001.
Alkofer, Reinhard, Fischer, Christian S., Llanes-Estrada, Felipe J, & Schwenzer, Kai. The quark-gluon vertex in Landau gauge QCD: Its role in dynamical chiral symmetry breaking and quark confinement. United States. https://doi.org/10.1016/j.aop.2008.07.001
Alkofer, Reinhard, Fischer, Christian S., Llanes-Estrada, Felipe J, and Schwenzer, Kai. Thu . "The quark-gluon vertex in Landau gauge QCD: Its role in dynamical chiral symmetry breaking and quark confinement". United States. https://doi.org/10.1016/j.aop.2008.07.001.
@article{osti_21167701,
title = {The quark-gluon vertex in Landau gauge QCD: Its role in dynamical chiral symmetry breaking and quark confinement},
author = {Alkofer, Reinhard and Fischer, Christian S. and Llanes-Estrada, Felipe J and Schwenzer, Kai},
abstractNote = {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 explicitly, 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.},
doi = {10.1016/j.aop.2008.07.001},
url = {https://www.osti.gov/biblio/21167701}, journal = {Annals of Physics (New York)},
issn = {0003-4916},
number = 1,
volume = 324,
place = {United States},
year = {2009},
month = {1}
}