The quarkgluon vertex in Landau gauge QCD: Its role in dynamical chiral symmetry breaking and quark confinement
Abstract
The infrared behavior of the quarkgluon vertex of quenched Landau gauge QCD is studied by analyzing its DysonSchwinger equation. Building on previously obtained results for Green functions in the YangMills sector, we analytically derive the existence of powerlaw infrared singularities for this vertex. We establish that dynamical chiral symmetry breaking leads to the selfconsistent generation of components of the quarkgluon vertex forbidden when chiral symmetry is forced to stay in the WignerWeyl 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 quarkgluon vertex DysonSchwinger equation which respects the analytically determined infrared behavior, numerical results for the coupled system of the quark propagator and vertex DysonSchwinger 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 quarkquark 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 »
 Authors:

 Institut fuer Physik der KarlFranzens Universitaet Graz, A8010 Graz (Austria)
 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: S00034916(08)00105X; Copyright (c) 2008 Elsevier Science B.V., Amsterdam, The Netherlands, All rights reserved; Country of input: International Atomic Energy Agency (IAEA); Journal ID: ISSN 00034916
 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; QUARKQUARK INTERACTIONS; QUARKONIUM; QUARKS; SINGULARITY; STRONGCOUPLING MODEL; SYMMETRY BREAKING; VAN DER WAALS FORCES; VERTEX FUNCTIONS; YANGMILLS THEORY
Citation Formats
Alkofer, Reinhard, Fischer, Christian S., LlanesEstrada, Felipe J, and Schwenzer, Kai. The quarkgluon 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., LlanesEstrada, Felipe J, & Schwenzer, Kai. The quarkgluon 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., LlanesEstrada, Felipe J, and Schwenzer, Kai. Thu .
"The quarkgluon 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 quarkgluon vertex in Landau gauge QCD: Its role in dynamical chiral symmetry breaking and quark confinement},
author = {Alkofer, Reinhard and Fischer, Christian S. and LlanesEstrada, Felipe J and Schwenzer, Kai},
abstractNote = {The infrared behavior of the quarkgluon vertex of quenched Landau gauge QCD is studied by analyzing its DysonSchwinger equation. Building on previously obtained results for Green functions in the YangMills sector, we analytically derive the existence of powerlaw infrared singularities for this vertex. We establish that dynamical chiral symmetry breaking leads to the selfconsistent generation of components of the quarkgluon vertex forbidden when chiral symmetry is forced to stay in the WignerWeyl 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 quarkgluon vertex DysonSchwinger equation which respects the analytically determined infrared behavior, numerical results for the coupled system of the quark propagator and vertex DysonSchwinger 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 quarkquark 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 longrange 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 = {00034916},
number = 1,
volume = 324,
place = {United States},
year = {2009},
month = {1}
}