Modelling the quark propagator

Journal Article · Sun Sep 01 04:00:00 EDT 1991 · Annals of Physics (New York); (United States)

DOI:https://doi.org/10.1016/0003-4916(91)90051-9· OSTI ID:5072487

Williams, A G; Krein, G ^[1]; Roberts, C D ^[2]

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1. Department of Physics Supercomputer Computations, Research Institute, Florida State University, Tallahassee, Florida (USA)
2. Theory Group, Bldg 203, Argonne National Laboratory, Argonne, Illinois (USA)

We are interested in developing covariant, confining, and asymptotically free models of hadrons. With this goal in mind we have carried out a study of dynamical chiral symmetry breaking without imposing the frequently used approximation {alpha}{sub {ital s}}({minus}({ital p}{minus}{ital k}){sup 2}){congruent}{alpha}{sub {ital s}}({minus}{ital p}{sup 2}{sub {gt}}), where {ital p}{sup 2}{sub {gt}}{equivalent to}max({ital p}{sup 2},{ital k}{sup 2}) for the running coupling constant in the quark Schwinger--Dyson equation. We present numerical results in Landau gauge and compare these with earlier results obtained when using this approximation. We see in this context that a gluon propagator which has the form 1/{ital q}{sup 4} in the infrared is too singular and must be regulated. We derive a suitably generalized expression for the pion decay constant {ital f}{sub {pi}}. With essentially one free parameter we are able to reproduce reasonable results for various physical quantities of interest including {ital f}{sub {pi}}, {l angle}{ital {bar q}q}{r angle}, and {Lambda}{sub QCD}. {copyright} 1991 Academic Press, Inc.

• DOE Contract Number: W-31109-ENG-38
• OSTI ID: 5072487
• Journal Information: Annals of Physics (New York); (United States), Journal Name: Annals of Physics (New York); (United States) Vol. 210:2; ISSN 0003-4916; ISSN APNYA
• Country of Publication: United States
• Language: English

Related Subjects

645204* -- High Energy Physics-- Particle Interactions & Properties-Theoretical-- Strong Interactions & Properties
72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS
BOSONS
CHARGED-PARTICLE REACTIONS
CHIRAL SYMMETRY
CONFINEMENT
ELEMENTARY PARTICLES
FERMIONS
FIELD THEORIES
GAUGE INVARIANCE
GLUONS
HADRON REACTIONS
HADRONS
INFRARED DIVERGENCES
INTERACTIONS
INVARIANCE PRINCIPLES
MESON REACTIONS
NUCLEAR REACTIONS
NUMERICAL SOLUTION
PARTICLE INTERACTIONS
PION REACTIONS
POSTULATED PARTICLES
PROPAGATOR
QUANTUM CHROMODYNAMICS
QUANTUM FIELD THEORY
QUARK-QUARK INTERACTIONS
QUARKS
RENORMALIZATION
SYMMETRY