The QCD {beta}-function from global solutions to Dyson-Schwinger equations

Journal Article · Mon Feb 15 00:00:00 EST 2010 · Annals of Physics (New York)

DOI:https://doi.org/10.1016/j.aop.2009.10.011· OSTI ID:21336090

Baalen, Guillaume van ^[1]; Kreimer, Dirk ^[2]; Uminsky, David; Yeats, Karen ^[1]

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1. Department of Mathematics and Statistics, Boston University, 111 Cummington Street, Boston, MA 02215 (United States)
2. CNRS-IHES, 91440 Bures sur Yvette (France)

We study quantum chromodynamics from the viewpoint of untruncated Dyson-Schwinger equations turned to an ordinary differential equation for the gluon anomalous dimension. This non-linear equation is parameterized by a function P(x) which is unknown beyond perturbation theory. Still, very mild assumptions on P(x) lead to stringent restrictions for possible solutions to Dyson-Schwinger equations. We establish that the theory must have asymptotic freedom beyond perturbation theory and also investigate the low energy regime and the possibility for a mass gap in the asymptotically free theory.

• OSTI ID: 21336090
• Journal Information: Annals of Physics (New York), Vol. 325, Issue 2; Other Information: DOI: 10.1016/j.aop.2009.10.011; PII: S0003-4916(09)00214-0; Copyright (c) 2009 Elsevier Science B.V., Amsterdam, The Netherlands, All rights reserved; Country of input: International Atomic Energy Agency (IAEA); ISSN 0003-4916
• Country of Publication: United States
• Language: English

Related Subjects

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS
ANOMALOUS DIMENSION
ASYMPTOTIC SOLUTIONS
DYSON REPRESENTATION
FUNCTIONS
GLUONS
NONLINEAR PROBLEMS
PERTURBATION THEORY
QUANTUM CHROMODYNAMICS
SCHWINGER FUNCTIONAL EQUATIONS