Asymptotically free gauge theories. I

Journal Article · Thu Nov 15 00:00:00 UTC 1973 · Physical Review, D

DOI:https://doi.org/10.1103/PhysRevD.8.3633· OSTI ID:4312175

Gross, D J; Wilczek, F

Asymptotically free gauge theories of the strong interactions are constructed and analyzed. The reasons for doing this are recounted, including a review of renormalization-group techniques and their application to scaling phenomena. The renormalization-group equations are derived for Yang-Mills theories. The parameter that enter into the equations are calculated to lowest order and it is shown that these theories are asymptotically free. More specifically the effective coupling constant, which determines the ultraviolet behavior of the theory, vanishes for large spacelike momenta. Fermions are incorporated and the construction of realistic models is discussed. We propose that the strong interactions be mediated by a color'' gauge group which commutes with SU(3) x SU(3). The problem of symmetry breaking is discussed. It appear likely that this would have a dynamical origin. It is suggested that the gauge symmetry might not be broken, and that the severe infrared singularities prevent the occurrence of noncolor singlet physical states. The deep-inelastic structure functions, as well as the electron-positron total annihilation cross section are analyzed. Scaling obtains up to calculable logarithmic corrections, and the naive light-cone or parton-model results follow. The problems of incorporating scalar mesons and breaking the symmetry by the Higgs mechanism are explained in detail.

• Research Organization: National Accelerator Laboratory, P. O. Box 500, Batavia Illinois 60510 (US); Joseph Henry Laboratories, Princeton University, Princeton, New Jersey 08540 (US)
• Sponsoring Organization: US Department of Energy (US)
• OSTI ID: 4312175
• Journal Information: Physical Review, D, Journal Name: Physical Review, D Journal Issue: 10 Vol. 8; ISSN PRVDA
• Country of Publication: United States
• Language: English

Related Subjects

71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS
COUPLING CONSTANTS
CROSS SECTIONS
ELECTRON-POSITRON INTERACTIONS
GAUGE INVARIANCE
LIGHT CONE
PARTON MODEL
QUANTUM FIELD THEORY
SCALAR MESONS
SCALING LAWS
STRONG INTERACTIONS
STRUCTURE FUNCTIONS
SU-3 GROUPS
SYMMETRY BREAKING
YANG-MILLS THEORY