Fine structure in non-Abelian gauge theories

Journal Article · Sat May 15 00:00:00 EDT 1976 · Phys. Rev., D; (United States)

DOI:https://doi.org/10.1103/PhysRevD.13.2866· OSTI ID:7192788

Duncan, A

Fine-structure effects of purely non-Abelian origin are isolated and evaluated for quark--antiquark bound states in a general massless non-Abelian gauge theory. The relevant kernels are identified by studying the threshold power singularities of the quark--antiquark scattering amplitude. The non-Abelian fine structure is shown to consist of (a) an O (..cap alpha../sub s//sup 3/) contribution ascribable to the (spatial) momentum dependence of the effective Coulomb-gluon--quark coupling, which is larger than the O (..cap alpha../sub s//sup 2/) Coulomb energy for a wide range of ..cap alpha../sub s/, and (b) O (..cap alpha../sub s//sup 4/) contributions comparable to the usual Abelian fine structure. A way is suggested of improving the threshold expansion to avoid the breakdown associated with the piling up of logarithmic singularities in higher order: In this approach the spin-independent fine structure is reasonably given by the Breit--Fermi interaction with a phenomenological potential, taken together with the purely non-Abelian contributions computed previously. The Breit--Fermi formula cannot be taken seriously for the hyperfine structure, however: Transverse- and Coulomb-gluon exchanges seem to be associated with different effective couplings. In addition, there are Pauli-type contributions to the transverse-gluon--quark vertex which involve logarithmic singularities. The threshold expansion is expected to be directly and unambiguously applicable, however, for threshold bound states of sufficiently heavy quarks (say, m/sub q/ > 15 GeV), should such exist. (AIP)

• Research Organization: The Institute for Advanced Study, Princeton, New Jersey 08540
• OSTI ID: 7192788
• Journal Information: Phys. Rev., D; (United States), Vol. 13:10
• Country of Publication: United States
• Language: English

Related Subjects

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS
COMPOSITE MODELS
FINE STRUCTURE
QUARKS
BOUND STATE
COULOMB FIELD
GAUGE INVARIANCE
GLUON MODEL
HYPERFINE STRUCTURE
SCATTERING AMPLITUDES
SINGULARITY
AMPLITUDES
ELECTRIC FIELDS
ELEMENTARY PARTICLES
INVARIANCE PRINCIPLES
MATHEMATICAL MODELS
PARTICLE MODELS
POSTULATED PARTICLES
645204* - High Energy Physics- Particle Interactions & Properties-Theoretical- Strong Interactions & Properties