Fine structure in non-Abelian gauge theories
- 15 May 1976
- journal article
- research article
- Published by American Physical Society (APS) in Physical Review D
- Vol. 13 (10), 2866-2880
- https://doi.org/10.1103/physrevd.13.2866
Abstract
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 contribution ascribable to the (spatial) momentum dependence of the effective Coulomb-gluon—quark coupling, which is larger than the Coulomb energy for a wide range of , and (b) contributions comparable to the usual Abelian fine structure. A way is suggested of improving the threshold expansion to avoid the breakdown associated with logarithmic singularities piling up 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, GeV), should such exist.
Keywords
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