Short-distance perturbation theory for the leading logarithm models

Abstract

I derive a short-distance perturbation expansion for the static potential of quasi-abelian quark and antiquark source charges, in the models in which renormalization group radiative corrections are retained in the gauge gluon effective dielectric functional. A natural running coupling parameter ζ for the models is identified, and the scale mass Λ P appearing in ζ is computed by requiring the vanishing of the O( ζ 2) term in the perturbation expansions. The models are shown to give unsatisfactory results beyond one-loop order in the short-distance expansion, as a result of the breakdown in the ultraviolet of the assumption that the effective action is a local functional of the field strength. The same argument indicates that the assumption of a local effective action becomes self-consistent in the large-distance limit. The coupling parameter ζ is identified as a running coupling which evolves in field strength, rather than momentum, and which becomes infinite in the large-distance limit.