Scale setting in QCD and the momentum flow in Feynman diagrams.

We present a formalism to evaluate QCD diagrams with a single virtual gluon using a running coupling constant at the vertices. This method, which corresponds to an all-order resummation of certain terms in a perturbative series, provides a description of the momentum flow through the gluon propagator. It can be viewed as a generalization of the scale-setting prescription of Brodsky, Lepage and Mackenzie to all orders in perturbation theory. In particular, the approach can be used to investigate why in some cases the “typical” momenta in a loop diagram are different from the “natural” scale of the process. It offers an intuitive understanding of the appearance of infrared renormalons in perturbation theory and their connection to the rate of convergence of a perturbative series. Moreover, it allows one to separate shortand long-distance contributions by introducing a hard factorization scale. Several applications to oneand two-scale problems are discussed in detail. CERN-TH.7487/94 December 1994