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. Moreover, it offers an intuitive understanding of the appearance of infrared renormalons in perturbation theory, their connection to the rate of convergence of a perturbative series, and the necessity to separate short- and long-distance contributions. Several applications to one- and two-scale problems are discussed in detail.