Resummation of renormalon chains for cross sections and inclusive decay rates

Recently, we have developed a new formalism to evaluate QCD loop diagrams with a single virtual gluon using a running coupling constant at the vertices. It corresponds to an all-order resummation of certain terms (the so-called renormalon chains) in a perturbative series and provides a generalization of the scale-setting prescription of Brodsky, Lepage and Mackenzie. In its original form the method is applicable to Green functions without external gluons and to euclidean correlation functions. Here we generalize the approach to the case of cross sections and inclusive decay rates, which receive both virtual and real gluon corrections. We encounter non-perturbative ambiguities in the resummation of the perturbative series, which may hinder the standard construction of the operator product expansion. The ratios R_{e^+ e^-} and R_\tau are discussed in detail.