Analytic continuation and perturbative expansions in QCD

Starting from the divergence pattern of perturbative quantum chromodynamics, we propose a novel, non-power series replacing the standard expansion in powers of the renormalized coupling constant a. The coefficients of the new expansion are calculable at each finite order from the Feynman diagrams, while the expansion functions, denoted as Wn(a), are defined by analytic continuation in the Borel complex plane. The infrared ambiguity of perturbation theory is manifest in the prescription dependence of the Wn(a). We prove that the functions Wn(a) have branch points and essential singularities at the origin a=0 of the complex a plane and that their perturbative expansions in powers of a are divergent, while the expansion of the correlators in terms of the Wn(a) set is convergent under quite loose conditions. (orig.)