Eur. Phys. J. C 24, 127-135 (2002)
https://doi.org/10.1007/s100520100880

Analytic continuation and perturbative expansions in QCD

¹ National Institute of Physics and Nuclear Engineering, POB MG 6, 76900 Bucharest, Romania
² The Abdus Salam International Centre for Theoretical Physics, 34014 Trieste, Italy
³ Institute of Physics, Academy of Sciences of the Czech Republic, 18221 Prague 8, Czech Republic

Received: 27 October 2001
Published online: 5 April 2002

Abstract

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 W_n(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 W_n(a). We prove that the functions W_n(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 W_n(a) set is convergent under quite loose conditions.