Achieving renormalization-scale- and scheme-independence in Padé-related resummation in QCD

Abstract

Previously developed Padé-related method of resummation for QCD observables, which achieves exact renormalization-scale-invariance, is extended so that the scheme-invariance is obtained as well. The dependence on the leading scheme parameter c 2 is eliminated by a variant of the method of the principle of minimal sensitivity. The subleading parameter c 3 in the approximant is then fixed in such a way that the correct known location of the leading infrared renormalon pole is reproduced. Thus, β-functions which go beyond the last perturbatively calculated order in the observable are used. The β-functions in the approximant are quasianalytically continued by Padé approximants. Two aspects of nonperturbative physics are accounted for in the presented resummation: a mechanism of quasianalytic continuation from the weak- into the strong-coupling regime, and the (approximant-specific) contribution of the leading infrared renormalon. The case of the Bjorken polarized sum rule is considered as a specific example of how the method works.