Renormalization - scale - invariant continuation of truncated QCD ( QED ) series – an analysis beyond large - β 0 approximation

An approximation algorithm is proposed to transform truncated QCD (or QED) series for observables. The approximation is a modification of the Baker–Gammel approximants, and is independent of the renormalization scale (RScl) µ – the coupling parameter α(µ) in the series and in the resulting approximants can evolve according to the perturbative renormalization group equation (RGE) to any chosen loop order. The proposed algorithm is a natural generalization of the recently proposed method of diagonal Padé approximants, the latter making the result RScl–invariant in large-β 0 approximation for α(µ). The algorithm described below can extract large amount of information from a calculated available truncated perturbative series for an observable, by implicitly resumming large classes of diagrams.