The QCD observables expansion over the scheme-independent two-loop coupling constant powers, the scheme dependence reduction

Abstract

The method suggested in this paper allows to express the n-th order renorm-group equation solutions over the powers of the two-loop solution, that can be obtained explicitly in terms of the Lambert function. On the one hand this expansion helps to get more reliable theoretical predictions, on the other hand the scheme dependence problem can be understood better. When using this method, Stevenson scheme invariant expressions can be obtained easily, the scheme dependence emerging from the perturbative series truncation can be estimated and reduced. The `optimal' choice of the scale parameter allows to have at the three-loop level the scheme dependence magnitude corresponding to the four-loop level etc. The new criterion, principally different from the Raczka criterion, is introduced.