Towards a physical expansion in perturbative gauge theories by using improved Baker-Gammel approximants
Applicability of the previously introduced method of modified diagonal Baker-Gammel approximants is extended to truncated perturbation series (TPS) of any order in gauge theories. The approximants reproduce the TPS when expanded in power series of the gauge coupling parameter to the order of that TPS. The approximants have the favorable property of being exactly invariant under the change of the renormalization scale, and that property is arrived at by a generalization of the method of the diagonal Padé approximants. The renormalization scheme dependence is subsequently eliminated by a variant of the method of the principle of minimal sensitivity (PMS). This is done by choosing the values of the renormalization-scheme-dependent coefficients ( β2, β3, …), which appear in the beta function of the gauge coupling parameter, in such a way that the diagonal Baker-Gammel approximants have zero values of partial derivatives with respect to these coefficients. The resulting approximants are then independent of the renormalization scale and of the renormalization scheme.