Towards a physical expansion in perturbative gauge theories by using improved Baker-Gammel approximants

Details Towards a physical expansion in perturbative gauge theories by using improved Baker-Gammel approximants Towards a physical expansion in perturbative gauge theories by using improved Baker-Gammel approximants

1998-02-04

arxiv.org/abs/hep-ph/9802248v2

Nucl.Phys. B522 (1998) 396-410

Physics

High Energy Physics

High Energy Physics - Phenomenology

LaTeX (REVTeX), 14 pages, one reference added, one affiliation updated

Scientific paper

10.1016/S0550-3213(98)00230-2

Applicability of the previously introduced method of modified diagonal Baker-Gammel approximants is extended to truncated perturbative 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 Pad\'e 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, 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.

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