Improvement of the method of diagonal Pade approximants for perturbative series in gauge theories

Details Improvement of the method of diagonal Pade approximants for perturbative series in gauge theories Improvement of the method of diagonal Pade approximants for perturbative series in gauge theories

1997-11-27

arxiv.org/abs/hep-ph/9711487v2

Phys.Rev. D57 (1998) 3209-3213

Physics

High Energy Physics

High Energy Physics - Phenomenology

LaTeX (REVTeX), 9 pages, minor changes, version to appear in Phys. Rev. D (Rapid Comm.) in March 1998

Scientific paper

10.1103/PhysRevD.57.R3209

Recently it has been pointed out that diagonal Pad\'e approximants to truncated perturbative series in gauge theories have the remarkable property of being independent of the choice of the renormalization scale as long as the gauge coupling parameter ${\alpha}(p^2)$ is taken to evolve according to the one-loop renormalization group equation -- i.e., in the large-${\beta}_0$ approximation. In this letter we propose and describe an improvement to the method of diagonal Pad\'e approximants. The improved method results in approximants which are independent of the chosen renormalization scale when ${\alpha}(p^2)$ evolves at any chosen (in principle arbitrary) loop-level.

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