Year: 1997
Type: article
Abstract: We prove that in the limit where the $\ensuremath{\beta}$ function is dominated by the one-loop contribution (``large ${\ensuremath{\beta}}_{0}$ limit'') diagonal Pad\'e approximants (PA's) of perturbative series become exactly renormalization-scale (RS) independent. This symmetry suggests that diagonal PA's are correctly resumming contributions from higher-order diagrams that are responsible for the renormalization of the coupling constant. Nondiagonal PA's are not exactly invariant, but generally reduce the RS dependence as compared to partial sums. In physical cases, higher-order corrections in the $\ensuremath{\beta}$ function break the symmetry softly, introducing a small scale and scheme dependence. We also compare the Pad\'e resummation with the Brodsky-Lepage-Mackenzie (BLM) method. We find that in the large-${N}_{f}$ limit using the BLM scale is identical to resumming the series by an $x[0/n]$ nondiagonal PA.
Author: Einan Gardi
Institution: Tel Aviv University
Language: English
Subfield: Nuclear and High Energy Physics
Field: Physics and Astronomy
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W1980818534