Asymptotic Padé-approximant predictions for renormalization-group functions of massive φ4 scalar field theory

Abstract

Within the context of massive N-component φ 4 scalar field theory, we use asymptotic Padé-approximant methods to estimate from prior orders of perturbation theory the five-loop contributions to the coupling-constant β-function β g , the anomalous mass dimension γ m , the vacuum-energy β-function β v , and the anomalous dimension γ 2 of the scalar field propagator. These estimates are then compared with explicit calculations of the five-loop contributions to β g , γ m , β v , and are seen to be respectively within 5%, 18%, and 27% of their true values for N between 1 and 5. We then extend asymptotic Padé-approximant methods to predict the presently unknown six-loop contributions to β g , γ m , and β v . These predictions, as well as the six-loop prediction for γ 2, provide a test of asymptotic Padé-approximant methods against future calculations.