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

Within the context of massive N-component phi(4) scalar field theory, we use asymptotic Pade-approximant methods to estimate from prior orders of perturbation theory the five-loop contributions to the coupling-constant beta-function beta(g), the anomalous mass dimension gamma(m), the vacuum-energy beta-function beta(v), and the anomalous dimension gamma(2) of the scalar field propagator. These estimates are then compared with explicit calculations of the five-loop contributions to beta(g), gamma(m), beta(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 Pade-approximant methods to predict the presently unknown six-loop contributions to beta(g), gamma(m), and beta(v). These predictions, as well as the six-loop prediction for gamma(2), provide a test of asymptotic Pade-approximant methods against future calculations. (C) 1999 Published by Elsevier Science B.V. All rights reserved.