Asymptotic Pade-approximant predictions for renormalization-group functions of massive phi(4) scalar field theory

Within the context of massive N-component phi(4) scalar field theory, we us e asymptotic Pade-approximant methods to estimate from prior orders of pert urbation theory the five-loop contributions to the coupling-constant beta-f unction beta(g), the anomalous mass dimension gamma(m), the vacuum-energy b eta-function beta(v), and the anomalous dimension gamma(2) of the scalar fi eld propagator. These estimates are then compared with explicit calculation s of the five-loop contributions to beta(g), gamma(m), beta(v), and are see n to be respectively within 5%, 18%, and 27% of their true values for N bet ween 1 and 5. We then extend asymptotic Pade-approximant methods to predict the presently unknown six-loop contributions to beta(g), gamma(m), and bet a(v). These predictions, as well as the six-loop prediction for gamma(2), p rovide a test of asymptotic Pade-approximant methods against future calcula tions. (C) 1999 Published by Elsevier Science B.V. All rights reserved.