Asymptotic Padé-Approximant Predictions for Renormalization-Group Functions of Massive φ Scalar Field Theory

Within the context of massive N -component φ scalar field theory, we use asymptotic Padéapproximant methods to estimate from prior orders of perturbation theory the five-loop contributions to the coupling-constant β-function βg, the anomalous mass dimension γm, the vacuum-energy βfunction βv, and the anomalous dimension γ2 of the scalar field propagator. These estimates are then compared with explicit calculations of the five-loop contributions to βg, γm, βv, 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 βg, γm, and βv. These predictions, as well as the five-loop prediction for γ2 , provide a test of asymptotic Padé-approximant methods against future calculations. A substantial body of work [1, 2, 3, 4, 5] already exists in which Padé-approximant methods are utilized to predict higher order corrections in quantum field theoretical calculations. In the present letter, we apply such methods to the coupling-constant β-function βg(g), the anomalous mass dimension γm(g), the anomalous scalar-field propagator dimension γ2(g), and the vacuum-energy β-function βv(g) for a massive φ N -component scalar field theory based on the Lagrangian