Asymptotic Pade-Approximant Predictions for Renormalization-Group Functions of Massive ${\varphi }^4$ Scalar Field Theory

Abstract

Within the context of massive N-component ${\varphi }^4$ 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.

latex2e, 5 pages, minor errors corrected and references updated

References in corpus (2)

• Asymptotic Pade Approximant Predictions: up to Five Loops in QCD and SQCD
• Five-Loop Vacuum Energy Beta Function in phi^4 Theory with O(N)-Symmetric and Cubic Interactions

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