Asymptotic Pade Approximant Predictions: up to Five Loops in QCD and SQCD

Abstract

We use Asymptotic Pade Approximants (APAP's) to predict the four- and five-loop \beta-functions in QCD and N=1 supersymmetric QCD (SQCD), as well as the quark mass anomalous dimensions in Abelian and non-Abelian gauge theories. We show how the accuracy of our previous \beta-function predictions at the four-loop level may be further improved by using estimators weighted over negative numbers of flavours (WAPAP's). The accuracy of the improved four-loop results encourages confidence in the new five-loop \beta-function predictions that we present. However, the WAPAP approach does not provide improved results for the anomalous mass dimension, or for Abelian theories.

Comments: Title page revised with deep regret following the untimely death of our friend and collaborator Mark Samuel; 25 pages, harvmac (b), including 3 figures; requires epsf.tex and tables.tex