Asymptotic Padé approximant predictions: Up to five loops in QCD and SQCD

Abstract

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