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arxiv: hep-ph/9710302 · v2 · submitted 1997-10-09 · ✦ hep-ph

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

J. Ellis (CERN) , I. Jack (Liverpool) , D.R.T. Jones (Liverpool) , Marek Karliner (Tel-Aviv) , Mark A. Samuel (deceased)
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classification ✦ hep-ph
keywords improvedpredictionsabelianaccuracyanomalousasymptoticbeta-functionfive-loop
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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.

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  1. Asymptotic Pad\'e Predictions up to Six Loops in QCD and Eight Loops in $\lambda\phi^4$

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    Asymptotic Padé approximants validated on five-loop QCD data now yield six-loop QCD beta-function and quark-mass anomalous-dimension predictions plus eight-loop results in scalar theory.