Exploring arbitrarily high orders of optimized perturbation theory in QCD with nf -> 16.5

Abstract

Perturbative QCD with nf flavours of massless quarks becomes simple in the hypothetical limit nf -> 16.5, where the leading beta-function coefficient vanishes. The Banks-Zaks (BZ) expansion in a0=(8/321)(16.5-nf) is straightforward to obtain from perturbative results in MSbar or any renormalization scheme (RS) whose nf dependence is `regular.' However, `irregular' RS's are perfectly permissible and should ultimately lead to the same BZ results. We show here that the `optimal' RS determined by the Principle of Minimal Sensitivity does yield the same BZ-expansion results when all orders of perturbation theory are taken into account. The BZ limit provides an arena for exploring optimized perturbation theory at arbitrarily high orders. These explorations are facilitated by a `master equation' expressing the optimization conditions in the fixed-point limit. We find an intriguing strong/weak coupling duality a -> a*^2/a about the fixed point a*.

arXiv comment32 pages, 4 figures

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• Calculation of the non-perturbative strong coupling from first principles
• One-loop RG improvement of the screened massive expansion in the Landau gauge
• Interplay Between Approximation Theory and Renormalization Group
• Thermal extension of the screened massive expansion in the Landau gauge
• The effective exponent gamma(Q) and the slope of the beta function
• The Nielsen identities in screened theories