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arXiv · hep-ph/9706365

A Convergent Reformulation of QCD Perturbation Theory

C. J. Maxwell
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Abstract

We propose a generalization of Grunberg's method of effective charges in which, starting with the effective charge for some dimensionless QCD observable dependent on the single energy scale $Q, R(Q)$, we introduce an infinite set of auxiliary effective charges, each one describing the sub-asymptotic Q-evolution of the immediately preceding effective charge. The corresponding infinite set of coupled integrated effective charge beta-function equations may be truncated. The resulting approximations for $R(Q)$ are the convergents of a continued function. They are manifestly RS-invariant and converge to a limit equal to the Borel sum of the standard asymptotic perturbation series in $α_s({μ^2})$, with remaining ambiguities due to infra-red renormalons. There are close connections with Pad{é} approximation.

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C. J. Maxwell. 1997-06-16. A Convergent Reformulation of QCD Perturbation Theory. https://doi.org/10.1016/s0370-2693(97)00882-4

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