A convergent reformulation of QCD perturbation theory

We propose a generalization of Grunbergʹs 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 αs(μ2), with remaining ambiguities due to infra-red renormalons. There are close connections with Padé approximation.