Method of effective charges and Brodsky-Lepage-Mackenzie criterion

A renormalization-scheme-invariant method to improve the QCD perturbative series when the Brodsky-Lepage-Mackenzie (BLM) criterion indicates large perturbative corrections is presented. The method, which is a variant of the effective-charge scheme, is specific to QCD and relies on a new renormalization-group equation describing the response of a physical quantity to a change in the BLM next-to-leading-order coefficient r₁*. Two alternative methods are also discussed: one of them consists in an improvement of the perturbative series for the effective charge β function, which also yields, as a byproduct, an improvement of the series for the perturbative infrared fixed point of QCD at f≈33/2 flavors; the other represents an improvement of the perturbative series specific to the BLM choice of renormalization point.