The gauge-independent QCD effective charge

It is shown how the QCD concept of a gauge-, scale-and scheme-independent one-loop effective charge can be extended directly at the diagrammatic level to QCD, thus justifying explicitly the 'naive non-abelialization' prescription used in renormalon calculus. It is first argued that, for one-shell external fields and at the strictly one-loop level, the required gluon self-energy-like function is precisely that obtained from S-matrix elements via the pinch technique. The generalization of the pinch technique to explicitly off-shell processes is then introduced. It is shown how, as a result of a fundamental cancellation among conventional perturbation theory diagrams encoded in the QCD Ward identities, the pinch technique one-loop gluon self-energy iΠμνab (q) remains gauge-independent and universal regardless of the fact that the 'external' fields in the given process are off-shell. This demonstration involves a simple technique enabling the isolation in a arbitrary gauge, of iΠμνab (q) from subclasses of up to several hundreds diagrams at once. Furthermore, it is shown how this one-loop cancellation mechanism iterates for the subclasses of n-loop diagrams containing implicitly the Dyson chains of n-loop self energies iΠμνab (q). The gauge cancellation required for the Dyson summation of iΠμνab (q) is thus demonstrated explicitly in the class of ghost-free gauges for all orders n. (authors)