THE GAUGE-INDEPENDENT QCD EFFECTIVE CHARGE

It is shown how the QED concept of a gauge-, scale- and scheme-indepen dent one-loop effective charge can be extended directly at the diagram matic level to QCD, thus justifying explicitly the ''naive non-abelian ization'' prescription used in renormalon calculus. It is first argued that, for on-shell external fields and at the strictly one-loop level , the required gluon self-energy-like function is precisely that obtai ned from S-matrix elements via the pinch technique. The generalization of the pinch technique to explicitly off-shell processes is then intr oduced. It is shown how, as a result of a fundamental cancellation amo ng conventional perturbation theory diagrams, encoded in the QCD Ward identities, the pinch technique one-loop gluon self-energy i<(Pi)over cap>(ab)(mu nu)(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 iso lation, in an arbitrary gauge, of i<(Pi)over cap>(ab)(mu nu)(q) from s ubclasses of up to several hundred diagrams at once. Furthermore, it i s shown how this one-loop cancellation mechanism iterates for the subc lasses of n-loop diagrams containing implicitly the Dyson chains of n one-loop self-energies i<(Pi)over bar>(ab)(mu nu)(q). The gauge cancel lation required for the Dyson summation of i<(Pi)over bar>(ab)(mu nu)( q) is thus demonstrated explicitly in a general class of ghost-free ga uges for all orders n. (C) 1997 Elsevier Science B.V.