Gauge-invariant on-shell Z2 in QED, QCD and the effective field theory of a static quark

We calculate the on-shell fermion wave-function renormalization constant Z2 of a general gauge theory, to two loops, in D dimensions and in an arbitrary covariant gauge, and find it to be gauge-invariant. In QED this is consistent with the dimensionally regularized version of the Johnson-Zumino relation: d logZ2/da0=i(2π)-De02∫dDk/k4=0. In QCD it is, we believe, a new result, strongly suggestive of the cancellation of the gauge-dependent parts of non-abelian UV and IR anomalous dimensions to all orders. At the two-loop level, we find that the anomalous dimension γF of the fermion field in minimally subtracted QCD, with NL light-quark flavours, differs from the corresponding anomalous dimension γ tildeF of the effective field theory of a static quark. A complete description of two-loop on-shell renormalization of one-lepton QED, in D dimensions, is also given. More generally, we show that there is no need of integration in the two-loop calculation of on-shell two- and three-point functions. (orig./HSI)