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(2-pi)-De0(2) integral d(D)k/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 gamma-F of the fermion field in minimally subtracted QCD, with N(L) light-quark flavours, differs from the corresponding anomalous dimension gamma-F approximately of the effective field theory of a static quark by the gauge-invariant amount [GRAPHICS] 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.