The three-loop on-shell renormalization of QCD and QED

We describe a calculation of the on-shell renormalization factors in QCD and QED at the three loop level. Explicit results for the fermion mass renormalization factor Z(m) and the on-shell fermion wave function renormalization constant Z(2) are given. We find that at O(alpha (3)(s)) the wave function renormalization constant Z(2) in QCD becomes gauge dependent also in the on-shell scheme, thereby disproving the gauge-independence conjecture based on an earlier two-loop result. As a byproduct, we derive an O(alpha (3)(s)) contribution to the anomalous dimension of the heavy quark field in HQET. (C) 2000 Elsevier Science B.V. All rights reserved.