The three-loop on-shell renormalization of QCD and QED Original Research Article

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 Zm and the on-shell fermion wave function renormalization constant Z2 are given. We find that at O(αs3) the wave function renormalization constant Z2 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(αs3) contribution to the anomalous dimension of the heavy quark field in HQET.