The Three Loop On-Shell Renormalization of QCD and QED

The authors 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. They find that at theta(alpha33) 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, they derive a theta(alphass) contribution to the anomalous dimension of the heavy quark field in HQET