Renormalization of gauge theories, W decay, and μ decay

We present a renormalization program for spontaneously broken gauge theories in the unitary formalism. It is compared with the renormalization program for renormalizable gauges and necessary constraints are discussed. We then explicitly formulate this program for the Weinberg SU(2)×U(1) theory of leptons and show how it provides the basis for the dispersive calculations of higher-order corrections to μ decay reported in a previous paper. As we pointed out there, certain symmetry-breaking effects are finite and calculable. In this paper, we calculate the breaking of μ-e universality in order α. We also explicitly verify the consistency of our renormalization procedure on the one-loop level. There are certain subtleties in the treatment of infrared divergences in gauge models, particularly in dispersive calculations. We give a method for handling this problem, calculate the rate for W decay, and complete the calculation of the photonic contributions to μ decay in the Weinberg SU(2)×U(1) model. Our predictions for the decay rate and the electron energy spectrum in μ decay for the Weinberg model are experimentally indistinguishable from those of the old current-current theory of weak interactions. Finally we make some comments about other gauge models and other physical processes.