The one-loop contributions to $\mu$ decay are calculated in Weinberg's model of the weak and electromagnetic interactions of leptons. The higher-order weak contributions are shown to be finite in this model, despite the high order of divergence of individual Feynman graphs. Thus this calculation is practical evidence in favor of the renormalizability of spontaneously broken gauge theories. The electromagnetic corrections to $\mu$ decay are finite after renormalization in the Weinberg model. The renormalized higher-order weak corrections do not affect the shape of the final electron spectrum. The effect on the $\mu$ decay rate is of the same order of magnitude as the electromagnetic correction, ∼½%. Since this is effectively just a small "renormalization" of the weak coupling constant, it appears to be impossible to detect this effect experimentally unless other weak processes can be calculated and measured with comparable precision. The calculation is done by evaluating Feynman graphs dispersively. This calculational technique may be of interest in further work with spontaneously broken gauge theories.

• Received 5 June 1972

DOI:https://doi.org/10.1103/PhysRevD.6.2998