Radiative Corrections to Muon and Neutron Decay

The corrections to muon decay due to electromagnetic interactions have been recalculated. Our results differ from those of Behrends, Finkelstein, and Sirlin, because those authors used an inconsistent method for handling the infrared divergences which arise separately in the real and virtual processes. The disagreement is especially significant near the end of the electron (positron) spectrum where our results indicate that the radiative correction to the Michel $\rho$ parameter is approximately 1% larger than previously supposed, a result in the direction of increasing agreement between experiment and theory. With the radiative corrections to muon decay given here, the predicted value of the muon lifetime using the universal theory is (2.27±0.04)×${10}^{-6\mathrm{}}$ sec. As a preliminary to studying the decay of particles with structure, the $\beta$ decay of the neutron is examined. This leads to an increase in the Coulomb $F$ factor independent of the nuclear charge and of amount approximately 2.6%. As a result the universal coupling constant obtained from the decay of ${\mathrm{O}}^{14}$ is decreased to $G=(1.37\mathrm{}\pm 0.02)\times {10}^{-49\mathrm{}}$ erg ${\mathrm{cm}}^3$ and increases the value of the muon lifetime to (2.33±0.05)×${10}^{-6\mathrm{}}$ sec.