Radiative Corrections to Fermi Interactions

The radiative correction to the decay spectrum of polarized muons is recalculated taking into account a mistake in our previous work which was recently pointed out by Berman. The revised values for the radiative correction to, , and integrated asymmetries for the high- as well as low-energy decay electrons have turned out to be practically identical with the old values. The value determined from experiments, on the other hand, has to be increased by about 1% because of the new correction. Thus the over-all effect of the radiative correction to the value is now an increase of the order of 5. 6% when the experimental and theoretical spectral distributions are compared in the region 0{p₌₀ₗ}0. 95. The radiative corrections to the spectrum and lifetime of the nuclear decay arising from the charge interactions of the electron and proton are also studied. Use of this expression gives a correction of -1. 7% for the lifetime of O^14. The corrected Feynman-Gell-Mann coupling constant is G= (1. 400. 01) 10^-49 erg/cm^3. In the universal V-A theory of weak interactions, the calculated muon mean life becomes _= (2. 310. 05) 10^-6 sec. (These three values depend logarithmically on the ultraviolet cutoff and the corrections to _ increase for increasing values of. ) It is found that the corrections to the spectral shape of decay are rather large in the case in which the end-point energy E₌m₄c^2. The radiative corrections to the lifetime and the total asymmetry for muon decay are found to be well defined and finite for m₄0 in spite of the fact that the differential spectrum itself diverges logarithmically in the same limit. The same situation is encountered in the case of radiative corrections to the nuclear decay. A physical explanation for such behavior of the radiative corrections is attempted. In Appendix A, a simplified expression is given for the determination of the Michel parameter.