Radiative Corrections to Fermi Interactions

This is the authors' abstract. We don't add key points for this paper.

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 δ, ξ, 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 ρ 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 ρ value is now an increase of the order of 5.6% when the experimental and theoretical spectral distributions are compared in the region 0≤ppₘₐₓ≤0.95. The radiative corrections to the spectrum and lifetime of the nuclear β 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 O¹⁴. The corrected Feynman-Gell-Mann coupling constant is G=(1.40±0.01)×10^-49 erg/cm³. In the universal V-A theory of weak interactions, the calculated muon mean life becomes τ_μ=(2.31±0.05)×10^-6 sec. (These three values depend logarithmically on the ultraviolet cutoff λ and the corrections to τ_μ increase for increasing values of λ.) It is found that the corrections to the spectral shape of β decay are rather large in the case in which the end-point energy Eₘmₑc². The radiative corrections to the lifetime and the total asymmetry for muon decay are found to be well defined and finite for mₑ→0 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 β 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.