Electromagnetic Corrections to Muon and Beta Decays when Mediated by a Vector Boson

Abstract

The radiative corrections to the weak decays have been calculated using two electromagnetic formalisms for the vector bosons. The energy spectrum for the electrons from muon decay is obtained and is found to reduce to the old form, obtained using the four fermion interaction, when the mass of the boson becomes infinite. The effective value of the Michel parameter is calculated. It seems unlikely that the electromagnetic effects of a boson would be observed through a study of the spectrum shape. The spectrum we have calculated satisfies Kinoshita's theorem. The results for muon decay are independent of the vector meson formalism employed. It is found that the bosons can reduce the corrections to the ${\mathrm{O}}^{14}$ decay lifetime to 1.2%, although the reduction depends upon the choice of formalism. The boson mass provides an effective cutoff which renders the over-all correction to the lifetime finite. This was not previously the case. Finally it is concluded that a vector meson can explain the muon lifetime discrepancy, but not if the current indications on its mass prove to be correct.