Muon Decay with Parity Nonconserving Interactions and Radiative Corrections in the Two-Component Theory

The decay of a polarized muon is studied in the case of the general four-component neutrino theory with the most general parity-nonconserving interaction. A three-parameter formula for the decay-electron distribution is obtained as a generalization of the Michel formula for an unpolarized muon. This general formula is examined to determine to what extent the observed spectrum enables one to decide whether any particular theory is correct or not. It is seen, among other things, that by the observation of the muon decay spectrum alone one cannot test the validity of the two-component neutrino theory. To facilitate a possible accurate experimental test of the two-component neutrino theory, the radiative correction for the decay of a polarized muon is worked out to the lowest order in $\alpha$. Although the correction is rather complicated, it can still be expressed approximately by the three-parameter formula mentioned above. It is found, in particular, that the corrected Michel parameter for the two-component theory is ${0.70}_6$ when a neutrino and an antineutrino are emitted in the final state, which is 6% smaller than the value 0.75 predicted by the simple theory.