Time-Reversal Invariance and Radiative Muon Decay

The radiative muon decay μ→e+ν+ν+γ is investigated as a source of information on the time-reversal properties of the muon decay interaction. It is shown that for any muon decay process, which may include electromagnetic interactions, terms in the transition probability which violate time-reversal invariance must be pseudoscalars. Further, only ten combinations of the coupling constants of the four-fermion interaction can occur in the transition probability. These may be classified in accordance with the types of terms in which they occur; a term which violates time-reversal invariance must contain as a factor either the electron mass or the transverse electron polarization. In the radiative muon decay, if such a term is proportional to the electron mass, it will also contain as a factor the longitudinal electron polarization.