Leptonic μ - and τ - decays : mass effects , polarization effects and O ( α ) radiative

Leptonic µ-and τ-decays: mass effects, polarization effects and O(α) radiative corrections Abstract We calculate the radiative corrections to the unpolarized and three polarized spectrum and rate functions in polarized µ-decays into polarized electrons. The new feature of our calculation is that we keep the mass of the final state electron finite. Analytical results are given for the energy spectrum and the polar angle distribution of the final state electron whose longitudinal polarization is calculated. We also provide analytical results on the integrated spectrum functions. We analyze the m e → 0 limit of our general results and investigate the quality of the m e → 0 approximation. In the m e → 0 case we discuss in some detail the role of the anomalous helicity flip contribution of the final electron which survives the m e → 0 limit. The results presented in this paper also apply to the leptonic decays of polarized τ-leptons for which we provide numerical results.