New Parameterization in Muon Decay and the Type of Emitted Neutrino

Normal muon decay, $\mu^{+} \to e^{+}\nu_{e}\bar{\nu_{\mu}}$, is studied as atool to discriminate between the Dirac and Majorana types of neutrinos and tosurvey the structure of the weak interaction. It is assumed that massiveneutrinos mix with one another and that the interaction Hamiltonian consists ofthe $V-A$ and $V+A$ charged currents. A new set of parameters used in place ofthe Michel parameters is proposed for the positron distribution. Explicit formsof these new parameters are obtained by assuming that the masses are less than10 eV for light neutrinos and sufficiently large for heavy Majorana neutrinos,which are not emitted in the muon decay. It is shown that a possible method todiscriminate between the Dirac and Majorana cases is to use a characterizationgiven by the $\chi^2$ fitting of their spectra. It is also confirmed that thetheoretical predictions in the Majorana neutrino case are almost the same asthose obtained from the standard model. Indeed, their differences cannot bedistinguished within the present experimental precision.Comment: 30 page