New Parameterization in Muon Decay and the Type of Emitted Neutrino. II

In a previous paper, new sets of parameters to replace the Michel parameterswere proposed to analyze data for the muon decay $\mu^{+} \toe^{+}\nu_{e}\bar{\nu_{\mu}}$. Both $(V-A)$ and $(V+A)$ charged currents withfinite neutrino mass have been used to study this decay. In the present paper,this parameterization is extended to a more general form, and a method for dataanalysis (least squares) is discussed for the propose of determining the rateof contribution from the $(V+A)$ current. We find that there is a simple formin which the set of parameters is related primitively to the physicalquantities. It is shown that the Michel parameters are one of the other setsthat are obtained from this simple form by rearranging one term. We derive thecondition to obtain the same information regarding unknown physical quantitiesin the case that the data are analyzed using these simple and rearranged formsseparately. We find that there is some possibility to get different resultsfrom these analyses, because the equivalent condition is very delicate and theQED radiative corrections should be treated carefully. We propose a consistentformula for data analysis. It is useful to compare the value obtained in theleast squares fit using the simple form with that obtained using the predictionof the standard model, because a large difference is not expected, especiallyin the case of the Majorana neutrino. Finally, we point out that the method weproposed to determine the type of neutrino in the previous paper is incorrect.Comment: 21 page