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

Abstract

In a previous paper, new sets of parameters to replace the Michel parameters were proposed to analyze data for the muon decay $μ^{+} \to e^{+}ν_{e}\bar{ν_μ}$. Both $(V-A)$ and $(V+A)$ charged currents with finite 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 data analysis (least squares) is discussed for the propose of determining the rate of contribution from the $(V+A)$ current. We find that there is a simple form in which the set of parameters is related primitively to the physical quantities. It is shown that the Michel parameters are one of the other sets that are obtained from this simple form by rearranging one term. We derive the condition to obtain the same information regarding unknown physical quantities in the case that the data are analyzed using these simple and rearranged forms separately. We find that there is some possibility to get different results from these analyses, because the equivalent condition is very delicate and the QED radiative corrections should be treated carefully. We propose a consistent formula for data analysis. It is useful to compare the value obtained in the least squares fit using the simple form with that obtained using the prediction of the standard model, because a large difference is not expected, especially in the case of the Majorana neutrino. Finally, we point out that the method we proposed to determine the type of neutrino in the previous paper is incorrect.