The kinematic of this decay follows from that of the pion beta process discussed in above:
The decay rate can also be calculated using the same approach as in the case of pibeta with the following modifications:
However, for the most general form of the four-fermion interaction, the positron spectrum has been shown to be [Sch-83]:
Figure: The energy spectrum of positrons from muon decays. This distribution is known as Michel spectrum and constitutes the major background in the study of pion beta decay in the stopped pion mode. The theoretical curve (dashed lines) is superimposed on the Monte Carlo generated distribution.
The energy spectrum of the positron is displayed in figure (). In the event of exact V-A structure of the weak charged current, the spectrum () reduces to () giving the Michel parameter .
The other decay modes of the muon are listed below: