Rare Decays

Apart from the dominant decay mode $\mu^+ \rightarrow e^+ + \nu_e + \overline{\nu}_\mu$, the only other decay modes with a significant branching ratio are the radiative decay

$$\mu^+ \rightarrow e^+ +\nu_e + \overline{\nu}_\mu + \gamma$$ (14)

which has a branching ratio of 1.4$\pm$0.4% and the five particle decay

$$\mu^+ \rightarrow e^+ + e^+ + e^- +\nu_e + \overline{\nu}_\mu$$ (15)

with a branching ratio of 3.4$\pm$0.4 x 10^-5. The rates of both decay modes have the same time dependence as the dominant one. These decay modes could mimic two or even three decay muons assuming several tiles had been struck. In our scheme, such events would in fact be counted as two (or three) muon decays at the same time. Because there is no higher probability for this to occur at early compared to late times, counting each decay positron independently has no influence on the shape of the observed decay rate. The only factor is a slight change in the statistical accounting for a given timing bin. This effect can be accounted for in the fitting procedure because the branching ratios of the above processes are known well enough.