Figure 5.8: CsI sum spectrum from 1996 data made by illuminating the CsI array with a 70 MeV positron beam.
spectrum. These spectra can be seen in Figure 5.9. The simulation was used because pion
decays cannot be experimentally observed without the presence of muon decays. The muon decays, however, can be observed experimentally without the presence of pions by waiting a sufficiently long time after stopping a pion in the target. This is because the
Figure 5.9 : Left: Experimental Michel spectrum from the CsI array Right: Simulated p -> e n ( g ) for the same CsI array
muon lifetime is about 85 times that of the pion; so muons created by pion decays will still exist in the target long after virtually all pions have decayed away.
There were 239,208 events in the simulated p -> e n ( g ) spectrum. The number of p -> e n ( g ) events simulated was chosen arbitrarily such the shape of p -> e n ( g ) peak was well defined and that the statistical errors introduced by the simulated spectrum were insignificant relative to those introduced by other sources.
The number of events in the low-threshold Michel spectrum was 40,888. This gives a value of Rraw =5.850 ± 0.031 where the uncertainty is obtained using the square roots of the number of events in the simulated p -> e n ( g ) and empirical Michel spectra.