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Muon stopping fraction determination

In order to obtain the normalization, we need to know the fraction of muons which stop in the hydrogen target with respect to the number of entering muons counted by the beam counter T1. Since our layer is rather thin, some of the muons stop in the Au target foils or possibly in the Cu thermal shield. We attempted to determine this fraction by two different methods, both of which use the decay electron time spectrum: (i) the amplitude ratio of different lifetime components in the electron time spectrum (Section 6.4: amplitude ratio method), and (ii) an absolute measurement of the number of electrons decaying with the hydrogen lifetime, with the detection efficiency determined using fusion signals in the silicon detectors (Section 6.5: absolute amplitude method). These methods are largely independent, but we initially observed an apparent discrepancy of some 20% between the two methods. This is why we go into great detail for the stopping fraction determination in the sections that follow.