Beam Telescope Amplitude Cut

The multi-$\pi$ stop events were distinguished from single $\pi$ stop events by applying a cut based on the beam telescope amplitude described in Section 5.3.2. The light output from the eight photo-multiplier tubes viewing the four individual beam scintillators were normalized and summed. The cut was imposed on this normalized sum. The final pulse height spectra shown in Figure 5.7 is obtained as follows. The ADC pulse heights from the four beam telescopes are read out by a pair of top and bottom mounted photo-multiplier tubes. The eight ADC spectra thus obtained were normalized to 100. The normalization factors were 0.79, 1.12, 0.83, 0.81, 0.88, 0.86, 0.67 and 0.92 respectively. The final spectra was obtained by adding the individual ADC readouts multiplied by their respective normalization factors. Based on this final spectra a beam telescope cut was applied at 1069 to reject the multi-$\pi$ peak.

The multi-pion background was about $900 \times$ our $\pi ^-p\rightarrow \gamma \gamma n$ signal and corresponds to the smaller second peak in Figure 5.7. The efficiency of passing the signal by the beam telescope amplitude cut was determined from analyzing the periodically recorded dedicated $\pi ^o$ runs. In such runs, the random coincident two-photon events are insignificant compared to the two-photon events due to $\pi ^o$ decay by several orders of magnitude. The $\pi ^o$ two-photon events are ideally expected to be unaffected by the beam telescope amplitude cut. Following this procedure, an individual beam telescope efficiency of selecting single pion events was found to be $>$ 95%. An efficiency of $>$ 99% was obtained for all four beam telescopes combined. The beam telescope amplitude cut removed about $0.8 \times 10^{6}$ accidental $\gamma$-$\gamma$ coincidences arising from the multi-$\pi$ stops. As described in Section 5.3.2, from the 100 events attributed the random multi-$\pi$ coincidences, the remaining inefficiency in rejecting the accidental coincidences was 100/ $0.8 \times 10^{6}$ =  $1.3 \times 10^{-4}$.