Lower Energy Cut

A lower energy cut at $E_{2\gamma} >$ 80 MeV was employed throughout the analysis of data to eliminate events due to a very small number of Dalitz $e^+e^-$ pairs originating from $\pi ^0$ decay (B.R. = 1.2%) and leaking through the $A$,$A'$ veto.

$$\pi^{o} \rightarrow \gamma + e^+e^- \quad (1.2\%) \quad \quad \mbox{ Dalitz}$$ (5.11)

Figure 5.10: The Monte Carlo generated spectrum with one of the photon pairs derived from a $e^+e^-$ pair due to Dalitz decay. The sum energy tails off at about 80 MeV.

Such events contribute one $e^+e^-$ pair that do not come from a photon converted in the lead. The $e^+e^-$ pairs that originate from the target lose considerable energy while passing through the target and the $A$,$A'$ plastic scintillators. A photon-pair derived from events that has one such $e^+e^-$ pair, has considerably lower energy sum, typically below 80 MeV as seen from Figure 5.10. Dedicated $\pi ^o$ runs were analyzed with the lower energy cut in order to asses the two-photon selection efficiency. The lower energy cut, together with the opening angle cut, was applied on the Monte Carlo generated $\pi ^-p\rightarrow \gamma \gamma n$ data (discussed in Section 6.1.3) in order to determine the efficiency of passing the $\pi ^-p\rightarrow \gamma \gamma n$ signal. The efficiency correspondign to the two data sets (see Section 6.1.1) was averaged weighted by the respective pion stops, and the resulting efficiency of these cuts was found to be $0.45\times 407/599 + 0.55\times 286/425 = 68$%.

The opening angle cut, together with the lower energy cut, removed about $1.4 \times 10^{6}$ real $\gamma$-$\gamma$ coincidences from $\pi ^o$ decays. As described in Section 6.2.1, 53 events attributed to $\pi ^o$ decays are estimated to remain in the two-photon signal surviving these cuts. Thus we estimate our $\pi ^o$ rejection inefficiency to be 53/ $1.4 \times 10^{6}$ = 3.8  $\times 10^{-5}$.

Figure 5.11: The two-photon energy distribution (left) and the opening angle distribution (right) of the 635 $\pi ^-p\rightarrow \gamma \gamma n$ events that pass all cuts.