$\gamma \gamma$ Acceptance from $\pi ^0$ Decay

The results of measurement and simulation were also compared for photon-pairs from at-rest charge exchange $\pi^- p \rightarrow \pi^o n$ followed by neutral pion decay $\pi^o\rightarrow\gamma\gamma$. This data was collected periodically from dedicated `$\pi ^0$ runs'. For these runs, a modified trigger for detecting the back-to-back photon pairs mC3_gC1_rD2 (see Section 3.4) was used. From analysis of two such `$\pi ^0$ runs' corresponding to AHC cut(4,6), 9.7 $\times$ 10$^{4}$ ($N_{\pi^0}$) photon-pairs were reconstructed from 3.2 $\times$ 10$^{8}$ incident pions ($N_{\pi}$). Using the known branching ratio of 60.7% ( ${B.R.}_{\pi^-p\rightarrow\pi^o n}$), the two-photon acceptance from $\pi ^0$ decay was calculated from the relation,

$$\begin{eqnarray*} \epsilon\Delta\Omega = \frac{ N_{\pi^o} }{ N_{\pi} \cdot \epsi... ...} \cdot B.R._{\pi^-p\rightarrow\pi^o n} } & = 5.9 \times 10^{-4} \end{eqnarray*}$$

From 1 $\times$ 10$^{6}$ Monte Carlo generated $\pi ^0$ events reproducing the same run conditions, 605 reconstructed photon-pairs were found resulting in a two-photon acceptance of 6.1 $\times$ 10$^{-4}$. Thus the agreement between experiment and simulation for data set (4,6) was found to be 5.9  $\times 10^{-4}$/6.1  $\times 10^{-4}$ = 96%. This can be compared with the agreement between experiment and simulation (96.8%) for the two-photon acceptance found from multi-$\pi$ stop data for AHC cut(4,6), described in section 6.1. Thus we conclude that the Monte Carlo program used for determination of the detector acceptance was adequately reliable.