$C$ Counter Timing Cut

To distinguish and reject two photon events coming from adjacent beam buckets, a cut was applied based on the difference of the $C$ scintillator timing. The two photons were determined to be coincident by requiring that the charged tracks constituting each of the two photons arrive at the $C$ counter within a certain time window as recorded by the FBTDC readout.

Figure 5.9: The two-photon FBTDC time difference spectra as recorded from the $C$ counter. The shallower peak corresponds to runs that passed the tracking and photon cuts and consisted of mostly random multi-$\pi$ events. The larger peaked histogram is obtained from analyzing a dedicated $\pi ^o$ run which shows a narrow window of about $\pm$ 4 ns. The cut is based on a time window that rejects all events occurring later or earlier than $\pm$4 ns.

In Figure 5.9, the broader and shallower peak shows the time difference between two photons from the analysis of several $\pi ^-p\rightarrow \gamma \gamma n$ runs. The events mostly consisted of multiple $\pi ^-$ stop events that passed the tracking and photon cuts. The narrower peak corresponds to the timing obtained from analysis of a dedicated $\pi ^o$ run which shows a clearer prompt time window of about $\pm 4$ ns. Thus, in order to reject photons coming from pions arriving in adjacent beam buckets, a $\pm$4 ns cut was applied.

Efficiency of the timing cut in selecting coincident two-photon events was obtained from analysis of dedicated $\pi ^o$ runs. Due to high trigger rates from the $\pi ^o$ decay, almost all events were expected to be prompt. This efficiency was found to be 99%. This efficiency factor was relevant when comparing with the Monte Carlo data, since all Monte Carlo events were generated prompt.

Table 5.3: The $C$ timing, beam telescope amplitude, opening angle, and lower energy cuts.

Cuts	Cut Parameter	Efficiency of	Inefficiency of
		passing signal	rejecting multi-$\pi$
			and $\pi ^o$ background
$C$ timing (TDC)	Two photon
	FBTDC time
	difference $\leq \pm$4 ns
		99%	1.3 $\times 10^{-4}$
Beam telescope	Beam ADC $\leq$ 1069
amplitude
Opening angle	$\cos{\theta_{\gamma\gamma}}\geq-0.1$
		68%	3.8 $\times 10^{-5}$
Lower energy	$E_{2\gamma} > 80$ MeV