$\pi ^o$-tail background subtraction

The $\pi ^o$ contamination that remained was subtracted using (i) the observed number of $\pi ^o$ events with $\cos{\theta} < -0.76$ and (ii) the simulated angular response of the photon-pair spectrometer for the $\pi ^o$ background.

Simulation of the $\pi ^o$-tail (30) background was a long and time consuming process. On a Pentium III 500 MHz Linux box, the Monte Carlo analysis (30) took about a month. With the advent of faster computers, the computing time could be considerably shortened.

The $\pi ^o$-tail simulation involved generation of enough $\pi ^o$ events in order to detect the very rare tail events which may arise due to unusual multiple scattering of the drift electrons, energy loss in the plastic scintillators and the drift chamber gas, and possible limitations in the photon-pair reconstruction (discussed in Section  5.3.1). A total of 9 $\times$ 10$^{7}$ $\pi^o\rightarrow\gamma\gamma$ Monte Carlo events were generated at which point enough $\pi ^o$-tail events with $\cos\theta > -0.1$ were found. These were analyzed by the two-photon trigger used for the $\pi ^-p\rightarrow \gamma \gamma n$ measurement (mC3_gC1_rD1_OC3) (discussed in Section 3.4). The angle distribution of the photon-pairs that passed the cuts were plotted (Figure 6.7), and the two-photon events with $\cos\theta > -0.1$ were counted.

Figure 6.7: $\pi ^o$-tail obtained from analysis of Monte Carlo generated data analyzed with the $\pi ^-p\rightarrow \gamma \gamma n$ trigger.

The Monte Carlo generated tail events were normalized from the $\pi ^-p\rightarrow \gamma \gamma n$ data by analyzing the $\pi ^o$ decay events with $\cos\theta < -0.1$. Thus, these events were found after analyzing the $\pi ^-p\rightarrow \gamma \gamma n$ data. While most back-to-back $\pi ^o$ two-photon events were rejected during data taking, there were still some clearly distinguishable $\pi ^o$ background events in the $-0.7 <\cos\theta <-0.1$ region. These $\pi ^0$ events were used to normalize the background from the Monte Carlo data in the $\cos\theta > -0.1$ region. The $\pi ^o$-tail background in the $\pi ^-p\rightarrow \gamma \gamma n$ signal was also estimated for different opening angle cuts. As seen from Table 6.3, even though the fractional $\pi ^o$-tail background contribution was statistically equivalent for different opening angle cuts, this $\pi ^o$-tail background contribution was the smallest at $\cos\theta > -0.1$, and was the determining factor for the applied opening angle cut at $\cos\theta > -0.1$ as was described earlier in Section 5.4.3.

Table 6.3: The fraction of $\pi ^o$-tail background events at different opening angle cuts.

Minimum $\cos\theta$	$\pi ^o$ background fraction
-0.2	(15.3 $\pm$ 5.8)%
-0.1	( 8.3 $\pm$ 4.8)%
+0.0	( 9.2 $\pm$ 5.3)%
+0.1	(11.0 $\pm$ 6.4)%

Thus the raw 635 signal events that passed all cuts contain an inferred 8.3% or 53 background events from the $\pi ^o$-tail. As seen from Figure 6.7, there were 3 Monte Carlo events in the $\cos\theta > -0.1$ region, and so, the statistical error in determining the $\pi ^o$ background was $\pm (8.3 \times 1/\sqrt{3})$% or $\pm$4.8%. Thus a ( 8.3 $\pm$ 4.8)% or (53 $\pm$ 30) $\pi ^o$-tail background subtraction was applied to the 635 raw signal events.