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Expected number of $\gamma$$\gamma$-Events

The expected $\gamma$$\gamma$-signal is extracted as the total number of events seen minus the expected background. There are two different ways to classify the total number of single and double tags. Either a trigger is accepted if there is nothing else in the other modules, or an event is tagged regardless of what is seen in the other VSAT modules.

The first method should be used if the physics in single tag events should be studied, as the second electron then is assumed to go in the beampipe with Q² $\approx$0. In this analysis the single tag events are mainly used to extract the expected size of the $\gamma$$\gamma$-signal, therefore the second method is to prefer.

The expected background can easily be extracted as the off-energy background probability times the number of notag events, as explained in section 3.3. This gives the correct value within 5-10%, due to systematical errors and off-energy background fluctuations over the data taking period. Therefore other methods of measuring the off-energy background also had to be adopted in order to get the best possible background estimation. In this analysis the background also was adjusted to the following measurements:

• The ratio of the number of $\gamma$$\gamma$ events between the modules fluctuates with the beamspot position, but should be quite stable for a whole data taking period.

• The relative number of recorded events should correspond to the relative luminosity.

• By adjusting the size of the cut maps and compare the impact on data, background and $\gamma$$\gamma$-Monte Carlo, it is possible to extract the expected background [18].

• The energy distribution of the data should be comparable to that of the Monte Carlo, or at least the same for all modules. The off-energy background and $\gamma$$\gamma$ energy distribution look quite different, so a change in the size of the subtracted background will directly reflect in the final energy distribution.

Taking these measurements into account, the off-energy background probability obtained from STIC and VSAT Bhabha measurements could be fine tuned. Once the expected number of background events (Table 3.1) have been obtained, the $\gamma$$\gamma$-signal is extracted as the remaining part of the data. This is presented in table 5.1 along with the probability to have a single tag event, when the hadronic system is triggered.

Table 5.1: The expected number and probability(in %) of single tag $\gamma$$\gamma$-events.

	Module 1		Module 2		Module 3		Module 4
Energy	Events	Prob.	Events	Prob.	Events	Prob.	Events	Prob.
189	2571	0.81	2234	0.71	2177	0.69	2290	0.72
192	415	0.73	360	0.64	347	0.61	369	0.65
196	1405	0.81	1216	0.71	1179	0.68	1252	0.73
200	1447	0.78	1250	0.67	1199	0.64	1277	0.69
202	678	0.74	584	0.64	569	0.62	599	0.65
206	2558	0.73	2288	0.65	2187	0.62	2348	0.67
TOT	9073	0.77	7932	0.67	7659	0.65	8135	0.68

If the two photons in a $\gamma$$\gamma$ collision were totally independent, the probability for a double tag would just be the joint combination of two single tags. The cuts on the particle system do however relate the two electrons and thereby increases the double tag probability. The expected number of double tags is therefore extracted by partly looking on the double tag data when the expected background has been subtracted and partly on the probability of a single tag [18]. This is presented in table 5.2 along with the Monte Carlo expectations.

Table 5.2: The expected number of double tag $\gamma$$\gamma$-events for different module combinations and the total sum compared with Monte Carlo

Energy	1+4	2+3	1+3	2+4	Tot	MC
189	27	22	26	22	97	92
192	4	3	4	3	14	16
196	15	12	14	12	53	48
200	14	11	14	12	51	52
202	6	5	6	5	23	25
206	24	20	23	21	89	93
Tot	90	74	87	75	326	327