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$\gamma$$\gamma$ Cut-maps

In order to achieve as good purity as possible in the final $\gamma$$\gamma$ sample, it is necessary to impose hard cuts on the data. As mentioned before all background cannot be removed, but any physical analysis of the final sample needs a signal purity of at least 70%. This requires background rejection in the order of 90%, and at the same time it is desirable not to loose more than 50% of the signal.

The off-energy background spreads out over the whole horizontal plane of the detector and can not be confined in x. The high energy background (mainly in the outer modules) is however very well confined in the y-plane of the beam (Fig. 3.3). Unfortunately the y-position experiences rapid changes during LEP-running (Fig. 3.7).

Figure 3.7: The y-position changes (equal for modules on the same side of the detector) of the off-energy background.
Figure 3.8: The energy and y-position of the off-energy background tagged in VSAT. The boxed area represent the cut-map used.

The low energy background is less confined in y, but as seen from Fig. 3.7 it follows the same changes in the beam position as the high energy background. Both the energy and y-position of the background are used for confinement. From Fig. 3.8 it is clear that no trivial mathematical expression can be used to define the rejection region for the off-energy background. Instead the imposed cut was defined with a grid map, as a function of the VSAT energy and y-position measurement [18]:

Y_map = (y_pos - $$\overline{y_{off}}$$ + 1.6)*25 + 1,        X_map = E_beam - E + 11

To improve and narrow down the distribution, the y-position changes of the background ( $\overline{y_{off}}$) shown in Fig. 3.7 was implemented on a run by run basis (blocks of about 20 minutes data taking in DELPHI). The grid size of the maps were set to 80, which is the origin of the constant numbers in the expressions. A map is created by filling it with off-energy electron events from the single electron trigger (Fig. 3.9). A map was defined for each module and energy interval of LEP, resulting in total of 24 different maps.

Figure 3.9: The distribution of events in a cut map, a cut is imposed by specifying a level on the Z-axis.
Figure 3.10: The amount of remaining background after imposing cuts at different cut limits.

The height of each bin in the maps is defined as the relative probability (in permill) for an off-energy electron to hit that bin. The total sum of all the bins is thus equal to one (or 1000 permill). The cut is then easily imposed by specifying a horizontal cut limit in the map, removing all events that are in bins that have a height above that limit.

As the outer modules have a more confined background than the inner modules, the cut limits has to be set separately. The impact of adjusting the cut limit is shown in Fig. 3.10, where cut limit of about 0.2 permill is needed for a background rejection over 90% in the outer modules. The background rate in the inner modules is smaller and less background need to be cut away (a cut limit at around 0.4-0.6 is normally enough for the inner modules).