Event reconstruction in pair production detectors

In the pair production telescopes, the $\gamma$ ray is annihilated with its energy transferred to an electron-positron pair which is created:

$$h\nu \rightarrow e^{+} + e^{-}$$

The interaction takes place in the electric field of a nucleus. The energy and the momentum of the $\gamma$-ray are taken by the electron-positron pair, and in a smaller part by the nucleus. Therefore, by measuring the energy and momentum of the pair, the energy and the momentum of the $\gamma$-ray are estimated. The reconstruction of the $\gamma$-ray direction proceeds through the identification and analysis of the $e^+ e^-$ tracks stemming from the production vertex. At each plane the microstrip on the silicon layers give, separately, the coordinates X and Y of the hits corresponding to the passage of the two electrons. The first step of the event analysis requires to find the two tracks among the possible associations of the hits detected by the tracker silicon layers.This means, in practical terms, dividing the hits among those belonging to each track and those external to both tracks. This operation is complicated by the fact that the tracks can have a complex morphology, especially at low energy, while at high energy the hits of the two tracks are very close. Moreover the hits of the $e^+ e^-$ pairs, are often superimposed over hits released by $\delta$-rays and other secondary phenomena.
Regarding the second step it is necessary to fit the hits of each track with a line which models the electron trajectory. This task is complicated by the fact that electrons path is not a straight line because of the multiple scattering. Moreover, measurements on the electrons passage through the silicon planes are affected by an intrinsic error of not negligible amplitude. The first two steps are performed separately for the hits corresponding to the X and Y coordinates. A total of four tracks (two for each projection) are then produced. In order to obtain the direction in the three-dimensional space of the electrons moment, it is required to correctly associate the two projection of each track. A technique which allows to maximize the probability of correct association of the projections is then necessary.