In the reconstruction the hits forming a track candidate have to be compared with a track template to make sure that they could have been left by a particle with given momentum and emission angle theta. As the deviations are calculated for fixed momentum and theta, the hits from real particle with slightly different momentum or theta have some systematic deviations which are added to the deviation due to the multiple scattering. For very close momenta it causes only a decrease of probability, but when the difference of momentum or theta is larger, the track candidate is rejected. To accept all tracks with continuous momentum and theta one thus needs templates close enough, so that a particle with momentum (or theta) between these of the templates is accepted by at least one of them. The study of the acceptance range of templates has shown that we can achieve this goal if templates are separated by no more than 1% in momentum and 0.1-0.3 degrees (closer templates are requited at high momenta) in theta. With such a grid a full set of templates for one type of particle should contain 4000 templates or more. As the template size is of the order of 2 kB the memory required to keep them all would be about 80 MB. Such requirements make the reconstruction very difficult or may be even impossible - we can not keep all templates in memory, and reading a subset really necessary in each event is probably not acceptable.
To reduce the number of templates some modifications are necessary. Simple reduction of the size of template is not sufficient, to be useful template has to contain all important information. A significant decrease of the number of templates is thus necessary.
If one would know the real momentum and theta of the particle, one could predict the position of the trajectory in the layer and then calculate deviations due to the multiple scattering only, without additional systematic deviations due to the difference of the track and template parameters. Such prediction can be obtained either by interpolation in which two or more neighbor templates are used, or by extrapolation from a given template using additional information of the change of trajectory with the change of momentum and theta. Here the second approach is presented.
The test of the acceptance of the templates were performed for Pi+ and Pi- for two values of momentum: 200 MeV/c and 1 GeV/c and for several values of the theta angle. Here are presented only the largest and lowest theta tested. The probability values for the tracks with momentum different up to 30% from that of the template and theta different up to 5 degrees were calculated and then for the points where they exceed 0.01 they were stored in a 2D histogram. They were calculated:
After looking at the pictures below it is immediately clear the the implemented method gives always much larger acceptance area than the original approach. This is especially striking at high energies, where previously difference only up to 0.2 degrees in theta and up to 4% in momentum was accepted.
The area of acceptance of the templates is much larger, one can assume that the grid 10% in momentum and 1 degree in theta should be sufficient to cover whole spectrometer without large gaps. The calculation of corrected theta and momentum is not very accurate (especially at low momenta), but gives better estimation than the values taken directly from the template.
