Improvements of track fitting with well tuned probability distributions for silicon strip detectors

Well tuned probability distributions are synthetically illustrated, their forms produce faithful realizations of the impact point distributions for particles in silicon strip detector. Their use in track fitting shows a drastic improvement of a factor two, for the low noise case, and a factor three, for the high noise case, in respect to the standard approach. The tracks are well reconstructed even in presence of hits with large errors (outliers), with a surprising effect of hit discarding. The applications illustrated are simulations of the PAMELA tracker, but other type of trackers can be handled similarly. The probability distributions are calculated for the center of gravity algorithms, and they are evidently non-gaussian. The non gaussian tails are crucial to accurately reconstruct tracks with high error hits and their effective discarding. Our distributions share strong similarities with the Cauchy distribution and this forced us to abandon the standard deviation for our comparisons and instead use the full width at half maximum. A set of mathematical approaches must be developed for these applications, some of which are standard in wide sense, even if very complex. One is essential and, in its absence, all the others are useless. Therefore, in this paper, we report the details of this critical approach. It extracts physical properties of the detectors, and allows the insertion of the functional dependence from the impact point in the probability distributions. Other papers will be dedicated to the remaining parts