Abstract
A very simple Gaussian model is used to illustrate an interesting fitting result: a linear growth of the resolution with the number N of detecting layers. This rule is well beyond the well-known rule proportional to N for the resolution of the usual fits. The effect is obtained with the appropriate form of the variance for each hit (observation). The model reconstructs straight tracks with N parallel detecting layers, the track direction is the selected parameter to test the resolution. The results of the Gaussian model are compared with realistic simulations of silicon micro-strip detectors. These realistic simulations suggest an easy method to select the essential weights for the fit: the lucky model. Preliminary results of the lucky model show an excellent reproduction of the linear growth of the resolution, very similar to that given by realistic simulations. The maximum likelihood evaluations complete this exploration of the growth in resolution.
Highlights
Essential sources of information in high energy physics experiments are the tracking of ionizing particles
Preliminary results of the lucky model show an excellent reproduction of the linear growth of the resolution, very similar to that given by realistic simulations
In refs. [1,2], we introduced for the first time very special probability density functions (PDFs), one for each hit, calculated for minimum ionizing particles (MIPs) crossing a micro-strip detector
Summary
Essential sources of information in high energy physics experiments are the tracking of ionizing particles. [1,2], we introduced for the first time very special probability density functions (PDFs), one for each hit, calculated for minimum ionizing particles (MIPs) crossing a micro-strip detector Extensive expressions of those PDFs and the detailed derivations are reported in ref. The complexity introduced by heteroscedasticity destroys the independence from the origin of the data, but adds substantial improvements to the fit quality To illustrate this point, beyond the results of refs. References [3,4] demonstrate the essentiality of our approach to get a statistical optimality of the least-squares fits To complete these fitting results a comparison with the maximum likelihood evaluations The usual fitting methods are a crude simplification of the methods discussed in ref. [13], tuned on the problems of that times, completely out of place with our very sophisticated silicon detectors
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