Abstract
Two new fitting methods are explored for momentum reconstruction. They give a substantial increase of momentum resolution compared to standard fit. The key point is the use of a different (realistic) probability distribution for each hit (heteroscedasticity). In the first fitting method an effective variance is calculated for each hit, the second method uses the search of the maximum likelihood. The tracker model is similar to the PAMELA tracker with its two sided detectors. Here, each side is simulated as a momentum reconstruction device. One of the two is similar to silicon micro-strip detectors of large use in running experiments. The gain obtained in momentum resolution is measured as the virtual magnetic field and the virtual signal-to-noise ratio required by the standard fits to overlap with the best of the new methods. For the low noise side, the virtual magnetic field must be increased 1.5 times to reach the overlap and 1.8 for the other. For the high noise side, the increases must be 1.8 and 2.0. The signal-to-noise ratio has to be increased by 1.6 for the low noise side and 2.2 for the high noise side ( η -algorithms). Each one of our two methods shows a very rapid linear increase of the resolution with the number N of detector layers, the two standard fits have the usual slow growth less than N .
Highlights
Momenta of charged particles are fundamental pieces of information in high energy particle physics
The gain obtained in momentum resolution is measured as the virtual magnetic field and the virtual signal-to-noise ratio required by the standard fits to overlap with the best of the new methods
In ref. [9] we indicated the principal steps required to obtain the probability density functions (PDFs) for the COG2, those steps followed the standard method described in the books about the theory of probability
Summary
Momenta of charged particles are fundamental pieces of information in high energy particle physics. For their acquisition, very complex instruments (trackers) have been developed and the key element of a tracker is a uniform (or near to) magnetic field. In a homogeneous magnetic field a free charged particle describes an helicoidal path, the radius of the helix is proportional to the momentum component orthogonal to the magnetic field. The precise reconstructions of these non linear paths allow the trackers to measure the particle momenta and to fix the charge signs. Among the degrading effects we quote the multiple (Coulomb) scattering, the energy loss, the inhomogeneities of the magnetic field and the systematic and statistical errors of the positioning algorithms. The handling of the full non linearity of the particle path is described in ref. [3]
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