Statistics for trajectometry
A trajectometer is made of layers of charged particle detectors which measure successive positions along the trajectories; it is generally immersed in a magnetic field, so the curvature of the trajectory provides a measurement of the momentum. A method to perform a progressive fitting of the trajectory (Kalman Filter formalism), incorporating the measurements one after one, with an optimal account for the perturbations (multiple scattering, energy loss), is described with some indications for practical implementations in realistic detector layouts. Useful byproducts of the method and tests of validity are discussed. The procedure appears to be a combination ad libitum of elementary operations on vectors and matrices of fixed dimension (the number of parameters needed to define the trajectory), affording very flexible strategies, including a coupling of the pattern recognition of tracks with the fit of the trajectory, and combination with calorimetric or timing measurements. Extension to non-gaussian errors is discussed.
Once the trajectories of an event are independently reconstructed, they may be extrapolated back to the region of production of the particles (target, or zone of intersection of the beams in a collider) and associated to one or several vertices (primary interaction, and possible secondary interactions or decays): a fast and flexible method is described to perform these operations and improve the geometrical reconstruction, hence the kinematical one, by the constraint of a common origin; additional constraints may be added. Here again, the elementary steps consist in linear operations on vector and matrices of fixed dimension, allowing the user to easily proceed by successive trials and to optimize the strategy.
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