Abstract
The bremsstrahlung energy loss distribution of electrons propagating in matter is highly non-Gaussian. Because the Kalman filter relies solely on Gaussian probability density functions, it is not necessarily the optimal reconstruction algorithm for electron tracks. A Gaussian-sum filter (GSF) algorithm for electron reconstruction in the CMS tracker has therefore been developed and implemented. The basic idea is to model the bremsstrahlung energy loss distribution by a Gaussian mixture rather than by a single Gaussian. It is shown that the GSF is able to improve the momentum resolution of electrons compared to the standard Kalman filter. The momentum resolution and the quality of the error estimate are studied both with a fast simulation, modelling the radiative energy loss in a simplified detector, and the full CMS tracker simulation.
Highlights
Modern track detectors based on semiconductor technologies contain larger amounts of material than gaseous detector types, partially due to the detector elements themselves and partially due to additional material required for on-sensor electronics, power, cooling, and mechanical support
Results from the reconstruction of data originating from a simplified simulation are shown. In this simulation multiple scattering and ionization energy loss are turned off, all the material is concentrated on the detector units, and the exact amount of material used in the simulation is known by the reconstruction program
The following results all refer to the quantity q/p recorded at the point of closest approach to the vertex in the transverse plane – the transverse impact point (TIP) – after a fit going from the outside towards the inside of the tracker
Summary
Modern track detectors based on semiconductor technologies contain larger amounts of material than gaseous detector types, partially due to the detector elements themselves and partially due to additional material required for on-sensor electronics, power, cooling, and mechanical support. The material effects are currently assumed to be concentrated in the active elements of the detector layers In this context the optimal treatment of radiative energy loss is to correct the momentum with t=0.2 t=0.1 t=0.05 t=0.02 101. The mean value of energy loss and to increase the variance of the momentum by adding the variance of the energy loss distribution This procedure should ensure unbiased estimates of the track parameters and of the associated uncertainties [3]. The Kalman filter is a linear least-squares estimator, and is proved to be optimal only when all probability densities encountered during the track reconstruction procedure are Gaussian. The resulting estimator resembles a set of Kalman filters running in parallel, where each Kalman filter corresponds to one of the components of the mixture describing the distribution of the state vector
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