A Gaussian-mixture approximation of the Bethe-Heitler model of electron energy loss by bremsstrahlung

The distribution of the energy loss by bremsstrahlung of electrons is very different from a Gaussian one. If the energy loss by bremsstrahlung is to be taken into account during track reconstruction, its distribution has to be approximated by a Gaussian mixture so that it can be used by a (generalized) Kalman filter. The distribution is taken from the Bethe-Heitler model of bremsstrahlung, which assumes that the bremsstrahlung spectrum can be described in terms of a reduced quantity, independent of the electron energy. In this case the parameters of the mixture can be parameterized as a function of the amount of material only. The algorithm for computing the approximating mixtures with one to six components is described, and results on the quality of the approximation are shown. Finally, the required parameterizations of the mixtures are obtained in terms of 5th order polynomials. (C) 2003 Elsevier B.V. All rights reserved.