Propagation of Covariance Matrices of Track Parameters in Homogeneous Magnetic Fields in CMS

In this paper, a set of Jacobians used for the propagation of track parameter covariance matrices in homogeneous magnetic fields in CMS is derived. Most of the presented formulas have been in widespread use in the high-energy physics community for many years, but have until now only existed in unpublished notes. Very precise, purely numerical schemes for calculating the same derivatives are also presented and used as a baseline for evaluating the correctness of the analytical terms.