The Passage of Ultrarelativistic Neutralinos through Matter

The origin of the most energetic cosmic ray events, with $E \gsim 10^{20}$ eV, remains mysterious. One possibility is that they are produced in the decay of very massive, long--lived particles. It has been suggested that these so--called ``top--down scenarios'' can be tested by searching for ultrarelativistic neutralinos, which would be produced copiously if superparticles exist at or near the TeV scale. In this paper we present a detailed analysis of the interactions of such neutralinos with ordinary matter. To this end we compute several new contributions to the total interaction cross section; in particular, the case of higgsino--like neutralinos is treated for the first time. We also carefully solve the transport equations. We show that a semi--analytical solution that has been used in the literature to treat the somewhat analogous propagation of $\tau$ neutrinos leads to large errors; we therefore use a straightforward numerical method to solve these integro--differential equations.