Use of energy loss mechanisms to constrain Lorentz invariance violations

In light of recent and probably incoming observations of very high energy astroparticles, such as those reported by the IceCube collaboration, we readdress the energy loss mechanism by Lorentz violating particles. We analytically show that Cohen-Glashow's formula for energy loss is connected with a Poisson distribution for the number of decays, for which the large fluctuations prevent placing bounds on Lorentz invariance violations. However, thismodel ignores the sharp change in the decay width after each process. We propose replacing Poisson statistics with a new distribution that takes this into account. We study the average final energy and its fluctuations according to the new statistics, contrasting it with Cohen-Glashow's result, and discussing the reliability of energy loss mechanisms to constrain violations of Lorentz invariance.