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In light of recent and probably upcoming observations of very high energyastroparticles, such as those reported by the IceCube collaboration, wereaddress the energy loss mechanism by Lorentz violating particles. Weanalytically show that Cohen-Glashow's formula for energy loss is connectedwith a Poisson distribution for the number of decays, whose large fluctuationsprevent placing bounds on Lorentz invariance violations. However, this modelignores the sharp change in the decay width after each process. We proposereplacing Poisson statistics with a new distribution that takes this intoaccount. We study the average final energy and its fluctuations according tothe new statistics, contrasting it with Cohen-Glashow's result, and discussingthe reliability of energy loss mechanisms to constrain violations of Lorentzinvariance.

On the use of energy loss mechanisms to constrain Lorentz invariance violations