Lorentz Invariance Violation on UHECR propagation

Abstract

In the present work possible consequences of the Lorentz symmetry breaking are presented. Those consequences are encoded through the modification of dispersion relations which are applied to the processes of pair and pion photo production generated at UHECR scale. The produced physics from such modifications contains scenarios where the expected photo production thresholds under Lorentz symmetry are shifted; the other scenarios predict that the cosmic ray flux will be recover at higher energies due to the suppression of the production processes. This phenomenon is repeated for different components of the diffuse photon background and generates opacity bands in distinct parts of the energy spectrum; we expose scenarios that have not been considered previously by other authors. Moreover, in contrast with previous studies, in this work the scenarios generated by the Lorentz symmetry breaking are measured by a generic parameter, unique for each process, independent of the correction origin (E2 or p2) in the dispersion relations, as well as the nature of the particle involved and possible corrections to the relations of conservation energy-momentum laws. Additionally, the Pierre Auger result for the pion photo production is used to estimate the energy scale parameter of the Lorentz symmetry breaking.