Threshold anomalies in Horava-Lifshitz-type theories

Recently the study of threshold kinematic requirements for particle-production processes has played a very significant role in the phenomenology of theories with departures from Poincare' symmetry. We here specialize these threshold studies to the case of a class of violations of Poincare' symmetry which has been much discussed in the literature on Horava-Lifshitz scenarios. These involve modifications of the energy-momentum ("dispersion") relation that may be different for different types of particles, but always involve even powers of energy-momentum in the correction terms. We establish the requirements for compatibility with the observed cosmic-ray spectrum, which is sensitive to the photopion-production threshold. We find that the implications for the electron-positron pair-production threshold are rather intriguing, in light of some recent studies of TeV emissions by Blazars. Our findings should also provide motivation for examining the fate of the law of energy-momentum conservation in Horava-Lifshitz-type theories.