Ultra High Energy Cosmic Rays in light of the Lorentz Invariance Violation Effects within the Proton Sector

Abstract

Tiny Lorentz Invariance Violation (LIV) effects, potentially arising from quantum gravity-induced spacetime structures, may also manifest in the proton sector, offering a plausible pathway to test Planck-scale physics through high-energy cosmic phenomena. Our analysis reveals that even minuscule LIV effects in the proton sector can significantly elevate the photon threshold energy for photopion production to $\cal {O}$(0.1 to $10^3$ eV), orders of magnitude higher than in Lorentz-symmetric scenarios. Consequently, protons in ultra-high-energy cosmic rays (UHECRs) can propagate for very long distances without significant energy loss via photopion interactions with cosmic microwave background (CMB) photons. This suppression of attenuation may provide a plausible explanation for the observed cosmic-ray events exceeding the Greisen-Zatsepin-Kuzmin (GZK) cutoff energy. We further demonstrate that when both leading-order and next-to-leading-order LIV effects are considered, higher-order LIV contributions induce discontinuous transitions in the GZK cutoff energy spectrum. Observations of proton-dominated UHECRs beyond the GZK threshold could provide constraints the LIV energy scale. Offering insights into the ultraviolet regime of LIV theories near the Planck scale, UHECRs may serve as a sensitive probe of LIV and provide a means to test quantum gravity predictions by constraining deviations from Lorentz symmetry in extreme-energy regimes.