https://doi.org/10.1140/epjc/s10052-025-14308-5
Regular Article - Theoretical Physics
Ultra high energy cosmic rays in light of the Lorentz invariance violation effects within the proton sector
School of Physics, Zhengzhou University, 450001, Zhengzhou, China
a
guoliliu@zzu.edu.cn
b
feiwang@zzu.edu.cn
Received:
13
November
2024
Accepted:
12
May
2025
Published online:
1
June
2025
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 
(0.1 to 
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.
© The Author(s) 2025
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