AUGER-HiRes results and models of Lorentz symmetry violation

The implications of AUGER and HiRes results for patterns of Lorentz symmetry violation (LSV) are examined, focusing on weak doubly special relativity (WDSR). If the Greisen-Zatsepin-Kuzmin (GZK) cutoff is definitely confirmed, the mass composition of the highest-energy cosmic-ray spectrum will be a crucial issue to draw precise theoretical consequences from the experimental results. Assuming that the observed flux suppression is due to the GZK mechanism, data will allow in principle to exclude a significant range of LSV models and parameters, but other important possibilities are expected to remain open : Lorentz breaking can be weaker or occur at a scale higher than the Planck scale, unconventional LSV effects can fake the GZK cutoff, threshold phenomena can delay its appearance… Space experiments appear to be needed to further test special relativity. We also examine the consequences of AUGER and HiRes data for superbradyons. If such superluminal ultimate constituents of matter exist in our Universe, they may provide new forms of dark matter and dark energy.

💡 Research Summary

This paper presents a detailed analysis of the implications of ultra-high-energy cosmic ray (UHECR) data from the AUGER and HiRes experiments for models of Lorentz symmetry violation (LSV), with a particular focus on the framework of “Weak Doubly Special Relativity” (WDSR). The central premise is that the experimental confirmation of the Greisen-Zatsepin-Kuzmin (GZK) cutoff provides a powerful tool to constrain LSV, but its interpretative power is critically dependent on the unknown mass composition (protons vs. nuclei) of the highest-energy cosmic rays.

The analysis centers on a specific LSV model: Quadratic Deformed Relativistic Kinematics (QDRK). This model introduces a fundamental length scale and a preferred vacuum rest frame, leading to a modification of the energy-momentum relation for particles at high energies, characterized by a correction term ΔE proportional to -α * p^3. This deformation generates two key energy scales: a transition energy (E_trans) where the deformation term begins to dominate over the mass term, and a limiting energy (E_lim) above which the phase space for two-body interactions (like proton-photon collisions responsible for the GZK effect) is severely suppressed.

The observed presence of the GZK cutoff rules out QDRK parameter sets where E_lim or E_trans fall below the observed cutoff energy (~10^20 eV). Under the assumption that UHECRs are pure protons, this sets an upper bound on the proton’s LSV parameter α_proton < ~10^-6, if the fundamental energy scale is the Planck energy. However, the paper strongly emphasizes that this bound is exquisitely sensitive to the nuclear composition of cosmic rays. If the primaries are nuclei composed of N nucleons, the derived upper bound on α_proton weakens significantly, scaling roughly with N^4. This introduces an uncertainty spanning several orders of magnitude, highlighting the paramount importance of future mass composition measurements for fundamental physics tests.

The discussion delves into deeper theoretical nuances. It questions whether the α parameter for composite particles like protons is the fundamental one, suggesting that the underlying value for quarks and gluons (α_QG) could be larger. It also explores the possibility that the fundamental length scale of new physics (a) could be smaller than the Planck length, meaning LSV effects might only become significant at energies higher than those currently probed, thereby delaying the suppression of the GZK cutoff and necessitating space-based experiments for further exploration.

Beyond kinematic suppression of the GZK process, the paper examines other potential LSV phenomena. It discusses “spontaneous decays,” where a difference in the α parameter between different particle species (e.g., photons and protons) could allow a high-energy proton to radiate a photon in vacuum. This process, kinematically forbidden in standard relativity, provides an alternative mechanism that could mimic the GZK flux suppression.

Finally, the paper explores the consequences for the “superbradyon” hypothesis. Superbradyons are postulated superluminal preons that could be the ultimate constituents of matter. If they exist as free particles in our universe, they could be sources of UHECRs through a form of “Cherenkov” radiation, or, having dissipated their energy, form a cosmological sea contributing to dark matter and dark energy.

In conclusion, while AUGER and HiRes data significantly constrain a class of LSV models, the paper argues that crucial uncertainties—primarily the UHECR mass composition and the possible higher energy scale for new physics—leave important possibilities open, underscoring the need for more precise composition measurements and observations at even higher energies.