Lorentz Violation for Photons and Ultrahigh-Energy Cosmic Rays

Lorentz symmetry breaking at very high energies may lead to photon dispersion relations of the form ω²=k²+ξₙk²(k/MPl)ⁿ with new terms suppressed by a power n of the Planck mass MPl. We show that first and second order terms of size |ξ₁|10^-14 and ξ₂-10^-6, respectively, would lead to a photon component in cosmic rays above 10¹⁹ eV that should already have been detected, if corresponding terms for e^± are significantly smaller. This suggests that LI breaking suppressed up to second order in the Planck scale is unlikely to be phenomenologically viable for photons.