GZK photon constraints on Planck scale Lorentz violation in QED

Abstract

We show how the argument exploited by Galaverni & Sigl in Phys. Rev. Lett., 100, 021102 (2008) (see also arXiv:0708.1737) to constrain Lorentz invariance violation (LV) using Ultra-High-Energy photon non observation by the AUGER experiment, can be extended to QED with Planck-suppressed LV (at order $O(E/M)$ and $O(E^2/M^2)$). While the original constraints given by Galaverni & Sigl happen to be weakened, we show that, when used together with other EFT reactions and the expected detection of photons at $E > 10^{19}$ eV by AUGER, this method has the potentiality not only to basically rule out order $O(E/M)$ corrections but also to strongly constrain, for the first time, the CPT-even $O(E^2/M^2)$ LV QED.