Lorentz Violation for Photons and Ultra-High Energy Cosmic Rays

TL;DR

This paper investigates how Lorentz symmetry breaking at high energies affects photon dispersion and cosmic rays, concluding that certain Lorentz-violating terms are incompatible with observed ultra-high energy cosmic ray data.

Contribution

It provides constraints on Lorentz violation parameters for photons based on cosmic ray observations, highlighting the unlikelihood of certain Lorentz invariance breakings up to second order.

Findings

Photon Lorentz violation parameters xi_1 > 10^(-14) are excluded.

Photon Lorentz violation parameters xi_2 < -10^(-6) are excluded.

Lorentz invariance breakings suppressed up to second order are phenomenologically unlikely.

Abstract

Lorentz symmetry breaking at very high energies may lead to photon dispersion relations of the form omega^2=k^2+xi_n k^2(k/M_Pl)^n with new terms suppressed by a power n of the Planck mass M_Pl. We show that first and second order terms of size xi_1 > 10^(-14) and xi_2 < -10^(-6), respectively, would lead to a photon component in cosmic rays above 10^(19) eV that should already have been detected, if corresponding terms for electrons and positrons are significantly smaller. This suggests that Lorentz invariance breakings suppressed up to second order in the Planck scale are unlikely to be phenomenologically viable for photons.