Lorentz Invariance Violation and Chemical Composition of Ultra High Energy Cosmic Rays

Motivated by experimental indications of a significant presence of heavy nuclei in the cosmic ray flux at ultra high energies ($\gtrsim 10^{19} \eV$), we consider the effects of Planck scale suppressed Lorentz Invariance Violation (LIV) on the propagation of cosmic ray nuclei. In particular we focus on LIV effects on the photodisintegration of nuclei onto the background radiation fields. After a general discussion of the behavior of the relevant quantities, we apply our formalism to a simplified model where the LIV parameters of the various nuclei are assumed to kinematically result from a single LIV parameter for the constituent nucleons, $\eta$, and we derive constraints on $\eta$. Assuming a nucleus of a particular species to be actually present at $10^{20}$ eV the following constraints can be placed: $-3\times10^{-2} \lesssim \eta \lesssim 4$ for $^{56}$Fe, $-2\times10^{-3} \lesssim \eta \lesssim 3\times10^{-2}$ for $^{16}$O and $-7\times10^{-5} \lesssim \eta \lesssim 1\times10^{-4}$ for $^{4}$He, respectively.