We investigate the consequences of higher dimension Lorentz violating, CPT
even kinetic operators that couple standard model fields to a non-zero vector
field in an Effective Field Theory framework. Comparing the ultra-high energy
cosmic ray spectrum reconstructed in the presence of such terms with data from
the Pierre Auger observatory allows us to establish two sided bounds on the
coefficients of the mass dimension five and six operators for the proton and
pion. Our bounds imply that for both protons and pions, the energy scale of
Lorentz symmetry breaking must be well above the Planck scale. In particular,
the dimension five operators are constrained at the level of $10^{-3} M_{\rm
Planck}^{-1}$. The magnitude of the dimension six proton coefficient is bounded
at the level of $10^{-6} M_{Planck}^{-2}$ except in a narrow range where the
pion and proton coefficients are both negative and nearly equal. In this small
area, the magnitude of the dimension six proton coefficient must only be below
$10^{-3} M_{\rm Planck}^{-2}$. Constraints on the dimension six pion
coefficient are found to be much weaker, but still below $M_{\rm Planck}^{-2}$.
