High-energy tests of Lorentz invariance

We develop a perturbative framework with which to discuss departures from exact Lorentz invariance and explore their potentially observable ramifications. Tiny noninvariant terms introduced into the standard model Lagrangian are assumed to be renormalizable (dimension \ensuremath{\leqslant}4), invariant under $\mathrm{SU}(3)\ensuremath{\bigotimes}\mathrm{SU}(2)\ensuremath{\bigotimes}U(1)$ gauge transformations, and rotationally and translationally invariant in a preferred frame. There are a total of 46 independent CPT-even perturbations of this kind, all of which preserve anomaly cancellation. They define the energy-momentum eigenstates and their maximal attainable velocities in the high-energy limit. The effects of these perturbations increase rapidly with energy in the preferred frame, more rapidly than those of CPT-odd perturbations. Our analysis of Lorentz-violating kinematics reveals several striking new phenomena that are relevant both to cosmic-ray physics (e.g., by undoing the Greisen, Zatsepin, and Kuz'min cutoff) and neutrino physics (e.g., by generating novel types of neutrino oscillations). These may lead to new and sensitive high-energy tests of special relativity.