Vacuum Cherenkov radiation in quantum electrodynamics with high-energy Lorentz violation

We study phenomena predicted by a renormalizable, CPT invariant extension of the standard model that contains higher-dimensional operators and violates Lorentz symmetry explicitly at energies greater than some scale Delta(L). In particular, we consider the Cherenkov radiation in vacuo. In a rather general class of dispersion relations, there exists an energy threshold above which radiation is emitted. The threshold is enhanced in composite particles by a sort of kinematic screening mechanism. We study the energy loss and compare the predictions of our model with known experimental bounds on Lorentz violating parameters and observations of ultrahigh-energy cosmic rays. We argue that the scale of Lorentz violation Delta(L) (with preserved CPT invariance) can be smaller than the Planck scale, actually as small as 10(14)-10(15) GeV. Our model also predicts the Cherenkov radiation of neutral particles.