  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 Lambda_{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 Lambda_{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.

High Energy Physics - Phenomenology;High Energy Physics - Theory