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.
Phys. Rev. D 83 (2011) 056010 | DOI: 10.1103/PhysRevD.83.056010
We study a QED extension that is unitary, CPT invariant and super-renormalizable, but violates Lorentz symmetry at high energies, and contains higher-dimension operators (LVQED). Divergent diagrams are only one- and two-loop. We compute the one-loop renormalizations at high and low energies and analyse the relation between them. It emerges that the power-like divergences of the low-energy theory are multiplied by arbitrary constants, inherited by the high-energy theory, and therefore can be set to zero at no cost, bypassing the hierarchy problem.
Phys. Rev. D 81 (2010) 085042 | DOI: 10.1103/PhysRevD.81.085042