Renormalization and phenomenology of quantum electrodynamics with high-energy Lorentz violation

Lorentz invariance is experimentally verified with a high degree of precision, so that to date it appears to be one of the most precise symmetries in nature. Nevertheless, Lorentz breaking at high energies is widely explored as a possible feature of new physics beyond the Standard Model. The point of view adopted in this thesis is that, if one relaxes the assumption of Lorentz invariance, the set of renormalizable quantum field theories can be enlarged. In fact the ultraviolet behaviour of propagators can be improved by means of higher space derivatives, preserving locality, causality and unitarity. We study explicitly the renormalization of the electromagnetic sector of this Lorentz violating extended Standard Model as well as the interplay between the high-energy and the low-energy theory. Doing so we realize that the power-like divergences of the low-energy theory become arbitrary, as they are multiplied by coefficients that incorporate an arbitrary renormalization scheme choice inherited from the high-energy theory. Consequently, if the elementary Higgs field is present, this arbitrariness makes the hierarchy problem disappear. Moreover, if one assume that Lorentz symmetry is not exact, several phenomena that are otherwise forbidden can occur, such as the Cherenkov radiation in vacuo. Comparing the predictions of the theory with experimental data and observations, we put bounds on the values of Lorentz-violating parameters and especially on the magnitude of the typical energy scale of Lorentz violation. Indeed, we argue that the scale of Lorentz violation may be smaller than the Planck scale, and if this were true, the understanding of physics around the Planck scale, in particular the formulation of gravity, should be completely reconsidered

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 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.Comment: 27 pages, 2 figures; v2: typos corrected, more references, some more comments - PR

Diffusion corrections to the hard pomeron

The high-energy behaviour of two-scale hard processes is investigated in the framework of small-x models with running coupling, having the Airy diffusion model as prototype. We show that, in some intermediate high-energy regime, the perturbative hard Pomeron exponent determines the energy dependence, and we prove that diffusion corrections have the form hinted at before in particular cases. We also discuss the breakdown of such regime at very large energies, and the onset of the non-perturbative Pomeron behaviour.Comment: 18 pages, 3 Postscript figure