Lorentz violation at high energy: concepts, phenomena and astrophysical constraints

TL;DR

This paper analyzes Planck-suppressed Lorentz violation within an effective field theory framework, focusing on dimension-5 operators in QED that modify photon and electron dispersion and enable LV processes like photon decay and vacuum Cherenkov radiation. By combining theoretical structure with high-energy astrophysical observations, it derives strong, multi-channel constraints on LV parameters, notably $|\xi|\lesssim 2\times10^{-4}$ from birefringence and $|\eta_{\pm}|\lesssim O(0.1)$ (and stronger in related bounds) from photon-decay, synchrotron, and Cherenkov processes, including detailed Crab Nebula modeling. The work also discusses naturalness concerns, potential SUSY protections, and how future facilities (GLAST/FERMI, Auger, EUSO/OWL, IceCube) could substantially tighten limits, thereby constraining or guiding quantum gravity scenarios that predict LV. Overall, the paper demonstrates that Planck-scale LV can be probed with current observations and emphasizes the role of EFT in providing robust, testable predictions and constraints.

Abstract

We consider here the possibility of quantum gravity induced violation of Lorentz symmetry (LV). Even if suppressed by the inverse Planck mass such LV can be tested by current experiments and astrophysical observations. We review the effective field theory approach to describing LV, the issue of naturalness, and many phenomena characteristic of LV. We discuss some of the current observational bounds on LV, focusing mostly on those from high energy astrophysics in the QED sector at order E/M_Planck. In this context we present a number of new results which include the explicit computation of rates of the most relevant LV processes, the derivation of a new photon decay constraint, and modification of previous constraints taking proper account of the helicity dependence of the LV parameters implied by effective field theory.

Figures (3)

• Figure 1: Constraints on LV in QED at $O(E/M)$ on a log-log plot. For negative parameters minus the logarithm of the absolute value is plotted, and region of width $10^{-10}$ is excised around each axis. The constraints in solid lines apply to $\xi$ and both $\eta_\pm$, and are symmetric about both the $\xi$ and the $\eta$ axis. At least one of the two pairs $(\eta_\pm,\xi)$ must lie within the union of the dashed bell-shaped region and its reflection about the $\xi$ axis. The IC and synchrotron Čerenkov lines are truncated where they cross.
• Figure 2: Graphical representation of energy-momentum conservation in a two-particle reaction. $\mathcal{R}$ is the region covered by all final energy curves $E_f^{\alpha,\beta,p_3} (p_1)$ for some fixed $p_2$, assuming momentum conservation holds to determine $p_4$. The curve $E_i(p_1)$ is the initial energy for the same fixed $p_2$. Where the latter curve lies inside $\mathcal{R}$ there is a solution to the energy and momentum conservation equations. In the example shown there is both a lower and an upper threshold for the reaction.
• Figure 3: Asymmetric pair production. The negative curvature of the outgoing particle dispersion relation allows to save energy by providing the pair partners with different portions of the initial momentum $p_{in}$.