Lorentz Violation: Loop-Induced Effects in QED and Observational Constraints

Lorentz invariance is a cornerstone of modern physics, yet its possible violation remains both theoretically intriguing and experimentally significant. In this work, using quantum electrodynamics as an example, we explore how Lorentz invariance violation, introduced into a specific sector of the theory, spreads through loop corrections, modifying the propagation and dispersion relations of other particles. Self-energy and vacuum polarization graphs reveal how LIV effects transfer across sectors, influencing particle kinematics. Due to these loop effects, constraints from cosmic-ray observations and other Earth-based experiments impose limits on induced LIV parameters that would otherwise be less constrained. We show that while interaction-based LIV effects require unrealistically large parameters for detection, modifications to dispersion relations can be probed down to $\delta \sim 10^{-8} \text{ to } 10^{-9}$ at the LHC. This suggests that accelerator-based resonance studies provide a promising avenue for stringent LIV constraints, potentially rivaling astrophysical observations.