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

Zurab Kepuladze

TL;DR

We study Lorentz-violation in QED within an effective-field-theory framework to determine whether LIV introduced in one sector can propagate to others via quantum loops. One-loop calculations of fermion self-energy and photon vacuum polarization show that LIV parameters transfer across sectors with a loop suppression, linking interaction-based LIV to observable kinematic effects. Constraints from astrophysical observations bound the cross-sector LIV coefficients, while dispersion-based LIV can be probed at high-energy colliders, with potential sensitivity to δ on the order of 10^-8 to 10^-9 at the LHC. The results suggest accelerator-based resonance studies can provide competitive, model-independent LIV constraints complementary to astrophysical bounds, motivating detailed collider analyses of LIV-induced resonance distortions.

Abstract

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 $δ\sim 10^{-8} \text{ to } 10^{-9}$ at the LHC. This suggests that accelerator-based resonance studies provide a promising avenue for stringent LIV constraints, potentially rivaling astrophysical observations.

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

TL;DR

We study Lorentz-violation in QED within an effective-field-theory framework to determine whether LIV introduced in one sector can propagate to others via quantum loops. One-loop calculations of fermion self-energy and photon vacuum polarization show that LIV parameters transfer across sectors with a loop suppression, linking interaction-based LIV to observable kinematic effects. Constraints from astrophysical observations bound the cross-sector LIV coefficients, while dispersion-based LIV can be probed at high-energy colliders, with potential sensitivity to δ on the order of 10^-8 to 10^-9 at the LHC. The results suggest accelerator-based resonance studies can provide competitive, model-independent LIV constraints complementary to astrophysical bounds, motivating detailed collider analyses of LIV-induced resonance distortions.

Abstract

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 at the LHC. This suggests that accelerator-based resonance studies provide a promising avenue for stringent LIV constraints, potentially rivaling astrophysical observations.

Paper Structure

This paper contains 11 sections, 52 equations, 1 figure.

Table of Contents

  1. Introduction
  2. Calculation of the loop correction
  3. LIV vs GI
  4. LIV interaction
  5. Transfer of LIV to fermion kinematics
  6. Transfer of LIV to the photon kinematics
  7. Modification of the dispersion relation of the fermion
  8. LIV modification of the photon
  9. About accelerator specific physics
  10. Conclusion
  11. Acknowledgments

Figures (1)

  • Figure 1: Relative deviation $\Delta\sigma/\sigma$ as a function of the invariant mass of the $Z$ resonance is plotted for $E=14$ TeV and $\delta_{B}=2\times10^{-9}$. The vertical dashed line marks the $Z$-boson mass $M_{Z}$. LIV effects are nonzero at $M_{Z}$ and reach a maximum of about $0.17\%$ around 1.2 GeV away from the $M_{Z}$ value.