Quantum Corrections to Lorentz Invariance Violating Theories: Fine-Tuning Problem

TL;DR

This paper investigates quantum corrections in Lorentz invariance violating theories, revealing that such models face severe fine-tuning issues to align with experimental constraints, particularly in the Myers-Pospelov QED framework.

Contribution

It demonstrates that the Myers-Pospelov LIV model suffers from large, non-suppressed quantum corrections, requiring extreme fine-tuning to match experimental bounds.

Findings

Quantum corrections induce large Lorentz violations at low energies.

The Myers-Pospelov model requires 21 orders of magnitude fine-tuning.

LIV theories face naturalness problems due to quantum effects.

Abstract

It is of general agreement that a quantum gravity theory will most probably mean a breakdown of the standard structure of space-time at the Planck scale. This has motivated the study of Planck-scale Lorentz Invariance Violating (LIV) theories and the search for its observational signals. Yet, it has been recently shown that, in a simple scalar-spinor Yukawa theory, radiative corrections to tree-level Planck-scale LIV theories can induce large Lorentz violations at low energies, in strong contradiction with experiment, unless an unnatural fine-tuning mechanism is present. In this letter, we show the calculation of the electron self-energy in the framework given by the Myers-Pospelov model for a Lorentz Invariance Violating QED. We find a contribution that depends on the prefered's frame four-velocity which is not Planck-scale suppressed, showing that this model suffers from the same disease. Comparison with Hughes-Drever experiments requires a fine-tuning of 21 orders of magnitude for this model not to disagree with experiment.