Quantum corrections to Lorentz invariance violating theories: Fine-tuning problem

• Published in: Physics letters. B Vol. 651; no. 4; pp. 313 - 318
• Main Authors: Crichigno, P.M., Vucetich, H.
• Format: Journal Article
• Language: English
• Published: Amsterdam Elsevier B.V 02.08.2007; Elsevier Science
• Subjects: Exact sciences and technology; Nuclear physics; Physics; The physics of elementary particles and fields; Space-time; Scale invariance; Spinor theory; Violations; Quantum electrodynamics; Quantum correction; Radiative corrections; Lorentz invariance; Models; Quantum gravity; Quantum theory
• ISSN: 0370-2693; 1873-2445
• DOI: 10.1016/j.physletb.2007.06.025

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 preferred 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.