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

P. M. Crichigno·H. Vucetich
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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.

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P. M. Crichigno, H. Vucetich. 2007-07-15. Quantum Corrections to Lorentz Invariance Violating Theories: Fine-Tuning Problem. https://doi.org/10.1016/j.physletb.2007.06.025

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