Quantum corrections to Lorentz invariance violating theories: Fine-tuning problem
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...
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Published in | Physics letters. B Vol. 651; no. 4; pp. 313 - 318 |
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Main Authors | , |
Format | Journal Article |
Language | English |
Published |
Amsterdam
Elsevier B.V
02.08.2007
Elsevier Science |
Subjects | |
Online Access | Get full text |
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Summary: | 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. |
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ISSN: | 0370-2693 1873-2445 |
DOI: | 10.1016/j.physletb.2007.06.025 |