Unitarity and non-relativistic potential energy in a higher-order Lorentz symmetry breaking electromagnetic model

TL;DR

This paper investigates a Lorentz-violating electromagnetic model with higher derivatives, demonstrating conditions under which unitarity is preserved and analyzing how the potential energy between particles deviates from Coulomb's law.

Contribution

It shows that unitarity can be maintained in a higher-derivative Lorentz-violating model and explores the non-relativistic potential energy modifications for various background vectors.

Findings

Unitarity is preserved at tree-level for specific background vectors.

The potential energy deviates from Coulomb's law depending on the background vector.

The model's spectrum includes ghost contributions but can be unitary under certain conditions.

Abstract

The Lorentz-violating model proposed by Myers and Pospelov suffers from a higher-derivative pathology due to a dimension-5 operator. In particular, its electromagnetic sector exhibits an spectrum which contains, in addition to an expected massless photon, ghost contributions that could (in principle) spoil the unitarity of the model. We find that unitarity at tree-level can be assured for pure spacelike, timelike and lightlike background four-vectors (the last two under restrictions upon the allowed momenta). We then analyze the non-relativistic interparticle potential energy behavior for different background four-vectors and compare to the usual Coulomb potential.