Low-energy Moller scattering in a Maxwell-Chern-Simons Lorentz-violating planar model

TL;DR

This paper investigates electron-electron interactions in a planar Maxwell-Chern-Simons model with Lorentz violation, revealing potential bound states due to attractive scalar and gauge-mediated forces.

Contribution

It provides an exact solution for the interaction potential in a Lorentz-violating planar model, highlighting the possibility of electron-electron bound states.

Findings

Scalar potential is always attractive.

Gauge interaction can also be attractive.

Potential for electron-electron bound states exists.

Abstract

One starts from a planar Maxwell-Chern-Simons model endowed with a Lorentz-violating term. The Dirac sector is introduced exhibiting a Yukawa and a minimal coupling with the scalar scalar and the gauge fields, respectively. One then evaluates the electron-electron interaction as the Fourier transform of the Moller scattering amplitude carried out in the non-relativistic limit. In the case of a purely time-like background, the interaction potential can be exactly solved, exhibiting a typical massless behavior far from the origin. The scalar interaction potential is always attractive whereas the gauge intermediation may also present attraction even when considered in the presence of the centrifugal barrier and the A^{2} term. Such a result is a strong indication that electron-electron bound states may appear in this theoretical framework.