Lorentz Violation, Gravitoelectromagnetic Field and Bhabha Scattering

Lorentz symmetry is a fundamental symmetry in the Standard Model (SM) and in General Relativity (GR). This symmetry holds true for all models at low energies. However at energies near the Planck scale, it is conjectured that there may be a very small violation of Lorentz symmetry. The Standard Model Extension (SME) is a quantum field theory that includes a systematic description of Lorentz symmetry violations in all sectors of particle physics and gravity. In this paper SME is considered to study the physical process of Bhabha Scattering in the Gravitoelectromagnetism (GEM) theory. GEM is an important formalism that is valid in a suitable approximation of general relativity. A new non-minimal coupling term that violates Lorentz symmetry is used in this paper. Differential cross section for gravitational Bhabha scattering is calculated. The Lorentz violation contributions to this GEM scattering cross section are small and are similar in magnitude to the case of the electromagnetic field.