Gravitational electron-positron scattering

TL;DR

This paper investigates electron-positron scattering mediated by gravitons using gravitoelectromagnetism, deriving gravitational cross-sections and comparing them to electromagnetic counterparts.

Contribution

It presents the first calculation of gravitational scattering cross-sections for electron-positron interactions within the gravitoelectromagnetism framework.

Findings

Derived gravitational cross-section for electron-positron scattering.

Compared gravitational and electromagnetic scattering cross-sections.

Showed gravitational effects are negligible compared to electromagnetic interactions.

Abstract

A scattering process with gravitons as an intermediate state is investigated. To study such a scattering, the Gravitoelectromagnetism theory is considered. It is a gravitational theory built on the analogy between gravity and electromagnetism. The complete Lagrangian formulation of the gravitoelectromagnetic theory includes interactions of gravitons with fermions and photons that leads us to calculate their scattering amplitudes and cross-sections. In this context, the gravitational cross-section of the $e^{-}+e^{+}\longrightarrow\mu^{-}+\mu^{+}$ scattering process is obtained. A comparison between the electromagnetic and gravitational cross-sections is made.