Eur. Phys. J. Plus (2022) 137: 260
https://doi.org/10.1140/epjp/s13360-022-02479-z

Regular Article

Gravitational electron–positron scattering

¹ Instituto Federal de Educação, Ciência e Tecnologia de Mato Grosso, 78043-409, Cuiabá, Mato Grosso, Brazil
² Instituto de Física, Universidade Federal de Mato Grosso, 78060-900, Cuiabá, Mato Grosso, Brazil
³ Department of Physics and Astronomy, University of Victoria, 3800 Finnerty Road, V8P 5C2, Victoria, BC, Canada
⁴ Physics Department, Theoretical Physics Institute, University of Alberta, Edmonton, Alberta, Canada

^c alesandroferreira@fisica.ufmt.br

Received: 19 January 2022
Accepted: 11 February 2022
Published online: 23 February 2022

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 $e^{-}+e^{+}⟶{\mu }^{-}+{\mu }^{+}$ scattering process is obtained. A comparison between the electromagnetic and gravitational cross sections is made.