Perturbative aspects of mass dimension one fermions non-minimally coupled to electromagnetic field

¹ Faculdade de Física, Universidade Federal do Pará - 66075-110, Belém, Pará, Brazil
² Universidade Federal de São Paulo, Departamento de Física - Rua São Nicolau 210, 09913-030, Diadema, São Paulo, Brazil
³ Departamento de Física, Universidade Estadual Paulista, UNESP - Av. Dr. Ariberto Pereira da Cunha, 333, Guaratinguetá, SP, Brazil

^(a) E-mail: marco.dias@unifesp.br (corresponding author)

Received: 5 June 2023
Accepted: 4 September 2023

Abstract

This paper addresses perturbative aspects of the renormalization of a fermion with mass dimension one non-minimally coupled to the electromagnetic field. Specifically, we calculate the one-loop corrections to the propagators and vertex functions of the model and determine the one-loop beta function of the non-minimal electromagnetic coupling. Additionally, we perform calculations of the two-loop corrections to the gauge field propagator, demonstrating that it remains massless and transverse up to this order. We also find that the non-minimal electromagnetic coupling can exhibit asymptotic freedom if a certain condition is satisfied. As a potential dark matter candidate, these findings suggest that the field may decouple at high energies. This aspect holds significance for calculating the relic abundance and freeze-out temperature of the field, particularly in relation to processes involving the ordinary particles of the Standard Model.