Physics Tomorrow Letters

Introduction

It dates from over two decades ago, the first version of fermionic mass dimension one fields as candidates to dark matter [1]. Since then, the field has undergone modifications in the formulation to conciliate it with Lorentz symmetries (for a broad discussion and physical consequences, see [2]). Recent advancements in the theory of fermionic fields characterized by mass dimension one have been made [3]. These developments have revealed that the field possesses a two-fold Wigner degeneracy [4], effectively doubling its degrees of freedom. Consequently, the field exhibits complete Poincar`e symmetry. The resulting construction provides a first-principle candidate for dark matter, considering that constraints significantly impact the feasible interactions with standard matter fields, necessitating perturbative renormalizability. While certain potential couplings can still be achieved through a Higgs portal (refer to [5] for an analysis based on the earlier version of the field), it is conceivable that an additional field associated with a hidden dark sector’s U(1) gauge symmetry may exist [6]. The renormalization of the previous version of the model, specifically in the absence of gauge interactions, was examined in Ref. [7]. The findings from that investigation indicate that the obtained physical results also apply to the current scenario. Building upon this prior work, the objective of our study is to extend the analysis by incorporating a gauge interaction. To accomplish this, we employ dimensional regularization to evaluate the one-loop renormalization of fermions with mass dimension one that are non-minimally coupled to the electromagnetic field. Notably, we consider the presence of a renormalizable non-minimal coupling term ˜eλ¯[γµ, γν]λFµν, which is allowed by gauge symmetry and has been proposed as a potential source for an effective mass term for the photon [1]. The primary result presented in this paper is the demonstration that photon propagation remains massless and transverse up to the two-loop order. This achievement corroborates the transverse aspect of photon self-energy tensor found very recently, via symmetry arguments, in the comprehensive study of Ref. [8].