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applciletetrsa>vol-02>issue-07>Perturbative aspects of mass dimension one fermions non-minimally coupled to electromagnetic field
Research
Perturbative aspects of mass dimension one fermions non-minimally coupled to electromagnetic field
Willian Carvalho
M. Dias
Applied Science Letters
2022 ° 04(06) ° 1685-6980
https://www.wikipt.org/applscilettersa
DOI: 10.1490/897511.661applsci
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.
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].
Conclusion
KS Our study focuses on investigating the role of the Elko field in Quantum Electrodynamics (QED) within the framework of renormalization at one and two-loop orders. Notably, we observe a distinction between Dirac and Elko fermions regarding the vanishing wave-function counterterm. Additionally, our results reveal that the photon propagation remains massless and transverse up to the two-loop order. An important result of our study is that the non-minimal electromagnetic coupling can exhibit asymptotic freedom if the condition g < 48Ëœe 2 is satisfied. This finding has profound implications for the behavior of the Elko field at high energies. It suggests that the Elko field has the potential to decouple from other particles and interactions at these energy scales. This aspect is relevant when considering the Elko field as a candidate for dark matter. It implies that the Elko field may behave differently from other matter fields at high energies, which has implications for calculating its relic abundance and freeze-out temperature. In particular, it impacts processes involving the interactions between the Elko field and the ordinary particles of the Standard Model. Furthermore, future investigations can expand upon our calculations by incorporating gravitational corrections and exploring higher energy scales. Such analyses would shed light on more intriguing aspects of the primordial universe and cosmological applications involving the Elko particle as a constituent of dark matt
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