Logo
ScienceStack
Table of Contents
Fetching ...
Sign In

On the structure of interactions of mass dimension one fermions: a functional renormalization group perspective

Gustavo P. de Brito

TL;DR

This work analyzes mass-dimension-one ELKO fermions through the functional renormalization group to map the structure of their interactions with scalars and gauge fields. By constructing a truncation that includes ELKO bilinears, scalar and gauge sectors, derivative Yukawa-like couplings, scalar portals, and four-fermion operators, the authors derive beta functions and anomalous dimensions, identifying conditions for UV completeness and asymptotic freedom. A key result is that derivative ELKO-scalar interactions do not generate non-derivative four-fermion terms due to a shift symmetry, while a scalar portal introduces a rich RG structure where UV-complete trajectories can exist, particularly for $N_ ext{E}>1$. When ELKO couples to a Pauli-like gauge term, additional four-fermion operators become dynamically required, and leading-order analysis suggests possible asymptotically free trajectories, though full stability beyond leading order remains to be established. Overall, the FRG approach reveals viable UV behaviors in these dark-sector couplings and sets the stage for further exploration of gravity–matter interplay and phenomenological implications of ELKO dark matter.

Abstract

In this paper, we provide the first systematic investigation of renormalization group properties of mass dimension one fermions described by ELKO spinors. By construction, ELKOs must be neutral under any Standard Model charge, therefore, providing a natural candidate for dark matter. We consider two versions of scalar-ELKO systems: the first characterized by a derivative Yukawa-like interaction, while the second involves ELKO four-fermion interactions as well as a scalar-ELKO portal. We also considered a system composed of ELKOs interacting with an Abelian gauge field via Pauli-like term. In all cases, we identified the minimal set of interactions that are required by a consistent renormalization group flow, and we discussed the possibility of constructing UV-complete trajectories based on asymptotic freedom. We used the functional renormalization group as a method of investigation.

On the structure of interactions of mass dimension one fermions: a functional renormalization group perspective

TL;DR

This work analyzes mass-dimension-one ELKO fermions through the functional renormalization group to map the structure of their interactions with scalars and gauge fields. By constructing a truncation that includes ELKO bilinears, scalar and gauge sectors, derivative Yukawa-like couplings, scalar portals, and four-fermion operators, the authors derive beta functions and anomalous dimensions, identifying conditions for UV completeness and asymptotic freedom. A key result is that derivative ELKO-scalar interactions do not generate non-derivative four-fermion terms due to a shift symmetry, while a scalar portal introduces a rich RG structure where UV-complete trajectories can exist, particularly for . When ELKO couples to a Pauli-like gauge term, additional four-fermion operators become dynamically required, and leading-order analysis suggests possible asymptotically free trajectories, though full stability beyond leading order remains to be established. Overall, the FRG approach reveals viable UV behaviors in these dark-sector couplings and sets the stage for further exploration of gravity–matter interplay and phenomenological implications of ELKO dark matter.

Abstract

In this paper, we provide the first systematic investigation of renormalization group properties of mass dimension one fermions described by ELKO spinors. By construction, ELKOs must be neutral under any Standard Model charge, therefore, providing a natural candidate for dark matter. We consider two versions of scalar-ELKO systems: the first characterized by a derivative Yukawa-like interaction, while the second involves ELKO four-fermion interactions as well as a scalar-ELKO portal. We also considered a system composed of ELKOs interacting with an Abelian gauge field via Pauli-like term. In all cases, we identified the minimal set of interactions that are required by a consistent renormalization group flow, and we discussed the possibility of constructing UV-complete trajectories based on asymptotic freedom. We used the functional renormalization group as a method of investigation.
Paper Structure (14 sections, 82 equations)

This paper contains 14 sections, 82 equations.

Table of Contents

  1. Introduction
  2. Methodology and setup
  3. Brief introduction to the functional renormalization group
  4. Defining the setup
  5. ELKO interacting with scalar fields
  6. Derivative Yukawa-like interaction
  7. Scalar-ELKO portal and four-fermion self-interactions
  8. Leading order flow for $N_\text{E}=1$
  9. Leading order flow for $N_\text{E}\geq 2$
  10. ELKO interacting with a gauge field via Pauli-like interaction
  11. The necessity of extra four-fermion channels
  12. The possibility of asymptotically free trajectories
  13. Final remarks
  14. Leading order flows around a free fixed-point