Symmetries and unitary interactions of mass dimension one fermionic dark matter

TL;DR

This paper investigates the symmetries and interactions of mass dimension one fermionic dark matter fields derived from Elko, revealing that their self-interactions violate unitarity, thus constraining their possible interactions and supporting their role as dark matter candidates.

Contribution

It provides a detailed analysis of the symmetries and interaction constraints of mass dimension one fermions, showing that only Yukawa interactions are compatible with unitarity and renormalisability.

Findings

Four-point fermionic self-interactions violate unitarity at high energies.

Only Yukawa interactions are allowed for spin-half fermions.

Higher-spin fermions lack renormalisable or unitary interactions.

Abstract

The fermionic fields constructed from Elko have several unexpected properties. They satisfy the Klein-Gordon but not the Dirac equation and are of mass dimension one instead of three-half. Starting with the Klein-Gordon Lagrangian, we initiate a careful study of the symmetries and interactions of these fermions and their higher-spin generalisations. We find, although the fermions are of mass dimension one, the four-point fermionic self-interaction violates unitarity at high-energy. Therefore, it cannot be a fundamental interaction of the theory. It follows that for the spin-half fermions, the demand of renormalisability and unitarity forbids four-point interactions and only allows for the Yukawa interaction. For fermions with spin j>1/2, they have no renormalisable or unitary interactions. Since the theory is described by a Klein-Gordon Lagrangian, the interaction generated by the local $U(1)$ gauge symmetry which contains a four-point interaction, is excluded by the demand of renormalisability. In the context of the Standard Model, these properties make the spin-half fermions natural dark matter candidates.