Symmetries and unitary interactions of mass dimension one fermionic dark matter

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.

20 pages, 5 figures

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Cited by in corpus (8)

• $\Lambda (t)$ cosmology induced by a slowly varying Elko field
• Localization of five-dimensional Elko spinors with non-minimal coupling on thick branes
• Further investigation of mass dimension one fermionic duals
• Unveiling Mapping Structures of Spinor Duals
• Fermionic degeneracy and non-local contributions in flag-dipole spinors and mass dimension one fermions
• Mass dimension one fermions and their gravitational interaction
• An alternative approach concerning Elko spinors and the hidden unitarity
• A note on hidden classes in spinor classification