Narrow Results

It has been taken as granted that the observation of two independent mass-squared differences necessarily fixes the number of underlying mass eigenstates as three, and that the addition of a sterile neutrino provides an additional mass-squared difference. The purpose of this letter is to argue that if one considers a sterile neutrino component that belongs to the CP² = -𝟙 sector, then both of the stated claims are false. We also outline how the results reported here, when combined with the forthcoming MiniBooNE data and other experiments, can help settle the issue of the CP properties of the sterile neutrino; if such a component does indeed exist.

According to Ahluwalia and Grumiller, massive spin-half fields of mass-dimension one can be constructed using the eigenspinors of the charge-conjugation operator (Elko) as expansion coefficients. In this paper, we generalize their result by constructing quantum fields from higher-spin Elko. The kinematics of these fields are thoroughly investigated. Starting with the field operators, their propagators and Hamiltonians are derived. These fields satisfy the higher-spin generalization of the Klein–Gordon but not the Dirac equation. Independent of the spin, they are all of mass-dimension one and are thus endowed with renormalizable self-interactions. These fields violate Lorentz symmetry. The violation can be characterized by a non-Lorentz-covariant term that appears in the Elko spin-sums. This term provides a decomposition of the generalized higher-spin Dirac operator in the momentum space thus suggesting a possible connection between the mass-dimension one fields and the Lorentz-invariant fields.

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 generalizations. We find, although the fermions are of mass dimension one, the four-point fermionic self-interaction violates unitarity at high-energy so it cannot be a fundamental interaction of the theory. Using the optical theorem, we derive an explicit bound on energy for the fermion–scalar interaction. It follows that for the spin-half fermions, the demand of renormalizability and unitarity forbids four-point interactions and only allows for the Yukawa interaction. For fermions with spin $j>\frac{1}{2}$, they have no renormalizable 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 renormalizability. In the context of the Standard Model, these properties make the spin-half fermions natural dark matter candidates. Finally, we discuss the recent developments on the introduction of new adjoint and spinor duals which may allow us to circumvent the unitarity constraints on the interactions.

Assuming the validity of the general relativistic description of gravitation on astrophysical and cosmological length scales, we analytically infer that the Friedmann–Robertson–Walker cosmology with Einsteinian cosmological constant, and a vanishing spatial curvature constant, unambiguously requires a significant amount of dark matter. This requirement is consistent with other indications for dark matter. The same space–time symmetries that underlie the freely falling frames of Einsteinian gravity also provide symmetries which, for the spin one half representation space, furnish a novel construct that carries extremely limited interactions with respect to the terrestrial detectors made of the standard model material. Both the "luminous" and "dark" matter turn out to be residents of the same representation space but they derive their respective "luminosity" and "darkness" from either belonging to the sector with (CPT)² = +𝟙, or to the sector with (CPT)² = -𝟙.

We review how Elko arise as an extension of complex-valued four-component Majorana spinors. This is followed by a discussion that constrains certain elements of phase freedom. A proof is reviewed that unambiguously establishes that Elko, and for that matter the indicated Majorana spinors, cannot satisfy Dirac equation. They, however do, as they must, satisfy spinorial Klein–Gordon equation. We then introduce a quantum field with Elko as its expansion coefficients and show that it is causal, satisfies Fermi statistics, and then refer to the existing literature to remind that its mass dimension is one. We conclude by providing an up-to-date bibliography on the subject.

If dark matter exists in the form of ultralight fermionic and bosonic species, then (a) it can accelerate evaporation of astrophysical black holes to the extent that their lifetimes can be reduced to astronomical time scales,^a and (b) if there are extremely large number of such species it has the potential to solve the hierarchy problem [H. Davoudiasl, P. B. Denton and D. A. McGady, Phys. Rev. D 103 (2021) 055014; G. Dvali, Fortschr. Phys. 58 (2010) 528]. Here, we put forward a proposal that darkness of many of these new particles is natural, and in addition, the net zero point energy of the fermions exactly cancels that coming from the new bosons. The needed fermion–boson equality, and matching the fermion–boson degrees of freedom, comes about naturally. A very direct argument that allows the departure from the spin–statistics theorem is presented.

This happens in two steps: first, the relatively rapid evaporation of the ultralight particles, and the second slower one associated with a hundred or so ‘heavier’ particles of the standard model.

Following the unexpected theoretical discovery of a mass dimension one fermionic quantum field of spin one half, we now present first results on two local versions. The Dirac and Majorana fields of the standard model of particle physics are supplemented by their natural counterparts in the dark matter sector. The possibility that a mass dimension transmuting symmetry may underlie a new standard model of particle physics is briefly suggested.

This article will provide the reader a short introduction to dark spinors, which are ELKO spinors, eingenspinors of the charge conjugation operator, applied to dark matter/energy.