Dark matter: A spin one-half fermion field with mass dimension one?

Abstract

We report an unexpected theoretical discovery of a spin one half matter field with mass dimension one. It is based on a complete set of eigenspinors of the charge conjugation operator. Due to its unusual properties with respect to charge conjugation and parity it belongs to a non standard Wigner class. Consequently, the theory exhibits non-locality with (CP T ) 2 = −I. Its dominant interaction with known forms of matter is via Higgs, and with gravity. This aspect leads us to contemplate it as a first-principle candidate for dark matter.

The Theory of Local Mass Dimension One Fermions of Spin One Half

“…Global phases associated with these eigenspinors, and the pairing of these eigenspinors with the creation and annihilation operators, influence the Lorentz covariance and locality of the fields. This last observation, often ignored in textbooks, when coupled with the discovery of a freedom in defining spinorial duals accounts for removal of the non-locality and restoring of the Lorentz symmetry for the mass dimension one fermions of [1,2].…”

“…Associated with this prediction was the charge conjugation symmetry. 1 In 1937 Majorana introduced a new class of particles for which the particles and antiparticles were identical [13]. They were described by a field which equaled its charge conjugate.…”

“…About a decade ago the present author in collaboration with Daniel Grumiller presented an 'unexpected theoretical discovery' of spin one-half fermions with mass dimension one [1,2]. In the decade that followed a significant number of groups explored intriguing mathematical and physical properties of the new construct.…”

From Dirac spinor fields to eigenspinoren des ladungskonjugationsoperators

“…Also, the Lounesto classification of spinor fields is presented together with the definition of ELKO spinor fields, 1 showing that ELKO is indeed a flagpole spinor field with opposite ͑dual͒ helicities. 1,2,22 In Sec. IV the mapping from Dirac spinor fields to ELKO is widely investigated in detail.…”

“…Any invertible map that takes Dirac particles and leads to ELKO is also capable to make mass dimension transmutations, since DSFs present mass dimension 3 / 2, instead of mass dimension 1 associated with ELKO. The main physical motivation of this paper is to provide the initial prerequisites to construct a natural extension of the standard model ͑SM͒ in order to incorporate ELKO, and consequently a possible description of dark matter 1,2,6 in this context.…”