Mass dimension one fermions: Constructing darkness

Abstract

Let $\Theta$ be the Wigner time reversal operator for spin half and let $\varphi$ be a Weyl spinor. Then, for a left-transforming $\varphi$, the construct ${\zeta }_{\lambda }\Theta {\varphi }^{\ast }$ yields a right-transforming spinor. If instead, $\varphi$ is a right-transforming spinor, then the construct ${\zeta }_{\rho }\Theta {\varphi }^{\ast }$ results in a left-transforming spinor (${\zeta }_{\lambda ,\rho }$ are phase factors). This allows us to introduce two sets of four-component spinors. Setting ${\zeta }_{\lambda }$ and ${\zeta }_{\rho }$ to $\pm i$ renders all eight spinors as eigenspinor of the charge conjugation operator $C$ (called ELKO). This allows us to introduce two quantum fields. A calculation of the vacuum expectation value of the time-ordered product of the fields and their adjoints reveals the mass dimension of the fields to be one. Both fields are local in the canonical sense of quantum field theory. Interestingly, one of the fields is fermionic and the other bosonic. The mass dimension of the introduced fermionic fields and the matter fields of the Standard Model carry an intrinsic mismatch. As such, they provide natural darkness for the new fields with respect to the Standard Model doublets. The statistics and locality are controlled by a set of phases. These are explicitly given. Then we observe that in $p_{\mu }{p}^{\mu }$= m${}^2$, Dirac took the simplest square root of the 4 × 4 identity matrix $I$ (in $I\times$m${}^2$, while introducing ${\gamma }_{\mu }{p}^{\mu }$ as the square root of the left hand side of the dispersion relation), and as such he implicitly ignored the remaining fifteen. When we examine the remaining roots, we obtain additional bosonic and fermionic dark matter candidates of spin half. We point out that by early nineteen seventies, Dirac had suspected the existence of spin half bosons, in the same space as his fermions. This is interweaved with a detailed discussion of duals and adjoints. We study the fermionic self-interaction and interactions with a real scalar field. We show that a consistent interacting theory can be formulated using the ELKO adjoint up to one-loop thus circumventing the earlier problem of unitarity violation. We then undertake quantum field theoretic calculation that establishes the Newtonian gravitational interaction for a mass dimension one dark matter candidate. The report ends: (a) by studying the partition function and main thermodynamic properties of the mass dimension one fermionic field in the context of the dark matter halo of galaxies. For the Milky Way, the observational data of rotation curve fits quite well for a fermionic mass of about 23 eV; and (b) by introducing higher-dimensional ELKOs in braneworld scenario. After a brief introduction of some braneworld models, we review the localization of higher-dimensional ELKOs on flat and bent branes with appropriate localization mechanisms. We discuss the massless and massive Kaluza–Klein modes of ELKO fields on branes and give a comparison with other fields.