From Dirac spinor fields to ELKO

TL;DR

This paper explores the algebraic and geometric relationship between Dirac and ELKO spinor fields, providing conditions for mapping between them to extend the Standard Model and better understand dark matter candidates.

Contribution

It establishes necessary and sufficient conditions for mapping Dirac spinors to ELKO, advancing the theoretical framework for incorporating mass dimension one spinors into particle physics.

Findings

Derived conditions for Dirac to ELKO mapping

Extended the Standard Model with ELKO spinors

Enhanced understanding of ELKO's properties and dark matter relevance

Abstract

Dual-helicity eigenspinors of the charge conjugation operator (ELKO spinor fields) belong, together with Majorana spinor fields, to a wider class of spinor fields, the so-called flagpole spinor fields, corresponding to the class (5), according to Lounesto spinor field classification based on the relations and values taken by their associated bilinear covariants. There exists only six such disjoint classes: the first three corresponding to Dirac spinor fields, and the other three respectively corresponding to flagpole, flag-dipole and Weyl spinor fields. This paper is devoted to investigate and provide the necessary and sufficient conditions to map Dirac spinor fields to ELKO, in order to naturally extend the Standard Model to spinor fields possessing mass dimension one. As ELKO is a prime candidate to describe dark matter, an adequate and necessary formalism is introduced and developed here, to better understand the algebraic, geometric and physical properties of ELKO spinor fields, and their underlying relationship to Dirac spinor fields.