Where are ELKO Spinor Fields in Lounesto Spinor Field Classification?

Abstract

This paper proves that from the algebraic point of view 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. The main algebraic difference between ELKO and Majorana spinor fields is that in the first case their respective two 2-component spinor fields present opposite helicities, while in the second case the helicity associated with the two 2-component of ELKO are not imposed to be flipped. The proof of our statement is based on Lounesto general classification of all spinor fields, according to the relations and values taken by their associated bilinear covariants, and can shed some new light on the algebraic investigations concerning dark matter.