Dynamical dispersion relation for ELKO dark spinor fields

TL;DR

This paper investigates a mass generation mechanism for ELKO dark spinor fields within the VSR framework, revealing how exotic couplings and spin structure inequivalences lead to intrinsic mass without gauge shifts.

Contribution

It introduces a novel dynamical mass generation mechanism for ELKO dark spinors based on inequivalent spin structures and their coupling to scalar field topological solutions within VSR.

Findings

Identifies an additional term in the Dirac operator for dark spinors.

Demonstrates mass generation without gauge shift absorption.

Proposes effective scenarios with dark spinor and scalar field couplings.

Abstract

An intrinsic mass generation mechanism for exotic ELKO dark matter fields is scrutinized, in the context of the very special relativity (VSR). Our results are reported on unraveling inequivalent spin structures that educe an additional term on the associated Dirac operator. Contrary to the spinor fields of mass dimension 3/2, this term is precluded to be absorbed as a shift of some gauge vector potential, regarding the equations for the dark spinor fields. It leads to some dynamical constraints that can be intrinsically converted into a dark spinor mass generation mechanism, with the encoded symmetries maintained by the VSR. The dynamical mass is embedded in the VSR framework through a natural coupling to the kink solution of a \lambda \phi^{4} theory for a scalar field \phi. Our results evince the possibility of novel effective scenarios, derived from exotic couplings among dark spinor fields and scalar field topological solutions.