The theory of local mass dimension one fermions of spin one half

TL;DR

This paper develops a consistent quantum theory for spin one-half fermions with mass dimension one, resolving previous issues of non-locality and Lorentz violation, and explores their interactions and implications for dark matter and lepton-number violation.

Contribution

It provides the first local, Lorentz-invariant quantum framework for mass dimension one fermions, clarifying their duals and field adjoints, and investigates their interactions with the Standard Model.

Findings

Resolved non-locality and Lorentz violation issues

Established consistent interactions with Higgs and neutrinos

Identified potential for dark matter and lepton-number violation

Abstract

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 [JCAP 2005, PRD 2005]. In the decade that followed a significant number of groups explored intriguing mathematical and physical properties of the new construct. However, the formalism suffered from two troubling features, that of non-locality and a subtle violation of Lorentz symmetry. Here, we trace the origin of both of these issues to a hidden freedom in the definition of duals of spinors and the associated field adjoints. In the process, for the first time, we provide a quantum theory of spin one-half fermions that is free from all the mentioned issues. The interactions of the new fermions are restricted to dimension-four quartic self interaction, and also to a dimension-four coupling with the Higgs. A generalised Yukawa coupling of the new fermions with neutrinos provides an hitherto unsuspected source of lepton-number violation. The new fermions thus present a first-principle dark matter partner to Dirac fermions of the standard model of high energy physics with contrasting mass dimensions -- that of three halves for the latter versus one of the former without mutating the statistics from fermionic to bosonic.