Scotoseesaw mechanism from a $Z_3$ symmetry of matter

TL;DR

This paper introduces a novel $Z_3$ symmetry-based mechanism linking neutrino mass generation and dark matter stability, utilizing the center of QCD, with potential extensions to $U(1)_{B-L}$ gauge symmetry.

Contribution

It proposes a $Z_3$ symmetry framework that unifies neutrino mass mechanisms and dark matter stability through the QCD center, introducing the scotoseesaw concept.

Findings

Neutrino masses are generated via a $Z_3$-based scotoseesaw mechanism.

Dark matter stability is achieved through the $Z_3$ symmetry, though relic density is not addressed.

Extension to $U(1)_{B-L}$ can resolve relic density and detection issues.

Abstract

We show that the neutrino mass generation and the dark matter stability can be governed by the center of the QCD group, which is a $Z_3$ group. Three right-handed neutrinos $N_{1,2,3R}$ transform under $Z_3$ as $1,w,w^2$, where $w=e^{i2\pi/3}$ is the cube root of unity, and they couple to usual lepton doublets via the usual Higgs doublet $H$ and two new scalar doublets $\eta,\chi$, which transform under $Z_3$ as $1,w^2,w$, respectively. This leads to a scotoseesaw mechanism in which the seesaw and scotogenic neutrino mass generations are induced by the Majorana $N_{1R}$ mass and the Dirac $N_{2,3R}$ mass, respectively. Although the lightest of the $Z_3$ fields is stabilized, responsible for dark matter, the model lacks an explanation for relic density and/or direct detection. The issue can be solved in a $U(1)_{B-L}$ gauge completion of the model, for which the center of the QCD group is isomorphic to $Z_3=\{1,T,T^2\}$ for $T=w^{3(B-L)}$.