Eur. Phys. J. C (2025) 85: 473
https://doi.org/10.1140/epjc/s10052-025-14206-w

Regular Article - Theoretical Physics

Scotoseesaw mechanism from a $Z_3$ symmetry of matter

Phenikaa Institute for Advanced Study, Phenikaa University, Yen Nghia, Ha Dong, 100000, Hanoi, Vietnam

^a dong.phungvan@phenikaa-uni.edu.vn

Received: 16 January 2025
Accepted: 21 April 2025
Published online: 30 April 2025

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 $T=w^{3(B-L)}$.