Dark symmetry implication for right-handed neutrinos

Abstract: We argue that the long-standing issues of neutrino mass and dark matter can be manifestly solved in a dark gauge symmetry $U(1)D$ that transforms nontrivially only for three right-handed neutrinos $\nu{1,2,3R}$ -- the counterparts of known left-handed neutrinos. This theory assigns $\nu_{1,2,3R}$ dark charge to be $D=0$, $-1$, and $+1$, respectively, in order for anomaly cancelation. Additionally, it imposes an inert Higgs doublet $\eta$ and two Higgs singlets $\xi,\phi$ with dark charge $D=+1$, $-1$, and $+2$, respectively. That said, the dark symmetry is broken by $\phi$ (by two units) down to a dark parity $P_D=(-1)^D$, for which $\nu_{2,3R}$ and $\eta,\xi$ are odd, whereas all other fields are even due to $D=0$. The lightest of these odd fields is stabilized by $P_D$, responsible for dark matter. Neutrino masses are generated by a scotoseesaw scheme, in which the seesaw part is mediated by $\nu_{1R}$, while the scotogenic part is mediated by $\nu_{2,3R}$, for which the hierarchy of atmospheric and solar neutrino mass splittings is explained.