Implications of a dark grand unification

TL;DR

This work proposes a dark grand unification framework based on $E_6$ that unifies dark and normal matter through a sequence of symmetry breakings. A trinification residual theory houses a built-in matter parity that stabilizes dark matter and facilitates neutrino mass generation via a canonical seesaw, while embedding in a larger GUT structure. The trinification can descend to a novel universal $3-3-1-1$ model at the TeV scale, which is family universal and predictive, featuring a rich set of dark matter candidates including a vector doublet $A_7$ whose relic density is fixed by a resonance with a heavy scalar $H_1$. Precision electroweak and collider constraints push the new states to the TeV range, yielding distinctive signatures at LEP II and the LHC and offering viable direct-detection prospects for TeV-scale dark matter.

Abstract

Given that dark matter and normal matter are nontrivially unified in a grand unified theory, called dark grand unification, we derive novel residual theories at low energy explaining dark matter and neutrino mass. The first chain of which is $E_6\to SU(3)_C\otimes SU(3)_L\otimes SU(3)_R$, which contains a matter parity by itself stabilizing a dark matter candidate and producing neutrino mass via a seesaw. The second chain is $\mathrm{Trinification}\to SU(3)_C \otimes SU(3)_L\otimes U(1)_X\otimes U(1)_N$, which results in a novel family-universal 3-3-1-1 model, opposite to the normal 3-3-1-1 (or corresponding 3-3-1) model. Surprisingly, it is a variant of both minimal 3-3-1 model and 3-3-1 model with right-handed neutrinos since both $e_R$ and $ν_R$ are located at the bottoms of lepton triplets. Since this universal 3-3-1-1 model is properly embedded in the trinification, the above matter parity works governing dark matter stability as well as suppressing unwanted fermion mixings. Further, neutrino masses are naturally generated by a canonical seesaw combined with a scotogenic scheme.

Figures (7)

• Figure 1: Radiative corrections of the dark gauge/Higgs fields to the neutrino mass.
• Figure 2: Radiative contribution to Majorana $N_L$ mass.
• Figure 3: The mixing parameters $\mathcal{E}_{1,2}$ and the $\rho$-parameter deviation $\Delta \rho$ contoured according to the current limits as functions of $v,w$ for $\kappa=1$, 3, and 6 GeV.
• Figure 4: Annihilation processes of the doublet vector dark matter $A_7$ to the standard model particles which set the relic abundance.
• Figure 5: Doublet vector dark matter abundance plotted as a function of its mass, where the horizontal dashed line is measured by experiment pdg.