The E6 route to multicomponent dark matter

TL;DR

This work embeds the SM inside $E_6$ and shows that a dark sector is automatically generated by the same fundamental multiplets, enabling a two-component dark matter scenario with a stable scalar $\eta$ and a metastable fermion $\chi$. The stability arises from a remnant discrete symmetry $Z_2$ (PD) that survives specific symmetry-breaking chains, while a hierarchical vev pattern places the dark states near the EW scale. DM interactions with the SM occur predominantly through the Higgs portal, and decays of the heavier DM component are suppressed by the unification and seesaw scales, ensuring compatibility with indirect-detection constraints. The viability of the framework is demonstrated across several maximal $E_6$ breaking routes with minimal scalar content and perturbative gauge coupling running up to the Planck scale, offering a testable path to connect neutrino physics, unification, and dark matter.

Abstract

We present a framework of dark- and visible-sector unification in the E6 embedding of the standard model. The demand for consistently getting the standard model leads to the existence of the dark-sector. We show that the hierarchy of vevs typifying unified models leads to multicomponent dark matter at the IR. The symmetry breaking itself categorises the matter content into dark- and visible-sector particles, the categorisation being uniform across different breaking chains. We discuss the stability of the dark matter particles and compare them to existing phenomenological models of dark matter. The central results follow from symmetry and hierarchy arguments. We present an indicative set of models of gauge coupling unification, to show that the framework can be embedded in realistic models of E6.

Figures (5)

• Figure 1: Symmetry breaking routes of $E_6$. We show only the non-abelian parts and drop the $U(1)$s. However, we indicate the number of broken generators by giving the ranks at each stage. We use a compact notation for the direct products of the $SU(N)$ symmetries, with MN representing $SU(M)\times SU(N)$.
• Figure 2: Hierarchy of scales in E6DM. The particles in Red are dark-sector scalars while those in Blue are dark-sector fermions. The ones in green are visible sector particles. In the text, we describe the masses of which particles are associated to symmetry breaking scales, which are fixed using the extended survival hypothesis, and which are (quasi-)free parameters. The scale extends from the masses of the light-neutrinos on the left to the Planck scale on the right. Between these two, are the EWSB scale, the unification scale ($X$ and $Y$ gauge bosons), and the intermediate rank breaking (neutrino seesaw) scale. The state $\phi$, the mass eigenstate corresponding to $s_8$, can vary over a range between the SM and the intermediate scales. The scale of $\phi$ is a parameter controlling the interaction strength between the LDSF and the SM Higgs. We describe the case where the LDSF and the LDSS are both at the EW scale. Other possibilities also exist.
• Figure 3: On the left we show the two body decay mode of the LDSS at tree level. On the top-row at right, we show the two one-loop diagrams leading to the decay of the LDSS to a neutrino (two-body) and to a neutrino and a photon (three-body). On the right bottom-row we show the $\xi^+$ mediated tree-level decay to a neutrino (three-body) and to a neutrino and a photon (four-body).
• Figure 4: Left: Partial decay lifetime for the channel $\eta\to \chi W^+ e^-$. We have plotted the lifetime as a function of $M_\eta$ for the different values of $M_\chi$ and the charged slepton mass is set to a value $M_{\xi^+}=(M_\eta + 100~\mathrm{GeV})$. Right: Partial decay lifetime for the channel $\eta\to \chi \nu_e e^+ e^-$. We have plotted the lifetime as a function of $M_\chi$ for a typical choice $M_\eta=300$ GeV and the charged slepton mass $M_{\xi^+}=350$ GeV using CalcHEPBelyaev:2012qa.
• Figure 5: A schematic of the two-component DM paradigm as obtained from the fundamental of $E_6$, E6DM. The lightest particles of the scalar and the fermionic dark-sectors, the LDSS and the LDSF respectively, are simultaneously the DM candidates. The lighter of the two is absolutely stable, while the heavier is metastable and decays to the lighter one through unification scale and seesaw scale suppressed operators. The lifetime of the metastable DM is safe from current bounds. Both the DM particles annihilate to the SM through marginal and irrelevant couplings with the SM Higgs. The two sectors can annihilate into each other through a unification scale and seesaw scale suppressed operator, which we ignore.