A minimal model for ${\rm SU}(N)$ vector dark matter

TL;DR

This work introduces a minimal classically conformal extension of the Standard Model with a hidden SU$(N)_D$ gauge sector and a bi-adjoint scalar that communicates with the SM via a Higgs portal. Electroweak symmetry breaking is generated radiatively in the hidden sector through the Coleman–Weinberg mechanism, giving degenerate massive vector bosons whose stability is protected by a residual SO$(N)$ symmetry, yielding vector dark matter. A detailed two-parameter scan over $N=2,3,4$ under collider, Planck-scale stability, perturbativity, relic abundance, and direct-detection constraints shows viable regions for $N=2$ and $N=3$ (but not $N=4$), with a predictively heavy Higgs state $h_2$ whose discovery at LHC Run II could confirm the model or rule out $N=3$. The direct-detection cross sections are well below current bounds, while the dark-matter relic density can be accommodated for surviving points; Run II collider data are expected to significantly probe the heavy-Higgs sector and the remaining parameter space.

Abstract

We study an extension of the Standard Model featuring a hidden sector that consists of a new scalar charged under a new SU$(N)_D$ gauge group, singlet under all Standard Model gauge interactions, and coupled with the Standard Model only via a Higgs portal. We assume that the theory is classically conformal, with electroweak symmetry breaking dynamically induced via the Coleman-Weinberg mechanism operating in the hidden sector. Due to the symmetry breaking pattern, the SU$(N)_D$ gauge group is completely Higgsed and the resulting massive vectors of the hidden sector constitute a stable dark matter candidate. We perform a thorough scan over the parameter space of the model at different values of $N=2$, $3$, and $4$, and investigate the phenomenological constraints. We find that $N=2,3$ provide the most appealing model setting in light of present data from colliders and dark matter direct search experiments. We expect a heavy Higgs to be discovered at LHC by the end of Run II or the $N=3$ model to be ruled out.

Figures (4)

• Figure 1: Portal coupling as a function of the dark gauge coupling for $N=2$ (left panel) and $N=3$ (right panel) in color for stable and perturbative data points, with color code function of $c_\alpha=\cos\alpha$ as given by the bar in the left panel. The data points that also produce an experimentally viable dark matter abundance are shown in black, and the gray points represent the unstable and/or non-perturbative data points which though feature a viable coupling coefficient $c_\alpha$.
• Figure 2: Dark scalar and dark vector masses for all the data points satisfying the LHC constraint, for $N=2$ (left panel) and $N=3$ (right panel), in color for those that also feature stability and perturbativity, in black those that satisfy the dark matter abundance constraint as well, while the data points that do not satisfy neither of the last two constraints are in gray.
• Figure 3: Portal coupling vs dark gauge coupling (left panel) and dark scalar vs dark gauge masses (right panel) for $N=4$, in color for stable and perturbative data points, with a color code function of $c_\alpha$ as given by the bar in the left panel, in black for data points that instead produce an experimentally viable dark matter abundance, and in gray for data points which satisfy only the LHC constraint on $c_\alpha$.
• Figure 4: CMS constraint (shaded region ruled out at 95%CL) on $s^2_\alpha=\sin^2\alpha$ in function of the heavy Higgs mass, together with the viable data points (in green those stable and with viable light Higgs couplings, and in black those that satisfy also DM constraints), for $N=2$ (left panel) and $N=3$ (right panel).