Light Dark Matter, Naturalness, and the Radiative Origin of the Electroweak Scale

TL;DR

This work addresses the naturalness problem by exploring classically scale-invariant extensions of the SM in which the Higgs mass arises through a Coleman-Weinberg-like mechanism in a dark sector that communicates with the SM via a Higgs portal. The authors construct a concrete model with SU(2)_X×U(1)_X gauge symmetry, a dark scalar, and fermionic states that yield TeV-scale dark matter and a long-range dark force, while enforcing vanishing mass parameters at the Planck scale and achieving vacuum stability up to that scale. They show that the dark sector dynamics generate electroweak symmetry breaking and constrain the dark scalar to lie in the 140–220 GeV range with a Higgs–dark-scalar mixing that reduces SM Higgs couplings and opens invisible Higgs decays; they also compute DM relic densities, direct-detection cross sections (below current limits but within reach of LZ), and dark-photon effects on N_eff. The framework yields distinctive collider and astroparticle signatures, including a detectable dark scalar at the LHC, invisible Higgs decays, and a multi-component dark matter sector with potential implications for galaxy structure and early-universe cosmology, offering a concrete path to test the radiative origin of the electroweak scale.

Abstract

We study classically scale invariant models in which the Standard Model Higgs mass term is replaced in the Lagrangian by a Higgs portal coupling to a complex scalar field of a dark sector. We focus on models that are weakly coupled with the quartic scalar couplings nearly vanishing at the Planck scale. The dark sector contains fermions and scalars charged under dark SU(2) x U(1) gauge interactions. Radiative breaking of the dark gauge group triggers electroweak symmetry breaking through the Higgs portal coupling. Requiring both a Higgs boson mass of 125.5 GeV and stability of the Higgs potential up to the Planck scale implies that the radiative breaking of the dark gauge group occurs at the TeV scale. We present a particular model which features a long-range abelian dark force. The dominant dark matter component is neutral dark fermions, with the correct thermal relic abundance, and in reach of future direct detection experiments. The model also has lighter stable dark fermions charged under the dark force, with observable effects on galactic-scale structure. Collider signatures include a dark sector scalar boson with mass < 250 GeV that decays through mixing with the Higgs boson, and can be detected at the LHC. The Higgs boson, as well as the new scalar, may have significant invisible decays into dark sector particles.

Figures (6)

• Figure 1: Vacuum stability properties in the $m_s$-$\sin\alpha$ plane. In the shaded region the Higgs quartic is positive up to the Planck scale. Between the two dashed contours the Higgs quartic touches zero close to the Planck scale within $2\sigma$. The dotted lines in the unstable region show the scale at which the Higgs quartic runs negative. The solid lines indicate contours of constant scalar vev, $w$. Note, that large mixing angles $\sin\alpha \gtrsim 0.5$ are phenomenologically strongly constrained by collider bounds, see Section \ref{['sec:higgs']}.
• Figure 2: The renormalization group evolution of the gauge couplings, the Yukawa couplings and the scalar quartic couplings for one example parameter point in the considered model that leads to an almost flat scalar potential at the Planck scale.
• Figure 3: Top: the invisible branching ratio of the Higgs boson as a function of the charged dark fermion mass, for example choices of the scalar mixing angle. Bottom: the scalar signal strength into SM particles as function of the charged dark fermion mass for example choices of the scalar mixing angle. The scalar mass is fixed to $m_s = 140$ GeV in the left and $m_s = 180$ GeV in the right plot.
• Figure 4: Feynman diagrams corresponding to the dominant processes contributing to dark matter annihilation (a), (b), and (c), as well as direct detection (d). In the case of annihilation into dark photons (a) an additional crossed diagram is not shown.
• Figure 5: The relic density of the light neutral dark fermion species as a function of its mass. In the left (right) plot, the $Z^\prime$ mass is fixed to $m_{Z^\prime} = 1 (2)$ TeV.