Higgs vacuum stability from the dark matter portal

TL;DR

The paper addresses the Higgs vacuum instability by embedding the Standard Model in classically scale-invariant extensions with hidden Coleman-Weinberg sectors. Through detailed RG analyses and constraints from LHC Higgs data, it finds that models without a real singlet struggle to stabilize the Higgs potential, whereas singlet-extended CSI ESMs stabilise the Higgs vacuum across viable parameter spaces. The work also explores dark matter phenomenology, showing that these models naturally host two DM candidates (a singlet scalar and, in non-Abelian cases, a hidden gauge boson), and computes relic densities and direct-detection prospects. Overall, the CSI ESM framework offers a predictive link between electroweak scale generation, Higgs stability, and multi-component dark matter, with testable implications for future experiments.

Abstract

We consider classically scale-invariant extensions of the Standard Model (CSI ESM) which stabilise the Higgs potential and have good dark matter candidates. In this framework all mass scales, including electroweak and dark matter masses, are generated dynamically and have a common origin. We consider Abelian and non-Abelian hidden sectors portally coupled to the SM with and without a real singlet scalar. We perform a careful analysis of RG running to determine regions in the parameter space where the SM Higgs vacuum is stabilised. After combining this with the LHC Higgs constraints, in models without a singlet, none of the regained parameter space in Abelian ESMs, and only a small section in the non-Abelian ESM survives. However, in all singlet-extended models we find that the Higgs vacuum can be stabilised in all of the parameter space consistent with the LHC constraints. These models naturally contain two dark matter candidates: the real singlet and the dark gauge boson in non-Abelian models. We determine the viable range of parameters in the CSI ESM framework by computing the relic abundance, imposing direct detection constraints and combining with the LHC Higgs constraints. In addition to being instrumental in Higgs stabilisation, we find that the singlet component is required to explain the observed dark matter density.

Figures (11)

• Figure 1: RG evolution in the Standard Model. The Higgs self-coupling turns negative at $\mu \gtrsim 10^9$ GeV thus signalling that the SM Higgs potential becomes unstable below the Planck scale. In this and all other Figures we use $M_t =173.1$ GeV.
• Figure 2: RG evolution in CSI $\mathrm{E}$SM theories with (a) $\mathrm{E}= \mathrm{U}(1)_{\bf B-L}$, (b) $\mathrm{E}=\mathrm{U}(1)_{\bf B-L} + s(x),$ and (c) $\mathrm{E}=\mathrm{SU}(2)_{ \mathrm{CW}}$. With these initial conditions the Higgs coupling $\lambda_H$ stays positive and satisfies the tree-level stability bound \ref{['treelst']}.
• Figure 3: Parameter space in the minimal U(1)$_{ \mathrm{CW}}\,\times$ SM classically scale invariant theory. The black wedge-shaped contour shows the region of the $(\lambda_{\rm P}, e_{ \mathrm{CW}})$ parameter space of the model where the Higgs potential is stabilised. The dotted lines represent contours of fixed values $\sin^2 \theta =$ 0.05, 0.1 and 0.2 of the Higgs mixing angle. Finally, the colour-coding indicates the mass of the second scalar $h_2$ in GeV.
• Figure 4: Parameter space of the U(1)$_{\bf B-L}\times$ SM theory showing the region where the Higgs potential is stabilised and the $\sin^2 \theta$ contours. The legend is the same as in Figure \ref{['U1Stab']}.
• Figure 5: Parameter space of the SU(2)$_{ \mathrm{CW}}\,\times$ SM theory showing the region where the Higgs potential is stabilised and the $\sin^2 \theta$ contours. The legend is the same as in Figure \ref{['U1Stab']}.