Classical scale invariance in the inert doublet model

TL;DR

The paper investigates whether the inert doublet model (IDM) can be embedded into a classically scale-invariant framework by linking the electroweak scale and dark matter to a hidden sector that breaks via the Coleman-Weinberg mechanism. A minimal hidden sector with a U(1)_CW gauge symmetry and a complex scalar Φ communicates a generated scale to the IDM through Higgs-portal couplings, producing mixing between the Coleman-Weinberg scalar and the SM Higgs. This setup introduces new DM annihilation channels (into the CW scalar and hidden gauge boson) and a new mediator for DM-nucleon scattering, altering relic-density calculations and direct-detection predictions relative to the ordinary IDM. RG analysis shows that high-scale validity up to the Planck scale is more restrictive in the CSI IDM, yielding tight bounds on couplings and DM mass (e.g., |λ_L|<0.13, |λ_P1|<0.012, M_H ≲ ~1.1 TeV) and highlighting phenomenological implications for current and future experiments. Overall, the work demonstrates a concrete CSI realization of the IDM with testable implications for direct detection and collider probes of the CW scalar.

Abstract

The inert doublet model (IDM) is a minimal extension of the Standard Model (SM) that can account for the dark matter in the universe. Naturalness arguments motivate us to study whether the model can be embedded into a theory with dynamically generated scales. In this work we study a classically scale invariant version of the IDM with a minimal hidden sector, which has a $U(1)_{\text{CW}}$ gauge symmetry and a complex scalar $Φ$. The mass scale is generated in the hidden sector via the Coleman-Weinberg (CW) mechanism and communicated to the two Higgs doublets via portal couplings. Since the CW scalar remains light, acquires a vacuum expectation value and mixes with the SM Higgs boson, the phenomenology of this construction can be modified with respect to the traditional IDM. We analyze the impact of adding this CW scalar and the $Z'$ gauge boson on the calculation of the dark matter relic density and on the spin-independent nucleon cross section for direct detection experiments. Finally, by studying the RG equations we find regions in parameter space which remain valid all the way up to the Planck scale.

Figures (5)

• Figure 1: Feynman diagrams for two of the new annihilation channels from adding a $U(1)_{\text{CW}}$ hidden sector to the inert doublet model. These contributions decrease the relic abundance in the classically scale invariant version of the IDM. Similar diagrams are also taken into account for coannihilations.
• Figure 2: Impact of adding a CW scalar in the calculation of the relic density, the introduction of a new annihilation into $h_{\text{\tiny CW}}$ means that the values for the relic density will be smaller, the effect becomes more relevant as we go to larger values of the DM mass $M_H$. The parameters we take are $\lambda_L\!=\!0$, $\lambda_2\!=\!0.15$, $e_{\text{\tiny CW}}\!=\!0.9$ and mass splittings $\Delta M_A\!=\!4$ GeV, $\Delta M_{H^{\pm}}\!=\!6$ GeV. We study three cases $\lambda_{\text{P1}}\!=\!0.001, 0.003$ and 0.005, which correspond to $M_{h_{\text{\tiny CW}}}\!=\!624, 360$ and 280 GeV, respectively. The light blue band corresponds to the measured dark matter relic abundance by the Planck collaboration to $2\sigma$Planck2015 .
• Figure 3: Spin-independent DM-nucleon cross section as a function of the DM candidate mass $M_H$. All points give the correct DM relic abundance from the latest Planck result to $2\sigma$. Left panel: Results for the ordinary IDM. Color coding corresponds to the RG analysis, points in light blue satisfy vacuum stability, perturbativity, and unitarity at the scale $\mu\!=\!m_t$. Right panel: Results for the for the CSI IDM, points in light blue satisfy all constraints up to the scale $\mu\!=\!\langle \phi \rangle$. In gray we show the points that do not satisfy condition \ref{['eq:laP1positive']}. In both plots points in dark blue are those that survive up to the Planck scale. We show current experimental limits from LUX LUX2013 (red line), future limits from LZ LZ (green line) and the neutrino coherent scattering limit NeutrinoScattering (black line).
• Figure 4: Left panel: Points in the IDM (high mass regime) that give the correct DM relic abundance from the latest Planck result to $2\sigma$, points in dark blue work well up to the Planck scale. Right panel: Points in the CSI IDM (high mass regime) that give the correct DM relic abundance from the latest Planck result to $2\sigma$, points in light blue satisfy all the constraints up to the scale $\mu\!=\!\langle \phi \rangle$ but develop a vacuum instability or a Landau pole before the Planck scale, points in dark blue satisfy all the constraints up to the Planck scale. In gray we show the unphysical points that do not survive up to $\mu\!=\!\langle \phi \rangle$, mainly due to condition \ref{['eq:laP1positive']}. We show in the $x$-axis the mass of the DM candidate $H$ and in the $y$-axis the quartic coupling $\lambda_L$.
• Figure 5: Plot of the portal couplings versus the DM mass $M_H$ for the same points as in Fig. \ref{['fig:lambdaL']}, same color coding. The upper limit on $\lambda_{\text{P1}}$ comes mainly from the experimental upper limit on the scalar mixing angle.