Constraints to the inert doublet model of dark matter with very high-energy gamma-rays observatories

We investigate the constraints on the Inert Doublet Model (IDM), a minimal extension of the Standard Model of Particle Physics featuring a scalar dark matter candidate, using data from recent and future gamma-ray observatories. The relevance of the model for indirect searches of dark matter stems from two key features: first, in the high-mass regime, IDM can achieve the correct dark matter relic abundance for masses between approximately 500 GeV and 25 TeV, aligning perfectly with the energy sensitivity of Imaging Atmospheric Cherenkov Telescopes. Second, this regime is dominated by co-annihilation processes, which elevate the thermal-relic velocity-weighted annihilation cross-section to the range of 0.5 $-$ 1.0$\times 10^{-25}$ cm$^3$ s$^{-1}$, thereby enhancing the potential gamma-ray signal from dark matter annihilation. Analyzing recent H.E.S.S. observations of the Galactic Center region, we find that dark matter particle masses within the 1 to 8 TeV range are excluded by current data. Furthermore, we project that the Cherenkov Telescope Array Observatory (CTAO) will comprehensively probe the remaining viable parameter space of the IDM. Our findings are further examined in the context of the most recent theoretical constraints, collider searches, and direct detection results from the LUX-ZEPLIN experiment.

💡 Research Summary

This paper presents a comprehensive study of the Inert Doublet Model (IDM) in the high‑mass regime (500 GeV – 25 TeV) using very‑high‑energy (VHE) gamma‑ray observations. The IDM extends the Standard Model by adding a second Higgs doublet that is odd under a Z₂ symmetry, rendering the lightest neutral component (usually denoted H) stable and a viable dark‑matter (DM) candidate. The model contains seven parameters; after fixing the SM Higgs mass and vacuum expectation value, four physical parameters remain: the DM mass m_H, the mass splittings Δ⁺ and Δ⁰ between H and its charged (H⁺) and pseudoscalar (A) partners, and the coupling λ₃₄₅ that controls the Higgs‑portal interaction.

Two distinct DM regimes exist. The low‑mass region (m_H < m_W) is already strongly constrained by LHC searches and direct‑detection experiments, so the paper focuses on the high‑mass region where co‑annihilation dominates. When Δ⁺, Δ⁰ ≲ 10 GeV, the three inert particles freeze out together, and the effective annihilation cross‑section ⟨σv⟩ is boosted to 0.5 – 1.0 × 10⁻²⁵ cm³ s⁻¹, well above the canonical thermal relic value. This enhancement makes the gamma‑ray flux from DM annihilation in the Galactic Center (GC) potentially observable with Imaging Atmospheric Cherenkov Telescopes (IACTs).

The authors performed a two‑step scan of the IDM parameter space. First, a broad random scan over 0 < λ₃₄₅ < 2π, 300 GeV < m_H < 30 TeV, and 0.5 GeV < Δ⁺, Δ⁰ < 10 GeV was subjected to theoretical constraints (vacuum stability, perturbative unitarity, inertness) and the Planck relic‑density measurement (Ωh² = 0.1200 ± 0.0012). MicrOMEGAs 5.3.35 was used to compute the relic density and co‑annihilation rates. In a second pass, points that also satisfied the latest LUX‑ZEPLIN (LZ) spin‑independent scattering limits were retained for indirect‑detection analysis.

For indirect detection, the gamma‑ray flux is expressed as dΦ/dE = ⟨σv⟩/(8π m_H²) × J × ∑_i B_i dN_i/dE, where the J‑factor encodes the line‑of‑sight integral of the DM density squared. The authors adopt a cuspy Einasto profile for the Milky Way halo (ρ_s = 0.079 GeV cm⁻³, r_s = 20 kpc, α = 0.17) and note that J‑factor uncertainties can reach an order of magnitude, directly propagating to the limits.

The H.E.S.S. Inner Galaxy Survey data were analyzed with a two‑dimensional (energy and spatial) binned likelihood method. Full annihilation spectra for each IDM point, generated by micrOMEGAs and CalcHEP, were convolved with the instrument response functions (effective area, energy dispersion) to obtain expected counts. The test statistic TS = −2 ln L(⟨σv⟩)/L(⟨σv⟩ = 0) was used to derive 95 % C.L. upper limits on ⟨σv⟩. The result is that IDM masses between roughly 1 TeV and 8 TeV are excluded, as the required cross‑section lies above the H.E.S.S. sensitivity.

Looking ahead, the authors project the performance of the Cherenkov Telescope Array Observatory (CTAO). Using the latest publicly available CTA IRFs and the same 2‑D likelihood framework, they estimate that a 100‑hour observation of the GC would probe ⟨σv⟩ down to the thermal‑relic level across the entire 0.5 TeV – 25 TeV mass range. In particular, for masses above 8 TeV CTAO improves upon H.E.S.S. limits by a factor of ~5, effectively covering the remaining viable IDM parameter space.

The paper also discusses the impact of Sommerfeld enhancement, which can further increase ⟨σv⟩ for multi‑TeV DM when electroweak gauge bosons act as light mediators. While the authors adopt tree‑level cross‑sections as a conservative baseline, they provide estimates showing that including Sommerfeld effects would only strengthen the exclusion power of both H.E.S.S. and CTAO.

Finally, the authors combine indirect‑detection limits with the LZ direct‑detection constraints and collider bounds (electroweak precision tests, Higgs signal strengths, LEP limits). The combined analysis shows that current H.E.S.S. data already eliminate a substantial fraction of the high‑mass IDM, LZ removes points with large λ₃₄₅, and CTAO is poised to close the remaining gap. This work is distinguished by using the full IDM annihilation spectra rather than simplified single‑channel assumptions, and by applying a realistic 2‑D likelihood analysis to both existing and future gamma‑ray data.

In summary, the study demonstrates that VHE gamma‑ray telescopes are powerful probes of the IDM high‑mass regime. Present H.E.S.S. observations exclude DM masses from 1 to 8 TeV, and the upcoming CTAO will be capable of testing the entire viable mass window up to 25 TeV, complementing collider and direct‑detection searches and potentially providing a definitive test of the Inert Doublet Model.