Invisible Higgs and Dark Matter

We investigate the possibility that a massive weakly interacting fermion simultaneously provides for a dominant component of the dark matter relic density and an invisible decay width of the Higgs boson at the LHC. As a concrete model realizing such dynamics we consider the minimal walking technicolor, although our results apply more generally. Taking into account the constraints from the electroweak precision measurements and current direct searches for dark matter particles, we find that such scenario is heavily constrained, and large portions of the parameter space are excluded.

💡 Research Summary

The paper investigates whether a single massive weakly interacting fermion can simultaneously account for the observed dark‑matter relic density and generate an invisible decay channel of the Higgs boson at the LHC. As a concrete realization the authors adopt the Minimal Walking Technicolor (MWT) framework, but they stress that the conclusions are applicable to any model featuring a Higgs‑portal fermionic dark‑matter candidate.

First, the authors introduce the theoretical motivation: an invisible Higgs branching ratio of order a few percent is still allowed by current LHC measurements, and a weakly interacting massive particle (WIMP) with a mass below the Higgs threshold can provide such a decay mode while also serving as a thermal relic. They then describe the MWT model in detail. The technicolor sector consists of an SU(2) gauge group with two Dirac fermion doublets. Confinement dynamically breaks electroweak symmetry, producing a composite scalar that mixes with the elementary Higgs doublet. A neutral technibaryon‑like fermion, denoted χ, emerges as a bound state and couples to the Higgs through a portal term −y χ̄ H χ. The effective Lagrangian therefore contains the Standard Model piece, the technicolor dynamics, and the portal interaction.

The relic‑density calculation follows the standard freeze‑out formalism. The thermally averaged annihilation cross‑section ⟨σv⟩ is dominated by s‑channel Higgs exchange into Standard Model fermions and gauge bosons. Matching the observed Ω_DM h² ≈ 0.12 fixes a relation between the coupling y and the dark‑matter mass m_χ. Typically, y ≈ 0.01–0.1 is required for m_χ in the 10 GeV–200 GeV range.

Next, the invisible Higgs width is computed. For m_χ < m_H/2 the decay H → χχ is kinematically allowed, with partial width
Γ(H→χχ) = (y² v²)/(8π m_H) √(1 − 4 m_χ²/m_H²).
Current LHC data constrain the invisible branching fraction to be below roughly 20 %, which translates into an upper bound on y for a given m_χ.

Electroweak precision observables (the S, T, U parameters) provide a powerful indirect test. The MWT sector typically yields a positive contribution to S, which must be kept within the experimental limit S = 0.00 ± 0.07. This forces the technifermion masses and the mixing angle between the composite and elementary Higgs to be tuned.

Direct‑detection experiments (XENON1T, LUX‑Zeplin, PandaX‑4T) constrain the spin‑independent χ‑nucleon scattering cross‑section, σ_SI ≈ (y² f_N² μ_N²)/(π m_H⁴). The most stringent limits are σ_SI ≲ 4 × 10⁻⁴⁷ cm² for m_χ ≈ 30 GeV, which again restricts y to the low‑10⁻² regime.

Combining all constraints, the authors perform a comprehensive scan over (m_χ, y). The viable region that simultaneously yields the correct relic density, respects the invisible‑Higgs bound, satisfies electroweak precision tests, and evades direct‑detection limits is found to be extremely narrow: roughly m_χ ≈ 50–70 GeV with y ≈ 0.01–0.03. Even this sliver is under pressure from the S‑parameter and upcoming direct‑detection upgrades.

The paper concludes that the scenario of a single fermionic WIMP providing both dark matter and an invisible Higgs decay is heavily constrained within the Minimal Walking Technicolor context. While modest parameter space remains, it is likely to be closed by near‑future precision measurements and next‑generation dark‑matter searches. The authors suggest that extensions—such as additional scalar mediators, alternative technicolor dynamics, or non‑thermal production mechanisms—might relax the tension, but the minimal setup examined here is essentially ruled out.