[Paper Review] Unitarity Constraints on Higgs Portals

Devin G. E. Walker|arXiv (Cornell University)|Oct 3, 2013

Dark Matter and Cosmic Phenomena3 citations

TL;DR

This paper derives unitarity and perturbativity constraints on Higgs portal dark matter models, showing that the mediator Higgs boson mass is bounded at 3 TeV (fermion-only annihilation) and 14.2 TeV (fermion and Higgs exchange), with dark symmetry breaking vevs constrained to 2.4 and 12 TeV, respectively. These bounds significantly reduce viable parameter space and imply future colliders like the ILC or VLHC are essential to test the mechanism.

ABSTRACT

Dark matter that was once in thermal equilibrium with the Standard Model is generally prohibited from obtaining all of its mass from the electroweak phase transition. This implies a new scale of physics and mediator particles to facilitate dark matter annihilation. In this work, we focus on dark matter that annihilates through a generic Higgs portal. We show how partial wave unitarity places an upper bound on the mass of the mediator (or dark) Higgs when its mass is increased to be the largest scale in the effective theory. For models where the dark matter annihilates via fermion exchange, an upper bound is generated when unitarity breaks down around 8.5 TeV. Models where the dark matter annihilates via fermion and higgs boson exchange push the bound to 45.5 TeV. We also show that if dark matter obtains all of its mass from a new symmetry breaking scale that scale is also constrained. We improve these constraints by requiring perturbativity in the Higgs sector up to each unitarity bound. In this limit, the bounds on the dark symmetry breaking vev and the dark Higgs mass are now 2.4 and 3 TeV, respectively, when the dark matter annihilates via fermion exchange. When dark matter annihilates via fermion and higgs boson exchange, the bounds are now 12 and 14.2 TeV, respectively. The available parameter space for Higgs portal dark matter annihilation is outlined. We also show how the bounds are improved if Higgs portal dark matter is only a fraction of the observed relic abundance. Finally, we discuss how to apply these arguments to other dark matter scenarios and discuss prospects for direct detection and future collider searches. If the Higgs portal is responsible for dark matter annihilation, planned direct detection experiments will cover almost all the parameter space. The ILC and/or VLHC, however, is needed to establish the Higgs portal mechanism.

Motivation & Objective

• To derive theoretical upper bounds on the mass of a dark Higgs mediator in Higgs portal dark matter models using unitarity and perturbativity constraints.
• To constrain the scale of new physics responsible for dark matter mass, particularly the dark Higgs vacuum expectation value (vev).
• To map the viable parameter space for Higgs portal dark matter annihilation under unitarity and perturbativity conditions.
• To assess the reach of direct detection experiments and future colliders (ILC, VLHC) in probing the Higgs portal mechanism.
• To improve existing bounds by incorporating perturbativity in the Higgs sector up to the unitarity limit.

Proposed method

• Applies partial wave unitarity to scattering amplitudes involving the SM Higgs and dark Higgs, identifying when unitarity is violated at high energies.
• Implements a parameter scan over Higgs portal couplings, mixing angles, and mediator masses to identify unitarity-violating regions.
• Imposes perturbativity constraints on the Higgs sector up to the unitarity bound, ensuring the theory remains weakly coupled.
• Uses the measured relic abundance to fix the mixing angle between SM and dark Higgses, translating unitarity bounds into mass and vev limits.
• Combines constraints from electroweak precision observables (S and T parameters) and Higgs signal strength measurements (μγγ+ZZ) to restrict the mixing angle.
• Evaluates direct detection cross sections and forecasts sensitivity of upcoming experiments based on the constrained parameter space.

Experimental results

Research questions

• RQ1 What is the maximum allowed mass of a dark Higgs mediator in Higgs portal dark matter models before unitarity is violated?
• RQ2 How do perturbativity constraints in the Higgs sector refine the upper bounds on the dark Higgs mass and dark vev?
• RQ3 How does the inclusion of Higgs exchange in dark matter annihilation processes affect the unitarity bounds compared to fermion-only annihilation?
• RQ4 To what extent does the observed Higgs signal strength (μγγ+ZZ) constrain the mixing angle between the SM and dark Higgs?
• RQ5 Can direct detection experiments within the next decade cover the remaining viable parameter space for Higgs portal dark matter?

Key findings

• For dark matter annihilating via fermion exchange alone, the unitarity bound on the dark Higgs mass is 8.5 TeV, reduced to 3 TeV when perturbativity is imposed.
• When both fermion and Higgs exchange contribute to annihilation, the unitarity bound rises to 45.5 TeV, but perturbativity reduces it to 14.2 TeV.
• The dark Higgs vacuum expectation value (vev) is constrained to 2.4 TeV (fermion-only annihilation) and 12 TeV (with Higgs exchange), under perturbativity.
• The mixing angle between the SM and dark Higgs is restricted to cosθ ∈ [1/√2, ≲1] based on current Higgs signal strength data (μγγ+ZZ ∈ [0.58, 2.15] at 95% c.l.).
• Direct detection experiments planned in the next decade are expected to cover nearly all of the remaining viable parameter space for Higgs portal dark matter.
• The ILC and/or VLHC are necessary to definitively establish the Higgs portal mechanism, as they can probe the high-scale physics beyond the reach of direct detection.