[Paper Review] More stringent constraints on the unitarised fermionic dark matter Higgs portal

S. Balaji, Archil Kobakhidze|arXiv (Cornell University)|Dec 28, 2018

Quantum and Classical Electrodynamics1 references4 citations

TL;DR

This paper applies K-matrix unitarisation to the fermionic Higgs portal dark matter model to resolve unitarity violations in effective field theory at high energies. It shows that unitarisation drastically reduces the required Higgs-dark matter coupling scale Λ, leading to the conclusion that the CP-conserving model is fully excluded by current direct detection experiments due to overproduced spin-independent scattering cross sections.

ABSTRACT

We revisit the simplest model of Higgs portal fermionic dark matter. The dark matter in this scenario is thermally produced in the early universe due to the interactions with the Higgs boson which is described by a non-renormalisable dimension-5 operator. The dark matter-Higgs scattering amplitude grows as $\propto \sqrt{s}$, signalling a breakdown of the effective description of the Higgs-dark matter interactions at large enough (compared to the mass scale $Λ$ of the dimention-5 operator) energies. Therefore, in order to reliably compute Higgs-dark matter scattering cross sections, we employ the K-matrix unitarisation procedure. To account for the desired dark matter abundance, the unitarised theory requires appreaciably smaller $Λ$ than the non-unitarised version, especially for dark matter masses around and below the Higgs resonance, $m_χ\lesssim 65$ GeV, and $m_χ\gtrsim $ few TeV. Consequently, we find that the pure scalar CP-conserving model is fully excluded by current direct dark matter detection experiments.

Motivation & Objective

• To address the breakdown of perturbative unitarity in the effective field theory description of fermionic Higgs portal dark matter at high energies.
• To improve the reliability of thermally produced dark matter relic abundance calculations by correcting overestimated annihilation cross sections from naive EFT.
• To re-evaluate direct detection constraints on the fermionic Higgs portal model using a unitarised scattering amplitude instead of truncated EFT.
• To determine whether the CP-conserving Higgs portal model remains viable after unitarisation, especially in light of recent direct detection limits.

Proposed method

• Apply the K-matrix unitarisation procedure to the tree-level scattering amplitude T₀, yielding the unitarised amplitude Tᵁ = T₀ / (1 - iT₀), ensuring unitarity is preserved at high energies.
• Use the unitarised Tᵁ to compute thermally averaged annihilation cross sections for dark matter relic density calculations, correcting the overestimation from naive EFT.
• Compute dark matter-nucleon spin-independent scattering cross sections using the unitarised amplitude, incorporating Higgs exchange and momentum-dependent form factors.
• Include contributions from Higgs invisible decays and Higgs-mediated processes to the full T-matrix in a 13-channel basis including hh, VV, and top/bottom/tau final states.
• Numerically evaluate the S-wave partial wave amplitude and cross sections using the unitarised T-matrix, accounting for resonance and high-energy behavior.
• Compare the unitarised results with non-unitarised EFT predictions and confront them with direct detection data from experiments like LUX and XENON1T.

Experimental results

Research questions

• RQ1 How does K-matrix unitarisation alter the required Higgs-dark matter coupling scale Λ to reproduce the observed dark matter relic density?
• RQ2 What is the impact of unitarisation on the spin-independent dark matter-nucleon scattering cross section in the fermionic Higgs portal model?
• RQ3 Does the CP-conserving fermionic Higgs portal model survive current direct detection constraints when unitarisation is properly applied?
• RQ4 How do the thermally averaged annihilation cross sections differ between unitarised and non-unitarised EFT treatments?
• RQ5 What is the role of high-energy scattering processes (e.g., χχ → hh, VV) in modifying the phenomenology of the model when unitarity is enforced?

Key findings

• The unitarised fermionic Higgs portal model requires significantly smaller Λ values than the non-unitarised version to reproduce the observed dark matter relic density, especially for mχ ≲ 65 GeV and mχ ≳ few TeV.
• The CP-conserving Higgs portal model is fully excluded by current direct detection experiments when unitarisation is applied, due to overproduced spin-independent scattering cross sections.
• The unitarised scattering amplitude grows as √s at high energies, but the K-matrix procedure prevents violation of unitarity and stabilizes the cross section at large energies.
• The thermally averaged annihilation cross section is substantially reduced in the unitarised framework compared to naive EFT, leading to a more accurate relic density calculation.
• The Higgs invisible decay width is modified by the unitarised dynamics, but the dominant constraint arises from direct detection, not Higgs invisible decay.