⚛️ phenomenology

Dark matter in composite Higgs models with a scotogenic EFT

This paper proposes a class of Composite Higgs models with a fermionic UV completion that yields a scotogenic effective theory where a stable pseudo-Nambu-Goldstone boson serves as dark matter, demonstrating through a specific $\mathrm{SU}(6)/\mathrm{Sp}(6)$ example and MCMC analysis that spin-1 resonances are crucial for achieving the observed relic density and predicting distinct LHC signatures.

Original authors: Yu Chen, Werner Porod

Published 2026-07-17

📖 5 min read🧠 Deep dive

CC BY 4.0

Original authors: Yu Chen, Werner Porod

Original paper licensed under CC BY 4.0 (http://creativecommons.org/licenses/by/4.0/). ✨ This is an AI-generated explanation of the paper below. It is not written or endorsed by the authors. For technical accuracy, refer to the original paper. Read full disclaimer

Imagine the universe as a giant, invisible ocean. We can see the ships sailing on the surface—the stars, the planets, and us—but we know there is something massive and invisible swimming underneath, holding the ships together. This invisible stuff is called Dark Matter. Scientists have been trying to figure out what it is for decades, but it's like trying to catch a ghost with a net; we know it's there because of how it pulls on things, but we can't see it or touch it.

To understand this paper, you need to know two big ideas. First, there's the Standard Model, which is like the periodic table for the tiny particles that make up everything we can see. But this table has holes in it. It doesn't explain why some particles are heavy and others are light, or why the universe has so much Dark Matter. Second, there's the Hierarchy Problem. Think of the Higgs boson (the particle that gives other particles mass) as a very delicate soap bubble. In the universe, there are forces that should pop that bubble instantly, making it heavy and unstable. Yet, it stays light and floaty. Why?

This paper explores a wild idea to fix these holes: what if the Higgs boson isn't a fundamental bubble at all, but a composite object? Imagine it's not a single marble, but a tightly bound cluster of smaller, invisible marbles held together by a super-strong glue. This "glue" comes from a new, hidden world of particles that interact so strongly they form these clusters. The authors of this paper built a specific model using this idea and asked a crucial question: Could the leftovers from this new world be the Dark Matter we've been looking for?

The Story of the Invisible Twins

The authors, Yu Chen and Werner Porod, decided to build a "toy universe" based on a specific mathematical shape called SU(6)/Sp(6). In this universe, there are six types of "hyper-fermions" (let's call them hyper-particles) that are charged with a new, super-strong force. When the universe cooled down, these particles got stuck together, forming a condensate. This process broke the symmetry of the universe, creating a zoo of new particles.

Among these new particles, there are some that are "even" (friendly with our world) and some that are "odd" (secretive). The paper focuses on the "odd" ones. Because of a special rule in this model called a Z2 symmetry, the lightest "odd" particle cannot decay into anything else. It's immortal. It's stable. And because it doesn't interact with light, it's invisible. This makes it a perfect candidate for Dark Matter.

The model predicts four different types of these immortal, invisible particles. The authors wanted to see if any of them could explain exactly how much Dark Matter we see in the universe today. They used a powerful computer method called MCMC (Markov Chain Monte Carlo), which is like a super-smart robot that tries millions of different combinations of numbers (masses, forces, angles) to see which ones work.

The Findings: Three Out of Four

Here is what the robot found:

The Loser: One of the four candidates, a particle called $\Delta^0$ , was a total bust. No matter how the authors tweaked the numbers, this particle would annihilate itself too efficiently in the early universe. It would disappear almost completely, leaving far too little Dark Matter to match what we observe. The paper explicitly rules this one out as a viable explanation for our universe's Dark Matter.
The Winners: The other three candidates— $\eta_3$ , $\eta_4$ , and $\phi^0$ —were much more promising. The authors found specific regions in the "parameter space" (the map of all possible numbers) where these particles could survive in just the right amount to match the observed Dark Matter density.
The Secret Weapon: A major discovery in the paper is that spin-1 resonances play a huge role. Think of these as heavy, short-lived "force carriers" that are much heavier than the Dark Matter itself. The authors found that these heavy particles act like a bridge or a funnel. They help the Dark Matter particles annihilate each other at just the right rate. Without these heavy bridges, the math doesn't work. The paper suggests that these heavy particles are essential for getting the numbers right.
The Tightrope Walk: The authors also checked if these particles would be detected by experiments on Earth, like the LUX-ZEPLIN detector. They found that while there are still "safe zones" where the Dark Matter could hide, a large chunk of the possible options has already been ruled out by these experiments. The surviving candidates have to be quite heavy (around 500 GeV or more) and have very specific, weak interactions with normal matter to avoid being caught.

The Bottom Line

This paper doesn't claim to have found Dark Matter. Instead, it builds a detailed, mathematically consistent map of a specific type of "Composite Higgs" universe. It shows that in this specific universe, it is possible for Dark Matter to exist as a stable, invisible particle made of the leftovers of a new strong force.

The authors suggest that if our universe works this way, we should look for two things:

Heavy Spin-1 Resonances: Giant, heavy particles that might be created in high-energy collisions at the Large Hadron Collider (LHC).
Missing Energy: Events where particles collide and suddenly vanish, leaving behind a trail of "missing" energy, which would be the Dark Matter escaping the detector.

The paper concludes that while the idea is fascinating and mathematically sound, it's a tightrope walk. The Dark Matter candidates must be heavy, and the heavy resonances must exist to make the math work. If future experiments at the LHC or new Dark Matter detectors find these heavy particles or see the missing energy, it could be a massive clue that the Higgs boson is indeed a composite object, and that we are finally catching a glimpse of the invisible ocean beneath the surface.

Technical Summary: Dark Matter in Composite Higgs Models with a Scotogenic EFT

Problem Statement
This work addresses the intersection of three major open questions in particle physics: the nature of Dark Matter (DM), the origin of neutrino masses, and the hierarchy problem of the Standard Model (SM). Specifically, the authors investigate a class of Composite Higgs models (CHMs) that feature a fermionic ultraviolet (UV) completion. The goal is to construct a low-energy effective field theory (EFT) that simultaneously explains the electroweak scale via a composite pseudo-Nambu-Goldstone boson (pNGB) Higgs, generates neutrino masses via a scotogenic mechanism (loop-level generation), and provides a viable DM candidate. The study focuses on the $SU(6)/Sp(6)$ coset model, which naturally yields a residual $Z_2$ symmetry, stabilizing a subset of pNGBs that can serve as DM.

Methodology
The authors analyze the phenomenology of the $SU(6)/Sp(6)$ model, which arises from the condensation of six hyper-fermions charged under an $Sp(4)$ gauge group. The low-energy spectrum includes the SM Higgs, additional pNGBs, and composite spin-1 resonances (vectors and axial-vectors).

Model Construction:
- The model identifies four neutral $Z_2$ -odd pNGBs ( $\Delta^0, \phi^0, \eta_3, \eta_4$ ) as potential DM candidates.
- The scalar potential is constructed using a simplified ansatz based on $SU(2)_L \times U(1)_Y$ invariance before electroweak symmetry breaking (EWSB), reducing the number of free quartic couplings.
- Spin-1 resonances are incorporated using the hidden gauge symmetry formalism. The mixing between these resonances and SM electroweak gauge bosons is calculated, generating mass eigenstates and determining couplings to SM fermions and pNGBs.
- Simplifying assumptions are made regarding pNGB masses: the DM candidate is the lightest, co-annihilating partners have a mass splitting $\Delta M$ , and heavier states are decoupled.
Computational Framework:
- The model was implemented in FeynRules and exported to CalcHEP.
- micrOMEGAs 6.2 was used to compute the thermal relic density ( $\Omega_{DM} h^2$ ) and spin-independent DM-nucleon scattering cross-sections ( $\sigma_{SI}$ ).
- A Markov Chain Monte Carlo (MCMC) scan was performed using the Metropolis–Hastings algorithm over an 8-dimensional parameter space: DM mass ( $M_\chi$ ), mass splitting ( $\Delta M$ ), Higgs-pNGB couplings ( $c_{\chi\chi hh}, c_{\pi\pi hh}$ ), vacuum misalignment angle ( $\theta$ ), spin-1 coupling ( $g_{V\pi\pi}$ ), resonance coupling ( $\tilde{g}$ ), and vector resonance mass scale ( $M_V$ ).
- Constraints applied include the Planck relic density measurement ( $\Omega_{DM} h^2 = 0.120 \pm 0.012$ ) and direct detection limits from LUX-ZEPLIN (LZ) 2025 data.

Key Contributions and Results

Viability of DM Candidates: Among the four $Z_2$ -odd neutral pNGBs, the authors find that only three ( $\eta_3, \eta_4, \phi^0$ ) can reproduce the observed relic density within the scanned parameter space. The fourth candidate, the $SU(2)_L$ triplet $\Delta^0$ , is excluded because its annihilation cross-section via SM vector bosons is too efficient, resulting in a relic density far below the observed value.
Role of Spin-1 Resonances: A significant finding is the importance of heavy spin-1 resonances in the relic density calculation.
- Resonant s-channel annihilation occurs when $M_\chi \approx M_V/2$ , significantly enhancing the cross-section and reducing the relic density.
- The opening of new channels involving one heavy resonance and one SM particle (when $M_\chi \approx M_V$ ) also reduces the relic density.
- The parameter space consistent with observations is heavily influenced by the mass scale $M_V$ and the coupling $g_{V\pi\pi}$ .
MCMC Scan Findings:
- $\eta_3$ Scenario: Viable regions exist for $M_\chi$ up to 1.5 TeV. The scan shows a preference for a vacuum misalignment angle $\theta \approx 0.1$ . Direct detection constraints push the Higgs coupling $c_3$ to values $\mathcal{O}(10^{-2})$ .
- $\eta_4$ and $\phi^0$ Scenarios: These scenarios require a strict upper bound on the mass splitting ( $\Delta M \lesssim 10$ GeV) to allow for destructive interference in the annihilation cross-section, which is necessary to achieve the correct relic density. They also exhibit a sharp lower bound on the DM mass ( $M_\chi \gtrsim 500$ GeV) due to efficient electroweak annihilation.
Direct Detection: A substantial portion of the parameter space that satisfies the relic density constraint is excluded by current LZ 2025 direct detection limits. The remaining viable points often lie within the "neutrino fog," suggesting that future experiments like DARWIN will be required to probe these regions.
LHC Phenomenology: The paper outlines potential signatures at the LHC and future colliders (FCC-hh).
- $Z_2$ -odd particles produce events with large missing transverse momentum ( $E_T^{miss}$ ), soft leptons/jets from cascade decays, and associated production with Higgs or vector bosons.
- $Z_2$ -even particles lead to high-energy leptons and jets typical of composite Higgs models.
- Spin-1 resonances, if light enough, could be produced in association with Higgs or vector bosons, leading to hard multi-lepton/jet final states.

Significance and Claims
The authors claim that this work demonstrates the feasibility of a "scotogenic" realization within a Composite Higgs framework, where the DM candidate and the mechanism for neutrino mass generation are intrinsically linked to the strong dynamics of the Higgs sector.

The paper emphasizes that:

Spin-1 resonances are not negligible: Unlike some approximations in CHM literature, the inclusion of spin-1 resonances is crucial for correctly calculating the relic density in this specific model class, particularly near resonance regions.
Parameter Space Constraints: The interplay between relic density requirements and direct detection limits severely restricts the viable parameter space, particularly for the triplet candidate which is ruled out, and for the singlet/doublet candidates where mass splittings and couplings must be finely tuned.
Testability: The model predicts distinct signatures at the LHC, combining features of both Composite Higgs models (resonances, heavy vectors) and Supersymmetry (missing energy from stable $Z_2$ -odd states), offering a unique phenomenological footprint for future collider searches.

The authors remain modest regarding the robustness of their results, acknowledging that simplifying assumptions were made to reduce the parameter space (e.g., specific scalar potential structures and neglecting top-partner contributions to DM annihilation). They suggest that a full analysis including top-partners and a more general scalar potential is a necessary step for future investigations.

The Story of the Invisible Twins

The Findings: Three Out of Four

The Bottom Line

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