⚛️ phenomenology

Opening the Topological Portal to Dark Sectors with Colliders

This paper investigates the collider phenomenology of a topological portal connecting QCD to pseudo-Nambu-Goldstone dark matter by constructing a weakly coupled ultraviolet completion with a vector mediator, which enables the calculation of thermal coannihilation and provides testable predictions for LHC, LEP, bottomonium, and future FCC-ee experiments.

Original authors: Joe Davighi, Admir Greljo, Lia Schöneweiß, Nudzeim Selimovic

Published 2026-09-11

📖 5 min read🧠 Deep dive

CC BY 4.0

Original authors: Joe Davighi, Admir Greljo, Lia Schöneweiß, Nudzeim Selimovic

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

Dark matter is the invisible substance that holds galaxies together, yet for decades, scientists have struggled to find it. The leading idea is that dark matter particles interact with ordinary matter only through gravity, making them nearly impossible to catch in a detector. However, if these particles interact even slightly through other forces, they might leave subtle traces. One promising theory suggests that dark matter could be made of particles that are very similar to the pions found in our own universe—particles that are usually short-lived and decay instantly. If a version of these particles exists in a hidden "dark sector," they might be stable enough to make up the dark matter we see in the cosmos. The challenge has been figuring out how these dark particles could talk to the normal matter we can see, without violating the strict rules of physics that govern how particles behave.

A team of physicists has now mapped out a specific way this connection could work, proposing a new kind of bridge between the visible and invisible worlds. They focused on a theoretical idea called a "topological portal," which acts like a special doorway that allows dark matter to interact with ordinary matter in a very specific, mathematically rigid way. Unlike other theories that rely on guesswork about how strong these interactions might be, this portal is built on deep mathematical principles that ensure the connection is consistent with the laws of physics. The researchers constructed a detailed model of how this portal would function at the highest energy levels, essentially reverse-engineering the universe to see what kind of invisible particles and forces would be required to create such a doorway. They found that this setup naturally leads to a scenario where dark matter particles are slightly heavier than their stable counterparts, creating a small but crucial difference in their mass that dictates how they behave.

The study reveals that for this model to work, there must be a new, heavy particle acting as a messenger, carrying forces between the dark sector and the quarks that make up protons and neutrons. This messenger particle would interact with the first two generations of quarks but ignore the third, a specific pattern that avoids conflicts with known physics. When the researchers simulated the early universe, they found that this setup allows dark matter to form in just the right amount to match what we observe today. The process relies on a "co-annihilation" mechanism, where two slightly different types of dark particles collide and destroy each other, leaving behind the stable version that survives to the present day. This happens at temperatures where the particles are moving fast enough to break through the usual barriers, a regime that previous, simpler theories could not accurately describe.

Crucially, the paper shows that this model makes very clear predictions that can be tested with current and future experiments. Because the dark particles are so light, they would be produced in high-energy collisions at particle accelerators like the Large Hadron Collider. The researchers calculated that these collisions would produce jets of particles accompanied by missing energy, a signature that experiments are already looking for. They also found that the model predicts a specific type of decay for the heavier dark particle, which would travel a short distance before turning into a lighter dark particle and a photon. This "displaced" decay would look like a particle appearing out of nowhere and vanishing a few meters away, a signature that is distinct from standard background noise.

The team also looked at how this model would affect the behavior of heavy particles like the bottom quark, which is found in particles called bottomonium. They determined that the new force would subtly change how these particles decay, a effect that could be measured with high precision. While current data does not rule out the model, it places tight limits on how strong the new force can be. The researchers identified a "sweet spot" in the parameters of their model where the dark matter abundance is correct, and this region is within reach of upcoming experiments. Future facilities, such as a proposed electron-positron collider that would produce millions of Z bosons, could probe this region with incredible sensitivity, potentially confirming or ruling out this specific type of dark matter.

One of the most significant findings is that this model naturally avoids detection by traditional methods. Because the interaction between dark matter and ordinary matter is so specific, it does not allow dark matter to bounce off atomic nuclei in underground detectors, nor does it produce the gamma-ray signals that telescopes look for in space. This explains why we have not found dark matter yet, even though it is likely right around us. The paper concludes that the search for dark matter needs to expand its toolkit, looking for these subtle, topological connections rather than just direct collisions. By building a complete picture of how this portal works from the smallest scales to the largest, the researchers have provided a concrete roadmap for the next generation of experiments to finally catch a glimpse of the dark sector.

Technical Summary: Opening the Topological Portal to Dark Sectors with Colliders

Problem Statement
The paper addresses the challenge of constructing a viable thermal dark matter (DM) model in the GeV mass range that evades stringent constraints from direct and indirect detection. Previous work [1] identified a "topological portal" connecting Quantum Chromodynamics (QCD) to a dark sector of pseudo-Nambu–Goldstone bosons (pNGBs). This portal arises from a topological interaction (analogous to the Wess–Zumino–Witten term) that couples the QCD baryon current to a dark topological current. While this mechanism naturally suppresses elastic scattering (evading direct detection) and elastic annihilation (evading indirect detection) due to its derivative and antisymmetric nature, the original formulation relied on an Effective Field Theory (EFT) valid only below the QCD scale.

For GeV-scale DM, the thermal freeze-out occurs at center-of-mass energies near or above the QCD scale ( $\sqrt{s} \sim m_{\chi_1} + m_{\chi_2}$ ), where the pion-based EFT description breaks down. Furthermore, the topological portal requires an ultraviolet (UV) completion to be consistent with the Standard Model (SM) and to define the mediator's properties. Without a UV completion, the model's predictions for relic abundance and collider signatures remain unreliable.

Methodology
The authors construct a weakly coupled UV completion of the topological portal to enable a rigorous calculation of the DM relic abundance and collider phenomenology.

Symmetry Matching and UV Construction:
- The authors identify that the topological portal matches a "2-group" generalized symmetry structure. To realize this, they introduce a massive vector mediator ( $X_\mu$ ) that gauges a specific baryonic current of the SM.
- They propose a concrete, anomaly-free model where the mediator couples to the generation-dependent combination $B_1 + B_2 - 2B_3$ (leptophobic). This choice avoids the need for additional colored or charged fermions to cancel anomalies.
- The dark sector consists of two complex scalars ( $\phi_1, \phi_2$ ) forming a doublet under an approximate global $SU(2)_D$ symmetry. Spontaneous symmetry breaking of this sector yields two pNGBs, $\chi_1$ and $\chi_2$ . An exact discrete parity ( $P_D$ ) ensures the stability of the lighter state ( $\chi_1$ ), while controlled explicit breaking generates a small mass splitting ( $\Delta m_\chi$ ) between them.
- The model includes vector-like quarks to generate the full CKM matrix and ensure gauge invariance of the Yukawa couplings.
Thermal Relic Abundance Calculation:
- Unlike previous EFT approaches, the authors calculate the thermal freeze-out directly using the full microscopic model with quark degrees of freedom and the full propagator of the vector mediator $X_\mu$ .
- They distinguish between non-resonant freeze-out (where the mediator is off-shell) and resonant freeze-out (where $m_X \approx m_{\chi_1} + m_{\chi_2}$ ), utilizing the full Breit-Wigner enhancement in the latter regime.
- They employ the co-annihilation formalism, as the relic density is determined by the process $\chi_1 \chi_2 \to X^* \to q\bar{q}$ .
Phenomenological Analysis:
- Decay of the Excited State: The authors analyze the decay of the heavier dark state $\chi_2$ . They show that for mass splittings $\Delta m_\chi \gtrsim 200$ MeV, the topological decay channel $\chi_2 \to \chi_1 \pi^0 \gamma$ dominates over the kinetically mixed leptonic channel $\chi_2 \to \chi_1 \ell^+ \ell^-$ . However, for the thermal target parameters, $\chi_2$ is long-lived on detector scales, appearing as missing energy in most collider searches.
- Collider Signatures: They recast existing LHC searches (CMS boosted dijet + photon, ATLAS monojet), LEP searches (acoplanar jets), and $B$ -physics constraints (bottomonium decays, rare $B$ decays, neutral meson mixing).
- Future Projections: They estimate the sensitivity of the High-Luminosity LHC (HL-LHC) and the future FCC-ee (specifically the Tera-Z factory) to this model.

Key Contributions and Results

Validated UV Completion: The paper provides the first consistent UV completion of the topological portal, demonstrating that it can be embedded in the SM via a leptophobic $Z'$ gauging $B_1 + B_2 - 2B_3$ . This resolves the EFT validity issue for GeV-scale DM.
Relic Abundance Target: The authors map out the thermal target in the $(m_X, g_X)$ plane for various dark matter masses and splittings. They show that the viable parameter space includes both non-resonant branches and a resonant region where $m_X \approx m_{\chi_1} + m_{\chi_2}$ .
Collider Constraints:
- LHC: The model is constrained by CMS boosted dijet searches (sensitive to $X \to q\bar{q}$ ) and ATLAS monojet searches (sensitive to $X \to \chi_1 \chi_2$ ). These searches exclude the non-resonant branches requiring large couplings ( $g_X \gtrsim 0.05$ ).
- Flavor Physics: The specific $B_1 + B_2 - 2B_3$ embedding predicts flavor-changing neutral currents (FCNCs) in the up-sector (e.g., $t \to cX$ , $D^0-\bar{D}^0$ mixing) and constraints from bottomonium ( $\Upsilon$ ) decays. The $\Upsilon$ decay constraint is particularly strong for $m_X < 13$ GeV, currently excluding parts of the parameter space that LHC searches cannot reach.
- Direct/Indirect Detection: The authors confirm that for the relevant mass splittings ( $\Delta m_\chi \sim m_\pi$ ), direct detection is kinematically forbidden, and indirect detection signals are negligible, consistent with the topological nature of the portal.
Future Sensitivity:
- FCC-ee: The paper projects that a future $Z$ -factory can probe the low-mass region ( $m_X \lesssim 50$ GeV) via recoil-mass searches in hadronic $Z$ decays ( $Z \to q\bar{q}X$ , $X \to \chi_1 \chi_2$ ) and visible dijet resonance searches ( $X \to b\bar{b}$ ). This offers a complementary probe to the LHC, particularly for the lower non-resonant thermal branch.
- Belle II: Improved measurements of $\Upsilon$ decays could significantly tighten constraints on the coupling $g_X$ . Additionally, if the coupling and mass splitting are at the upper edge of the viable range, displaced vertex signatures ( $\chi_2 \to \chi_1 \pi^0 \gamma$ ) could be observable.

Significance and Claims
The paper claims that the topological portal offers a robust and testable framework for GeV-scale thermal dark matter. Its primary significance lies in:

Decoupling Detection: The topological structure naturally suppresses elastic scattering and annihilation, allowing the model to satisfy current null results from direct and indirect detection experiments while remaining thermal.
UV Consistency: By constructing a specific UV completion, the authors demonstrate that the topological portal is not merely an IR artifact but can be realized in a renormalizable theory consistent with the SM.
Distinctive Signatures: The model predicts unavoidable collider signatures (dijets, monojets, displaced vertices) that are directly tied to the symmetry structure required to match the topological portal.
Complementarity: The paper emphasizes that different energy regimes require different descriptions: the UV model governs hard production and freeze-out, while the IR topological operator governs soft transitions (like $\chi_2$ decay). This necessitates a multi-front experimental strategy involving the LHC, flavor factories (Belle II), and future $Z$ factories (FCC-ee) to fully test the parameter space.

The authors conclude that while the specific flavor predictions depend on the concrete UV realization (e.g., the choice of $B_1 + B_2 - 2B_3$ ), the core phenomenology of the topological portal—specifically the interplay between resonant co-annihilation, long-lived dark states, and specific collider signatures—provides a coherent and testable target for the next generation of particle physics experiments.

Technical Summary: Opening the Topological Portal to Dark Sectors with Colliders

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