⚛️ phenomenology

Heavy Dark Baryons at Large $N$ : Self-Interactions across All Scales

This paper proposes that heavy dark baryons in a moderately large- $N$ confining $SU(N)$ sector can naturally explain the full range of observed dark matter self-interactions across astrophysical scales through van der Waals forces, while simultaneously accounting for the dark matter abundance via a baryon asymmetry and allowing the number of colors $N$ to be inferred from observational data.

Original authors: Giovani Dalla Valle Garcia, Juan Herrero-Garc\'ıa

Published 2026-10-01

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CC BY 4.0

Original authors: Giovani Dalla Valle Garcia, Juan Herrero-Garc\'ıa

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 scaffolding of the universe, a substance that does not emit light but holds galaxies together with its gravity. For decades, the leading theory has treated this matter as "cold" and "collisionless," meaning the particles pass right through one another like ghosts, interacting only through gravity. However, astronomers have begun to notice that this simple picture struggles to explain the detailed shapes of small galaxies and the behavior of galaxy clusters. In some cases, the centers of these galaxies seem too dense, while in others, they appear too diffuse. This has led scientists to consider a different possibility: that dark matter particles might bump into each other, exchanging energy and reshaping the structures they inhabit. The challenge is that these interactions cannot be constant; they must be strong in slow-moving environments like dwarf galaxies but weak in the high-speed collisions of massive galaxy clusters. Finding a physical mechanism that naturally produces this specific, velocity-dependent behavior has been a major puzzle.

A new study by researchers at the University of Melbourne and the University of Valencia proposes a solution rooted in the idea that dark matter is not a single, simple particle, but a composite object, much like an atom is made of smaller parts. They suggest that dark matter consists of heavy "baryons"—complex structures made of many smaller constituents held together by a force similar to the one that binds protons and neutrons in our own universe. In this model, the dark matter particles are not point-like dots but compact, cloud-like bundles. When two of these bundles approach each other, they do not simply bounce off or pass through. Instead, their internal structures distort slightly, creating a temporary attraction that pulls them together, much like how neutral atoms can stick together to form molecules. This attraction is not uniform; it changes dramatically depending on how fast the particles are moving relative to one another.

The researchers focused on a specific scenario where the dark sector contains a large number of colors, a property analogous to the electric charge in our world but with many more variations. They calculated how these heavy, composite dark particles would scatter off one another across a wide range of speeds. Their calculations revealed a striking pattern: at the slow speeds found in dwarf galaxies, the particles interact very strongly, with a cross-section per unit mass ranging from 30 to 100 square centimeters per gram. As the speed increases to the levels seen in galaxy clusters, this interaction drops sharply to less than 1 square centimeter per gram, satisfying the strict limits observed in those massive systems. Most remarkably, at very low speeds of just a few kilometers per second, the interaction strength surges again, reaching values between 100 and 1,000 square centimeters per gram. This surge aligns with recent observations of a dense, collapsed substructure near a distant galaxy, which appears to require such intense self-interaction to exist.

This behavior arises from the unique way these composite particles interact. Because they are neutral overall, they do not feel a simple force at long distances. Instead, their internal components shift in response to each other, creating a fleeting, induced attraction known as a van der Waals force. This force is strong when the particles are close and moving slowly, allowing them to resonate and interact intensely. However, as they move faster, this delicate connection breaks down, and the interaction weakens significantly. The researchers found that this mechanism works best if the dark matter particles have a mass around 10 times that of a proton, placing them in the range of a few billion electron volts. This mass scale is not arbitrary; it is precisely the region where the symmetric population of these particles would have annihilated away in the early universe, leaving behind only a small excess of matter. This leftover asymmetry would naturally account for the total amount of dark matter we see today, linking the particle's physical properties directly to the history of the cosmos.

The study suggests that the number of "colors" in this dark sector is likely between 7 and 80, with a specific example of 20 colors providing a robust fit to the data. This framework offers a unified explanation for several seemingly unrelated astronomical observations. It resolves the tension between the need for strong interactions in slow-moving dwarf galaxies and the need for weak interactions in fast-moving clusters. It also provides a natural setting for the existence of extremely dense, collapsed dark matter clumps that have been detected through gravitational lensing. By treating dark matter as a complex, composite system rather than a simple point particle, the researchers have shown that the universe's dark sector could be far richer and more dynamic than previously imagined. The findings imply that the diversity of galactic structures we observe may be a direct consequence of these particles bumping into each other, reshaping the invisible web that holds the cosmos together.

Technical Summary: Heavy Dark Baryons at Large N: Self-Interactions across All Scales

Problem Statement
Self-interacting dark matter (SIDM) offers a potential resolution to small-scale structure anomalies in the otherwise successful cold dark matter paradigm, such as the diversity of galactic rotation curves. However, observational constraints require the self-interaction cross-section per unit mass ( $\sigma/m_{DM}$ ) to be highly velocity-dependent. Dwarf spheroidal galaxies favor $\sigma/m_{DM} \sim 30\text{--}100 \text{ cm}^2/\text{g}$ at velocities $\sim 30 \text{ km/s}$ , while galaxy clusters require $\sigma/m_{DM} \lesssim 1 \text{ cm}^2/\text{g}$ at $\sim 1500 \text{ km/s}$ . Furthermore, strong lensing observations of the dense second perturber in JVAS B1938+666 suggest a need for even stronger interactions ( $\sigma/m_{DM} \sim 10^2\text{--}10^3 \text{ cm}^2/\text{g}$ ) at very low velocities ( $\sim \text{few km/s}$ ). The central challenge is to construct a model where self-interactions are sizable but vary by orders of magnitude across these astrophysical velocity scales.

Methodology
The authors propose a minimal confining dark sector based on an $SU(N)$ gauge theory with a single vector-like quark flavor ( $Q$ ) of mass $m_Q$ significantly larger than the confinement scale $\Lambda_d$ ( $m_Q \gg \Lambda_d$ ). The dark matter candidate is identified as the lightest stable dark baryon, a color singlet composed of $N$ heavy quarks.

Theoretical Framework: In the heavy-quark limit, the baryon is treated as a compact Coulombic bound state. The interaction between two such baryons is not mediated by one-gluon exchange (which vanishes for color singlets) but arises from chromo-electric polarizability. This induces a non-Abelian van der Waals force, analogous to interactions between neutral atoms or heavy quarkonium in QCD.
Potential Construction: The interaction potential $V(r)$ $V (r)$ is derived across three regimes:
- Short-range ( $r \ll \epsilon_B^{-1}$ ): A non-retarded London dispersion force ( $r^{-6}$ ).
- Intermediate-range ( $\epsilon_B^{-1} \lesssim r \lesssim \Lambda_d^{-1}$ ): A retarded Casimir–Polder force ( $r^{-7}$ ).
- Long-range ( $r \gtrsim \Lambda_d^{-1}$ ): A Yukawa tail mediated by the exchange of the lightest dark glueball.
- Regularization: To handle the breakdown of the multipole expansion at short distances, the authors introduce a repulsive core arising from fermion exchange (Pauli repulsion) and suppress the attractive potential below a matching radius $r_{in}$ .
Scattering Calculation: The velocity-dependent viscosity cross-section ( $\sigma_V$ ) is computed by solving the radial Schrödinger equation for the regularized potential. The analysis focuses on the large- $N$ limit (specifically using $N=20$ as a representative case) where the attractive potential becomes approximately $N$ -independent, while the repulsive core scales linearly with $N$ .
Parameter Scan: The study scans the parameter space defined by the baryon mass $m_B$ and confinement scale $\Lambda_d$ , constrained by the hierarchy ratio $\xi = m_Q/\Lambda_d$ .

Key Contributions and Results

Velocity-Dependent Phenomenology: The authors demonstrate that for moderately large $N$ $N$ ( $N \sim 10\text{--}100$ $N \sim 10 - 100$ ) and a hierarchy $\xi \sim 10\text{--}100$ $ξ \sim 10 - 100$ , the model naturally generates the required velocity dependence.
- At dwarf-galaxy velocities ( $\sim 30 \text{ km/s}$ ), the cross-section is enhanced to $\sigma/m_{DM} \sim 30\text{--}100 \text{ cm}^2/\text{g}$ .
- At cluster velocities ( $\sim 1500 \text{ km/s}$ ), the cross-section drops to satisfy the constraint $\sigma/m_{DM} \lesssim 1 \text{ cm}^2/\text{g}$ .
- At very low velocities ( $\sim \text{few km/s}$ ), resonant-like enhancements drive the cross-section to $10^2\text{--}10^3 \text{ cm}^2/\text{g}$ , consistent with the JVAS B1938+666 perturber.
Parameter Space Selection: A specific benchmark region is identified where $m_B \sim 10 m_p$ (tens of GeV) and $\Lambda_d \sim \Lambda_{QCD}$ (tens of MeV). For an $SU(20)$ theory with $\xi = 35$ , the best fit yields $m_B \approx 11 \text{ GeV}$ and $\Lambda_d \approx 16 \text{ MeV}$ .
Dependence on $N$ : The paper notes that while the qualitative velocity dependence persists for $N \sim 7\text{--}80$ , the precise location of the resonant enhancement depends on $N$ . In the limit of very large $\xi$ , the ratio of cross-sections at different velocities approaches an $N$ -dependent plateau, potentially allowing $N$ to be inferred from observations.
Cosmological Viability: The model supports an asymmetric dark matter origin. The symmetric component of heavy dark quarks efficiently annihilates ( $Q\bar{Q} \to gg$ ) and undergoes re-annihilation via baryon-antibaryon rearrangement, leaving a negligible symmetric relic. The observed dark matter abundance is thus naturally explained by a primordial dark baryon asymmetry comparable in magnitude to the visible baryon asymmetry.

Significance and Claims
The paper claims to provide a minimal, theoretically consistent framework that simultaneously addresses the small-scale structure problems of the CDM model and the specific strong-lensing anomaly of JVAS B1938+666 without requiring multiple quark flavors, CP-violating dynamics, or narrow resonances.

The authors emphasize that the velocity dependence arises intrinsically from the composite nature of the dark baryons and the interplay between chromo-electric polarizability and Pauli repulsion. They assert that this scenario favors GeV-scale dark baryons and an asymmetric origin, independent of the relic abundance requirement. The work suggests that the robustness of this velocity-dependent enhancement across a broad range of $N$ motivates further searches for low-velocity collapsed substructures. However, the authors remain modest regarding the short-distance dynamics, noting that the specific resonant features depend on the regularization of the potential and that a dedicated cosmological analysis is required to fully connect the model to potential gravitational wave signals from the confinement phase transition.

Technical Summary: Heavy Dark Baryons at Large N: Self-Interactions across All Scales

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