Heavy Dark Baryons as Self-Interacting Dark Matter: A GeV-Scale Coincidence

As a fastidious and diligent researcher, I have thoroughly analyzed both provided texts from the arXiv preprint Heavy Dark Baryons as Self-Interacting Dark Matter: A GeV-Scale Coincidence. The following synthesis combines the findings regarding self-interaction phenomenology with those concerning spectral analysis of the dark sector's interactions, providing a detailed overview of the paper's core contributions.

This research investigates a model where self-interacting dark matter (DM) is composed of heavy baryons arising from a confining dark SU(N) gauge theory, featuring a single heavy vector-like quark (m Q d). The central theme revolves around deriving and analyzing the long-distance baryon-baryon interaction potential and its resulting self-interaction phenomenology, which is critically dependent on the number of colors, N.

The study adapts the quarkonium operator-product-expansion formalism to heavy baryons to derive the leading baryon-baryon interaction. The resulting long-distance potential is characterized by three distinct physical regimes:

1. Non-retarded London dispersion.

2. Retarded Casimir–Polder interaction.

3. Yukawa contributions stemming from the exchange of dark glueballs (non-perturbative effects).

The baryon-baryon potential is successfully reproduced by combining these asymptotic contributions, with numerical reconstruction confirming that the full spectral representation accurately reflects this sum throughout the region where retardation effects are relevant. Specifically, for larger distances, the potential is well approximated by a pure Yukawa form. Crucially, the analysis demonstrates that the full spectral reconstruction provides no appreciable correction to the simple potential obtained by summing only the Yukawa and Casimir–Polder contributions, validating this approximation across all relevant scales.

The behavior of key observables, such as the chromo-electric polarizability (d 2), is highly sensitive to N:

• Small N (e.g., N=2, 3): The free-adjoint approximation provides an excellent description of the continuum contribution. For these cases, the free-adjoint approximation captures most of the chromo-electric polarizability.

• Large N: The situation shifts dramatically; for large N, the chromo-electric polarizability becomes dominated by contributions from intermediate adjoint bound states, analogous to the hydrogen atom spectrum. This behavior justifies adopting a bound-state approximation, particularly for SU(10).

The analysis compares analytical results with prior literature, finding exact reproduction of semianalytical results for mesons at N=3 and convergence to the free-particle result as N to infinity.

The self-interaction phenomenology is analyzed using a partial-wave formalism for identical particle scattering, employing the viscosity cross section as the natural quantity for asymmetric dark-baryon abundance. The findings reveal a strong dependence on N:

• Small N (N=2, 3): The attractive interaction is too weak to overcome the short-distance Pauli repulsion. Consequently, these minimal realizations do not exhibit phenomenologically relevant velocity dependence.

• Large N (e.g., N about 10): In contrast, for sufficiently large N, the attractive interaction remains competitive with the repulsive core and is capable of generating strong velocity-dependent cross sections. Numerical results show that in this regime, the self-interaction cross section can rise by orders of magnitude towards low velocities (v about 5 km/s), reaching values like O(100 cm 2/g).

The model successfully navigates complex astrophysical constraints:

• Scale Consistency: The viable parameter space simultaneously satisfies self-interaction requirements at dwarf, galaxy, and cluster scales.

• Mass and Confinement Scale Selection: Astrophysical requirements strongly select dark baryon masses and confinement scales close to the ordinary baryon mass (GeV scale) and the QCD confinement scale (d about QCD).

The confluence of these findings motivates a specific cosmological interpretation:

1. Asymmetric Origin: The model naturally suggests an asymmetric dark matter origin, where the dark baryon asymmetry is comparable in magnitude to the visible baryon asymmetry, addressing the observed DM abundance.

2. Phenomenological Success: The resulting velocity dependence provides a substantially better description of cluster data than a simple Yukawa benchmark, while offering a comparable fit to dwarf-spheroidal data.

As a fastidious researcher, I have analyzed this paper on heavy dark baryons as self-interacting dark matter (SIDM). The framework provides a highly structured, composite model for dark matter interactions that bridges particle physics and astrophysical observations across multiple scales.

Here are the specific improvements to AI systems that could be derived from this scientific framework:

The improved AI system would be a sophisticated Multi-Scale Dark Sector Simulation Engine capable of generating, testing, and interpreting complex physical models where the fundamental dark matter particle itself is a composite object.

Specific capabilities include:

1. [If the AI system incorporates Section 3 & 4 methods] It can perform high-fidelity simulations of dark matter halo dynamics by calculating velocity-dependent self-interaction cross sections (using viscosity and transfer cross sections) based on the derived baryon–baryon potential, accurately predicting core formation in dwarf galaxies versus cluster constraints.

2. [If the AI system incorporates Section 5 & 6 methods] It can simulate cosmological production scenarios (Asymmetric Dark Matter, ADM) by modeling the interplay between perturbative and non-perturbative annihilation processes (e.g., QQ̄ → gg vs. baryon re-annihilation), allowing it to predict dark matter relic abundance based on different thermal histories (symmetric vs. asymmetric).

3. [If the AI system incorporates Section 6 & 7 methods] It can identify the preferred parameter space for dark matter masses and confinement scales by simultaneously satisfying multiple astrophysical constraints (dwarf cores, cluster bounds, and extremely large cross-sections at low velocities), effectively using observations to select particle physics parameters.

4. [If the AI system incorporates Section 5.3 & 6 methods] It can map the resulting preferred mass scales onto visible matter physics, predicting dark baryon masses that are remarkably close to proton/neutron masses, suggesting a common origin for visible and dark matter abundances (ADM).

5. [If the AI system incorporates Section 7 methods] It can predict potential observable signals from high-energy physics phenomena related to the confinement transition, such as nanohertz gravitational waves from the first-order phase transition in SU(N) gauge theories, providing a target for next-generation gravitational wave detectors (like NANOGrav).

This system moves beyond standard dark matter models by treating DM not as a point particle or light mediator, but as a composite heavy baryon whose interactions are governed by QCD-like confinement and the dynamics of its internal structure.

We study self-interacting dark matter composed of heavy baryons in a confining dark SU(N) gauge theory with a single heavy vector-like quark, m Q Λ d. In this regime, the dark baryons are compact Coulombic bound states whose long-distance interactions can be described by a multipole expansion. We derive the leading baryon-baryon interaction by adapting the quarkonium operator-product-expansion formalism to heavy baryons. The resulting force contains non-retarded London dispersion, retarded Casimir-Polder, and Yukawa contributions from dark glueball exchange. We find that the self-interaction phenomenology depends strongly on the number of colors. For N=2,3, the attractive interaction is too weak to overcome the short-distance Pauli repulsion, and no phenomenologically relevant velocity dependence is obtained within our minimal set-up. For sufficiently large N, the attractive interaction remains competitive with the repulsive core and can generate strong velocity dependent cross sections. Taking SU(10) as a representative finite- N realization, we find regions compatible with self-interaction requirements inferred from dwarf galaxies and clusters, while allowing much larger cross sections at low velocities relevant for gravothermal evolution. These regions correspond to GeV-scale dark baryons and a confinement scale close to that of QCD, which naturally motivate an asymmetric dark matter origin.