⚛️ phenomenology

Comparable Dark Matter and Baryon energy densities from Dark Grand Unification

This paper proposes an $SU(9)$ dark grand unification model where a shared asymmetry mechanism and similar gauge coupling running naturally explain the comparable energy densities of dark matter and baryons by predicting GeV-scale dark baryons and a TeV-scale $Z'$ mediator.

Original authors: Yi Chung

Published 2026-02-03

📖 5 min read🧠 Deep dive

CC BY 4.0

Original authors: Yi Chung

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, bustling city. For a long time, we knew about the "visible" citizens: the atoms, stars, and planets that make up everything we can see. We call this Baryonic Matter. But astronomers also know there is a massive, invisible population living in the shadows, exerting gravity but refusing to interact with light. This is Dark Matter.

Here is the mystery: If you count the total "weight" (energy density) of the visible citizens and the invisible citizens, they are surprisingly similar. The invisible crowd is only about five times heavier than the visible one. In the world of physics, this is like finding that the number of people in a small town is almost exactly the same as the number of people in a massive metropolis next door. It's a strange coincidence that suggests the two groups might be related, like siblings rather than strangers.

This paper proposes a theory called "Dark Grand Unification" to explain this coincidence. Here is the story in simple terms:

1. The Two Families (The Model)

The author suggests that the visible world and the dark world aren't just neighbors; they are part of the same extended family tree.

The Visible Family: Our world is built on a force called "Color" (part of the Strong Nuclear Force) that binds quarks together to make protons and neutrons.
The Dark Family: The author proposes a "Dark Color" force that works almost exactly the same way, but in a hidden sector. It binds "Dark Quarks" together to make "Dark Baryons" (the dark matter).

The key idea is Grand Unification. Just as a family tree branches out from a single ancestor, this theory says that at extremely high energies (like right after the Big Bang), the visible force and the dark force were actually one single force. They only split apart later as the universe cooled down.

2. Why the Weights Match (The Analogy)

Why are the two groups so similar in weight?

The Recipe: Because they came from the same "ancestor" force, they inherited the same recipe. The paper argues that the "ingredients" (particles) in the dark sector are arranged almost identically to the visible sector.
The Cooking Time: In physics, forces get stronger or weaker as you change the energy scale (like a recipe changing as you cook). Because the ingredients are so similar, the "cooking time" (how the forces evolve) is almost identical for both families.
The Result: This leads to the "Dark Baryons" (dark matter particles) having a mass very close to our "Protons" (visible matter). If the dark matter is about the same size as a proton, and the numbers of particles are similar, their total weights will be similar too. This solves the "coincidence" mystery.

3. The "Dark Baryon" (The Candidate)

In our world, protons are stable. In this dark world, the dark matter is made of Dark Baryons.

The paper suggests these dark baryons are a bit exotic. They are made of "Dark Quarks" that behave like a mix of different types.
Crucially, there is a "Dark Baryon Number" (a rule that says dark matter can't just disappear). This ensures the dark matter we see today is the leftover overabundance from the early universe, just like our visible matter.

4. The Messenger (The Z' Boson)

How do these two separate worlds talk to each other?

The paper introduces a new particle called a Z' boson. Think of this as a diplomat or a bridge.
This diplomat is heavy (about 10,000 times heavier than a proton) and acts as a messenger. It allows the dark sector to interact with our visible sector, but only very weakly.
This diplomat is the key to testing the theory. If we build a big enough particle collider (like a super-powered microscope), we might be able to spot this diplomat, proving the two worlds are connected.

5. The "Dark Pions" (The Light Messengers)

The theory also predicts lighter particles in the dark sector called "Dark Mesons" (specifically a particle called $\eta$ ).

These are like the "messenger pigeons" of the dark world.
They are unstable and decay quickly into visible particles (like electrons or muons).
The paper suggests that experiments looking for rare particle decays (like smashing beams of particles into a wall) could find traces of these dark messengers.

6. The "Coincidence" Explained

The paper argues that the reason the dark matter and visible matter have such similar densities is a two-part lock:

Same Number: A shared history created an equal number of dark particles and visible particles.
Same Mass: The shared "recipe" and "cooking time" ensured that the dark particles ended up weighing about the same as visible particles (around 1 to 2 GeV, which is roughly the weight of a proton).

Summary

The author has built a mathematical model where the visible universe and the dark universe are twins separated at birth. They share the same DNA (gauge groups and particle content), which explains why they are so similar in size and weight today.

What can we do with this?

Look for the Diplomat: We can search for the heavy Z' boson at future particle colliders (like the 100 TeV collider mentioned).
Listen for the Pigeons: We can look for the light dark mesons in beam-dump experiments or rare decay measurements.
Check the Neighbors: We can look for dark matter hitting our detectors (direct detection), though the signal might be very faint.

The paper concludes that this is a "testable" theory. It doesn't just explain the mystery; it gives us a specific map of where to look to prove it's true. If we find the Z' boson or the dark mesons, we will have confirmed that the dark matter and the visible matter are indeed part of the same grand family.

Technical Summary: "Comparable Dark Matter and Baryon energy densities from Dark Grand Unification"

Problem Statement
The paper addresses the "Dark Matter-Baryon Coincidence," the observation that the energy densities of dark matter ( $\rho_D$ ) and baryons ( $\rho_B$ ) are comparable, with a ratio $\rho_D/\rho_B \approx 5$ . Standard cosmological models suggest these sectors are unrelated, making such a ratio require extreme fine-tuning. Previous Asymmetric Dark Matter (ADM) models successfully linked the number densities ( $n_D \approx n_B$ ) via a shared global $U(1)$ symmetry but failed to explain the comparable masses ( $m_D \approx m_B$ ). Since baryon masses are set by the QCD confinement scale ( $\Lambda_{QCD}$ ), a viable solution requires a dark sector with a similar strong interaction (Dark QCD) and a mechanism to ensure the dark confinement scale ( $\Lambda_{DC}$ ) is of the same order as $\Lambda_{QCD}$ , despite the exponential sensitivity of confinement scales to ultraviolet (UV) parameters.

Methodology and Model Construction
The authors propose a "Dark Grand Unification" framework based on an $SU(9)$ gauge group that unifies the Standard Model (SM) gauge group with a dark color gauge group. The construction proceeds through the following steps:

Gauge Group Selection: To ensure similar running of the coupling constants, the authors select a dark color group $Sp(4)_D$ rather than the more intuitive $SU(3)_D$ . This choice is motivated by the requirement that the quadratic Casimir $C_2(G)$ of the dark group matches that of $SU(3)_C$ ( $C_2=3$ ). The $Sp(4)$ group avoids certain quantum anomaly issues associated with $SU(3)$ unification and allows for a desired fermion spectrum.
Fermion Content: The model extends the $SU(5)$ Georgi-Glashow GUT fermion content to $SU(9)$. This introduces new fermions, including dark quarks ( $\chi$ ) and exotic fermions ( $\psi$ ). Crucially, the extension naturally provides three generations of dark quarks analogous to SM quarks, introducing flavor structure and new CP-violating sources.
Symmetry Breaking: The symmetry breaking chain proceeds from $SU(9) \times Sp(4)' \times U(1)_5$ $S U (9) \times S p (4)^{'} \times U (1)_{5}$ down to the SM and $Sp(4)_D$ $S p (4)_{D}$ via several scalar fields ( $\Gamma, \Delta, \Phi, \Phi'$ $Γ, Δ, Φ, Φ^{'}$ ) at distinct scales:
- $\Lambda_{GUT} \sim 10^{16}$ GeV: Breaks $SU(9)$ to $SU(7)_{DU} \times SU(2)_W$ .
- $\Lambda_{DU} \sim 10^{15}$ GeV: Unifies QCD and Dark QCD into $SU(7)_{DU}$ and breaks $Sp(4) \times Sp(4)'$ to the diagonal $Sp(4)_D$ .
- $\Lambda_5 \sim 10^5$ GeV: Breaks a residual $U(1)'_5$ symmetry, generating a massive $Z'$ boson and giving masses to specific dark quarks.
- $\Lambda_{EW}$ : Electroweak symmetry breaking.
Mass Generation: The model utilizes a seesaw mechanism for the antisymmetric dark quarks ( $\chi_a$ ) and hierarchical Yukawa couplings to generate a spectrum where the lightest dark quarks ( $\chi_{a,1}$ and $\chi_{f,1}$ ) have masses $\sim 0.1$ GeV, well below the confinement scale.

Key Contributions and Results

Unified Origin of Asymmetry: The model identifies a conserved global $U(1)$ symmetry, $D - (B-L)$ , where $D$ is the dark baryon number. This symmetry is preserved during the generation of asymmetries, ensuring that the number densities of dark baryons and SM baryons are comparable ( $n_D \approx n_B$ ). The asymmetry is generated via the out-of-equilibrium decay of heavy fermions ( $\psi_a$ ) at the Dark Unification scale, satisfying the Sakharov conditions.
Comparable Confinement Scales: By unifying the gauge groups and ensuring the dark sector has a matter content (fermion spectrum) that mirrors the SM QCD sector, the model achieves similar one-loop beta function coefficients ( $b_s \approx b_D$ $b_{s} \approx b_{D}$ ) across a wide energy range. This results in comparable running of the couplings from the unification scale down to the confinement scales.
- The calculated confinement scale is $\Lambda_{DC} \sim 3.3$ GeV (one-loop) or $\sim 7.5$ GeV (two-loop), which is within an order of magnitude of $\Lambda_{QCD}$ .
- This proximity explains why dark baryon masses ( $m_D \sim \Lambda_{DC}$ ) are comparable to visible baryon masses ( $m_B \sim \Lambda_{QCD}$ ).
Dark Sector Spectrum: The low-energy dark spectrum consists of:
- Dark Baryons: The lightest stable dark matter candidate is identified as a vector diquark baryon ( $\rho$ ) with mass $m_\rho \approx 1.6$ GeV (for benchmark parameters). Its stability is protected by the $D-(B-L)$ symmetry and kinematic constraints (decay is forbidden due to the absence of light fermionic dark hadrons with the necessary quantum numbers).
- Dark Mesons: A light pseudoscalar meson ( $\eta$ ) with mass $\sim 1.0$ GeV serves as the decay channel for the symmetric component of the dark sector.
Phenomenology:
- $Z'$ Boson: The model predicts a $Z'$ boson with mass $M_{Z'} \sim \mathcal{O}(10)$ TeV, mediating interactions between the dark and visible sectors. This particle is a primary target for future hadron colliders.
- Direct Detection: Dark baryons interact with nucleons via the $Z'$ , yielding a spin-independent cross-section potentially within reach of next-generation detectors (e.g., DarkSide-20k).
- Dark Meson Searches: The light $\eta$ meson behaves like an axion-like particle (ALP) coupling to SM fermions. Current constraints from beam-dump experiments (CHARM) and $B$ -meson decays (LHCb) set lower bounds on the symmetry breaking scale $f'$ .
- Self-Interactions: The model predicts dark matter self-interactions with a cross-section per unit mass $\sigma_D/m_D \sim 10^{-4}$ cm $^2$ /g, consistent with current astrophysical constraints (e.g., Bullet Cluster), though resonant enhancements could alter this.

Significance and Claims
The paper claims that Dark Grand Unification provides a natural, non-fine-tuned explanation for the Dark Matter-Baryon coincidence. By extending the SM fermion sector rather than introducing a "mirror" sector, the model simultaneously solves the number density problem (via the $D-(B-L)$ symmetry) and the mass problem (via the unified running of couplings and similar matter content).

The authors emphasize that the model is fully testable. The finite parameter space allows for specific predictions regarding the mass of the dark baryon (GeV scale), the mass of the $Z'$ boson (TeV scale), and the existence of light dark mesons. The paper notes that while the $SU(3)_D$ alternative was considered, it faces significant drawbacks regarding anomaly cancellation and the difficulty of generating light dark quark masses, reinforcing the choice of $Sp(4)_D$ . The work concludes that the observed similarity in energy densities is a direct consequence of a deep connection between the visible and dark sectors rooted in grand unification.