Neutron Portal and Dark Matter-Baryon Coincidence: from UV Completion to Phenomenology

This paper proposes a dynamical framework linking the dark matter-baryon coincidence to a GeV-scale asymmetric dark matter scenario, where a strongly supercooled dark confinement phase transition—potentially responsible for observed nano-Hz gravitational waves—naturally correlates the dark matter mass with the ultraviolet completion of the neutron portal operator.

The Gist

The Big Mystery: Why is the Universe Balanced?

Imagine the universe as a giant bank account. It has two main types of currency:

1. Visible Matter (Baryons): The stuff we see—stars, planets, you, me.
2. Dark Matter: The invisible "ghost" stuff that holds galaxies together but doesn't shine.

Scientists have a puzzle: These two currencies are strangely similar in total amount. If you look at the energy density of the universe, Dark Matter is only about 5 times heavier than Visible Matter.

In the world of physics, this is like finding a bag of gold coins next to a bag of silver coins, and they happen to weigh almost exactly the same. Usually, you'd expect one to be a mountain and the other a pebble. This is the "Coincidence Puzzle." Why are they so close?

The Proposed Solution: The "Neutron Portal"

The authors of this paper propose a solution involving a secret tunnel called the Neutron Portal.

Think of the "Visible World" and the "Dark World" as two separate rooms. Usually, they don't talk to each other. But the Neutron Portal is a small, hidden door connecting them.

• The Door: It allows a specific type of particle (let's call it a "Dark Messenger") to turn into a regular neutron (or vice versa).
• The Mechanism: In the early universe, this door allowed the "Dark Room" to share its imbalance with the "Visible Room." If the Dark Room had a surplus of particles, the door let some of that surplus spill over into our room, creating the matter we see today.

The Problem: The "Heavy Door" vs. The "Light Room"

Here is the catch. For this door to work, it needs to be built with very heavy materials (high energy). The paper suggests the door is built at a scale of Tera-electronvolts (TeV)—think of this as a massive, industrial-grade steel door.

However, the Dark Matter particles that walk through this door are surprisingly light, sitting at the Giga-electronvolt (GeV) scale. That's like building a massive steel door to let in a tiny, lightweight mouse.

The Question: Why is the door so heavy (TeV) while the mouse is so light (GeV)? Why are these two scales connected?

The Magic Trick: The "Infrared Fixed Point"

The authors explain this connection using a concept called an Infrared Fixed Point.

Imagine the Dark World is a giant, stretching rubber band.

1. The Stretch (UV Completion): To build that heavy "Neutron Portal" door, you need to introduce new, heavy particles into the Dark World. These particles are like heavy weights attached to the rubber band.
2. The Snap (Confinement): When you attach these heavy weights, the rubber band (the Dark World's force) gets stressed. It snaps out of its stretched state and suddenly contracts.
3. The Result: This contraction creates a new, smaller scale. The authors show that if you build the door at the TeV scale, the rubber band naturally snaps and contracts to the GeV scale.

The Analogy: It's like tuning a guitar string. If you tighten the tuning peg (the heavy door) to a specific tension, the string naturally vibrates at a specific, lower note (the light Dark Matter). You don't need to manually set the note; the physics of the string forces it to happen.

The "Supercooled" Event: The Big Bang's Ice Age

The paper also connects this to a recent discovery: Gravitational Waves (ripples in space-time) detected by pulsar timing arrays.

The authors suggest that the Dark World underwent a Phase Transition (like water freezing into ice) that was "supercooled."

• Imagine water that stays liquid even when it's far below freezing. Then, suddenly, it freezes all at once, releasing a massive burst of energy.
• This "freezing" event created the gravitational waves we are seeing now.
• Crucially, this event also diluted everything that existed before it. It wiped the slate clean.
• The Twist: Because the slate was wiped clean, the Dark Matter and Visible Matter had to be created after this freezing event. The Neutron Portal is the mechanism that created them after the freeze, ensuring they are perfectly balanced.

The "Ghost" Messenger and the "Dark Pions"

The paper also discusses what happens to the Dark Matter particles.

• The Messenger ($\chi$): This is the particle that walks through the Neutron Portal. It has to be heavy enough to not mess up the formation of atoms (Big Bang Nucleosynthesis), but light enough to be produced.
• The Decay: The messenger must decay (die) quickly, turning into regular neutrons and protons to populate our universe. If it lives too long, it ruins the chemistry of the early universe. The paper calculates that it must die within about 0.1 seconds after the Big Bang.

How Do We Find This? (The Hunt)

The authors aren't just doing math; they are telling experimentalists where to look.

1. Beam Dump Experiments: Imagine firing a giant cannonball (a proton beam) into a thick block of lead (a "beam dump"). If the Neutron Portal exists, some particles might bounce off the lead, turn into our "Dark Messenger," and then decay inside a detector further down the line. Experiments like SHiP and NA62 are looking for these ghosts.
2. Colliders: The Large Hadron Collider (LHC) could also produce these particles, though they are harder to catch because they might be too heavy or decay too fast.

Summary: The Grand Story

1. The Puzzle: Why is Dark Matter only 5x heavier than normal matter?
2. The Bridge: A "Neutron Portal" connects the two worlds, allowing them to share their creation story.
3. The Mechanism: The heavy door (TeV scale) forces the Dark World to contract, naturally creating light Dark Matter (GeV scale).
4. The Timing: A "supercooled" freezing event in the Dark World wiped the universe clean, forcing the creation of matter after the event, linking the two scales perfectly.
5. The Proof: We can test this by looking for specific particles in beam dump experiments and checking if the math matches the gravitational waves we hear from the universe.

In short, the paper argues that the "Coincidence" isn't a coincidence at all. It's the inevitable result of a heavy door forcing a light room to exist, all triggered by a cosmic freeze that reset the universe's clock.

Technical Summary

1. Problem Statement

The paper addresses two major cosmological puzzles simultaneously:

1. The Dark Matter-Baryon Coincidence Puzzle: The observed energy densities of Dark Matter ($\Omega_{DM}$) and baryons ($\Omega_b$) are of the same order of magnitude ($\Omega_{DM} \approx 5.4 \Omega_b$), despite potentially distinct origins. In the Asymmetric Dark Matter (ADM) paradigm, this implies the Dark Matter mass ($m_{DM}$) must be in the GeV range ($m_{DM} \approx 5$ GeV) to satisfy $n_{DM} \approx n_b$.
2. The Origin of the GeV Scale: While the coincidence puzzle suggests a GeV-scale DM, the physical mechanism generating this specific mass scale in the Dark Sector (DS) remains unexplained.
3. Gravitational Wave (GW) Connection: Recent nano-Hz stochastic gravitational wave signals detected by Pulsar Timing Arrays (PTA) suggest a first-order phase transition (PT) in a dark sector with a confinement scale $\Lambda_{dQCD} \sim \mathcal{O}(\text{GeV})$. This PT must be strongly supercooled, which dilutes any pre-existing baryon asymmetry.

Core Challenge: How to dynamically generate a GeV-scale confinement in the dark sector that is naturally correlated with the multi-TeV scale cutoff ($\Lambda_n$) of the "neutron portal" operator required to transfer asymmetry from the dark sector to the visible sector after the phase transition.

2. Methodology

The authors propose a framework where the neutron portal operator connects the visible and dark sectors, and its Ultraviolet (UV) completion dictates the dynamics of the dark sector.

A. The Neutron Portal Operator

The effective operator transferring asymmetry is:
$$\mathcal{O}_{n\chi} = \frac{1}{\Lambda_n^2} (\chi^c d_R^c) (u_R d_R^c)$$
where $\chi$ is a dark fermion, $u, d$ are SM quarks, and $\Lambda_n$ is the effective cutoff scale. To satisfy cosmological constraints (BBN, CMB) and transfer asymmetry efficiently, $\Lambda_n$ is constrained to the range $2 \text{ TeV} \lesssim \Lambda_n \lesssim 15 \text{ TeV}$.

B. UV Completions

The paper analyzes two mechanisms to UV-complete this operator, introducing new colored and dark-charged particles:

1. Tree-Level Completion: Introduces a colored scalar $\Phi$ coupling to SM quarks and $\chi$. The cutoff is $\Lambda_n \sim m_\Phi / \sqrt{y}$.
2. Loop-Level Completion: Introduces a box diagram involving dark fermions ($\Psi, \psi$) and scalars ($\sigma, \phi$). This is the primary focus for connecting to the dark sector dynamics.

C. Fixed-Point Dynamics and Confinement

The dark sector is modeled as a "Dark QCD" ($SU(N_D)$) governed by an approximate Infrared (IR) fixed point in the UV.

• Mechanism: New heavy particles (from the UV completion) acquire TeV-scale masses (e.g., via a Giudice-Masiero mechanism in a SUSY extension) and are integrated out.
• Flow: Removing these degrees of freedom perturbs the conformal field theory, causing the dark gauge coupling to run away from the fixed point.
• Result: The theory becomes asymptotically free in the IR, leading to confinement at a scale $\Lambda_{dQCD}$. The authors demonstrate that for specific particle contents and mass hierarchies, this dynamically generates $\Lambda_{dQCD} \sim \mathcal{O}(\text{GeV})$.

D. Cosmological and Phenomenological Analysis

• Asymmetry Transfer: The PT generates an asymmetry in $\chi$, which is transferred to SM baryons via the neutron portal decay $\chi \to n + \pi/\gamma$.
• Constraints: The paper rigorously analyzes constraints from Big Bang Nucleosynthesis (BBN) and the Cosmic Microwave Background (CMB) on the lifetime of $\chi$ ($\tau_\chi$).
• Experimental Probes: The authors calculate production cross-sections for $\chi$ in beam-dump experiments (CHARM, NA62, SHiP) and colliders (LHC mono-jet searches).

3. Key Contributions

1. Dynamical Correlation of Scales: The paper establishes a direct link between the multi-TeV scale of the neutron portal ($\Lambda_n$) and the GeV scale of dark confinement ($\Lambda_{dQCD}$). The mass of the UV completion particles ($M_D \sim \text{TeV}$) sets the scale for the fixed-point perturbation, which naturally yields $\Lambda_{dQCD} \sim \text{GeV}$.
2. Loop-Level UV Completion: The authors detail a specific box-diagram loop completion that avoids tree-level dominance and allows for a light dark fermion ($\psi$) to form the stable Dark Matter candidate (Dark Baryon).
3. ALP Portal Emergence: They show that integrating out the heavy messenger quarks inevitably generates an effective Axion-Like Particle (ALP) portal between dark mesons and SM gauge bosons ($G\tilde{G}$ and $B\tilde{B}$), which can facilitate the decay of symmetric dark matter components.
4. Comprehensive Constraints:
   • BBN/CMB: They derive a strict exclusion window for the $\chi$ lifetime: $0.1 \text{ s} \lesssim \tau_\chi \lesssim 10^{25} \text{ s}$ (for $A_0 \gtrsim 1$). Viable scenarios require $\tau_\chi \lesssim 0.1 \text{ s}$ (to decay before BBN) or $\tau_\chi \gtrsim 10^{25} \text{ s}$ (stable DM).
   • Experimental Reach: They project that future beam-dump experiments like SHiP can probe $\Lambda_n$ up to $\sim 5$ TeV and $m_\chi$ up to $\sim 14$ GeV.

4. Results

• Mass Scale Generation: For a loop-level completion with dark particles at $M_D \sim 1\text{--}3$ TeV and specific flavor counts (e.g., $n_\psi=5, n_\phi=0$), the model yields $\Lambda_{dQCD} \approx 1.1$ GeV. This results in a Dark Baryon mass $m_{BD} \approx 4\text{--}6$ GeV, perfectly matching the ADM requirement.
• Cutoff Correlation: The model predicts $\Lambda_n \approx 7.76$ TeV for specific benchmark parameters ($m_\psi = 500$ MeV, $m_\chi = 5$ GeV, $M_D \sim \text{TeV}$), fitting within the required $2\text{--}15$ TeV window.
• Lifetime Constraints:
  • If $\chi$ decays after neutron freeze-out but before BBN ($t \sim 1\text{--}200$ s), it alters the neutron-to-proton ratio, violating observed Helium-4 abundance ($Y_p$).
  • If $\chi$ decays after recombination, it distorts the CMB.
  • Conclusion: The viable parameter space for the asymmetry-sharing scenario is restricted to $\tau_\chi \lesssim 0.1$ s.
• Experimental Sensitivity:
  • Beam Dumps: SHiP is projected to cover the region $2 \text{ TeV} \lesssim \Lambda_n \lesssim 100 \text{ TeV}$ for $m_\chi \lesssim 14$ GeV.
  • Colliders: Current LHC mono-jet searches set a lower bound of $\Lambda_n \gtrsim 1.5$ TeV.

5. Significance

This work provides a dynamical solution to the "why GeV?" question in Asymmetric Dark Matter. Instead of postulating the GeV scale, it derives it from the requirement of UV-completing the neutron portal operator within a theory featuring an IR fixed point.

• Unification of Phenomena: It connects three distinct observations: the DM-Baryon coincidence, the PTA gravitational wave signal (requiring a GeV-scale PT), and the neutron portal phenomenology.
• Testability: The framework is highly testable. The specific correlation between $\Lambda_n$ and $\Lambda_{dQCD}$ means that if beam-dump experiments (like SHiP) discover a long-lived fermion in the GeV mass range with a specific coupling scale, it would strongly support this UV completion mechanism.
• Theoretical Robustness: By utilizing fixed-point dynamics, the model avoids ad-hoc mass parameters for the dark sector, offering a more natural explanation for the hierarchy between the TeV scale (portal) and the GeV scale (confinement).

The paper concludes that while the loop-level completion requires a Higgs portal to ensure thermalization, the core mechanism successfully links the high-energy UV physics to the low-energy dark matter phenomenology, offering a compelling narrative for the origin of the dark matter mass.