Annihilating to the Darker: Thermal Relic Dark Matter with an Ultraweak Portal to the Standard Model

This paper proposes that thermal relic dark matter can remain viable despite ultraweak couplings to the Standard Model by annihilating primarily into a hidden "darker" sector through strong hidden-concealed interactions, a mechanism demonstrated via coupled Boltzmann equations in two specific $U(1)$ gauge models.

The Gist

Imagine the universe is a massive, bustling city. For decades, scientists have been looking for a specific type of "ghost" living in this city: Dark Matter. They expected these ghosts to be like shy neighbors who occasionally bump into regular people (the Standard Model particles we can see and touch). If they bumped into us often enough, we would have found them by now using giant underground detectors or telescopes.

But we haven't found them. The "ghosts" seem to be even shyer than we thought.

This paper proposes a clever new way to explain why we can't find them, using a story about three neighborhoods in our cosmic city:

1. The Visible Neighborhood: This is our world, full of stars, planets, and us.
2. The Hidden Neighborhood: This is where the Dark Matter we usually look for lives. It's connected to our world by a very thin, almost invisible thread (an "ultraweak portal").
3. The Darker Neighborhood: This is a secret, secluded area even further away. It's connected to the Hidden Neighborhood by a wide, busy highway.

The Old Problem: The "Too Shy" Ghost

For many years, scientists viewed dark matter with a mass close to that of the Higgs boson as one of the most promising possibilities. Many experiments were therefore designed to search precisely in this mass range. At the same time, scientists generally believed that dark matter in this mass range had to interact with the visible world with enough strength to explain the abundance of dark matter we see in the universe today. In other words, the conventional thinking was: to leave the right amount of Dark Matter after the Big Bang, it must have been able to bump into regular matter strongly enough.

But if it bumped into us that much, our detectors would have seen it by now. The fact that we haven't seen it suggests the connection between Dark Matter and our world is incredibly weak—too weak to explain how the Dark Matter population got so small naturally.

The New Idea: "Annihilating to the Darker"

The authors suggest a different story. Imagine the Dark Matter in the Hidden Neighborhood is trying to reduce its own population to match the universe's rules.

Instead of trying to bump into us (which is hard because the door is locked), they decide to interact with their neighbors in the Darker Neighborhood.

• The Mechanism: The Dark Matter particles in the Hidden Neighborhood are very friendly with the particles in the Darker Neighborhood. They have a strong "party" there.
• The Result: Instead of disappearing by bumping into us, they disappear by turning into particles that live in the Darker Neighborhood, or by annihilating each other into energy that stays in that dark sector.

Because they are busy interacting with the "Darker" neighbors, they don't need to interact with us at all. This explains why they are so hard to find: they are essentially ignoring us to hang out with their own secret society.

Two Ways This Plays Out

The paper describes two specific scenarios for how this "party" works:

1. The "Assisted Depletion" (The Helper)
Imagine the Dark Matter in the Hidden Neighborhood is the main character. It wants to reduce its numbers. It calls in the Darker Neighborhood to help. The Darker Neighborhood acts like a giant vacuum cleaner, sucking up the excess Dark Matter.

• Outcome: The Dark Matter we are looking for is still the main type in the universe, but its numbers were successfully lowered by the help of the secret neighbors. We still haven't found it because it barely talks to us, but the math works out perfectly.

2. The "Darker Conversion" (The Transformation)
In this scenario, the Dark Matter in the Hidden Neighborhood doesn't just get help; it actually moves or transforms into the Darker Neighborhood.

• Outcome: The "ghosts" we were looking for (in the Hidden Neighborhood) mostly turned into a different, even more secret type of ghost (in the Darker Neighborhood). So, the dominant Dark Matter today is actually the one living in the deepest secret, which is even harder for us to detect. The original type we were hunting is now just a tiny, leftover remnant.

Why This Matters

The paper uses complex math (called "Boltzmann equations") to prove that this scenario is possible. They built two specific models:

• Model A: Uses invisible "force fields" (gauge bosons) to connect the neighborhoods.
• Model B: Uses a "messenger particle" (a real scalar) to carry messages between the neighborhoods.

In both models, they show that Dark Matter can exist at masses we can test (between 1 and 200 GeV) without breaking any of the rules set by our current experiments. The key is that the "door" to our world is tiny (so we don't see it), but the "door" to the secret neighborhood is wide open (so the population dynamics work out).

The Takeaway

This paper suggests that the reason we haven't found Dark Matter isn't because it doesn't exist, but because we've been looking in the wrong place. We've been waiting for it to knock on our door, but it's actually spending all its time in a secret room next door, interacting with a darker, more secluded group. As long as that secret group is busy, the Dark Matter population stays just right, and we remain none the wiser.

Technical Summary

Technical Summary: Annihilating to the Darker

Problem Statement
Thermal relic dark matter (DM) candidates, particularly Weakly Interacting Massive Particles (WIMPs) in the 1–200 GeV mass range, face severe constraints from direct detection experiments, indirect searches, and multi-messenger probes. Conventional models require sizable couplings between DM and Standard Model (SM) particles to achieve the correct relic abundance via freeze-out. However, these same couplings typically induce large elastic scattering cross-sections with hadrons, which are increasingly excluded by direct detection limits, and produce indirect signals that have not been observed. The central problem addressed is how to reconcile the existence of an electroweak-scale thermal relic with the ultraweak portal constraints imposed by current experiments, without rendering the DM cosmologically ineffective.

Methodology
The authors propose a framework where thermal DM resides in a "hidden sector" that couples only ultraweakly to the SM, while interacting significantly with a "darker concealed sector." The cosmological evolution of the DM abundance is governed not by the SM portal, but by interactions within and between these dark sectors.

To analyze this, the paper employs the following methodology:

1. Portal Classification: A model-independent summary of renormalizable portal interactions (scalar, gauge, fermion, and axion-like particle portals) connecting the SM, hidden, and concealed sectors. The authors distinguish between portals constrained by experimental data (SM–hidden) and those that are less constrained (hidden–concealed).
2. Model Realizations: Two specific $U(1)$ gauge extensions are constructed to illustrate the mechanism:
   • Prototype Framework ($U(1)_X \times U(1)_C$): A generic setup with kinetic and mass mixing between a hidden $U(1)_X$ and a concealed $U(1)_C$. The hidden sector communicates with the SM via ultraweak kinetic mixing ($\delta_1$), while the hidden–concealed connection is mediated by stronger kinetic ($\delta_2$) and mass ($M_m$) mixing.
   • Motivated Framework ($U(1)_{B-L} \times U(1)_C$): A setup where the hidden sector is gauged $U(1)_{B-L}$, which is strongly constrained by SM interactions. The connection to the concealed $U(1)_C$ sector is mediated primarily by a real scalar field $\phi$, which couples to hidden and concealed fermions via Yukawa interactions ($y_x, y_c$) but does not mix with the SM Higgs.
3. Dynamical Evolution: The authors solve the full set of coupled Boltzmann equations for all relevant dark sector particles (fermions, gauge bosons, and scalars). This approach avoids the assumption that dark mediators remain in thermal equilibrium with the SM bath, a condition that may fail when the SM portal is ultraweak.

Key Contributions and Mechanisms
The paper identifies two distinct phenomenological scenarios enabled by the "Annihilating to the Darker" mechanism:

• Assisted Depletion: The hidden sector DM ($\chi_x$) remains the dominant component of the universe today. However, its relic abundance is efficiently depleted not by annihilating into SM particles, but through annihilation into the darker sector (e.g., $\chi_x \chi_x \to \chi_c \chi_c$ or $\chi_x \chi_x \to Z'_c Z'_c$). The darker sector acts as a sink, reducing the $\chi_x$ abundance to the observed value ($\Omega h^2 \approx 0.12$) despite the ultraweak SM coupling.
• Darker Conversion: The hidden sector DM ($\chi_x$) is not the dominant relic. Instead, its abundance is predominantly transferred into the darker sector states ($\chi_c$) via efficient conversion channels. In this scenario, the dominant DM component today resides in the concealed sector, while the state directly connected to the SM ($\chi_x$) survives only as a subdominant remnant.

Results
The authors present benchmark models for both frameworks across the 1–200 GeV mass range:

• $U(1)_X \times U(1)_C$ Benchmarks: Models (e.g., a1, b1, c1) demonstrate successful assisted depletion where $\chi_x$ achieves the correct relic density with a tiny kinetic mixing parameter $\delta_1$ (satisfying direct detection) but a sizable hidden–concealed mixing $\delta_2$. Models (e.g., a2, b2, c2) illustrate darker conversion where $\chi_c$ becomes the dominant relic.
• $U(1)_{B-L} \times U(1)_C$ Benchmarks: Due to the strong constraints on $U(1)_{B-L}$, direct annihilation into SM fermions or $Z'_{BL} Z'_{BL}$ is insufficient. The scalar-mediated channels ($\chi_x \chi_x \to \phi \phi$ and $\chi_x \chi_x \to \chi_c \chi_c$) successfully drive the depletion or conversion.
  • The models satisfy constraints from direct detection, indirect detection (CMB, AMS02, Fermi), and collider/low-energy searches (LHCb, NA62, COHERENT).
  • A specific benchmark (Model f1') demonstrates that this framework can accommodate asymmetric dark matter scenarios with $\mathcal{O}(1)$ GeV masses, efficiently depleting the symmetric component to below 1% of the total relic density.
  • Special cases (Models c2' and f2') show scenarios where the DM candidate is the lightest particle in the entire dark sector, differing from typical secluded scenarios where the mediator is lighter.

Significance
The paper claims that the "Annihilating to the Darker" mechanism provides a viable pathway for electroweak-scale thermal relic dark matter to survive current experimental constraints. The primary significance lies in decoupling the interaction responsible for experimental visibility (the SM portal) from the interaction governing cosmological evolution (the hidden–concealed portal). By solving the full coupled Boltzmann equations, the authors demonstrate that thermal relics can remain viable even when the SM portal is ultraweak, provided that sufficiently strong interactions exist within a multi-sector dark framework. This approach extends the viable parameter space for thermal DM and offers a general mechanism that can be applied to various mass ranges and additional dark sector structures.