WIMP-like Dark Matter Without Thermalization At Freeze-Out

This paper proposes a hidden-sector dark matter model where the dark matter and Standard Model decouple at high temperatures yet evolve to similar temperatures at freeze-out, allowing for the observed relic abundance with standard annihilation cross sections while rendering direct detection and collider signals potentially unobservable due to extremely weak couplings.

The Gist

The Big Picture: A Cosmic Coincidence

For decades, physicists have had a favorite theory about what Dark Matter is. They call it the WIMP (Weakly Interacting Massive Particle). The idea is that Dark Matter particles were once swimming in the same "hot soup" as normal matter (like atoms and light) in the early universe. As the universe cooled, they stopped interacting, leaving behind just the right amount of Dark Matter to explain what we see today.

This theory is popular because it predicts that Dark Matter should interact with normal matter just enough to be detected by sensitive experiments on Earth. However, after years of searching, we haven't found any WIMPs. This has led scientists to consider a "Hidden Sector" theory: Dark Matter lives in its own separate world, barely talking to us.

The Problem with the Hidden Sector:
If Dark Matter lives in a separate world, why should it have the same temperature as our world? If they are separate, they could be at totally different temperatures. If they are different, the math breaks, and we can't predict how much Dark Matter should exist. To fix this, previous theories demanded that the two worlds must stay connected (in thermal equilibrium) until the very end, which implies Dark Matter must be detectable by our current machines.

The New Discovery:
This paper argues that we don't need to keep the two worlds connected until the end. We just need them to have been connected very early on.

The Analogy: The Two Rooms and the Heavy Door

Imagine the early universe as a giant building with two rooms: Room A (Our Visible World) and Room B (The Hidden Dark Matter World).

1. The Early Party (High Temperature):
   In the very beginning, the building is incredibly hot. There is a massive, heavy door between the rooms. Even though the door is heavy, the heat is so intense that particles can smash through it easily. The air in both rooms mixes perfectly. They reach the same temperature.

2. The Cooling Down (Freeze-Out):
   As the universe expands, it cools down. The "heavy door" (mediated by very heavy particles) becomes too heavy for the cooling particles to push through. The door effectively slams shut.

   • Crucial Point: The door shuts before the Dark Matter particles stop interacting with each other.
   • Because the door was open long enough to equalize the temperature, Room A and Room B are still at the same temperature when the door closes.

3. The Separation:
   Now, the two rooms are isolated. Room B (Dark Matter) evolves on its own. Because it started at the same temperature as Room A, it naturally ends up with the exact same "recipe" for how much Dark Matter is left over.

The Result:
Even though the door is now so heavy and the connection between the rooms is so weak that we can't detect it with our current machines (like direct detection experiments or colliders), the Dark Matter still behaves exactly like a standard WIMP. It has the right amount to explain the universe, but it is "invisible" to us because the link is too faint.

The "Entropy Dilution" Mechanism: The Water Cooler

The paper also explains a second mechanism that helps this work, which they call Entropy Dilution.

Imagine the Dark Matter room has a lot of "heavy furniture" (unstable mediator particles) that eventually breaks down into dust (normal matter) and falls into our room.

• When this furniture breaks down, it dumps a huge amount of energy (heat) into our room.
• This is like pouring a giant bucket of water into a small cup. The water level (our visible matter) rises, but the amount of "stuff" (Dark Matter) relative to the water gets diluted.
• This dilution allows the Dark Matter to have a much higher mass or different properties than a standard WIMP, while still ending up with the correct amount we observe today.

Why This Matters

1. It Solves the "Why?" Question: It explains why Dark Matter has the "WIMP miracle" abundance (the perfect amount) without requiring it to be easily detectable right now.
2. It Explains the Silence: It suggests that the reason we haven't found Dark Matter yet isn't because our theories are wrong, but because the connection between our world and the Dark Matter world is incredibly weak—so weak that it might be below the sensitivity of even our most advanced future detectors (a limit they call the "neutrino fog").
3. It's Natural: The authors show that this scenario happens naturally in many theoretical models where heavy particles exist at very high energies (like those found in Grand Unified Theories).

Summary

The paper claims that Dark Matter could be a "WIMP-like" particle that naturally has the right abundance for our universe, even if it is completely decoupled from us today. This happens because the two sectors (our world and the dark world) were once hot enough to mix and equalize their temperatures long ago. Now, they are separated by a "heavy door" that is too hard to open, making Dark Matter incredibly hard to find, even though it follows the same rules as the standard theory.

Technical Summary

Technical Summary: WIMP-like Dark Matter Without Thermalization At Freeze-Out

Problem Statement
In the standard Weakly Interacting Massive Particle (WIMP) paradigm, dark matter (DM) is assumed to remain in chemical equilibrium with the Standard Model (SM) radiation bath until freeze-out occurs at a temperature $T \sim m_X/20$. This scenario, often termed the "WIMP miracle," predicts a thermal relic abundance consistent with observations for an annihilation cross section of $\sigma v \sim 10^{-26} \text{ cm}^3/\text{s}$. However, stringent constraints from direct detection experiments and collider searches have motivated models where DM resides in a "hidden sector" that does not couple directly to SM particles.

A significant challenge in hidden sector models arises if the SM and hidden sectors never achieve thermal equilibrium. In such non-equilibrated scenarios, the relative temperatures of the two sectors are set by initial conditions (e.g., reheating), leading to arbitrary relic abundances that lack the predictive power of the WIMP miracle. Consequently, previous studies often imposed the requirement that the sectors remain in thermal equilibrium during freeze-out to justify a WIMP-like cross section. This requirement, however, imposes a lower bound on the portal coupling between the sectors, which in turn implies a lower bound on the DM-SM scattering cross section probed by direct detection experiments.

Methodology
The authors propose a mechanism where the SM and hidden sectors decouple at a very high temperature ($T \gg m_X$) but still achieve thermal equilibrium at earlier times. The methodology involves:

1. High-Temperature Thermalization: The authors argue that while the portal coupling ($\epsilon$) may be too feeble to maintain equilibrium at the DM freeze-out temperature, heavy particles (mass $M \gg T_{\text{freeze-out}}$) charged under both sectors can mediate efficient scattering at high temperatures ($T \sim M$). Because the interaction rate for processes mediated by heavy particles scales as $\Gamma \propto T^5$ (while the Hubble rate scales as $H \propto T^2$), equilibrium is established at high $T$ but decouples as the universe cools.
2. Entropy Conservation and Temperature Tracking: Once decoupled, the two sectors evolve with separate thermal histories. However, because they started with equal temperatures ($T_{\text{hidden}} = T_{\text{SM}}$) and the entropy injection from non-relativistic particle decays is comparable in both sectors, the ratio of hidden-to-SM temperatures ($\xi = T_h/T$) remains of order unity throughout the freeze-out epoch.
3. Numerical Simulation: The authors solve a coupled system of Boltzmann equations for the number densities of the DM particle ($X$) and the hidden-sector mediator ($Y$), along with the energy conservation equation for the hidden sector. The system accounts for:
   • $X\bar{X} \to YY$ annihilation.
   • $3 \to 2$ "cannibal" processes within the hidden sector ($YYX \to YX$, etc.).
   • The decay of the mediator $Y$ into SM particles via the portal coupling $\epsilon$.
   • Entropy injection into the SM bath from the late decay of $Y$, which dilutes the pre-existing comoving abundances.
4. Benchmark Models: The mechanism is explicitly realized using the Hypercharge Portal (kinetic mixing between a hidden $U(1)'$ and SM hypercharge). The authors also extend the analysis to the Higgs Portal, $B-L$ Portal, and Baryon Portal in the supplementary material.

Key Contributions and Results

• Restoration of the WIMP Miracle: The paper demonstrates that even if the portal coupling is too small to maintain equilibrium at freeze-out, the prior high-temperature thermalization ensures that the hidden sector temperature tracks the SM temperature ($\xi \approx 1$). Consequently, the required annihilation cross section to match the observed relic density remains comparable to the canonical WIMP value ($\sigma v \sim 10^{-26} \text{ cm}^3/\text{s}$).
• Decoupling of Scattering and Annihilation: A primary result is that the DM annihilation cross section (determined by hidden sector dynamics) can be WIMP-like, while the DM-SM scattering cross section (determined by the portal coupling $\epsilon$) can be arbitrarily small.
• Entropy Dilution Mechanism: For very small portal couplings, the mediator $Y$ decays late, injecting significant entropy into the SM bath. This dilutes the DM relic abundance. To compensate and match the observed density, the initial annihilation cross section must be slightly lower than the canonical WIMP value, but it remains within the same order of magnitude.
• Parameter Space Viability: Numerical results for the Hypercharge Portal model (with parameters $m_X = 100$ GeV, $m_{Z'} = 40$ GeV, $\alpha_X = 10^{-3}$) show that the observed relic density can be reproduced for portal couplings $\epsilon$ as low as $10^{-12}$ to $10^{-13}$.
• Observational Constraints:
  • Direct Detection: The predicted spin-independent DM-nucleon cross sections for these low-$\epsilon$ scenarios are many orders of magnitude below current sensitivities (LZ, XENONnT) and even below the "neutrino fog" limit.
  • Big Bang Nucleosynthesis (BBN): The lower bound on $\epsilon$ is set by BBN constraints. If the mediator decays too late (very small $\epsilon$), the injection of hadronic energy disrupts light element abundances. The paper identifies a lower limit of $\epsilon \gtrsim 10^{-13}$ (depending on mediator mass) to satisfy BBN bounds.
  • Indirect Detection: The paper notes that these models, with WIMP-like cross sections, remain potentially accessible to indirect detection searches (e.g., gamma-ray excesses), as the annihilation signal is not suppressed by the small portal coupling.

Significance and Claims
The authors claim to challenge the conventional logic that hidden sector DM models must maintain thermal equilibrium during freeze-out to be theoretically motivated. They argue that it is natural to expect equilibrium at much earlier times due to the presence of heavy states in UV completions (e.g., GUTs), even if the effective portal coupling at low energies is negligible.

The significance of this work lies in its ability to decouple the DM annihilation cross section from the direct detection cross section. This implies that:

1. The "WIMP miracle" (a thermal relic abundance with a weak-scale cross section) can persist even in hidden sector models where the DM is effectively "secluded" from the SM at the time of freeze-out.
2. Direct detection and collider searches may fail to detect such DM candidates not because the models are incorrect, but because the coupling between the sectors is simply too feeble, potentially placing signals far below foreseeable experimental sensitivities.
3. The viable parameter space for hidden sector DM is significantly larger than previously thought, specifically in the region of extremely small portal couplings that evade current direct detection limits while maintaining a WIMP-like thermal history.

The paper concludes that while these scenarios are difficult to probe via direct detection, they remain a plausible and well-motivated class of models that could potentially be tested through indirect detection or future precision cosmological measurements.