Freeze-in $SU(2)$ vector dark matter at low reheating temperature

This paper proposes a freeze-in mechanism for $SU(2)$ vector dark matter in a low-reheating-temperature cosmology, demonstrating that the non-abelian structure allows for sizable couplings consistent with observed relic abundance that are potentially detectable by current and future direct detection experiments.

The Gist

The Big Picture: A "Cold Start" for the Universe

Imagine the early universe as a giant, chaotic kitchen. Usually, scientists think that when the universe was born, it was a super-hot, boiling soup where everything mixed together perfectly. In this "hot soup" scenario, Dark Matter (the invisible stuff that holds galaxies together) would have been created easily, but it would have interacted so weakly with normal matter that we can't find it today. This is the standard "Freeze-in" theory: the Dark Matter particles are like ghosts that never quite got into the party.

This paper proposes a different story.

The authors suggest that maybe the universe didn't get as hot as we thought. Imagine the kitchen didn't turn on the full blast of the stove; instead, it only got "warm" before cooling down. This is called a low reheating temperature.

Because the kitchen wasn't hot enough, the "ghosts" (Dark Matter) couldn't easily form. To get enough of them to fill the universe today, they needed a little help. The paper argues that if the universe was cooler, the Dark Matter particles must have had stronger connections to normal matter than we previously thought. This makes them much easier to catch in experiments today.

The Characters: The "Triplet" of Dark Matter

The authors are studying a specific type of Dark Matter made of Vector Bosons (think of them as heavy, invisible force-carriers).

• The Standard Model (The Normal Crowd): These are the particles we know (electrons, quarks, etc.).
• The Hidden Sector (The VIPs): The paper introduces a hidden group of three particles (let's call them X1, X2, and X3).
• The "Bodyguard" Symmetry: Usually, to keep Dark Matter stable (so it doesn't just disappear), scientists have to invent a special rule (like a "Z2 symmetry") to lock it in place. This paper is clever because it doesn't need that extra rule. The three particles are protected by a natural "custodial symmetry" (like a perfect trio of bodyguards). Because they are so perfectly matched, they can't decay; they are stuck together forever.

The Mechanism: The "Higgs Portal"

How do these invisible VIPs talk to the normal crowd? They use a "Higgs Portal."

Think of the Higgs boson as a universal translator or a bridge. The Dark Matter particles don't talk to normal matter directly. Instead, they talk to a new, hidden particle (a scalar), which then talks to the Higgs, which talks to us.

In a normal, hot universe, this bridge is very narrow and hard to cross. But in this paper's "cool universe" scenario, the bridge is wider. Because the universe was cooler, the Dark Matter particles had to be more "aggressive" (have stronger couplings) to cross that bridge and get created.

The Results: Why This Matters for Detection

Here is the exciting part for real-world science:

1. The "Goldilocks" Coupling: In old theories, Dark Matter was so weakly connected to us that we could never hope to find it. In this new "cool universe" theory, the connection is much stronger. It's like the difference between trying to hear a whisper from a mile away versus hearing someone shout from the next room.
2. The "Triplet" Advantage: Because there are three types of Dark Matter particles (X1, X2, X3) instead of just one, the math works out differently. It's like having three people trying to fill a bucket instead of one. This allows the model to work with a wider range of settings, making it more flexible and robust.
3. We Can Actually Look for It: The paper shows that with these stronger connections, existing experiments like PandaX-4T and LZ (which use giant tanks of liquid xenon to catch Dark Matter) might already be seeing hints of it, or at least have ruled out some possibilities.
   • The "Neutrino Floor": There is a limit to how sensitive our detectors can get because neutrinos (tiny particles from the sun) create background noise. The paper shows that while some of their ideas are blocked by this noise, a significant "safe zone" remains where future experiments like DARWIN could definitely find these particles.

The Conclusion: A New Way to Look

The authors conclude that if the universe started with a lower temperature than we assumed, Dark Matter might be much more "tangible" than we thought.

Instead of being an invisible ghost that we can never catch, this Dark Matter might be a "heavy, slightly visible" particle that interacts strongly enough to be detected by our current or next-generation machines. The fact that there are three of them (a triplet) and they are naturally stable makes this a very attractive and testable idea.

In short: The paper suggests the universe was cooler than we thought, which means Dark Matter is "louder" and "heavier" than we expected, giving us a much better chance of catching it in our detectors.

Technical Summary

Technical Summary: Freeze-in SU(2) Vector Dark Matter at Low Reheating Temperature

Problem and Motivation
The standard paradigm for Weakly Interacting Massive Particles (WIMPs) relies on thermal freeze-out, but null results from direct, indirect, and collider searches have significantly constrained this scenario. Conversely, the "freeze-in" mechanism, where Dark Matter (DM) is produced via extremely feeble couplings ($\lesssim 10^{-10}$) that prevent thermal equilibrium, offers an alternative. However, conventional freeze-in models are notoriously difficult to test experimentally due to these minute couplings. Furthermore, the assumption of a negligible initial DM density is increasingly challenged.

Recent studies suggest that the assumption of suppressed couplings can be relaxed if the reheating temperature ($T_{RH}$) of the early universe is sufficiently low ($T_{RH} < m_{DM}$). In such a low-$T_{RH}$ cosmology, DM production is Boltzmann-suppressed ($\sim \exp(-m_{DM}/T_{RH})$), requiring larger DM couplings to achieve the observed relic abundance. This work investigates this specific regime within the context of a non-Abelian $SU(2)_{HS}$ vector dark matter (VDM) model, contrasting it with Abelian $U(1)_X$ models.

Model Framework
The authors propose a minimal Beyond-the-Standard-Model (BSM) extension featuring:

1. Hidden Gauge Sector: A non-Abelian $SU(2)_{HS}$ gauge symmetry under which Standard Model (SM) particles are singlets. This sector contains three spin-1 gauge bosons, $X_i$ ($i=1,2,3$), which serve as the DM candidates.
2. Scalar Sector: A BSM scalar doublet $\phi$ charged under $SU(2)_{HS}$ and a singlet under the SM. The vacuum expectation value (VEV) of $\phi$ spontaneously breaks $SU(2)_{HS}$, generating a common mass $m_X = \frac{1}{2}g_\phi v_\phi$ for the three vector bosons.
3. Stability Mechanism: Unlike Abelian models that require an ad hoc $Z_2$ symmetry to ensure stability and forbid kinetic mixing, the $SU(2)_{HS}$ breaking pattern leaves an accidental custodial $SO(3)$ symmetry. This symmetry ensures the three vector states remain mass-degenerate and stable, as interactions occur only via $SO(3)$-singlet combinations (e.g., $X^a_\mu X^{a\mu}$), forbidding single-particle decay vertices.
4. Portal Interaction: The DM interacts with the SM via a Higgs portal. The CP-even scalar components of the SM Higgs ($S$) and the hidden scalar ($\phi^0$) mix with an angle $\beta$, producing physical mass eigenstates $h$ (identified with the 125 GeV SM Higgs) and $\eta$.

Methodology
The production of DM is analyzed in the low-$T_{RH}$ regime where $T_{RH} < m_{DM}$. The evolution of the comoving number density $Y_X$ is determined by solving the Boltzmann equation, which includes:

• Annihilation Channels: $f\bar{f} \to XX$, $VV \to XX$ (where $V=W,Z$), and scalar annihilations ($hh, \eta\eta, h\eta \to XX$) mediated by $h$ and $\eta$.
• Decay Channels: Decays of scalars $h, \eta \to XX$ (kinematically allowed when $2m_X \le m_{scalar}$).
• Thermal Suppression: The integration over the thermal distribution is dominated by the high-energy tail when $T < m_{DM}$, leading to an exponential suppression of the production rate.

The authors perform numerical scans over the parameter space defined by the DM mass ($m_{DM}$), the gauge coupling ($g_\phi$), the scalar mixing angle ($\sin \beta$), and the heavy scalar mass ($m_\eta$). They calculate the relic abundance $\Omega h^2$ and compare it against the observed value ($0.12$).

Key Results and Constraints

1. Coupling vs. Reheating Temperature: The study confirms that for $T_{RH} < m_{DM}$, the required gauge coupling $g_\phi$ is significantly larger than in standard freeze-in scenarios. For instance, to satisfy the relic density with $m_{DM} \sim 100$ GeV and $T_{RH} = 5$ GeV, a coupling of $g_\phi \sim \mathcal{O}(10^{-1})$ is required, compared to $\mathcal{O}(10^{-10})$ in vanilla freeze-in.
2. Multiplicity Effect: The $SU(2)_{HS}$ model features three degenerate DM components. The total relic abundance is $Y_{DM} = 3Y_X$. This multiplicity allows the model to satisfy the observed relic density with a slightly smaller individual coupling compared to a single-component $U(1)_X$ model, thereby opening a larger viable parameter space.
3. Direct Detection: The enhanced couplings in the low-$T_{RH}$ regime bring the model into the sensitivity range of current and future direct detection experiments.
   • Current Limits: A significant portion of the parameter space is already excluded by the LZ 2024 and PandaX-4T experiments, particularly for lower DM masses.
   • Future Prospects: Despite these constraints, a viable region remains, largely below the "neutrino floor," which is accessible to future experiments like DARWIN.
   • Comparison: The $SU(2)_{HS}$ model allows for slightly higher DM masses to evade current direct detection limits compared to single-component models (e.g., up to 92 GeV vs. 89 GeV for $T_{RH}=5$ GeV in the specific benchmark analyzed).
4. Indirect Detection: Constraints from Fermi-LAT and AMS on the annihilation channel $XX \to W^+W^-$ are analyzed. The study finds that indirect detection bounds are significantly weaker than direct detection limits for the parameter space satisfying the relic density.
5. Theoretical Consistency: The model parameters are constrained by perturbative unitarity, vacuum stability, and collider bounds (specifically Higgs invisible decay widths and signal strengths).

Significance and Claims
The paper claims that the interplay between a low reheating temperature and a non-Abelian hidden sector offers a distinct and testable dark matter scenario. The primary significance lies in:

• Testability: By invoking low $T_{RH}$, the model shifts the required couplings from the untestable "feeble" regime to a "sizable" regime, rendering the DM discoverable in next-generation direct detection experiments.
• Structural Advantage: The non-Abelian $SU(2)_{HS}$ structure naturally provides stability via custodial symmetry without ad hoc discrete symmetries and enhances the viable parameter space through the multiplicity of three degenerate DM states.
• Bridging Paradigms: This scenario bridges the gap between the parameter spaces of thermal freeze-out and vanilla freeze-in, offering a new viable pathway for DM genesis that is consistent with current null results but predictive for future searches.

The authors conclude that while stringent direct detection constraints exclude parts of the parameter space, a significant region remains viable and testable, highlighting the importance of considering low reheating temperatures in DM model building.