⚛️ phenomenology

A Freeze-In Interpretation of the LZ High-Energy Nuclear Recoil Event

This paper proposes a pseudo-Dirac fermion dark matter model with a vector mediator and freeze-in production via low reheating temperatures to explain the high-energy nuclear recoil event observed by the LUX-ZEPLIN experiment, demonstrating how this framework allows for a continuous parameter space that decouples the dark matter mass from the direct-detection cross section.

Original authors: D. Cabo-Almeida, F. Costa, D. Feiteira, V. Oliveira

Published 2026-09-14

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CC BY 4.0

Original authors: D. Cabo-Almeida, F. Costa, D. Feiteira, V. Oliveira

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

The universe is filled with invisible matter that holds galaxies together, yet we have never seen a single particle of it. This "dark matter" is a fundamental mystery in physics, and for decades, scientists have searched for it by building massive detectors deep underground, hoping to catch a rare collision between a dark matter particle and an ordinary atom. The most sensitive of these experiments, located in a former gold mine in South Dakota, recently reported a single, puzzling event: a heavy atomic nucleus recoiled with a surprisingly high amount of energy, far more than typical background noise would predict. While one event is not enough to prove the existence of dark matter, its unusual energy level has sparked a new wave of theoretical work. Researchers are now asking if this specific signal could be explained by a particular type of dark matter that behaves differently than the standard models predict, and if the history of the universe's cooling could change how we look for it.

A team of physicists has taken this single event and explored a new way to explain it, moving beyond the traditional ideas about how dark matter was created. In the standard view, dark matter particles were once hot and energetic, interacting frequently with the rest of the universe before cooling down and freezing into their current abundance. This process, known as thermal freeze-out, tightly links the mass of the dark matter particle to how strongly it interacts with normal matter. However, the authors of this study considered a different possibility: that dark matter was created when the universe was much cooler, a scenario called freeze-in. In this version, the particles were never hot enough to interact much; instead, they were slowly produced in tiny amounts from the energy of the early universe. Crucially, this team introduced a new variable: the temperature at which the universe reheated after a period of rapid expansion. By allowing this temperature to be lower than the mass of the dark matter particle, they found that the rules change. The strict connection between the particle's mass and its interaction strength is broken, opening up a wide range of possibilities that were previously closed off.

The researchers focused on a specific model where dark matter consists of two nearly identical particles that can switch places. One is stable and makes up the dark matter we see today, while the other is slightly heavier. When the stable particle hits an atomic nucleus in a detector, it must absorb energy to flip into the heavier state. This requirement acts like a speed bump, filtering out slow-moving particles and only allowing the fastest ones to cause a collision. This mechanism naturally explains why the detector saw a high-energy hit and not a flood of low-energy ones. The team tested this idea using two different versions of the model: one where the force carrier connecting dark matter to the visible world only talks to quarks, and another where it talks to all particles equally. They used powerful computer simulations to calculate how much dark matter would be produced in the early universe under these new conditions and whether those same particles would create the single event seen by the LUX-ZEPLIN experiment.

The results show that this scenario works remarkably well. The authors found that for a wide range of dark matter masses, specifically between 0.5 and 10 trillion electron volts, there is a continuous line of solutions that fit both the amount of dark matter in the universe and the single event observed. In the traditional thermal model, a specific mass would point to only one specific interaction strength. Here, because the reheating temperature is a free parameter, the same mass can work with many different interaction strengths. This means the dark matter could be lighter or heavier, and interact more or less strongly, than previously thought, as long as the universe cooled down at just the right rate. The study identifies the most promising candidates as dark matter particles with a mass between 0.5 and 1 trillion electron volts, which would produce a recoil spectrum that aligns best with the observed 248 kiloelectron volt event.

The team also checked whether these new models would run into trouble with other known physics. They confirmed that the heavier particle in the pair would not decay inside the detector in a way that would create a confusing signal, and they verified that the models are not ruled out by searches for new particles at the Large Hadron Collider. Furthermore, they addressed a previous concern about "solar capture," where the sun might trap dark matter and create too many signals; they found that for the masses they favor, this effect is actually weaker than in the standard thermal models, keeping the theory safe. The paper concludes that while this single event is not a definitive discovery, it is a compelling hint that fits a coherent picture of dark matter that was created through a non-thermal process in a cooler early universe. The findings suggest that the story of dark matter is more flexible than we thought, and that future data from the same experiment could help distinguish between these different possibilities, potentially revealing the true nature of the invisible mass that shapes our cosmos.

Technical Summary: A Freeze-In Interpretation of the LZ High-Energy Nuclear Recoil Event

Problem Statement
The LUX-ZEPLIN (LZ) experiment recently reported a single high-energy nuclear recoil candidate with a reconstructed energy of $E_R \simeq 248$ keV. While the statistical significance is insufficient to claim a discovery, the unusually large recoil energy distinguishes it from the standard thermal WIMP spectrum, which typically predicts a rapid fall-off at high energies and a surplus of low-energy events. Standard elastic spin-independent scattering struggles to explain an isolated high-energy event without predicting a large, unobserved population of lower-energy recoils. Previous interpretations have explored thermal pseudo-Dirac dark matter (DM) and thermal Higgsinos, though the latter face constraints from solar capture and the prediction of excessive high-energy events. This paper investigates whether the LZ candidate can be explained by inelastic dark matter produced via freeze-in at a low reheating temperature, a scenario that relaxes the strict constraints linking DM mass and interaction strength found in thermal freeze-out models.

Methodology
The authors analyze the LZ event within a pseudo-Dirac fermion model mediated by a heavy vector boson $Z'$ . The model consists of two nearly degenerate Majorana fermions ( $\chi_1$ and $\chi_2$ ) with a small mass splitting $\delta$ . The interaction is off-diagonal in the Majorana basis, leading to endothermic scattering ( $\chi_1 + N \to \chi_2 + N$ ), which suppresses low-energy recoils and shifts the spectrum toward higher energies.

The study employs two distinct coupling scenarios:

Leptophobic Model: The $Z'$ couples to the dark sector and quarks only.
Universal Coupling Model: The $Z'$ couples universally to all SM fermions.

The core methodological innovation is the application of freeze-in production in a low reheating temperature regime ( $T_R \ll m_{\chi}$ ). Unlike standard freeze-in (where couplings are feeble) or thermal freeze-out (where DM is in equilibrium), this regime assumes DM production is Boltzmann-suppressed. To reproduce the observed relic abundance, larger couplings are required to compensate for the suppression. The reheating temperature $T_R$ acts as a free parameter, breaking the one-to-one correspondence between the DM mass and the direct-detection cross-section ( $\sigma_N$ ).

The authors:

Derived analytical estimates for the DM yield and cross-section, validated against numerical solutions of the Boltzmann equation using micrOMEGAs.
Calculated the differential scattering rate for LZ, incorporating the Helm form factor, xenon isotope abundances, and the Standard Halo Model.
Imposed a "one-event benchmark" condition, normalizing the predicted signal to match the observed candidate ( $N_{sig} \approx 0.99$ ) while simultaneously satisfying the observed relic density ( $\Omega h^2 \approx 0.12$ ).
Checked constraints from dilepton resonance searches (ATLAS) and solar capture limits.

Key Contributions and Results
The paper demonstrates that the LZ high-energy recoil candidate can be accommodated over a continuous region of parameter space rather than at a single thermal benchmark point.

Decoupling of Mass and Cross-Section: In thermal freeze-out, the relic density fixes $\sigma_N$ for a given mass. In low- $T_R$ freeze-in, $T_R$ provides an additional degree of freedom. For a fixed DM mass, varying $T_R$ allows the model to reproduce the correct relic abundance across a wide range of $\sigma_N$ (spanning 4–5 orders of magnitude).
Viable Parameter Space: The model successfully reproduces both the relic density and the LZ event for DM masses ( $m_{\chi_1}$ $m_{χ_{1}}$ ) ranging from 0.5 TeV to 10 TeV.
- The required reheating temperatures satisfy $m_{\chi_1}/T_R \simeq 19\text{--}27$ . For example, for $m_{\chi_1} = 1$ TeV, $T_R \approx 39\text{--}47$ GeV.
- The mass splitting $\delta$ can range from $\sim 10$ keV to $\sim 300$ keV, including values below the thermal freeze-out benchmark.
Model Comparison: The leptophobic and universal coupling scenarios yield nearly identical direct-detection phenomenology because leptonic couplings do not enter the DM-nucleon cross-section at tree level. The universal model is slightly more constrained by collider dilepton searches, but these constraints do not exclude the parameter space required to explain the LZ event.
Spectral Analysis:
- Benchmarks with $m_{\chi_1} = 0.5$ and $1.0$ TeV are identified as the most favorable. They allow for mass splittings that shift the characteristic recoil energy ( $E_R^*$ ) close to the 248 keV candidate while suppressing the low-energy tail.
- Heavier candidates ( $m_{\chi_1} \ge 2.5$ TeV) tend to produce spectra where the second maximum lies below the observed event or where the signal is concentrated at lower energies, making them less suitable for explaining an isolated high-energy recoil.
Indirect Detection and Stability: The off-diagonal nature of the interaction suppresses present-day annihilation rates if the excited state $\chi_2$ is depleted after freeze-out. The paper notes that $\chi_2$ decays (e.g., $\chi_2 \to \chi_1 \gamma\gamma\gamma$ ) have large lifetimes and do not produce observable signals within the detector. Solar capture constraints, which ruled out thermal Higgsinos, are satisfied for $m_{\chi_1} \gtrsim 1$ TeV in this scenario.

Significance and Claims
The authors claim that this work provides a viable non-thermal interpretation of the LZ high-energy recoil event. The primary significance lies in demonstrating that the reheating temperature is a critical parameter that decouples the direct-detection cross-section from the relic density requirement. This allows the LZ candidate to be reproduced along a continuous line in the $(\delta, \sigma_N)$ plane, rather than being restricted to the specific thermal freeze-out benchmark.

The paper modestly concludes that while the model can produce an isolated event at the required rate, a definitive fit requires a full likelihood analysis of the LZ data. The results suggest that future high-energy recoil data from LZ and other xenon experiments will be essential to distinguish between thermal and non-thermal production mechanisms and to constrain the properties of inelastic dark matter. The interpretation of the candidate is shown to depend equally on particle physics model parameters and the cosmological history (specifically $T_R$ ) of the early universe.

Technical Summary: A Freeze-In Interpretation of the LZ High-Energy Nuclear Recoil Event

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