⚛️ phenomenology

Exothermic dark-photon dark matter and the LZ high-recoil event: finite-reheating constraints

Motivated by the LUX-ZEPLIN high-recoil candidate, this paper investigates the viability of exothermic dark-photon dark matter with a 45 GeV pseudo-Dirac particle and 1 MeV splitting, demonstrating that finite-reheating scenarios with reheating temperatures between 0.588 GeV and 3.09 GeV can simultaneously satisfy the observed relic abundance, the INTEGRAL/SPI gamma-ray limits, and the predicted event rate of 0.43 in the LZ window.

Original authors: Kuldeep Deka

Published 2026-10-15

📖 5 min read🧠 Deep dive

CC BY 4.0

Original authors: Kuldeep Deka

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 outweighs the stars and planets we can see, yet we have never directly caught a single particle of it. This "dark matter" is known only because its gravity holds galaxies together, but its true nature remains one of the biggest mysteries in physics. Scientists have proposed many ideas about what it could be, ranging from heavy, slow-moving particles to lighter, more exotic ones. One intriguing possibility involves a hidden sector of particles that interact with our world only very weakly, perhaps through a new kind of force carrier that acts like a shadow version of the photon, the particle of light. If such particles exist, they might not be stable in a single form; they could have a heavier, excited version that eventually settles into a lighter, stable state, releasing a tiny burst of energy in the process. Understanding how these particles were created in the early universe and how they might reveal themselves in modern detectors is crucial for solving the puzzle of what dark matter actually is.

A recent study by physicist Kuldeep Deka investigates a specific scenario where a heavy, excited dark matter particle collides with an atomic nucleus and releases its stored energy, creating a detectable flash of motion. This idea was sparked by a single, unusual event recorded by the LUX-ZEPLIN experiment, a massive detector buried deep underground that looks for dark matter by watching for tiny recoils in liquid xenon. That event involved a nucleus being kicked back with an energy of about 248 keV, a value that is surprisingly high for standard dark matter theories. Deka explored whether this event could be explained by a model where a 45 GeV dark matter particle, split into two states with a tiny mass difference of 1 MeV, releases that difference as kinetic energy during a collision. The study focuses on a particle called a dark photon, which acts as a bridge between the dark sector and our visible world, allowing these rare interactions to happen.

To make sense of this single event, the researcher had to look back at the very beginning of the universe. Standard theories often assume that the universe cooled down instantly after a period of rapid expansion, but this study considers a more gradual process called "reheating," where the universe slowly fills with heat and particles over time. This period is critical because it determines how many dark matter particles were created and how their numbers were diluted as the universe expanded. Deka calculated the production of these particles during this finite reheating phase, taking into account that the temperature of the universe did not drop instantly but followed different cooling patterns depending on the physics of the early cosmos. The goal was to find a set of conditions that would produce exactly the right amount of dark matter to match what we see today, while also predicting the correct number of events for the detector.

The calculations revealed that the timing of the universe's cooling is just as important as the temperature itself. If the universe cooled in a specific way, known as "quadratic constant-width reheating," the temperature at which radiation domination began would need to be about 1.32 GeV. Other cooling patterns required different temperatures, such as 3.09 GeV or 0.588 GeV, to achieve the same result. Interestingly, the study found that if the universe cooled too quickly or followed certain other expansion patterns, it would be impossible to get the right amount of dark matter without violating other known physical limits. For instance, a scenario where the universe expanded in a specific "kination" phase was ruled out for the temperatures relevant to this model, as it would have produced too much dark matter or failed to produce enough within the allowed time frame.

The model also had to pass a strict test regarding the stability of the excited dark matter particle. Because the particle is slightly heavier than its stable counterpart, it eventually decays, and if it decays too quickly, it would produce a glow of light that telescopes like INTEGRAL/SPI would have already seen. The study confirmed that the chosen parameters for the dark matter and the dark photon result in a decay rate slow enough to avoid detection by current telescopes, keeping the model consistent with observations of the diffuse light in the universe. Furthermore, the researcher checked whether the dark matter particles might convert back and forth between their heavy and light states, which could alter the number of particles available to cause a recoil. The results showed that this conversion is negligible, meaning the population of excited particles remains stable enough to explain the detector signal.

When all these factors were combined, the model predicted that the LUX-ZEPLIN detector should have seen about 0.43 events in the energy window where the candidate event was found. This is a statistically reasonable expectation for a single event, suggesting that the model is a viable explanation for the observation. The study also confirmed that the shape of the energy signal matches what was observed, reinforcing the idea that this specific type of dark matter interaction is a plausible candidate. By linking the single event in the detector to the complex history of the early universe, the research provides a concrete path forward for testing these ideas. It shows that the answer to the dark matter puzzle might lie not just in the particles themselves, but in the precise thermal history of the cosmos that brought them into existence.

Technical Summary: Exothermic Dark-Photon Dark Matter and the LZ High-Recoil Event

Problem Statement
The LUX–ZEPLIN (LZ) experiment reported a single nuclear recoil event at $E_R = 248 \pm 23 \pm 23$ keV with a global significance of $2.6\sigma$ . While a single event does not confirm a dark matter (DM) signal, its high energy and the absence of companion events motivate an inelastic scattering interpretation. Specifically, an exothermic scenario where a long-lived excited DM state ( $\chi_H$ ) releases its mass splitting ( $\delta$ ) during a collision with a nucleus ( $\chi_H N \to \chi_L N$ ) can produce high-energy recoils without requiring the DM to originate from the high-velocity tail of the halo distribution.

Existing studies of such models typically assume instantaneous reheating, where the universe transitions immediately to a radiation-dominated era at a temperature $T_{rh}$ . This assumption neglects particle production occurring during the finite reheating phase, where the temperature can exceed $T_{rh}$ , and subsequent entropy dilution. Furthermore, the cosmological abundance of the excited state must satisfy constraints from the three-photon decay ( $\chi_H \to \chi_L + 3\gamma$ ), which is the dominant decay mode when the mass splitting is below the electron-pair threshold.

Methodology
The author analyzes a specific benchmark model motivated by the LZ event: a 45 GeV pseudo-Dirac fermion with a 1 MeV mass splitting ( $\delta$ ) and a 1 GeV dark photon mediator ( $A'$ ). The interaction is mediated by kinetic mixing between the dark photon and the Standard Model hypercharge, as well as $Z$ -boson exchange.

Signal Normalization: The author adjusts the signal normalization ( $C_{LZ}$ ) to be consistent with the published INTEGRAL/SPI limit on the three-photon decay flux. This reduces the expected event count in the LZ window from 1.04 (in the reference benchmark) to 0.43 events, while maintaining the reference recoil spectral shape.
Finite Reheating Framework: Instead of assuming instantaneous reheating, the paper parameterizes the post-inflationary cooling branch using a maximum temperature $T_{max}$ , a cooling exponent $\alpha$ (where $T \propto a^{-\alpha}$ ), and an equation-of-state parameter $\omega$ for the dominant component. The Hubble rate during reheating is derived accordingly.
Production Calculation: The relic abundance is calculated via the freeze-in mechanism. The production integral includes contributions from:
- Standard Model fermion annihilation ( $f\bar{f} \to \chi_L \chi_H$ ) via off-shell $A'$ and $Z$ exchange (including the $Z$ resonance).
- Thermal dark-photon annihilation ( $A'A' \to \chi_L \chi_H$ ), estimated using detailed balance.
- The integral is performed from $T_{max}$ down to $T_{rh}$ , followed by the standard radiation-dominated contribution.
Excited State Evolution: The evolution of the excited fraction $f_H = n_H / (n_L + n_H)$ is tracked. The author evaluates depletion due to self-conversion ( $\chi_H \chi_H \leftrightarrow \chi_L \chi_L$ ) and radiative decay, ensuring that the surviving population is sufficient to explain the recoil event without violating photon flux limits.

Key Contributions and Results

Reheating Temperature Constraints: The study determines the required reheating completion temperature ( $T_{rh}$ ) to match the observed dark matter abundance ( $\Omega_\chi h^2 \approx 0.12$ ) for various reheating histories, assuming $T_{max} = m_\chi = 45$ GeV:
- Instantaneous Reheating: $T_{rh} = 4.10$ GeV.
- Quadratic Oscillations (Constant Width): $T_{rh} = 1.32$ GeV.
- Quartic Oscillations (Scalar Decay): $T_{rh} = 3.09$ GeV.
- Quartic Oscillations (Constant Width): $T_{rh} = 0.588$ GeV.
- Adiabatic Kination: No solution exists for $T_{rh} > 5.96$ MeV (the BBN cutoff) when $T_{max} \ge m_\chi$ .
- Quartic Fermion Decay: No solution exists above the BBN cutoff.
Insensitivity to $T_{max}$ : For $T_{max} \ge m_\chi$ , the required $T_{rh}$ is largely insensitive to increases in $T_{max}$ (changing by less than 0.03% when $T_{max}$ increases from $m_\chi$ to $5m_\chi$ ). This indicates that the production is dominated by the temperature range near $T_{rh}$ for these specific histories.
Mediator and Conversion Effects:
- At the reference dark coupling $\alpha_D = 10^{-10}$ , the thermal-mediator source ( $A'A'$ ) contributes less than 0.2% of the Standard Model fermion yield.
- Self-conversion ( $HH \leftrightarrow LL$ ) depletes the excited population by less than $10^{-7}$ , which is negligible compared to the radiative decay depletion ( $\sim 10^{-5}$ ).
- The paper establishes that the "source-free" upper bound on depletion is sufficient for the reference coupling, though exact collision terms would be required for larger $\alpha_D$ .
Mass Dependence: A comparison with a 200 GeV benchmark (with $\delta = 0.5$ MeV) shows that the adiabatic kination scenario remains viable only for $T_{max}/m_\chi \lesssim 0.389$ , compared to 0.155 for the 45 GeV case. In both cases, kination fails to produce the correct abundance for $T_{max} \ge m_\chi$ within the allowed parameter space.

Significance and Claims
The paper claims to provide a rigorous connection between an exothermic recoil benchmark and the pre-radiation-dominated thermal history of the universe. By incorporating finite reheating, the author demonstrates that the required reheating temperature $T_{rh}$ can be significantly lower than in instantaneous scenarios (e.g., dropping from 4.10 GeV to 0.588 GeV depending on the equation of state).

The work emphasizes that:

Finite reheating is critical: Calculations starting strictly at radiation domination may miss the dominant production contribution or misestimate the required $T_{rh}$ .
Photon constraints are robust: The chosen normalization satisfies the INTEGRAL/SPI three-photon decay limit while retaining the interpretation of the LZ event.
Model consistency: For the reference coupling, the thermal-mediator channel and self-conversion processes do not appreciably alter the relic density or the excited-state fraction, validating the use of simplified source terms in this regime.

The author concludes that while the single LZ event does not uniquely select a specific reheating history, the framework allows for the mapping of exothermic benchmarks to specific production and dilution histories, constrained by the interplay of recoil rates, photon flux limits, and cosmological abundance.

Technical Summary: Exothermic Dark-Photon Dark Matter and the LZ High-Recoil Event

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