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Model-Independent Sideband Constraints on Inelastic Dark Matter at the LZ High-Recoil Candidate

This paper presents a model-independent analysis of the LUX-ZEPLIN experiment's high-energy nuclear recoil candidate, demonstrating that while inelastic dark matter with specific mass and splitting parameters can naturally explain the event's location, the associated kinematic suppression and Helm form factor effects create tension with sideband data, suggesting that a dedicated search in the 271–800 keV range is necessary to decisively test this hypothesis.

Original authors: David Delepine, Shaaban Khalil

Published 2026-09-23

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CC BY 4.0

Original authors: David Delepine, Shaaban Khalil

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

Deep in the quiet of the cosmos, a vast sea of invisible particles is thought to drift through everything we see, including our own bodies. Scientists call these particles dark matter, and while they do not emit light or interact with ordinary matter in ways we can easily detect, their gravity shapes the structure of the universe. For decades, researchers have built massive, ultra-sensitive detectors deep underground to catch a glimpse of these particles. The most recent of these, the LUX-ZEPLIN experiment, sits in a mine in South Dakota, filled with tons of liquid xenon. The goal is simple yet profound: to spot a tiny flash of light caused when a dark matter particle bumps into an atom of xenon. Recently, this detector recorded a single, unusual event that has sparked a new line of inquiry. It was a collision that happened with far more energy than scientists typically expect from a standard dark matter encounter, prompting a fresh look at what these invisible particles might actually be.

The standard picture of dark matter suggests that when these particles hit an atom, they bounce off gently, transferring a small amount of energy. However, the single event recorded by the LUX-ZEPLIN experiment was unusually energetic, occurring at a recoil energy of 248 kiloelectronvolts. This high energy is difficult to explain with the usual model of dark matter, which would produce a flood of low-energy hits that the detector did not see. Instead, this specific event fits a different idea known as inelastic dark matter. In this scenario, the dark matter particle is not a single, unchanging object but has a slightly heavier version of itself. When it strikes a xenon atom, it does not just bounce; it transforms into that heavier version. This transformation requires a specific amount of energy to happen, acting like a threshold that blocks the low-energy collisions while allowing the high-energy ones to pass through. This mechanism naturally explains why the detector saw a high-energy hit but missed the swarm of low-energy ones that would be expected from other theories.

Two researchers, David Delepine and Shaaban Khalil, decided to test this idea without making any assumptions about the specific nature of the dark matter particle or the forces that govern it. They treated the problem as a puzzle of pure geometry and statistics. They took the data from the LUX-ZEPLIN experiment and divided the possible energy levels into three zones. The middle zone contained the single high-energy event that sparked the interest. The other two zones, one below and one above this event, served as control areas. If the inelastic dark matter theory were correct, the rules of physics would dictate a very specific relationship between the number of events in the middle zone and the number of events in the zones above and below it. The researchers calculated what the detector should have seen in those control zones if the single event was indeed caused by this type of dark matter.

Their analysis revealed a precise balance point. For any given mass of the dark matter particle, there is a specific energy gap between its two states that makes the number of predicted events in the low-energy zone equal to the number predicted in the high-energy zone. At this balance point, the theory makes its most conservative prediction, minimizing the number of extra events it expects to see. For a dark matter particle with a mass of one thousand gigaelectronvolts, this balance occurs when the energy gap is 339 kiloelectronvolts. At this setting, the theory predicts that for every event seen in the middle, there should be about 1.77 events in the low-energy zone and another 1.77 in the high-energy zone. Since the detector has seen zero events in both of those control zones so far, the theory is not completely ruled out, but it is under significant pressure. The statistical tension between the prediction and the observation is about 1.9 standard deviations, which is a hint of a problem but not enough to declare the theory false.

The situation becomes more complicated when looking at the specific properties of the xenon atoms inside the detector. The way xenon atoms respond to a collision depends heavily on the energy of the hit, and at the specific energy of the observed event, xenon is remarkably unresponsive. The atomic structure of xenon causes a suppression effect, making it about four thousand times harder to detect a collision at this energy than at lower energies. This means that for the dark matter to have produced the single event seen, it must have interacted with a force much stronger than previously thought. Furthermore, this suppression effect is unique to xenon. If the same dark matter particles were hitting a different type of atom, or even a different isotope of xenon, the suppression would not be nearly as strong, and the detector would likely have seen many more events. This creates a tight constraint: the theory works only if the dark matter interacts with xenon in a very specific, suppressed way.

The researchers conclude that the best way to settle this question is to look at the high-energy zone that has not yet been fully analyzed. If the inelastic dark matter theory is correct, the detector should find a cluster of events in the energy range between 271 and 800 kiloelectronvolts. Finding nothing there would strongly suggest that the single event was a fluke or caused by something else entirely. Conversely, finding a pattern of events matching the predicted shape would provide strong evidence that dark matter can change its internal state when it collides with ordinary matter. Until that search is completed, the idea remains a plausible but unproven explanation for a single, mysterious flash of light in the deep dark.

Technical Summary: Model-Independent Sideband Constraints on Inelastic Dark Matter at the LZ High-Recoil Candidate

Problem Statement
The LUX-ZEPLIN (LZ) experiment recently reported a single nuclear-recoil (NR) event at an energy of $E_R = 248 \pm 23_{stat} \pm 23_{sys}$ keV within a 2.84 tonne-year exposure. This event exhibits a local significance of $3.4\sigma$ . While not a discovery, the unusually high recoil energy motivates the hypothesis of inelastic (endothermic) dark matter (DM) scattering, defined by the transition $\chi_1 + N \to \chi_2 + N$ with a mass splitting $\delta = m_{\chi_2} - m_{\chi_1} > 0$ . In this scenario, the kinematic threshold $\delta$ suppresses low-energy recoils, shifting the signal spectrum toward higher energies. Previous analyses, such as those focusing on Higgsino scenarios, have identified tensions between the observed event and the predicted background in sideband regions, but often relied on specific ultraviolet (UV) completions or cross-section parametrizations.

Methodology
The authors perform a model-independent analysis of the LZ data to constrain inelastic DM scenarios without specifying a UV completion or a particular cross-section parametrization. The analysis relies on the following physical inputs:

Kinematics: The minimum speed required for a recoil $E_R$ is determined by the DM mass ( $m_\chi$ ), the nucleus mass ( $m_N$ ), and the mass splitting $\delta$ .
Halo Model: The Standard Halo Model (SHM) with a truncated Maxwellian velocity distribution is adopted ( $v_0 = 238$ km/s, $v_E = 232$ km/s, $v_{esc} = 544$ km/s).
Nuclear Response: Coherent spin-independent (SI) scattering is assumed, utilizing the Helm form factor for natural xenon.
Sideband Ratios: The core of the analysis defines two sideband-to-signal ratios relative to the signal region $[225, 271]$ keV:
- Low sideband: $[14, 225]$ keV ( $N_{low}/N_{sig}$ )
- High sideband: $[271, 800]$ keV ( $N_{>271}/N_{sig}$ )
For a given $(m_\chi, \delta)$ , the cross-section $\sigma_p$ is fixed such that the predicted count in the signal region is exactly one event ( $N_{sig} = 1$ ). Consequently, the overall normalization $\rho_\chi \sigma_p$ cancels out in the ratios, leaving the predictions dependent only on the spectral shape determined by $(m_\chi, \delta)$ , the SHM, and the xenon form factor.

Key Contributions

Model Independence: The analysis extends sideband arguments beyond specific $Z$ -exchange realizations (like Higgsinos) to the broader class of inelastic DM models characterized by coherent SI nuclear scattering.
Balanced Splitting ( $\delta^\star$ ): The authors identify a unique mass splitting $\delta^\star$ for each DM mass where the low-energy and high-energy sideband ratios are equal ( $N_{low}/N_{sig} = N_{>271}/N_{sig} \equiv N^\star$ ). This point minimizes the joint prediction for sideband events, representing the "best-case" scenario for an inelastic DM explanation of the single LZ event.
Systematic Envelope: A joint grid scan over halo parameters ( $v_0, v_{esc}, v_E$ ) and the nuclear skin radius ( $R_T$ ) quantifies the sensitivity of the constraints to astrophysical and nuclear uncertainties.

Results

Balanced Point for $m_\chi = 1$ TeV: The analysis yields a balanced splitting of $\delta^\star = 339$ keV. At this point, the predicted count in each sideband is $N^\star = 1.77$ events. Assuming zero observed events in the sidebands, this corresponds to a combined Poisson tension of approximately $1.9\sigma$ .
Mass Dependence: Over the mass range $m_\chi = 500$ GeV to $3$ TeV, the tension at the balanced point increases. For $m_\chi \lesssim 700$ GeV, the tension is negligible ( $\lesssim 1.3\sigma$ ). For $m_\chi = 3$ TeV, the tension rises to approximately $2.5\sigma$ ( $N^\star \approx 2.51$ ).
Nuclear Suppression: A critical finding is the strong suppression of the xenon nuclear response at the candidate energy. At $E_R = 248$ keV, the Helm form factor squared is $|F_{Xe}^{Helm}|^2 \simeq 3 \times 10^{-4}$ , which is close to the second diffraction zero near 284 keV. This suppression is a factor of $\sim 4000$ relative to the zero-momentum limit. Consequently, to produce the single signal event, the required cross-section is enhanced to $\sigma_{req} \approx 2 \times 10^{-40}$ cm $^2$ for $m_\chi = 1$ TeV.
Systematics: The escape speed ( $v_{esc}$ ) is the dominant halo systematic, shifting $\delta^\star$ from 315 to 373 keV and $N^\star$ from 1.1 to 2.5. The skin radius uncertainty significantly amplifies effects due to the signal window's proximity to the form factor zero. The full systematic envelope results in $\delta^\star \in [310, 379]$ keV and a significance range $Z \in [0.6, 3.5]\sigma$ .

Significance and Claims
The paper claims that its results provide a robust, model-independent constraint on inelastic dark matter scenarios explaining the LZ high-recoil candidate. By optimizing the mass splitting to minimize sideband tension, the authors demonstrate that the "best-fit" inelastic interpretation still faces a non-negligible tension (up to $2.5\sigma$ ) with the null observation in sidebands, particularly for higher DM masses.

The authors emphasize that the strong suppression of the xenon form factor at 248 keV is a decisive feature: any coherent SI model explaining the event must accommodate this near-zero nuclear response. They conclude that a dedicated LZ search in the high-energy window ( $271 < E_R < 800$ keV) would provide a decisive test. A null result in this region would impose strong constraints on the parameter space, while an excess with the predicted spectral shape would constitute strong evidence for inelastic dark matter. The analysis remains conditional on the assumed Standard Halo Model, coherent spin-independent interaction, and the specific recoil-spectrum dependence.

Technical Summary: Model-Independent Sideband Constraints on Inelastic Dark Matter at the LZ High-Recoil Candidate

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