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Inelastic Signatures of Electroweak Dark Matter

This paper proposes a minimal electroweak dark matter model involving coupled Majorana and Dirac multiplets that explains the high-energy nuclear recoil events observed by the LUX-ZEPLIN collaboration through inelastic scattering with specific mass splittings, while simultaneously predicting correlated elastic spin-independent signals for various multiplet representations.

Original authors: Juri Smirnov, Spencer Griffith, John F. Beacom

Published 2026-09-04

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CC BY 4.0

Original authors: Juri Smirnov, Spencer Griffith, John F. Beacom

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

Dark matter is the invisible substance that makes up most of the matter in the universe, holding galaxies together with its gravity, yet it refuses to reveal itself by reflecting light or interacting with ordinary matter in any obvious way. For decades, scientists have searched for it using massive detectors buried deep underground, hoping to catch a rare collision between a dark matter particle and an atomic nucleus. The leading theory for what this particle might be involves "weakly interacting massive particles," or WIMPs, which are heavy and interact only through the weak nuclear force and gravity. However, a recent signal from the LUX-ZEPLIN experiment in South Dakota has thrown a wrench into the standard expectations. The detector recorded a single event where a xenon nucleus recoiled with an unusually high amount of energy, far higher than what typical dark matter models predict. This anomaly has left physicists puzzled, as standard theories suggest that such a high-energy hit should be accompanied by a flood of lower-energy hits that simply were not seen.

A new study proposes a solution that turns this puzzle into a precise prediction. The researchers, Juri Smirnov, Spencer Griffith, and John F. Beacom, suggest that the dark matter particle is not a simple, solitary entity but part of a more complex family structure involving two different types of particles that are nearly identical in mass but slightly different in energy. They call this setup "Higgs-coupled minimal dark matter." In this model, the dark matter particles can exist in a low-energy state or a slightly higher-energy state, separated by a tiny gap of a few hundred thousand electron volts. When a dark matter particle from the low-energy state strikes a xenon nucleus, it must absorb energy to jump up to the higher-energy state. This process, known as inelastic scattering, acts like a filter: it prevents low-energy collisions from happening because there isn't enough energy to bridge the gap, but it allows high-energy collisions to occur if the dark matter particle is moving fast enough. This mechanism perfectly explains why the LUX-ZEPLIN detector saw a single high-energy event while missing the expected swarm of low-energy ones.

The brilliance of this proposal lies in how it connects the behavior of dark matter in the early universe to what we see in detectors today. The researchers show that for a specific range of particle masses and interaction strengths, the energy gap required to explain the LUX-ZEPLIN event is exactly the same as the gap needed to produce the correct amount of dark matter in the universe through natural cosmic processes. They calculated that for several different possible sizes of these dark matter families, there is a unique combination of mass and interaction strength that satisfies both conditions simultaneously. This creates a "universal" relationship where the high-energy signal is the same regardless of which specific family size nature chose, but the mass of the particle changes depending on that choice.

By matching the single observed event to their calculations, the team identified specific benchmark scenarios for each possible family size. For the smallest viable family, the dark matter particle would weigh about 1.44 TeV, while for the largest family considered, it would weigh about 131.14 TeV. Crucially, this model does not just explain the high-energy hit; it also predicts a second, quieter signal. While the high-energy event comes from the energy-absorbing jump, the model predicts that a much smaller number of standard, low-energy collisions should also occur, driven by quantum loops rather than the direct jump. The strength of this low-energy signal depends directly on the size of the dark matter family. For the smaller families, this signal is faint and might be hidden by background noise, but for the larger families, it should be strong enough to be detected by future experiments.

The study effectively narrows down the possibilities for what dark matter could be. It rules out the simplest versions of the theory where the dark matter is a single, unchanging particle, because those cannot produce the high-energy hit without also producing a flood of low-energy hits that were never seen. Instead, the data points toward a more complex structure where the dark matter has a split personality, existing in two states separated by a tiny energy gap. The researchers emphasize that while the LUX-ZEPLIN event is currently just a single data point and not a confirmed discovery, this framework offers a coherent and testable explanation. If future detectors with larger exposures continue to see high-energy events and begin to detect the predicted low-energy signals, it would provide a direct way to measure the size and structure of the dark matter family, turning a mysterious anomaly into a clear map of the invisible universe.

Technical Summary: Inelastic Signatures of Electroweak Dark Matter

Problem Statement
The LUX-ZEPLIN (LZ) collaboration recently reported a single nuclear recoil event reconstructed at $248 \pm 23_{\text{stat}} \pm 23_{\text{sys}}$ keV within an extended energy window ($5.4 $–$ 270$ keV). While the local significance is $3.4\sigma$ , the event lies in a region of very low expected background. Standard elastic Weakly Interacting Massive Particle (WIMP) interpretations are strongly disfavored because the nuclear form factor suppresses high-momentum transfers, and increasing the elastic cross-section to produce such a high-energy event would generically predict an unobserved excess of lower-energy recoils. Conversely, endothermic inelastic dark matter (DM) naturally suppresses low-energy spectra. The paper investigates whether Higgs-coupled Minimal Dark Matter (HC-MDM), a framework extending the Standard Model with coupled Majorana (M) and Dirac (D) electroweak multiplets, can provide a predictive explanation for this high-energy event while remaining consistent with thermal relic abundance constraints.

Methodology
The authors analyze a specific class of HC-MDM models involving adjacent multiplet sizes (e.g., $3_M 2_D$ , $5_M 4_D$ , up to $13_M 12_D$ ) coupled via Higgs interactions. The analysis proceeds through the following steps:

Theoretical Framework: The study focuses on the "custodial point" where the Majorana and Dirac masses are equal ( $m_M = m_D \equiv m_\chi$ ) and the Yukawa couplings satisfy $y_1 = -y_2 \equiv y$ . At this point, tree-level diagonal Higgs couplings to the lightest neutral state vanish, suppressing standard elastic scattering.
Universal Inelastic Physics: The authors demonstrate that for the entire sequence of multiplet combinations, the neutral-state mass splitting ( $\delta$ $δ$ ) and the leading off-diagonal $Z$ $Z$ -boson interaction are universal. They depend only on the DM mass ( $m_\chi$ $m_{χ}$ ) and Yukawa coupling ( $y$ $y$ ), not on the specific electroweak representation size.
- The splitting is derived as $\delta \simeq y^2 v^2 / (4m_\chi)$ for $yv \ll m_\chi$ .
- The inelastic scattering cross-section is fixed by the pseudo-Dirac neutral-current strength, $\sigma_n^{\text{inel}} \simeq 1.9 \times 10^{-39} \text{ cm}^2$ .
Rate Matching: Instead of directly equating the splitting to the recoil energy, the authors calculate the expected number of inelastic events ( $N_{\text{inel}}$ ) in the LZ exposure ($2.84$ tonne-yr) as a function of $m_\chi$ and $\delta$ . They define a "universal relation" $\delta_{\text{LZ}}(m_\chi)$ by requiring $N_{\text{inel}} = 1$ (with a two-sided 90% Poisson band for statistical uncertainty). This maps the observed event rate to a specific band in the $(m_\chi, y)$ plane.
Thermal Intersection: The universal rate-matched band is intersected with representation-dependent thermal relic trajectories ( $m_\chi = m_{\text{th}}^{(R_M, R_D)}(y)$ ) calculated in previous work (Ref. [37]), which account for Sommerfeld enhancement and bound-state formation.
Elastic Prediction: Once $(m_\chi, y)$ is fixed by the intersection, the authors predict the corresponding loop-induced elastic spin-independent cross-section, which is representation-dependent.

Key Contributions and Results

Universal Inelastic Signal: The paper establishes that the high-energy inelastic scattering signature is independent of the electroweak representation size for the coupled multiplet sequence. The splitting and interaction strength are determined solely by $(m_\chi, y)$ .
Benchmark Selection: By intersecting the universal LZ-selected band with thermal relic trajectories, the authors identify specific benchmark points for each multiplet combination ( $3_M 2_D$ $3_{M} 2_{D}$ through $13_M 12_D$ $1 3_{M} 1 2_{D}$ ).
- The selected splittings are consistently in the range of $\sim 350$ –$380$ keV.
- The selected masses range from $\sim 1.4$ TeV ( $3_M 2_D$ ) to $\sim 131$ TeV ( $13_M 12_D$ ).
Correlated Elastic Signal: The framework predicts a correlated low-energy elastic signal arising from electroweak loops. The magnitude of this signal is fixed by the representation size.
- For the $3_M 2_D$ and $5_M 4_D$ models, the predicted elastic cross-sections are near or slightly above the "neutrino floor," making them potentially detectable by next-generation experiments.
- For higher multiplets (e.g., $11_M 10_D$ , $13_M 12_D$ ), the required elastic cross-sections are significantly larger and are currently disfavored by null results from LZ and PandaX-4T.
Model Viability: The analysis suggests that the $3_M 2_D$ , $5_M 4_D$ , and $7_M 6_D$ scenarios are the most viable candidates consistent with both the LZ high-energy event and current direct detection limits.

Significance and Claims
The paper claims that HC-MDM provides a "natural inelastic interpretation" of the LZ 248 keV event. Its primary significance lies in the predictive power derived from the universality of the inelastic interaction combined with the representation-dependence of the thermal relic abundance.

Distinctiveness: Unlike generic inelastic DM fits, this framework links the inelastic splitting, the thermal freeze-out, and the elastic scattering rate through a single set of parameters.
Testability: The model offers a clear path to verification: if the LZ event persists, the framework predicts a specific high-energy recoil spectrum shape and a representation-dependent low-energy elastic signal. The relative size of the inelastic and elastic channels can distinguish between different multiplet combinations.
Modesty: The authors explicitly state that the LZ event is a single-event excess with modest global significance ( $2.6\sigma$ ) and that this work does not constitute evidence for HC-MDM. Rather, it demonstrates that HC-MDM is a "simple and well-motivated model" capable of accounting for the observation without violating other constraints. The work serves to identify a specific, testable correlation between inelastic scattering, thermal history, and elastic signals that would otherwise remain unexplored.

Technical Summary: Inelastic Signatures of Electroweak Dark Matter

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