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Inelastic $B-L$ scalar dark matter and the LUX-ZEPLIN event

This paper demonstrates that a previously proposed inelastic scalar dark matter model within a gauged $U(1)_{B-L}$ framework naturally explains the recent high-energy recoil event observed by the LUX-ZEPLIN collaboration while satisfying thermal relic constraints, offering a testable scenario for future $Z'$ boson searches.

Original authors: Nobuchika Okada, Osamu Seto

Published 2026-09-09

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CC BY 4.0

Original authors: Nobuchika Okada, Osamu Seto

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 universe, a vast majority of matter remains invisible to our eyes and our most powerful telescopes. Scientists call this invisible substance dark matter, and for decades, the leading theory has been that it consists of heavy, slow-moving particles that rarely interact with the ordinary matter making up stars, planets, and us. These hypothetical particles, known as weakly interacting massive particles, are expected to occasionally bump into atomic nuclei, leaving behind a tiny, measurable flash of energy. However, the nature of these collisions has been a subject of intense debate, particularly after a recent, puzzling signal appeared in data collected by a massive detector buried deep underground.

The LUX-ZEPLIN experiment, located in a former gold mine in South Dakota, is designed to catch these rare whispers from the dark sector. In its recent analysis of data collected over 220 days, the collaboration reported a single, anomalous event. Unlike the gentle taps expected from standard dark matter theories, this event showed a significantly higher energy deposit, a signal that stood out with a statistical weight that cannot be easily dismissed as random noise or known background interference. While this single event is not yet a confirmed discovery, it has sparked a vigorous search for new physics that could explain why a dark matter particle would hit a nucleus with such unexpected force.

A team of physicists, Nobuchika Okada and Osamu Seto, has proposed a specific explanation for this anomaly that fits neatly into a broader framework of particle physics. They suggest that the dark matter in question is not a single, uniform particle, but rather exists in two very similar states that are nearly identical in mass but not quite the same. In their model, these particles are part of a theoretical extension to the Standard Model of physics, which includes a new force carried by a heavy particle called a Z-prime boson. This new force is linked to a property called "baryon minus lepton number," a concept that helps explain why neutrinos have mass, but in this scenario, it also governs how dark matter behaves.

The researchers show that when a dark matter particle from this model strikes an atomic nucleus, it does not simply bounce off. Instead, the collision forces the particle to jump from its lighter state to a slightly heavier state. This transition requires energy, much like a ball rolling up a small hill. Because the particle must spend some of its kinetic energy to make this jump, the resulting recoil of the nucleus is pushed to a higher energy level than what would be seen in a standard elastic collision. This mechanism naturally accounts for the high-energy signal observed by the LUX-ZEPLIN team, turning a confusing outlier into a predictable outcome of a specific physical process.

To make this scenario work, the model requires the dark matter particles to have a mass in the range of a few trillion electron volts, a scale that is heavy but within the reach of future particle accelerators. The researchers found that for the dark matter to exist in the correct amount to fill the universe today, the mass of the dark matter particle must be roughly half the mass of the heavy Z-prime boson that mediates the force. Furthermore, the strength of the new force must be tuned to a specific value, roughly half the strength of the electromagnetic force, to ensure the particles annihilated at the right rate in the early universe. When these conditions are met, the model predicts that the probability of a dark matter particle hitting a nucleus and causing this high-energy jump is about one in ten to the power of 45 square centimeters. This predicted rate aligns perfectly with the single event seen by the LUX-ZEPLIN detector.

The beauty of this proposal lies in its testability. Unlike many dark matter theories that remain in the realm of speculation, this model makes a sharp prediction about the existence and mass of the Z-prime boson. Because the dark matter mass and the force carrier mass are locked together by the requirement to produce the correct amount of dark matter in the universe, future high-energy collider experiments should be able to find this Z-prime particle if the model is correct. If these machines can produce the Z-prime boson at the predicted mass, it would provide decisive confirmation that the dark matter responsible for the LUX-ZEPLIN event is indeed this inelastic scalar particle. The paper does not claim to have solved the mystery of dark matter, but it offers a concrete, mathematically consistent path forward that turns a single strange event into a roadmap for discovery.

Technical Summary: Inelastic $B-L$ Scalar Dark Matter and the LUX-ZEPLIN Event

Problem Statement
The LUX-ZEPLIN (LZ) collaboration recently reported an anomalous single-particle interaction event in 220 live days of data, exhibiting a 2.6 $\sigma$ deviation characterized by a significantly higher energy deposition than expected from standard elastic WIMP-nucleus scattering. While inelastic dark matter (DM) scenarios—where DM transitions to a slightly heavier state upon scattering—naturally explain such high-energy recoil signals by kinematically suppressing standard elastic scattering, existing interpretations face challenges. Specifically, strongly degenerate Higgsino-like neutralino candidates have been proposed but may encounter severe astrophysical constraints. This paper addresses whether a previously proposed inelastic scalar DM model based on gauged $U(1)_{B-L}$ symmetry can naturally accommodate the LZ event while satisfying thermal relic abundance and current experimental constraints.

Methodology and Model Framework
The authors analyze a model extending the Standard Model (SM) with a gauged $U(1)_{B-L}$ symmetry. The particle content includes the SM fields, three right-handed (RH) neutrinos ( $N_R^i$ ), and two $U(1)_{B-L}$ Higgs fields ( $\phi_1, \phi_2$ ). The model is anomaly-free and generates light neutrino masses via the seesaw mechanism.

Scalar Potential and Mass Splitting: The scalar potential involves the SM Higgs $\Phi$ and the $B-L$ Higgs fields. Upon symmetry breaking, the complex scalar $\phi_1$ splits into two real scalar states, $S$ (lighter) and $P$ (heavier). The mass splitting is controlled by a trilinear coupling parameter $A$ , resulting in a splitting $\sqrt{m_P^2 - m_S^2} \sim \mathcal{O}(100)$ keV.
Dark Matter Candidate: The lighter state $S$ serves as the DM candidate. The $Z_2$ parity stabilizing $S$ is automatically realized by charge assignments rather than being imposed by hand.
Interaction Mechanism: Crucially, the $Z'$ gauge boson couples off-diagonally to the DM states ( $Z'_\mu (\partial^\mu S)P - S\partial^\mu P$ ). There is no diagonal $Z'$ -DM-DM coupling. Consequently, $Z'$ -mediated scattering off nucleons is strictly inelastic. For mass splittings larger than the energy transfer in standard low-energy recoils, elastic scattering is suppressed, shifting the differential event rate peak to higher energies.

Key Contributions and Analysis
The paper performs a phenomenological analysis to determine if the model parameters can simultaneously satisfy:

Thermal Relic Abundance: The observed DM density $\Omega h^2 \simeq 0.1$ .
LZ Event Characteristics: The specific energy and rate of the reported high-energy recoil.
Experimental Bounds: Constraints from LEP, Tevatron, and LHC Run 2 on the $Z'$ mass.

The authors solve the Boltzmann equation to calculate the thermal relic abundance, accounting for co-annihilation effects ( $SP \to f\bar{f}$ ) and annihilation channels ( $SS \to Z'Z'$ ). They derive the spin-independent (SI) inelastic scattering cross-section $\sigma_{SI}$ mediated by the $Z'$ boson.

Results
The analysis yields the following specific parameter space required to explain the observations:

Mass Relation: To achieve the correct thermal relic abundance at the TeV scale via resonant annihilation ( $s$ -channel $Z'$ exchange), the DM mass must satisfy $m_S \simeq m_{Z'}/2$ .
Coupling Strength: A gauge coupling constant of $g_{B-L} \sim 0.5$ is required to generate a sufficiently large annihilation cross-section.
Scattering Cross-Section: Under these conditions ( $m_S \sim \text{few TeV}$ , $g_{B-L} \sim 0.5$ ), the predicted inelastic DM-nucleon cross-section is $\sigma_{SI} \sim 10^{-45} \text{ cm}^2$ .
Consistency: This predicted cross-section magnitude is in excellent agreement with the rate required to explain the LZ anomaly. The model naturally suppresses standard elastic scattering while enhancing the high-energy inelastic channel.

Significance and Claims
The paper claims that the inelastic scalar DM model in a gauged $U(1)_{B-L}$ framework provides a natural and self-consistent explanation for the LZ event. The small mass splitting between DM states arises naturally from the $B-L$ symmetry breaking mechanism. The scenario is highly predictive because the key parameters ( $m_S$ , $m_{Z'}$ , $v_{B-L}$ , and $g_{B-L}$ ) are tightly constrained by the combination of thermal relic requirements and direct detection data.

The authors assert that this scenario can be decisively tested by future collider searches for the $Z'$ boson resonance, specifically looking for the resonant production predicted by the mass relation $m_S \simeq m_{Z'}/2$ . The work does not propose new experimental setups but highlights that existing and upcoming high-energy collider experiments are sufficient to validate or rule out this specific interpretation of the LZ anomaly.

Technical Summary: Inelastic B−LB-LB−L Scalar Dark Matter and the LUX-ZEPLIN Event

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Technical Summary: Inelastic $B-L$ Scalar Dark Matter and the LUX-ZEPLIN Event