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Effect of inelastic scalar dark matter in hidden $U(1)$ scenario after the LZ nuclear recoil

This paper investigates a hidden $U(1)_H$ extension of the Standard Model featuring inelastic scalar dark matter to explain a recent high-energy nuclear recoil event observed by the LZ collaboration, while deriving constraints on the kinetic mixing parameter and comparing them with existing experimental bounds.

Original authors: Arindam Das, Takaaki Nomura

Published 2026-09-15

📖 5 min read🧠 Deep dive

CC BY 4.0

Original authors: Arindam Das, Takaaki Nomura

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 scaffolding of our universe, a substance that outweighs all the stars and galaxies combined yet refuses to reveal itself through light or ordinary touch. 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 atom in the detector. Most theories assume these particles bounce off atoms like billiard balls, but a different possibility has gained traction: what if dark matter is "inelastic"? In this scenario, a dark matter particle does not simply bounce; it must absorb a tiny bit of energy to transform into a slightly heavier version of itself before it can interact. This subtle difference changes the rules of the game, requiring the incoming particle to be moving at a specific speed to trigger the event. Recently, the LUX-ZEPLIN experiment, a massive detector filled with liquid xenon, reported a single, puzzling event where a nucleus recoiled with an energy of 248 keV, a signal that fits this inelastic picture better than the standard one.

Two physicists, Arindam Das and Takaaki Nomura, have taken this intriguing signal and built a theoretical model to explain how it could happen. They propose a hidden world of particles that interacts with our own only through a faint, shadowy force. In their framework, the universe contains a hidden symmetry, a kind of invisible charge that ordinary matter does not possess. To make this work, they introduce two new types of particles that are invisible to our standard instruments but carry this hidden charge. One of these particles acquires a "vacuum expectation value," a technical way of saying it settles into a stable state that gives mass to a new force carrier, which they call a dark photon. This dark photon acts as a messenger, capable of interacting with both the hidden sector and our visible world, albeit very weakly. The second particle, which is the candidate for dark matter, carries exactly half the hidden charge of the first. This specific arrangement creates a situation where the dark matter particle exists in two states: a lighter, stable version and a slightly heavier, excited version.

The researchers estimated a parameter region where these particles could account for the amount of dark matter we observe today. They found that if the dark matter particles are about one thousand times heavier than a proton, they can annihilate each other in the early cosmos at just the right rate to leave behind the correct amount of residue. This calculation relies on the particles colliding and turning into the dark photons or other new scalar particles predicted by their model. Once they established that their model could produce the right amount of dark matter, they turned their attention to the specific event seen by the LUX-ZEPLIN experiment. They simulated how a dark matter particle from our galaxy would travel through space and strike a xenon atom in the detector. Because the dark matter must transform into its heavier state to interact, it needs a minimum speed to succeed. Their calculations showed that for a dark matter particle with a mass of one teraelectronvolt, a mass splitting of 350 keV can fit the data well, matching the recoil energy observed in the LUX-ZEPLIN data and suggesting that the single event they saw could indeed be the result of this inelastic transformation.

However, for this story to hold together, the forces involved must be just right. The interaction is mediated by the dark photon, which must be light enough to allow the interaction to happen but heavy enough to avoid detection by previous experiments. The authors mapped out the properties of this dark photon, specifically its mass and how strongly it mixes with ordinary light. They found that a dark photon with a mass less than 10 gigaelectronvolts fits the data well while remaining hidden from current searches. They also examined other ways the dark matter could interact, such as through the Higgs boson, the particle that gives mass to ordinary matter. They determined that these other interactions must be extremely weak, or else they would have been seen in other experiments already. This places strict limits on the strength of the connections between the new particles and the known world, effectively narrowing down the possible properties of this hidden sector.

The paper concludes by outlining how this theory could be tested in the near future. Because the model requires a relatively light dark photon and new scalar particles, future experiments at high-energy colliders and specialized beam-dump facilities could produce them directly. The researchers suggest that machines like the Large Hadron Collider, or future detectors designed to look for long-lived particles, could find evidence of these hidden interactions. If the dark photon exists as they describe, it would decay into pairs of lighter particles like electrons or muons, creating a distinct signature that current and upcoming experiments are poised to catch. While the model remains a theoretical proposal, it offers a coherent explanation for a specific, unexplained signal in the data, turning a single statistical fluctuation into a potential window into a hidden layer of reality.

Technical Summary: Effect of Inelastic Scalar Dark Matter in Hidden U(1) Scenario after the LZ Nuclear Recoil

Problem Statement
The nature and interaction type of Dark Matter (DM) remain unknown despite its established relic abundance. Recently, the LUX-ZEPLIN (LZ) collaboration reported a candidate event with a nuclear recoil energy of $248 \pm 23(\text{stat}) \pm 23(\text{syst})$ keV, exhibiting a global significance of 2.6 $\sigma$ . This high-energy event, observed in an exposure of 2.84 tonne-years, constitutes a larger share of the expected recoil spectrum compared to standard spin-independent (SI) scattering. While previous experiments like DAMA/LIBRA and XENON1T have motivated inelastic DM scenarios, the LZ result specifically suggests the viability of an inelastic DM candidate where the scattering process is endothermic. The authors aim to explain this event within a theoretically motivated framework while satisfying constraints from relic density and direct detection.

Methodology and Model Framework
The authors propose a hidden $U(1)_H$ extension of the Standard Model (SM) containing two SM singlet complex scalar fields, $S$ and $\phi$ , with $U(1)_H$ charges of 1 and 2, respectively.

Symmetry Breaking: The field $\phi$ acquires a vacuum expectation value (VEV), spontaneously breaking the $U(1)_H$ symmetry and generating a mass for the dark gauge boson, $A'$ (dark photon).
Dark Matter Candidate: The field $S$ does not acquire a VEV. Due to the charge assignment, a remnant $Z_2$ symmetry exists where the CP-even ( $s$ ) and CP-odd ( $a$ ) components of $S$ are odd, while other particles are even. This ensures the stability of $s$ and $a$ .
Mass Splitting: A trilinear scalar coupling ( $\mu$ ) induces a mass splitting ( $\delta m = m_a - m_s$ ) between the $s$ and $a$ states. This splitting enables inelastic scattering.
Mediators: Interactions are mediated by the dark photon $A'$ (via kinetic mixing with the SM photon) and by scalar mixing between the SM Higgs ( $h$ ) and the real part of $\phi$ ( $\tilde{\phi}$ ).

The study utilizes the following steps:

Relic Density Calculation: The authors estimate the DM relic abundance using the annihilation channels $ss/aa \to A'A'$ (gauge interaction) and $ss/aa \to \phi\phi$ (scalar interaction), employing the micrOMEGAs package.
Direct Detection Analysis: They model the inelastic scattering process $sA \to aA$ (where $A$ is the target nucleus) mediated by $A'$ . They calculate the minimum DM velocity required to produce the observed LZ recoil energy ( $E_R \approx 248$ keV) and determine the necessary spin-independent (SI) cross-section.
Parameter Constraints: They derive bounds on the kinetic mixing parameter ( $\epsilon$ ) as a function of the dark photon mass ( $m_{A'}$ ) and gauge coupling ( $g_H$ ), comparing these against existing experimental limits from beam-dump and collider experiments.

Key Contributions and Results

Explanation of the LZ Event: The model successfully reproduces the LZ candidate event under a benchmark scenario with a DM mass ( $m_{DM}$ ) of 1 TeV and a mass splitting $\delta m = 350$ keV. The inelastic nature of the scattering ( $s \to a$ ) requires a minimal incoming DM velocity that reaches the tail of the Galactic DM velocity distribution; this kinematic threshold explains the observed high-energy event while naturally accounting for the absence of events with lower recoil energy.
Relic Density Viability: The authors identify parameter regions where the observed relic density ( $0.11 < \Omega h^2 < 0.13$ ) is satisfied. They find that for $O(1)$ TeV DM, $O(1)$ gauge couplings ( $g_H$ ) can accommodate the relic density via gauge interactions, while smaller couplings ( $g_H \sim 0.01$ ) can satisfy it via scalar interactions.
Kinetic Mixing Bounds: For the benchmark scenario ( $m_{DM} = 1$ TeV), the required SI cross-section ( $2 \times 10^{-40} \text{ cm}^2 < \sigma_{SI} < 3 \times 10^{-39} \text{ cm}^2$ ) implies that a relatively light dark photon ( $m_{A'} \lesssim 10$ GeV) is preferred to explain the LZ event while evading current experimental exclusions.
Scalar Sector Constraints: The study imposes constraints on scalar couplings ( $\lambda_{HS}, \lambda_{S\phi}$ ) and mixing angles to ensure the elastic scattering cross-section remains below current direct detection limits ( $\sim 3 \times 10^{-47} \text{ cm}^2$ ). This typically requires small couplings or specific cancellations between Higgs and $\phi$ mediation amplitudes.
Astrophysical Considerations: The authors note that solar neutrino constraints are relaxed in this scenario because $A'$ -neutrino couplings are suppressed, though decay chains involving $A' \to \tau^+\tau^-, \mu^+\mu^-$ or hadrons may require further analysis.

Significance and Future Probes
The paper claims that the proposed hidden $U(1)_H$ scenario provides a viable theoretical explanation for the recent LZ high-energy nuclear recoil event through inelastic scalar DM scattering. The significance lies in connecting the specific kinematic requirements of the LZ data (high recoil energy, specific mass splitting) with a concrete particle physics model involving a dark photon and scalar mixing.

The authors assert that the derived parameter space, particularly the kinetic mixing parameter $\epsilon$ as a function of $m_{A'}$ , is within the reach of future experiments. They specifically identify that the preferred region (light $A'$ ) can be probed by:

Lifetime Frontier: Dark photon searches such as FASER2.
Energy Frontier: High-luminosity LHC (3 ab $^{-1}$ ), future 100 TeV hadron colliders, and beam-dump facilities at lepton colliders.
Collider Signatures: Future Higgs and Z factories could detect processes like $h \to A'A'$ , $h \to \phi\phi \to A'A'A'A'$ , and $Z \to A'\phi$ , leading to multi-lepton final states.

The study concludes that while the scenario faces constraints from direct detection and stability (requiring the decay of the excited state $a$ ), it remains a testable framework for explaining the LZ anomaly.

Technical Summary: Effect of Inelastic Scalar Dark Matter in Hidden U(1) Scenario after the LZ Nuclear Recoil

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