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Cosmological Constrained Axion-Portal Inelastic Dark Matter for the LZ Event

This paper proposes a cosmologically constrained inelastic dark matter model where the long-lived excited state's relic abundance is dynamically determined by early-Universe conversion processes and the Lorentz structure of axion-portal couplings, offering a viable explanation for the high-recoil LZ event through either endothermic or exothermic scattering scenarios that can be distinguished by future annual modulation measurements and collider probes.

Original authors: Haipeng An, Fei Gao, Jia Liu, Minghao Liu, Changlong Xu

Published 2026-09-16

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CC BY 4.0

Original authors: Haipeng An, Fei Gao, Jia Liu, Minghao Liu, Changlong Xu

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

For decades, the most persistent mystery in physics has been the nature of dark matter. We know it exists because its gravity holds galaxies together, yet it refuses to interact with light or ordinary matter in any way we can easily detect. Scientists have spent years building massive, ultra-sensitive detectors deep underground, hoping to catch a rare moment when a dark matter particle bumps into an atom in the detector. The standard expectation has been that these collisions would be gentle, low-energy events. However, a recent report from the LUX-ZEPLIN experiment in South Dakota has shaken up this quiet expectation. The detector, filled with liquid xenon, recorded a single, unusually energetic collision that hit with a force far greater than the standard models predicted. This high-energy "recoil" is difficult to explain with the usual theories, suggesting that if dark matter is indeed responsible, it might behave in a much more complex and dynamic way than previously imagined.

A team of physicists has now proposed a specific scenario to explain this strange event, suggesting that dark matter is not a single, uniform substance but comes in two distinct states, like a ground state and an excited state. In their model, these two states are nearly identical in mass but separated by a tiny energy gap. The researchers built a framework where these two states interact with a hypothetical particle called an axion-like particle, which acts as a bridge between the dark world and the visible world. Crucially, they did not just assume one state exists today; they traced the entire history of these particles from the birth of the universe to the present day. They found that the way these two states convert into one another in the early universe determines which state is dominant today, and this history directly controls how the dark matter would behave in a detector on Earth.

The researchers discovered that the outcome depends entirely on the specific mathematical nature of the connection between the dark matter and the axion-like particle. If the connection is of a "scalar" type, the conversion process in the early universe is very efficient, stripping away almost all of the excited state. In this case, the dark matter reaching us today is almost entirely in the lower-energy state. To create the high-energy collision seen by the detector, a particle would have to absorb energy from the collision to jump up to the excited state, a process that requires a very specific, high-speed impact. Conversely, if the connection is of a "pseudoscalar" type, the conversion is inefficient, leaving roughly half of the dark matter in the excited state. In this scenario, the dominant process is the excited state dropping down to the lower state, releasing extra energy that boosts the collision. Both scenarios can produce a collision peak at the exact energy observed by the LUX-ZEPLIN experiment, around 250 keV, but they predict very different behaviors for the rest of the data.

This distinction offers a way to test the theory with future observations. The researchers calculated that if the excited state is rare, the signal would show a strong seasonal variation, peaking in June when the Earth moves fastest through the dark matter halo. If the excited state is common, the signal would be much steadier throughout the year. The single event reported by LUX-ZEPLIN happened on June 16, which aligns perfectly with the timing expected for the scenario where the excited state is rare. While this single event is not enough to prove the theory, the researchers show that with more data from current and future detectors, scientists could distinguish between these two possibilities. Their work demonstrates that the history of the universe is written into the way dark matter might scatter today, linking the conditions of the early cosmos directly to the signals we hope to catch in our laboratories. Furthermore, they note that the same particles involved in this dark matter model could be produced and studied directly in high-energy particle colliders, offering a second path to confirm or rule out this explanation.

Technical Summary: Cosmological Constrained Axion-Portal Inelastic Dark Matter for the LZ Event

Problem Statement
The LUX-ZEPLIN (LZ) collaboration recently reported a candidate nuclear-recoil event with an energy of $E_R \approx 248 \pm 23$ keV. Standard spin-independent elastic scattering models struggle to accommodate such high-energy recoils due to the suppression from the xenon nuclear form factor and the preference for lower recoil energies. This anomaly motivates alternative dark matter (DM) scenarios involving nonstandard kinematics, such as inelastic scattering, or momentum-dependent interactions. While previous works have explored inelastic DM (iDM) and axion-like particle (ALP) portals, many treatments assume a single DM state exists today or do not fully track the cosmological evolution of the excited state's abundance relative to the ground state.

Methodology
The authors propose a two-state inelastic DM model where two nearly degenerate fermionic states, $\chi_1$ (ground) and $\chi_2$ (excited), couple off-diagonally to an ALP ( $a$ ). The ALP also couples to gluons and photons. The model is analyzed through four benchmark scenarios (S1–S4) distinguished by the fermionic nature of the DM (Majorana vs. Dirac) and the Lorentz structure of the transition coupling (scalar vs. pseudoscalar).

The study employs a comprehensive cosmological and phenomenological framework:

Cosmological Evolution: Unlike previous studies, the authors track the evolution of both $\chi_1$ and $\chi_2$ from freeze-out to the present. They calculate the relic abundance determined by annihilation into ALP pairs ( $\chi\chi \to aa$ ) and the subsequent redistribution between states via dark-sector conversion processes ( $\chi_2\chi_2 \leftrightarrow \chi_1\chi_1$ ).
Lifetime Analysis: The decay $\chi_2 \to \chi_1 \gamma \gamma$ (mediated by the photon coupling) is calculated. The authors demonstrate that for parameters relevant to the LZ signal, this decay is sufficiently slow that $\chi_2$ survives to the present day, making its abundance a function of conversion rates rather than decay.
Direct Detection Calculation: Using tools like DirectDM and DMFormFactor, the authors match the partonic axion-gluon interaction to nucleon operators. They compute nuclear recoil spectra, retaining the full momentum dependence of the $t$ -channel axion propagator, which is crucial given the mediator masses ( $m_a \sim 0.01\text{--}1$ GeV) are comparable to the momentum transfer.
Modulation Analysis: The paper models the annual modulation of the event rate based on a truncated Maxwellian velocity distribution, comparing the expected timing of events for endothermic (up-scattering) versus exothermic (down-scattering) scenarios.

Key Contributions and Results
The central finding is that the Lorentz structure of the DM-ALP interaction dynamically selects the dominant direction of inelastic scattering in direct detection, linking the observed signal to early-Universe evolution:

Scalar Transition Couplings (S1, S3): In scenarios where the coupling is scalar (e.g., $\bar{\chi}_1 \chi_2$ ), the conversion process $\chi_2\chi_2 \leftrightarrow \chi_1\chi_1$ is highly efficient. This depletes the excited state fraction to $f_2 \sim 10^{-7} - 10^{-5}$ . Consequently, the recoil spectrum is dominated by endothermic scattering ( $\chi_1 N \to \chi_2 N$ ).
Pseudoscalar Transition Couplings (S2, S4): In scenarios with pseudoscalar couplings (e.g., $\bar{\chi}_1 i\gamma_5 \chi_2$ ), the conversion is inefficient, preserving an excited-state fraction of $f_2 \simeq 1/2$ . The recoil spectrum is therefore dominated by exothermic scattering ( $\chi_2 N \to \chi_1 N$ ).
Recoil Spectra: In all four scenarios, benchmark points can be tuned such that the recoil spectrum peaks near the observed LZ energy of $\sim 250$ keV. The gluonic coupling provides a momentum-dependent, spin-dependent nuclear response well-suited to the high-recoil regime.
Constraints: The authors show that the decay $\chi_2 \to \chi_1 \gamma \gamma$ is sufficiently suppressed to satisfy Cosmic Microwave Background (CMB) and Galactic X-ray constraints, particularly because the energy injection is suppressed by the small mass splitting relative to the DM mass.
Annual Modulation: The paper predicts distinct temporal signatures. Endothermic scenarios (S1/S3) exhibit a strong annual modulation (peaking in June) because the scattering threshold lies in the high-velocity tail of the DM distribution. In contrast, exothermic scenarios (S2/S4) show negligible modulation because the mass splitting provides the necessary energy, reducing sensitivity to the DM velocity distribution. The LZ candidate event occurred on June 16, aligning with the expected maximum for the endothermic scenarios.

Significance
The paper claims that the dominant direction of inelastic scattering (endothermic vs. exothermic) is not an arbitrary model choice but is dynamically determined by the cosmological evolution of the dark sector, specifically the efficiency of the $\chi_2\chi_2 \leftrightarrow \chi_1\chi_1$ conversion process. This establishes a direct link between early-Universe physics and the specific kinematic features of the LZ signal.

The authors suggest that with additional data from LZ, PandaX-4T, and XENONnT, the combined event yield could be sufficient to distinguish between these scenarios via recoil-energy distributions and, crucially, annual modulation measurements. Furthermore, the paper notes that the ALP portal can be directly probed at colliders, offering a complementary test to direct detection. The work underscores that the interpretation of the LZ event depends critically on the underlying Lorentz structure of the DM-ALP interaction.

Technical Summary: Cosmological Constrained Axion-Portal Inelastic Dark Matter for the LZ Event

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