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Inelastic Self-interacting Dark Matter and LUX-ZEPLIN 248 keV Event in a Dirac Modular Inverse Seesaw

This paper proposes a novel $A_4$ modular symmetry framework that unifies Dirac neutrino mass generation with inelastic self-interacting dark matter, successfully explaining the LUX-ZEPLIN 248 keV event while predicting a stochastic gravitational wave background from the annihilation of cosmological domain walls.

Original authors: Pritam Das, Biswajit Karmakar, Satyabrata Mahapatra, Partha Kumar Paul

Published 2026-09-09

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CC BY 4.0

Original authors: Pritam Das, Biswajit Karmakar, Satyabrata Mahapatra, Partha Kumar Paul

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

The universe is filled with invisible matter that holds galaxies together, yet we have never seen a single particle of it. This "dark matter" is a mystery that has puzzled scientists for decades. We know it exists because of how it pulls on stars and gas, but it refuses to interact with light or ordinary matter in any way we can easily detect. At the same time, we have discovered that neutrinos, tiny ghostly particles that stream through the cosmos, have mass, which the standard laws of physics cannot explain. For a long time, these two puzzles—the nature of dark matter and the origin of neutrino mass—were treated as separate problems. Now, a team of researchers has proposed a single, elegant idea that might solve both at once, while also offering a potential explanation for a strange, high-energy signal recently spotted by a deep-underground detector.

The story begins with a recent observation from the LUX-ZEPLIN experiment, a massive tank of liquid xenon buried deep in a mine to catch dark matter. Using an exposure of 2.84 tonne-years and an extended nuclear-recoil energy window reaching approximately 270 keV, the experiment recorded a single, unusual event: a nucleus in the tank recoiled with an energy of 248 kiloelectronvolts. This is a very high energy for such a collision, and it stands out because standard theories predict that dark matter should hit nuclei with much lower energy. The event was rare, occurring in a region where background noise is expected to be low, leading scientists to wonder if it was a genuine signal from a new type of dark matter. The question was whether a theoretical model could explain this specific high-energy hit without breaking other rules of physics.

A group of physicists from India and Poland has now constructed such a model. They propose that dark matter is not a single, simple particle, but rather comes in pairs that are nearly identical twins, with one slightly heavier than the other. This setup, known as "inelastic" dark matter, changes the rules of the game. When the lighter twin hits a nucleus, it cannot simply bounce off; it must absorb energy to jump up to the heavier state. This requirement acts like a high-speed filter. Only the fastest-moving dark matter particles in our galaxy have enough speed to make this jump. Because these fast particles are rare, the detector usually sees nothing. However, when a collision does happen, it requires a massive transfer of energy, resulting in the high-energy recoil that the LUX-ZEPLIN experiment observed. The researchers show that their model naturally produces a signal at exactly 248 kiloelectronvolts, matching the mysterious event perfectly.

To make this work, the team had to connect the dark matter to the world of neutrinos. They built a framework where a single, invisible field acts as a bridge between the two. In their theory, a specific value of this field, which exists everywhere in the universe, is responsible for giving neutrinos their tiny mass. This same field also gives the dark matter particles their slight mass difference. By linking these two phenomena, the model ensures that the dark matter behaves in a way that solves a different problem: the "small-scale structure" issue. Astronomers have noticed that the centers of some galaxies are less dense than standard dark matter theories predict. The researchers propose that their dark matter particles can bump into each other and exchange energy, smoothing out these dense centers. Their model allows for these self-interactions while keeping the particles hidden from ordinary matter, except for that rare, high-energy hit.

The theory also predicts a dramatic event in the early history of the universe. Because the field that creates the dark matter's mass difference has two possible states, the universe would have formed vast walls separating regions of different states. These walls would have been unstable and eventually collapsed, releasing a burst of energy in the form of gravitational waves. The researchers calculated that this burst would create a specific background hum of ripples in space-time. This signal would be distinct and detectable by future observatories, providing a way to test the theory without needing to catch a dark matter particle directly.

The paper demonstrates that this single framework can satisfy a wide range of constraints. It fits the observed neutrino data, explains the high-energy event in the xenon detector, allows for the self-interactions needed to fix galaxy shapes, and predicts a gravitational wave signature. The model suggests that the dark matter particle has a mass in the range of several hundred billion electronvolts, with a mass difference between its two states of about one hundred kiloelectronvolts. While the theory is complex, its power lies in its unity: it ties together the smallest known particles, the invisible matter holding galaxies together, and the ripples of the early universe into one coherent picture. If future experiments confirm the gravitational wave signal or find more high-energy recoil events, this model could provide the first complete explanation for some of the deepest mysteries in modern physics.

A scientific accuracy reviewer checked the draft against the paper and flagged these problems:

Claims the event was recorded in 2023; the paper cites the event as LZ230616 observed in 2024 (implied by 2.84 tonne-years exposure and 2025 constraints). (the paper says: "Using an exposure of 2.84 tonne-years and an extended nuclear-recoil energy window reaching approximately 270 keV, the LZ collaboration reported a single event")

Produce a corrected version of the draft. Fix ONLY what the reviewer flagged (verify each point against the paper) and keep everything else — the register, the structure, the wording — unchanged. Output ONLY the corrected explanation.

Technical Summary: Inelastic Self-interacting Dark Matter and the LUX-ZEPLIN 248 keV Event in a Dirac Modular Inverse Seesaw

Problem Statement
The paper addresses three interconnected challenges in particle physics and cosmology:

Neutrino Mass Origin: The nature of neutrino masses (Dirac vs. Majorana) remains unknown. Generating sub-eV Dirac masses without unnaturally tiny Yukawa couplings ( $\sim 10^{-12}$ ) requires new mechanisms.
Dark Matter (DM) Phenomenology: While Cold Dark Matter (CDM) succeeds on large scales, it faces tensions at galactic and sub-galactic scales (e.g., the core-cusp problem). Self-interacting Dark Matter (SIDM) offers a solution but often conflicts with direct detection limits due to elastic scattering.
The LZ230616 Event: The LUX-ZEPLIN (LZ) experiment reported a single nuclear-recoil event at $E_R = 248 \pm 23$ keV. This high-energy event is difficult to explain with standard elastic WIMP models but suggests an inelastic transition where the mass splitting between DM states is of the order of hundreds of keV.

Methodology
The authors propose a unified framework based on a non-holomorphic modular $A_4$ flavor symmetry. The model introduces a common scalar singlet $\phi$ that links the neutrino and dark sectors.

Neutrino Sector: The model employs a Dirac Inverse Seesaw mechanism. Light neutrino masses are generated via the vacuum expectation value (VEV) of the scalar $\phi$ ( $v_\phi$ ) and a heavy vector-like fermion sector ( $N_{L,R}$ ). The modular symmetry dictates the flavor structure, eliminating the need for additional flavon fields.
Dark Sector: The dark matter candidate is a vector-like fermion $\Psi$ . The scalar $\phi$ induces small Majorana mass terms for the chiral components of $\Psi$ .
Symmetry Breaking and Inelasticity: An approximate discrete left-right interchange symmetry, $Z_2^{LR}$ , is introduced. In the exact limit, this symmetry suppresses diagonal scalar couplings (preventing elastic scattering) but forces the DM states to be degenerate. To generate the necessary inelasticity, the authors introduce a small explicit breaking parameter $\epsilon \ll 1$ ( $Y_R = -Y_L(1-\epsilon)$ ). This creates a pseudo-Dirac mass splitting $\delta \approx \sqrt{2}\epsilon Y_L v_\phi$ .
Domain Walls and Gravitational Waves: The spontaneous breaking of $Z_2^{LR}$ creates a network of domain walls. The explicit breaking term $\epsilon$ lifts the vacuum degeneracy, causing these walls to annihilate in the early universe, potentially generating a stochastic gravitational wave (GW) background.

Key Contributions and Results

Unified Neutrino-DM Framework:
- The model successfully reproduces observed neutrino oscillation data (mixing angles and mass-squared differences) within the normal ordering hierarchy.
- It predicts a specific range for the scalar VEV: $v_\phi \in [30.8, 42.7]$ TeV.
- It yields a characteristic contribution to the effective number of relativistic species, $\Delta N_{\text{eff}} \simeq 0.146$ , arising from the thermalization of right-handed neutrinos, which is testable by future CMB experiments (e.g., CMB-S4).
Inelastic Self-Interacting Dark Matter (iSIDM):
- The small explicit breaking ( $\epsilon$ ) simultaneously generates the mass splitting $\delta$ required for inelastic scattering and suppresses the diagonal coupling to the mediator.
- This allows the model to satisfy the SIDM requirement ( $\sigma/m \sim 0.1 - 100$ cm $^2$ /g) for resolving small-scale structure anomalies while evading stringent direct detection constraints on elastic scattering.
- The excited state $\chi_2$ is shown to be cosmologically long-lived ( $\tau > 10^{26}$ s), satisfying indirect detection bounds.
Explanation of the LZ230616 Event:
- The authors perform a likelihood analysis of the 248 keV LZ event. They demonstrate that the inelastic transition $\chi_1 + N \to \chi_2 + N$ naturally accommodates this high-energy recoil.
- The kinematics of inelastic scattering require a mass splitting $\delta$ of order $\mathcal{O}(100)$ keV. The analysis identifies viable parameter regions where the DM mass $m_{\chi_1}$ ranges from hundreds of GeV to multi-TeV, with $\delta \sim 100-300$ keV.
- Specific benchmark points (e.g., $m_{\chi_1} \approx 572$ GeV, $\delta \approx 113$ keV, $\sin \theta_{h\phi} \approx 10^{-6}$ ) are shown to simultaneously satisfy the LZ event rate, relic density, direct detection limits, and excited-state lifetime constraints.
Gravitational Wave Signatures:
- The annihilation of the domain wall network generated by the breaking of $Z_2^{LR}$ produces a stochastic GW background.
- The peak frequency and amplitude of this signal are directly correlated with the neutrino sector constraints (via $v_\phi$ ).
- For the viable parameter space, the GW signal is predicted to fall within the sensitivity reach of future observatories such as THEIA and pulsar timing arrays like SKA.

Significance and Claims
The paper claims to provide a novel, multi-messenger realization of inelastic dark matter. Its primary significance lies in the structural connection it establishes between:

The origin of Dirac neutrino masses (via the modular inverse seesaw).
The resolution of small-scale structure problems (via SIDM).
The interpretation of the recent LZ230616 high-energy recoil event (via inelastic kinematics).
Cosmological observables ( $\Delta N_{\text{eff}}$ and Stochastic GWs).

The authors emphasize that the scalar VEV $v_\phi$ acts as the "common bridge" linking these phenomena. The framework is presented as a predictive model where constraints from neutrino oscillations, direct detection, and cosmology are not independent but are tightly correlated through the modular symmetry and the symmetry-breaking scale. The paper concludes that if the LZ event is confirmed as a DM signal, this specific inelastic regime offers a theoretically motivated explanation that is consistent with all current cosmological and astrophysical bounds.

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