⚛️ phenomenology

Testing Higgs-Coupled Minimal Dark Matter with Solar Neutrinos after the LZ High-Recoil Event

This paper investigates the Higgs-coupled Minimal Dark Matter interpretation of a recent LZ nuclear-recoil event and finds that, while the model successfully reproduces the terrestrial signal, the resulting high-energy solar neutrino flux from DM annihilation strongly conflicts with IceCube constraints for most thermal mass benchmarks, particularly those below 48 TeV.

Original authors: Mattia Di Mauro

Published 2026-09-18

📖 4 min read🧠 Deep dive

CC0 1.0

Original authors: Mattia Di Mauro

Original paper dedicated to the public domain under CC0 1.0 (http://creativecommons.org/publicdomain/zero/1.0/). ✨ 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, astronomers have known that the visible stars and galaxies in the universe are only a small fraction of what exists. The rest is an invisible substance called dark matter, which holds galaxies together through its gravity but refuses to interact with light. While we know it is there, we have never directly caught a single particle of it. One leading idea suggests that dark matter consists of heavy, slow-moving particles that occasionally bump into normal atoms. However, as detectors on Earth have become more sensitive, they have found nothing, forcing scientists to consider more complex scenarios where these particles might be harder to catch.

A recent clue appeared from the LUX-ZEPLIN experiment, a massive detector buried deep underground. The team reported seeing a single, unusual event where a nucleus in the detector received a very strong kick, far more energetic than typical background noise. This high-energy kick suggested a specific type of interaction: the dark matter particle might need to absorb a small amount of energy to change its state before it can bounce off an atom. This process, known as endothermic scattering, pushes the signal to higher energies, explaining why the detector saw such a powerful hit.

A new study takes this single event and asks a critical question: if this interpretation is correct, what should we see happening in the Sun? The researchers focused on a specific theoretical model where dark matter particles interact with the Higgs field, the same field that gives particles mass. In this model, the same force that causes the high-energy kick on Earth also pulls dark matter into the Sun. Once trapped by the Sun's immense gravity, these particles would sink to the core, collide, and eventually destroy each other, releasing a flood of high-energy neutrinos. These ghostly particles would travel to Earth, where a massive detector called IceCube, buried in the Antarctic ice, could spot them.

The researchers performed a detailed, step-by-step calculation to see if this scenario holds up. They did not simply assume the dark matter particles would behave perfectly; instead, they modeled the complex reality of the Sun's interior. They accounted for the fact that the Sun is not a solid block but a hot gas where atomic nuclei are constantly jiggling. They also considered that the dark matter particles might not start in their lowest energy state and would need to lose energy through various collisions before settling down to annihilate. By running these simulations with extreme precision, they determined exactly how many neutrinos should be arriving at Earth for each of the six proposed versions of this dark matter model.

The results were decisive. For the two lightest versions of the model, which fit the mass range of the single event seen on Earth, the predicted number of neutrinos from the Sun is thousands of times higher than what IceCube has actually observed. The detectors have seen far fewer neutrinos than this theory predicts, effectively ruling out these two versions of the model. The situation is similar for the next two heavier versions; while the gap is smaller, the predicted signal is still significantly higher than the observed limit, placing these models under severe strain.

For the heaviest versions of the model, the situation is more nuanced because they fall outside the standard range of data that IceCube has published. The researchers had to carefully estimate how the detector's sensitivity changes for such massive particles. Even with a very conservative estimate that assumes the detector becomes much less efficient at these extreme masses, the heaviest models still predict more neutrinos than are seen, though the margin is tighter. The 82 TeV benchmark is highly sensitive to these assumptions, while the 130 TeV benchmark remains below the extrapolated sensitivity, making it the only candidate that currently survives this test.

Ultimately, this work demonstrates that a single event on Earth can be tested against the entire solar system. By using the Sun as a giant trap and the Antarctic ice as a listening post, the researchers showed that the most popular explanations for the high-energy kick are likely incorrect. The study does not prove what dark matter is, but it successfully narrows the field, showing that if this specific type of interaction is responsible for the signal, the universe must be populated by much heavier particles than previously thought, or the model itself needs to be abandoned.

Technical Summary: Testing Higgs-Coupled Minimal Dark Matter with Solar Neutrinos after the LZ High-Recoil Event

Problem Statement
The LUX-ZEPLIN (LZ) collaboration recently reported a single nuclear-recoil candidate event at $E_R = 248 \pm 23 \text{ (stat)} \pm 23 \text{ (sys)} \text{ keV}$ . This high-energy event motivates interpretations involving endothermic dark matter (DM), where the incoming DM particle must supply a mass splitting ( $\delta$ ) to excite a heavier state. The specific model under investigation is Higgs-coupled Minimal Dark Matter (HC-MDM), which posits a Majorana multiplet and an adjacent Dirac multiplet coupled via the Higgs field. In this framework, the same electroweak interaction responsible for the terrestrial recoil induces DM capture in the Sun. Once captured, DM particles can thermalize, concentrate at the Solar center, and annihilate into Standard Model states, producing high-energy neutrinos detectable by IceCube. The central problem addressed is whether the HC-MDM parameter space that reproduces the LZ event is compatible with existing IceCube limits on Solar DM neutrinos.

Methodology
The author performs an independent reassessment of the HC-MDM interpretation of the LZ event, employing a more complete treatment of Solar capture and post-capture evolution than previous analyses. The methodology involves several distinct technical components:

Model Definition and Benchmark Selection: The study utilizes six thermal benchmark points (3M2D through 13M12D) corresponding to different electroweak representations. The author independently determines the mass splittings ( $\delta^\star$ ) required to reproduce the single LZ event rate, correcting the neutral-current normalization used in prior work.
Solar Capture Calculation: The capture rate is calculated using a sampled BS05(AGS,OP) Standard Solar Model. Key improvements over stationary-target approximations include:
- Natural Isotope Mixtures: Explicit treatment of isotope abundances, crucial near kinematic closure.
- Finite-Temperature Nuclear Motion: For high-mass splittings (specifically the $\delta = 570 \text{ keV}$ high-velocity solutions), the author averages the capture probability over the thermal Maxwell-Boltzmann velocity distribution of Solar nuclei. This accounts for the "reopening" of kinematically forbidden channels by nuclei moving toward the incoming DM.
- Exact Kinematics: Implementation of exact inelastic kinematics and finite-momentum nuclear form factors (Helm response).
Post-Capture Evolution: The study treats capture, cooling, and annihilation as distinct steps:
- De-excitation: Radiative and collisional de-excitation of excited states ( $\chi_{2,3} \to \chi_1$ ) are evaluated. Radiative decay is found to be rapid for lighter representations, while collisional de-excitation is treated conservatively.
- Orbital Cooling: The cooling of captured DM via loop-induced elastic scattering is calculated explicitly. The author verifies that even if the loop-induced cross-section is suppressed by factors of 100, the majority of the captured population thermalizes within the Solar age.
- Equilibrium Test: The capture-annihilation equilibrium is explicitly verified. The equilibration time ( $\tau_{eq}$ ) is found to be orders of magnitude smaller than the Solar age, justifying the use of the equilibrium relation $\Gamma_A \approx C_\odot / 2$ .
IceCube Comparison:
- For benchmarks within the published 10 TeV IceCube grid (3M2D and 5M4D), predictions are compared directly to the $W^+W^-$ response.
- For heavier benchmarks (7M6D to 13M12D), which lie above the 10 TeV grid, the author constructs a response-matched extrapolation. This extrapolation is anchored to the 10 TeV endpoint sensitivity and uses the logarithmic slope of the published high-mass curve. A conservative "response-loss" stress test is also applied to test the robustness of conclusions against weaker high-mass sensitivity.

Key Contributions

Independent Rate Matching: The author derives new mass splittings ( $\delta^\star$ ) for the six HC-MDM benchmarks based on the corrected neutral-current normalization, finding values systematically larger (by 1–7 keV) than those in the original LZ interpretation paper.
Finite-Temperature Capture Kernel: The paper develops and implements a finite-temperature capture kernel that significantly enhances capture rates for high-mass splittings ( $\delta = 570 \text{ keV}$ ) by accounting for the thermal motion of heavy Solar nuclei (Fe, Ni).
Systematic Stress Testing: The study explicitly tests the robustness of the thermalization and equilibrium assumptions against large reductions in the loop-induced elastic cross-section and variations in the high-mass IceCube response extrapolation.
High-Mass Extrapolation: A response-based diagnostic is constructed to extend IceCube constraints to DM masses up to 130 TeV, distinguishing between models that are robustly excluded and those that depend on the specific form of the high-mass response.

Results

Thermal Benchmarks (Standard Halo Model):
- The two lightest benchmarks, 3M2D ( $\sim 1.4 \text{ TeV}$ ) and 5M4D ( $\sim 7.7 \text{ TeV}$ ), predict Solar annihilation rates that exceed the mass-matched IceCube $W^+W^-$ response by factors of approximately $2.2 \times 10^3$ and $91$, respectively. These solutions are under strong tension.
- For the heavier benchmarks, the predicted annihilation rates are compared against the extrapolated response:
  - 7M6D ( $22 \text{ TeV}$ ): Remains in strong tension with IceCube even under the conservative response-loss extrapolation.
  - 9M8D ( $48 \text{ TeV}$ ): Remains above the extrapolated response, though closer to the sensitivity boundary.
  - 11M10D ( $82 \text{ TeV}$ ): The result is response-dependent; it lies modestly above the central extrapolation but below the conservative stress curve.
  - 13M12D ( $130 \text{ TeV}$ ): Remains below the extrapolated IceCube sensitivity in both treatments.
High-Velocity Solutions ( $\delta = 570 \text{ keV}$ ):
- For the proposed high-velocity solutions, the inclusion of finite-temperature nuclear motion enhances the Solar capture rate by a factor of $\sim 11\text{--}12$ compared to stationary-target calculations.
- The 1.47 TeV trajectory remains significantly constrained by IceCube (exceeding the response by a factor of $\sim 6$ ).
- The 8.5 TeV trajectory remains compatible with IceCube bounds, even assuming a fully $W^+W^-$ -equivalent spectrum.
Discrepancy with Previous Work: The author identifies that the difference between their Solar predictions and those in Ref. [25] for the high-velocity solutions arises from the treatment of the halo velocity distribution and the omission of finite-temperature nuclear motion in the previous analysis. The previous work's suppression factors were consistent with assuming a subdominant fast component density, but the author argues that the ordinary Galactic halo population remains available for capture and is efficiently captured by Fe and Ni.

Significance
The paper claims that the HC-MDM interpretation of the LZ high-recoil event is strongly constrained by Solar neutrino limits for the lightest thermal benchmarks. The study demonstrates that the tension is robust against variations in nuclear physics inputs, isotope mixtures, and the theoretical uncertainties of loop-induced elastic scattering. While the heaviest representations (specifically 13M12D) survive the current constraints, the exclusion of the lighter thermal solutions suggests that if the LZ event is indeed DM, it likely requires non-standard halo components or specific model variations beyond the standard thermal HC-MDM benchmarks. The work provides a rigorous framework for testing endothermic DM models against Solar capture and neutrino data, emphasizing the necessity of finite-temperature effects near kinematic thresholds.

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