⚛️ phenomenology

Escaping Solar Capture: Majoron mediated Elastic Dark Matter for the LZ 248~keV Event

This paper proposes that the 248 keV nuclear-recoil event observed by LZ can be explained by Majoron-mediated elastic dark matter scattering, a mechanism that naturally links neutrino mass generation to the signal while simultaneously reproducing the observed thermal relic abundance and suppressing solar capture through specific spin and kinematic properties.

Original authors: Salvador Centelles Chuliá, Ayan Chattaraj, Rahul Srivastava, Surabhi Srivastava

Published 2026-09-29

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CC0 1.0

Original authors: Salvador Centelles Chuliá, Ayan Chattaraj, Rahul Srivastava, Surabhi Srivastava

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

Deep in the quiet of the Earth, beneath layers of rock that shield them from the chaos of the surface, sits a tank of liquid xenon waiting to catch a ghost. This is the LUX-ZEPLIN experiment, a massive detector designed to find dark matter, the invisible substance that makes up most of the matter in the universe but refuses to interact with light or ordinary matter in any way we can easily see. For decades, scientists have watched these tanks, expecting to see a tiny, sudden flash of light when a dark matter particle bumps into an atom of xenon. The problem is that dark matter is supposed to be slow and heavy, moving through our galaxy like a gentle breeze. When such a particle hits an atom, it should give it a tiny, gentle nudge, creating a very low-energy signal. But recently, the LZ experiment saw something strange: a single, very energetic event, a hard kick to a xenon atom that happened at an energy level far higher than the gentle breeze of standard dark matter theories would predict. This single event sits near the top of the energy range the detector can see, and it does not fit the pattern of a quiet, slow collision.

The researchers behind this new study, working from institutions in Spain and India, asked a simple question: what if this strange, high-energy kick is not a mistake, but a clue to a different kind of dark matter? They proposed that the dark matter particle is not just bumping into atoms, but is interacting with them through a very specific, unusual force carried by a light particle called a Majoron. In the world of particle physics, forces are often carried by invisible messengers. The Majoron is a special kind of messenger that arises naturally if we assume that the universe has a hidden symmetry related to the number of particles called leptons, which includes electrons and neutrinos. When this symmetry breaks, it creates the Majoron, a particle that also helps explain why neutrinos have mass. The authors suggest that this same Majoron acts as the bridge between the dark matter and the atoms in the detector.

The key to their idea lies in how this interaction works. Unlike a standard collision where the force is constant, the force carried by the Majoron depends heavily on how fast the particles are moving and how hard they hit. It is a force that gets much stronger as the collision becomes more violent. This explains the strange LZ event perfectly: the interaction is too weak to create many of the small, low-energy bumps that would usually flood the detector, but it is just right to create that single, rare, high-energy kick. The model predicts that the dark matter particle, which they identify as a heavy, invisible fermion, travels through space and occasionally strikes a xenon atom. Because of the unique nature of the Majoron force, the atom receives a sharp, high-energy jolt rather than a gentle tap. This specific type of interaction, which relies on the spin of the particles involved, changes the rules of the game entirely.

One of the biggest hurdles for any theory trying to explain high-energy dark matter events is the Sun. The Sun is a massive gravitational trap that constantly captures dark matter particles passing through it. Once captured, these particles sink to the core, collide with solar atoms, and eventually annihilate, producing a flood of neutrinos that can be detected by telescopes on Earth. For many theories that try to explain the LZ event, the Sun would act as a filter, capturing so many dark matter particles that the resulting neutrino signal would be far too strong and would have already been seen by observatories like IceCube. However, the authors show that their specific model avoids this trap. The force they propose interacts very differently with the elements found in the Sun. The Sun is mostly made of hydrogen and helium, with a small amount of heavier elements like iron. The interaction they describe does not work well with the heavy elements that usually capture dark matter, and it is also very poor at capturing the light hydrogen atoms because the physics of the collision simply does not match up. As a result, the Sun captures almost none of these dark matter particles, leaving the neutrino telescopes quiet and allowing the theory to survive a test that would have killed other explanations.

To make this idea concrete, the team built a complete mathematical model of the universe that includes this new particle and force. They started with a known framework for how neutrinos get their mass, known as the scotogenic model, and added the necessary ingredients to create the Majoron and the dark matter particle. In their construction, the dark matter particle gets its mass from the same process that gives mass to the neutrinos, linking the mystery of dark matter directly to the mystery of neutrino mass. They also introduced a new, heavy type of quark to help transmit the force from the dark sector to the visible world. When they ran the numbers, they found that this model could reproduce the single high-energy event seen by LZ without creating a flood of low-energy events that would contradict other data. Furthermore, they calculated how much of this dark matter would have been left over from the Big Bang, and found that the amount matches exactly what astronomers observe in the universe today.

The result is a coherent picture where a single, rare event in a deep underground tank is not an anomaly, but a signature of a deeper connection between the invisible mass of the universe and the tiny masses of neutrinos. The theory suggests that the dark matter particle is a heavy, solitary traveler that interacts with our world only through a subtle, spin-dependent force carried by the Majoron. This force is weak enough to avoid detection in most places but strong enough to deliver that one surprising, high-energy blow to a xenon atom. By explaining the event while simultaneously avoiding the constraints of solar capture and matching the cosmic abundance of dark matter, the study offers a plausible, unified explanation for some of the most puzzling data in modern physics. It does not claim to have solved the mystery of dark matter, but it provides a clear, consistent path forward that links the smallest particles in the universe to the largest structures in the cosmos, all centered around a single, unexpected flash of light in a tank of liquid xenon.

Technical Summary: Escaping Solar Capture via Majoron-Mediated Elastic Dark Matter

Problem Statement
The LUX-ZEPLIN (LZ) collaboration reported a candidate nuclear recoil event at $E_R = 248 \pm 23_{stat} \pm 23_{syst}$ keV $_{nr}$ , located near the upper edge of their analysis window. Conventional elastic dark matter (DM) scattering predicts a steeply falling spectrum, making a single high-energy event difficult to reconcile without overproducing events in lower-energy bins. While inelastic DM scattering (where DM transitions to a heavier state) can kinematically shift the spectrum to high energies, it faces a critical constraint: the same mass splitting ( $\delta \sim 300$ keV) required to explain the LZ event allows for efficient solar capture on heavy elements (like iron). The annihilation products of this captured population are tightly constrained by neutrino telescopes (IceCube, Super-Kamiokande), effectively ruling out standard inelastic interpretations for this specific event. Furthermore, previous attempts to suppress solar capture via isospin-violating couplings fail because scattering on hydrogen is kinematically closed for the required mass splittings, leaving heavy element capture channels open.

Methodology
The authors propose an alternative mechanism: elastic scattering mediated by a light pseudoscalar, specifically the Majoron ( $J$ ), which arises from spontaneous lepton number breaking. The methodology proceeds in three stages:

Model-Independent Effective Operator Analysis:
The authors analyze the scattering of fermionic DM ( $F$ ) off nucleons via a pseudoscalar mediator. This interaction generates the non-relativistic operator $\mathcal{O}_6 = (\vec{S}_F \cdot \vec{q})(\vec{S}_N \cdot \vec{q})$ .
- Momentum Dependence: The differential cross-section scales as $q^4 / (q^2 + m_J^2)^2$ . This $q^4$ dependence suppresses low-energy recoils (where momentum transfer $q$ is small) while enhancing the rate at high recoil energies (where $q \sim 250$ MeV for the LZ event).
- Solar Capture Suppression: The operator $\mathcal{O}_6$ $O_{6}$ requires non-zero nuclear spin ( $I_A \neq 0$ $I_{A} \neq = 0$ ). The dominant solar capture targets (Iron-56, Helium-4, Oxygen-16) have zero spin, rendering them invisible to this interaction. The remaining target, Hydrogen, suffers from two suppression mechanisms:
  - Kinematic Mismatch: For heavy DM ( $\sim$ TeV), the maximum momentum transfer on protons is $\lesssim 9$ MeV, far below the characteristic scale of the LZ event ( $\sim 250$ MeV).
  - Momentum Suppression: The derivative nature of the interaction further suppresses the rate at these low momentum transfers.
Ultraviolet (UV) Completion (Scotogenic Majoron Model):
To realize this interaction concretely, the authors construct a scotogenic extension of the Standard Model:
- Field Content: The model includes the standard scotogenic sector (inert doublet $\eta$ , singlet Majorana fermions $N_i$ ) and a complex scalar singlet $\Phi$ that breaks lepton number ( $U(1)_L$ ).
- Dark Matter: The lightest singlet fermion $N_1$ is the DM candidate.
- Portal to Visible Sector: A vector-like up-type quark ( $U$ ) and a Type-I Dirac seesaw mechanism in the quark sector communicate the Majoron interaction to the up quark. This setup generates the physical up quark mass while decoupling the visible sector coupling from the DM coupling.
- Symmetry Breaking: The vacuum expectation value (VEV) of $\Phi$ ( $v_\phi$ ) generates the Majoron mass (via soft breaking) and the DM mass.
Phenomenological Analysis:
The authors perform a numerical scan to verify if this model can simultaneously:
- Reproduce the LZ 248 keV event rate without exceeding background limits in lower energy bins ( $E_R < 225$ keV).
- Satisfy the observed thermal relic abundance ( $\Omega h^2 \approx 0.12$ ).
- Satisfy theoretical constraints (vacuum stability, perturbativity) and experimental bounds (Higgs invisible decays, collider limits on vector-like quarks).

Key Contributions and Results

Reproduction of the LZ Spectrum: The model successfully reproduces the high-recoil event. By tuning the Majoron mass ( $m_J$ ) to the sub-GeV to GeV range and the coupling strengths, the $q^4$ momentum dependence shifts the signal to the 248 keV region. The analysis shows that for a mediator mass $m_J \sim 1$ GeV and DM mass $M_1 \sim 1$ TeV, the model yields exactly one expected event in the signal region ( $R_{II}=1$ ) while keeping the low-energy background contribution below the statistical uncertainty ( $R_I < 39$ ).
Suppression of Solar Capture: The specific spin structure of the $\mathcal{O}_6$ interaction eliminates the dominant capture channels on heavy solar elements (Iron). Capture on hydrogen is suppressed by orders of magnitude ( $\sim 10^{-6}$ to $10^{-5}$ ) due to the small momentum transfer available in the solar core compared to the detector scale. Consequently, the model evades the stringent constraints from IceCube and Super-Kamiokande that rule out inelastic DM interpretations.
Thermal Relic Abundance: The model accounts for the correct relic density through Majoron-mediated annihilation channels ( $N_1 N_1 \to JJ$ and $N_1 N_1 \to J\rho$ ). The annihilation cross-section is governed by the Yukawa coupling $Y_{N1} \propto M_1/v_\phi$ . The authors find that for a wide range of DM masses (up to a few TeV), there exists a corresponding VEV scale $v_\phi$ that yields the correct relic density.
Consistency with Constraints: The parameter space favored by the LZ event (moderate $M_1$ and $v_\phi$ ) overlaps with the region satisfying the relic density constraint. The model remains consistent with limits on Higgs invisible decays, charged lepton flavor violation (which constrains lighter masses not relevant here), and collider bounds on vector-like quarks (set at $M_U = 2$ TeV).

Significance
The paper claims that this construction provides a viable, neutrino-mass-motivated explanation for the LZ high-recoil event that was previously considered excluded by solar capture constraints. By utilizing a light Majoron mediator, the model achieves two goals simultaneously:

It generates the necessary momentum-dependent enhancement to explain the high-energy recoil without populating low-energy bins.
It naturally suppresses solar capture through the spin-dependent nature of the interaction and kinematic mismatches, bypassing the "solar capture problem" that plagues inelastic DM models.

The authors emphasize that this realization connects the LZ signal directly to the mechanism of radiative neutrino mass generation (scotogenic models) and spontaneous lepton number breaking, offering a coherent framework where the DM candidate, the mediator, and the neutrino mass origin are intrinsically linked. They suggest that similar consistent realizations may exist in other Majoron-based neutrino mass models, including those involving Dirac neutrinos (Diracon models).

Technical Summary: Escaping Solar Capture via Majoron-Mediated Elastic Dark Matter

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