⚛️ phenomenology

Environment-dependent mass splitting to suppress solar capture in the inelastic-doublet interpretation of the LZ event

This paper proposes an environment-dependent mass splitting mechanism driven by an ultralight scalar coupled to electrons to suppress solar capture constraints on the inelastic-doublet interpretation of the LZ experiment's 248 keV event, demonstrating its phenomenological viability despite severe fine-tuning requirements.

Original authors: Sudhakantha Girmohanta, Tae Hyun Jung

Published 2026-09-24

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CC BY 4.0

Original authors: Sudhakantha Girmohanta, Tae Hyun Jung

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

Deep in the silence of the universe, invisible particles known as dark matter are constantly drifting through the Earth. Scientists have spent decades building massive detectors, buried deep underground to shield them from cosmic noise, hoping to catch a glimpse of these elusive particles as they bump into the atoms inside their instruments. Recently, the LUX-ZEPLIN experiment, a state-of-the-art detector located in a former gold mine in South Dakota, recorded a single, startling event. A particle struck the detector with an energy of 248 kiloelectronvolts, a value significantly higher than what most standard theories of dark matter predict. While this single event is not enough to claim a discovery on its own, its unusual energy level sparked a new line of thinking among physicists. They began to wonder if this signal could be explained by a specific, slightly more complex version of dark matter that behaves differently depending on how fast it is moving or how heavy it is.

This specific theory, known as the inelastic doublet model, suggests that dark matter comes in two versions: a lighter state and a heavier state. For the dark matter to leave a mark in a detector on Earth, the lighter version must bump into an atomic nucleus and instantly transform into the heavier version. This transformation requires a specific amount of energy, like a key fitting into a lock. The energy measured in the LUX-ZEPLIN event fits perfectly with this idea, but only if the difference in weight between the two dark matter states is about 350 kiloelectronvolts. However, this same theory faces a major problem when applied to our Sun. The Sun is a massive furnace of density and gravity, acting as a giant trap for dark matter. If these particles exist, they should be captured by the Sun's gravity, sink to the core, and eventually collide with each other to produce high-energy neutrinos that we could detect on Earth. Observations from the IceCube neutrino observatory in Antarctica have found no such signal. This absence implies that if this theory is correct, the weight difference between the two dark matter states must be much larger—around 570 kiloelectronvelts or more—to prevent them from being captured by the Sun in the first place. This creates a contradiction: the Earth experiment needs a small difference to see the signal, while the Sun's silence demands a large difference to avoid detection.

A team of researchers has proposed a clever solution to this puzzle, suggesting that the rules of the game might change depending on where you are playing them. They argue that the difference in weight between the two dark matter states is not a fixed number carved in stone, but rather a value that shifts based on the density of the surrounding environment. In this scenario, the dark matter particles interact with a very light, invisible field that permeates the universe. This field behaves like a switch that remains off in the empty space around the Earth, keeping the weight difference small at 350 kiloelectronvolts, which allows the LUX-ZEPLIN detector to see the event. However, deep inside the Sun, where the density of matter is incredibly high, this field flips on. The presence of so much matter causes the field to take on a new value, which in turn increases the weight difference between the dark matter states to over 570 kiloelectronvolts. This larger gap makes it too difficult for the Sun to capture the particles, effectively silencing the neutrino signal that IceCube would otherwise see.

To test this idea, the researchers built a mathematical model describing how this invisible field responds to the density of electrons, which are abundant in both the Earth's crust and the Sun's core. They calculated that for this mechanism to work, the field must remain dormant in the laboratory but become active in the solar core. They then checked this proposal against other known laws of physics, specifically looking at how stars cool down and how the mass of electrons might change in dense environments. They found that the model holds up against observations of white dwarf stars and the early universe, provided that the parameters of the theory are set within a very specific range. The researchers identified that the field must be light enough to react to the Sun's density but heavy enough to ignore the Earth's, and the interaction strength must be tuned precisely to avoid conflicting with stellar cooling data.

The study concludes that this environment-dependent explanation is a viable way to reconcile the LUX-ZEPLIN event with the lack of solar signals. It offers a consistent picture where the same dark matter particles can produce a signal on Earth while remaining invisible to the Sun's gravitational trap. However, the authors are careful to note that achieving this balance requires a significant amount of fine-tuning in the underlying physics. The numbers in their equations must be set with extreme precision to ensure the field stays off on Earth but turns on in the Sun, a level of exactness that some physicists might find unnatural. Despite this theoretical hurdle, the work provides a concrete path forward, showing that the tension between the Earth-based signal and the solar silence does not necessarily rule out the inelastic doublet theory. Instead, it suggests that the properties of dark matter might be more fluid and context-dependent than previously imagined, changing their behavior as they move from the quiet void of space to the dense heart of a star.

Technical Summary: Environment-Dependent Mass Splitting to Suppress Solar Capture

Problem Statement
The LUX-ZEPLIN (LZ) collaboration reported a single nuclear recoil event at $E_R = 248 \pm 23 \text{ (stat)} \pm 23 \text{ (sys)}$ keV. While the global significance is modest ( $2.6\sigma$ ), the unusually high recoil energy motivates an inelastic dark matter (DM) interpretation involving a vector-like pair of pseudo-Dirac electroweak doublets. In this scenario, DM scattering ( $\chi_1 + N \to \chi_2 + N$ ) requires a mass splitting $\delta \approx 350$ keV to explain the LZ signal under the Standard Halo Model. However, the same interaction mediates the capture of DM in the Sun. The absence of high-energy neutrino signals from solar DM annihilation in the IceCube observatory imposes a stringent constraint: the mass splitting in the solar core must be $\delta_\odot \gtrsim 570$ keV to suppress capture. This creates a direct tension, as the pure doublet model cannot simultaneously satisfy $\delta \approx 350$ keV at Earth and $\delta \gtrsim 570$ keV in the Sun.

Methodology
The authors propose a mechanism where the mass splitting $\delta$ is environment-dependent, specifically sensitive to the local electron density ( $n_e$ ).

Model Construction: They introduce a complex scalar field $\Phi$ (with radial component $\phi$ ) coupled quadratically to the dark sector fermions ( $N, N^c$ ) via effective operators $\frac{\phi^2}{2\Lambda_N} NN + \text{h.c.}$ . The Majorana masses $m_M$ and $m'_M$ become functions of the scalar expectation value $v_\phi$ .
Density-Dependent Potential: The scalar potential $V(\phi)$ is constructed to be sensitive to the background electron density. Specifically, the term $\frac{\mu_\phi^2}{2}\phi^2$ is modified by an interaction with the electron bilinear $\bar{e}e$ :
$V(\phi) = \frac{\lambda_\phi}{4}\phi^4 + \left( \frac{\mu_\phi^2}{2} - \frac{m_e}{2\Lambda_e^2}\bar{e}e \right)\phi^2$
In a non-relativistic electron medium, $\langle \bar{e}e \rangle \simeq n_e$ . This creates a critical density $n_e^c$ . Below this density (e.g., in the laboratory), the potential minimum is at $v_\phi = 0$ . Above this density (e.g., in the solar core), $v_\phi$ becomes non-zero.
Mass Splitting Mechanism:
- At Earth (LZ): $n_e < n_e^c \implies v_\phi = 0$ . The splitting is determined solely by the bare Majorana masses: $\delta_{LZ} = 2m_{M0} \approx 350$ keV.
- At the Sun: $n_e > n_e^c \implies v_\phi \neq 0$ . The splitting receives an additional contribution: $\delta_\odot = 2(m_{M0} + v_\phi^2/\Lambda_N)$ . By tuning parameters, $\delta_\odot$ can exceed 570 keV, suppressing solar capture while preserving the LZ signal.

Key Constraints and Analysis
The authors derive conditions for the scalar mass $\mu_\phi$ , the cutoff scales $\Lambda_N$ and $\Lambda_e$ , and the quartic coupling $\lambda_\phi$ by examining several phenomenological constraints:

Stellar Cooling: The non-zero $v_\phi$ in stellar cores generates an effective electron Yukawa coupling $y_{\text{eff}} = m_e v_\phi / \Lambda_e^2$ . This leads to energy loss via scalar emission. Constraints from White Dwarfs (WD), Red Giants (RG), and Horizontal Branch (HB) stars limit $y_{\text{eff}}$ . The WD luminosity function provides the most stringent bound ( $y_{\text{eff}} \lesssim 4 \times 10^{-16}$ ).
Electron Mass Variation: The density-dependent $v_\phi$ induces a shift in the electron mass $\Delta m_e / m_e \propto v_\phi^2$ . This is constrained by the mass-radius relation of the white dwarf Sirius B ( $|\Delta m_e/m_e| \lesssim 1\%$ ) and Big Bang Nucleosynthesis (BBN) limits on the electron mass shift at $T \sim \text{MeV}$ .
EFT Validity: The effective field theory treatment requires $\Lambda_N > 10 M_D$ (where $M_D$ is the Dirac mass, $\sim \text{TeV}$ ).

Results
The authors identify a phenomenologically viable parameter space (shown in Fig. 2 of the paper) where:

$\mu_\phi \gtrsim 10^{-15}$ eV (to ensure the scalar Compton wavelength is smaller than the solar core size).
$\Lambda_e$ is constrained within a narrow window ( $\sim 10^{11} - 10^{12}$ GeV) to satisfy both the critical density condition for the Sun and the Earth-bound condition.
A benchmark scenario with $\mu_\phi = 4 \times 10^{-12}$ eV, $\Lambda_N = 7 \times 10^{13}$ GeV, and $\Lambda_e \approx 5 \times 10^{10}$ GeV successfully yields $\delta_{LZ} \approx 350$ keV and $\delta_\odot \approx 600$ keV.
In this region, constraints from WD cooling, Sirius B mass-radius measurements, and BBN are satisfied.

Significance and Limitations
The paper claims to provide a mechanism that resolves the tension between the LZ high-energy recoil event and the solar capture bounds within the inelastic doublet DM framework. By decoupling the mass splitting in the laboratory from that in the solar core via an environment-dependent scalar field, the model allows for a pure doublet interpretation of the LZ event without violating neutrino observatory limits.

However, the authors explicitly note a significant theoretical drawback: the scenario requires severe fine-tuning of the scalar potential. The quartic coupling $\lambda_\phi$ must be extremely small (e.g., $\lambda_\phi \sim 10^{-50}$ ) to maintain the flatness of the potential against quantum corrections from the heavy DM sector and electron loops. The authors acknowledge this unnaturalness, comparing it to the fine-tuning of the Standard Model Higgs potential, but accept it as a necessary feature of this specific low-energy effective theory. They suggest that a UV completion involving gauge-invariant operators (e.g., connecting $\Phi$ to the Higgs sector) could potentially address this, but such a detailed study is left for future work.

Technical Summary: Environment-Dependent Mass Splitting to Suppress Solar Capture

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