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Generalized Chiral $U(1)_{B-L}$ with Inelastic Scalar Dark Matter for the LZ 248 keV Event

This paper proposes a generalized chiral $U(1)_{B-L}$ model featuring inelastic scalar dark matter to explain the 248 keV nuclear recoil event observed by the LZ collaboration, where a small mass splitting between nearly degenerate states suppresses low-velocity scattering while enhancing high-energy interactions consistent with current experimental constraints and relic abundance.

Original authors: Ranjeet Kumar, Hemant Kumar Prajapati

Published 2026-09-11

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CC BY 4.0

Original authors: Ranjeet Kumar, Hemant Kumar Prajapati

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 universe has kept a quiet secret: most of its matter is invisible. Astronomers know this dark matter exists because its gravity holds galaxies together, yet no telescope has ever captured a single particle of it. The leading theory suggests these particles are heavy and move slowly, bumping into ordinary atoms in a way that should be detectable if we build sensitive enough instruments. For years, scientists have built massive detectors deep underground, waiting for a faint flash of light from such a collision. However, these experiments have found nothing but silence, forcing researchers to reconsider what dark matter might actually be. Perhaps the particles do not bounce off atoms like billiard balls, as the standard theory predicts, but instead undergo a more complex transformation upon impact. This shift in thinking has gained new urgency following a recent, puzzling signal from one of the world's most advanced detectors.

A team of physicists has proposed a specific explanation for a strange event recorded by the LUX-ZEPLIN experiment, a massive tank of liquid xenon buried deep in a South Dakota mine. The detector recently registered a high-energy collision where a nucleus recoiled with an energy of approximately 248 keV. In the language of dark matter searches, this is an unusually energetic hit, far stronger than the gentle taps expected from standard, slow-moving particles. While the statistical evidence for this single event is not yet strong enough to claim a discovery, its unusual energy level has sparked a new line of inquiry. The researchers suggest that this event could be the signature of "inelastic" dark matter, a scenario where the incoming particle does not simply bounce off but changes its identity, transforming into a slightly heavier version of itself.

To explore this possibility, the authors constructed a theoretical model based on a generalized version of a known force called the U(1) B-minus-L symmetry. In this framework, they introduced a new, invisible force carrier, a particle similar to the photon but much heavier, which mediates interactions between dark matter and ordinary matter. They also proposed that the dark matter particle is not a single, solid object but a complex field that, after the universe cooled down, split into two distinct states: a lighter, stable version and a slightly heavier partner. The mass difference between these two states is tiny, yet it is crucial. When the lighter dark matter particle collides with an atomic nucleus in the detector, it must absorb energy to transform into the heavier state. This process is endothermic, meaning it requires an input of energy to occur, much like a chemical reaction that needs heat to start.

This requirement for extra energy changes the rules of the game for detection. Because the collision demands a minimum amount of energy to trigger the transformation, slow-moving dark matter particles simply cannot cause the event; they lack the necessary speed to overcome the energy threshold. Only the fastest, most energetic particles in the dark matter cloud can succeed. This mechanism naturally filters out the vast majority of dark matter, which moves at lower speeds, while allowing the rare, high-speed tail of the distribution to produce the high-energy recoil seen in the LZ data. The researchers calculated that for their model to explain the 248 keV event, the mass splitting between the two dark matter states must be on the order of a few hundred keV, and the interaction strength must fall within a specific range that avoids detection by previous, less sensitive experiments.

The team then tested whether this scenario could also explain how much dark matter exists in the universe today. They simulated the early universe, tracking how these particles would have annihilated each other as the cosmos expanded and cooled. Their calculations showed that if the dark matter particles have a mass of roughly 2.5 TeV and interact through a new force carrier with a mass of 5 TeV, the remaining amount of dark matter would match the precise amount observed by cosmologists. Furthermore, they checked if their model would have been caught by other experiments, such as those at the Large Hadron Collider. They found that their specific choice of particle charges suppresses the new force carrier's branching fraction into charged leptons, effectively hiding it from the most stringent searches for new forces. This allows the model to survive current experimental limits while still predicting a signal for the LZ detector.

The work does not claim to have solved the mystery of dark matter, but it offers a coherent and testable path forward. It demonstrates that a high-energy nuclear recoil, which might otherwise be dismissed as noise or a statistical fluke, could be the result of a very specific type of dark matter interaction. By connecting the thermal history of the early universe with the kinematics of a single collision event, the study provides a concrete framework for future investigations. If the LZ experiment continues to observe similar high-energy events, or if future runs confirm this specific pattern, it would strongly support the idea that dark matter is not a simple, elastic scatterer, but a dynamic particle capable of changing its state when struck. Until then, the 248 keV event remains a compelling hint, waiting for more data to reveal whether it is the first glimpse of a new kind of physics or merely a rare fluctuation in the background noise.

Technical Summary: Generalized Chiral U(1) $_{B-L}$ with Inelastic Scalar Dark Matter for the LZ 248 keV Event

Problem Statement
The paper addresses the recent report by the LUX-ZEPLIN (LZ) collaboration of a high-energy nuclear recoil event with energy $E_R \simeq 248$ keV. While the statistical significance of this event is currently low (2.6 $\sigma$ ), its energy lies substantially above the recoil region typically associated with conventional elastic Weakly Interacting Massive Particle (WIMP) searches. This observation motivates the exploration of non-standard scattering kinematics, specifically Inelastic Dark Matter (iDM) scenarios. In standard elastic scattering, low-velocity dark matter (DM) dominates the signal; however, the high-energy nature of the LZ event suggests a mechanism where low-velocity DM is suppressed, and the high-velocity tail of the Galactic DM distribution becomes dominant. The authors propose a specific theoretical framework to explain this anomaly while remaining consistent with cosmological relic abundance and current collider constraints.

Methodology
The authors construct a model based on a generalized chiral U(1) $_X$ framework (extending the Standard Model with an additional Abelian gauge symmetry and three right-handed neutrinos). The methodology involves the following steps:

Model Construction:
- Gauge Structure: The U(1) $_X$ charges are parametrized by two independent parameters, $X_L$ and $\kappa$ . The authors adopt the benchmark choice $X_L = \kappa = 1$ , which recovers the conventional chiral $B-L$ assignment for Standard Model fermions but assigns non-universal charges $(-4, -4, 5)$ to the right-handed neutrinos.
- Dark Sector: A complex SM singlet scalar $\chi_d$ is introduced. The charge assignment is modified to allow a gauge-invariant trilinear term in the scalar potential: $V_{split} = \frac{\mu_d}{2}(\chi_d^2 \eta^* + \text{H.c.})$ , where $\eta$ is the SM singlet scalar responsible for breaking U(1) $_X$ .
- Mass Splitting: Upon symmetry breaking, the trilinear term generates a small mass splitting between the real ( $\chi_1$ ) and imaginary ( $\chi_2$ ) components of the dark scalar. The lighter state $\chi_1$ is the stable Dark Matter candidate, while $\chi_2$ is a slightly heavier partner. The mass splitting is defined as $\delta \equiv m_{\chi_2} - m_{\chi_1}$ .
Interaction Mechanism:
- The gauge interaction between the dark scalars and the new $Z'$ boson is off-diagonal ( $Z'\chi_1\chi_2$ ), with no diagonal couplings ( $Z'\chi_1\chi_1$ or $Z'\chi_2\chi_2$ ).
- This leads to an intrinsically inelastic scattering process in direct detection: $\chi_1 + N \to \chi_2 + N$ .
- The positive mass splitting $\delta$ introduces an endothermic threshold, raising the minimum velocity ( $v_{min}$ ) required for a nuclear recoil of a given energy. This suppresses contributions from low-velocity DM and shifts the recoil spectrum to higher energies.
Numerical Analysis:
- The authors fix a benchmark point (BP) with $M_{Z'} = 5$ TeV, gauge coupling $g_x = 0.3$ , and a mass splitting $\delta \sim \mathcal{O}(100)$ keV.
- They utilize SARAH to generate the model spectrum and vertices, SPheno for mass spectra and decay widths, MadGraph5 for collider cross-section calculations at $\sqrt{s} = 13$ TeV, and micrOMEGAs for relic abundance calculations.

Key Contributions and Results

Explanation of the LZ Event: The model successfully reproduces the kinematics required for the 248 keV LZ event. An inelastic scattering cross section of $\sigma_{SI} \approx 3 \times 10^{-45} \text{ cm}^2$ with a mass splitting of $\sim 100$ keV is shown to be consistent with the observed high-energy recoil, a regime where standard elastic WIMP models are heavily constrained or excluded.
Relic Abundance: The analysis identifies a viable parameter space where the observed relic density ( $\Omega h^2$ ) is achieved. For the benchmark $M_{Z'} = 5$ TeV, the DM mass is fixed to $m_{\chi_1} \simeq 2.5$ TeV. In this region, the annihilation cross section is resonantly enhanced via s-channel $Z'$ exchange ( $m_{\chi_1} \simeq M_{Z'}/2$ ). The authors note that co-annihilation between the nearly degenerate $\chi_1$ and $\chi_2$ states plays a role in the thermal history.
Collider Constraints: A critical contribution of the model is the suppression of the $Z'$ branching fraction into charged leptons ( $Br(Z' \to \ell^+\ell^-)$ ). Due to the non-universal charges of the right-handed neutrinos, the $Z'$ decays significantly into the invisible sector (neutrinos and dark scalars). Consequently, the benchmark point lies well below the exclusion limits set by ATLAS dilepton resonance searches at the LHC, evading constraints that would typically rule out a $Z'$ with these mass and coupling parameters in a minimal $B-L$ scenario.
Direct Detection Kinematics: The study demonstrates that the inelastic nature of the scattering decouples the nominal interaction strength from standard direct detection exclusion limits. The kinematic threshold imposed by $\delta$ allows for a relatively large cross section without violating constraints from low-energy recoil experiments.

Significance
The paper claims to provide a coherent theoretical framework that connects three distinct phenomenological aspects: the thermal history of scalar dark matter, the specific kinematics of inelastic scattering required to explain the high-energy LZ event, and the phenomenology of an additional $Z'$ boson. The authors emphasize that their generalized chiral U(1) $_X$ framework naturally accommodates the necessary mass splitting and off-diagonal couplings while simultaneously satisfying relic density requirements and evading stringent LHC dilepton constraints through the specific charge assignment of the neutrino sector. The work suggests that the LZ event, if confirmed, could be a signature of inelastic scalar dark matter mediated by a $Z'$ boson with specific non-universal couplings.

Technical Summary: Generalized Chiral U(1)B−L_{B-L}B−L​ with Inelastic Scalar Dark Matter for the LZ 248 keV Event

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Technical Summary: Generalized Chiral U(1) $_{B-L}$ with Inelastic Scalar Dark Matter for the LZ 248 keV Event