⚛️ phenomenology

Pseudo-Dirac Inelastic Dark Matter in the Leptophobic $U(1)_B$ Model: Confronting the LUX-ZEPLIN High-Recoil Event with Collider Searches

This paper proposes a minimal leptophobic $U(1)_B$ model with pseudo-Dirac inelastic dark matter that naturally explains the LUX-ZEPLIN 248 keV recoil event while simultaneously satisfying relic density and LHC dijet constraints, predicting specific mediator masses and couplings that can be definitively tested by current and future collider data.

Original authors: Xin-Yu Du, Wenjie Huang, Keping Xie

Published 2026-09-09

📖 5 min read🧠 Deep dive

CC BY 4.0

Original authors: Xin-Yu Du, Wenjie Huang, Keping Xie

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, physicists have searched for dark matter, the invisible substance that makes up most of the universe's mass but refuses to interact with light. The leading theory for years was that these particles are heavy and sluggish, bumping into ordinary atoms like billiard balls in a slow, elastic collision. However, a recent report from the LUX-ZEPLIN experiment in South Dakota has thrown a wrench into this simple picture. The detector, buried deep underground to shield it from cosmic noise, recorded a single, high-energy flash of light that looks like a heavy particle hitting a xenon atom. The problem is that this event happened at an energy level where the standard theory predicts almost nothing should occur, while the lower-energy region, where most events should pile up, remained completely empty. This mismatch suggests that dark matter might not be bouncing off atoms at all, but rather absorbing energy to jump to a heavier state, a process known as an inelastic transition.

A new study by researchers at Shanghai Jiao Tong University takes this puzzling signal and builds a complete, self-consistent theory around it. Instead of treating the strange behavior as a lucky accident or adding arbitrary rules to make the math work, the authors propose that dark matter is governed by a fundamental force of nature related to the number of protons and neutrons in ordinary matter. They describe a model where dark matter particles carry a specific "charge" linked to this baryon number, which forces them to interact with the atomic nuclei in the detector in a very specific way. This setup naturally explains why the dark matter particles are stable, why they only interact through a transition that requires energy, and why the interaction strength matches what was seen in the detector. The researchers found that if the dark matter particle weighs about one thousand times more than a proton and the energy gap between its two states is roughly three hundred thousand electron volts, the entire picture falls into place.

The beauty of this proposal is that it does not rely on guesswork. In many theories, scientists must manually insert a rule to keep the lightest dark matter particle from decaying, but here, the mathematical structure of the theory automatically creates a symmetry that protects it. Similarly, the requirement that the particles only interact by changing states, rather than bouncing off elastically, emerges naturally from the way the particles gain their mass. When the team plugged the specific numbers from the LUX-ZEPLIN event into their equations, they discovered that the model is "over-determined." This means that three completely different pieces of information—the energy of the single event, the expected amount of dark matter in the universe from the Big Bang, and the limits set by particle colliders—converge on a single, precise point. At this point, the force carrier that mediates the interaction would have a mass of about 1.44 trillion electron volts, and the strength of the force would be a specific, calculable value.

This convergence is significant because it turns a vague possibility into a sharp, testable prediction. The model predicts that the force carrier is too heavy to decay into dark matter particles at this specific energy, meaning it should only be seen decaying into pairs of quarks, which appear as jets of particles in a collider. This is the opposite of what most simplified theories predict, where the force carrier usually disappears into invisible dark matter. Because the particle decays into visible jets, the Large Hadron Collider (LHC) at CERN should be able to see it. The researchers compared their prediction against existing data from the ATLAS detector and found that the predicted signal sits just below the current limit of detection. It is not ruled out, but it is also not confirmed; it lives in a narrow window where the data is currently inconclusive.

The authors emphasize that this is not a solved mystery, but a clear target for the next round of experiments. The data needed to confirm or rule out this specific point has already been recorded by the LHC during its recent run at a higher collision energy. A simple re-analysis of this existing data, without needing new equipment or years of waiting, could settle the question. If the signal is there, it would confirm that dark matter interacts through a force tied to the very building blocks of ordinary matter. If the signal is absent, this specific interpretation of the LUX-ZEPLIN event would be discarded. The study also notes that if the energy gap between the dark matter states were slightly different, the theory would predict a much heavier force carrier, which would require the future High-Luminosity LHC to find. Until then, the single 248 keV event remains a tantalizing clue, pointing toward a universe where the invisible sector is tightly woven into the fabric of the visible one, waiting for the next look to reveal its true nature.

Technical Summary: Pseudo-Dirac Inelastic Dark Matter in the Leptophobic $U(1)_B$ Model

Problem Statement
The LUX-ZEPLIN (LZ) collaboration reported a single nuclear-recoil candidate event at $E_{obs} = 248 \pm 23_{stat} \pm 23_{sys}$ keV. Interpreting this event as an endothermic transition of inelastic dark matter (iDM) typically requires two structural assumptions often introduced "by hand": (1) a stable dark state protected by an imposed symmetry (e.g., a $Z_2$ parity), and (2) a coherent transition current that is purely off-diagonal (vector coupling), rather than a free mixing angle. Furthermore, standard elastic scattering interpretations struggle with this event due to the steeply falling spectrum and momentum transfer lying beyond the first diffraction minimum of the xenon form factor.

Methodology and Model Construction
The authors propose a gauge-complete framework based on a leptophobic $U(1)_B$ symmetry (gauged baryon number) to naturally supply the required ingredients for iDM.

Gauge Structure: The model extends the Standard Model (SM) with $G = G_{SM} \times U(1)_B$ . To cancel mixed anomalies, a set of colorless Weyl fermions is introduced. The authors focus on a specific benchmark with dark charges $B(\chi_L) = -3/2$ and $B(\chi_R) = -9/2$ .
Mass Generation: A scalar sector generates the dark fermion masses. A scalar $S_B$ with charge $B=-3$ generates a Dirac mass $M_D$ , while scalars $\Phi_L$ and $\Phi_R$ (charges $+3$ and $-9$) generate Majorana masses $\mu_L$ and $\mu_R$ .
Residual Parity: The vacuum expectation values (VEVs) of these scalars leave an exact residual parity $P = (-1)^{6B}$ . Under this symmetry, the SM and scalars are even, while the new fermions are odd. This naturally stabilizes the lightest dark state ( $\chi_1$ ) without imposing an ad-hoc $Z_2$ .
Inelasticity and Currents: The small Majorana masses split the pseudo-Dirac pair into two Majorana eigenstates ( $\chi_1, \chi_2$ ) with a splitting $\delta$ . Crucially, because the mass eigenstates are Majorana fermions, the diagonal vector current vanishes identically ( $\bar{\chi}_i \gamma^\mu \chi_i = 0$ ). The coherent vector current is therefore purely off-diagonal ( $\bar{\chi}_2 \gamma^\mu \chi_1$ ) as an identity of the theory, not a choice of mixing parameters. The splitting $\delta$ is technically natural, as $\mu_{L,R} \to 0$ restores a conserved dark Dirac number.
Parameters: The model is constrained by the four-parameter set $(m_\chi, \delta, M_{Z_B}, g_B)$ . The study fixes $m_\chi = 1$ TeV and $\delta = 300$ keV to confront the LZ data.

Key Results

Direct Detection Consistency:
- The model predicts an isoscalar nucleon coupling ( $f_p = f_n$ ) because the mediator couples to quarks only.
- At $m_\chi = 1$ TeV and $\delta = 300$ keV, the observed LZ event corresponds to a specific interaction strength. The recoil rate maps the LZ interval to a band in the $(M_{Z_B}, g_B)$ plane, selecting a ratio $M_{Z_B}/g_B \simeq 6.23$ TeV.
- The candidate event sits at the kinematically most accessible energy ( $E_R^* \approx 265$ keV) for this splitting, while the inelastic threshold naturally suppresses low-energy events, explaining the "empty" low-energy region.
Relic Density and Perturbativity:
- A leading-order thermal relic estimate (considering $\chi_1 \chi_2 \to Z_B^* \to q\bar{q}$ and $\chi_1 \chi_2 \to Z_B Z_B$ channels) intersects the LZ-derived band at a single perturbatively acceptable point:
  $(M_{Z_B}, g_B) \simeq (1.44 \text{ TeV}, 0.233)$
- A second intersection exists at $M_{Z_B} \approx 7.24$ TeV, but it is discarded because the coupling $g_B \approx 1.16$ drives the Landau pole to only $1.8 M_{Z_B}$ , violating perturbativity.
- The thermal target is reached not via resonant enhancement, but by the switching off of sub-threshold suppression as $M_{Z_B}$ approaches $2m_\chi$ .
Collider Constraints (LHC):
- Dijets vs. Missing Energy: Since $M_{Z_B} \approx 1.44$ TeV is below the invisible threshold ( $2m_\chi = 2$ TeV), the mediator decays exclusively to quarks ( $BR(Z_B \to q\bar{q}) = 1$ ). Consequently, missing energy (monojet) searches are insensitive, while dijet searches are the primary constraint.
- Current Status: The benchmark point lies just below the current ATLAS trigger-level dijet exclusion boundary (approx. 10% margin). It is currently allowed but not yet decided by existing Run-2 data.
- Future Projections: Re-running the existing analysis on Run-3 data ( $\sqrt{s} = 13.6$ TeV) is predicted to shift the exclusion boundary, placing the benchmark point 15–20% above the limit (i.e., excluding it). The High-Luminosity LHC (HL-LHC) would exclude it with high significance.
- Alternative Branch: For a smaller splitting ( $\delta = 200$ keV), the model predicts a heavier mediator ( $M_{Z_B} \simeq 2.4\text{--}3.0$ TeV) which is a target for the HL-LHC dijet program.
Kinetic Mixing:
- The model induces kinetic mixing between $U(1)_B$ and hypercharge, leading to a dilepton branching ratio. For the benchmark, $|\epsilon(M_{Z_B})| \simeq 9.5 \times 10^{-3}$ . This must be tested against high-mass dilepton searches; suppressing it to $<10^{-3}$ requires an 89% cancellation against an ultraviolet threshold.

Significance and Claims
The paper claims that the leptophobic $U(1)_B$ model provides a structural, rather than ad-hoc, explanation for the LZ candidate event. It simultaneously solves the stability problem (via residual parity) and the current structure problem (via Majorana nature) within a single gauge framework.

Over-determined Nature: The model is described as "over-determined" because the LZ recoil interval, a leading-order relic estimate, and LHC dijet limits all converge on a single, specific point in parameter space.
Testability: The authors emphasize that the model's fate is imminent. The point is "alive and not yet decided" by current data but will be definitively excluded or confirmed by re-analyzing existing Run-3 data.
Modesty: The authors explicitly state that the relic density calculation is a "leading-order estimate" and not a full gauge-complete freeze-out calculation (which requires scalar sector details). Therefore, the identified point is a "sharply defined target" rather than a demonstrated solution. The existence of the intersection is robust, but its precise location depends on higher-order thermal averaging.

In summary, the paper presents a specific, testable realization of inelastic dark matter where a single 248 keV event, if confirmed, would locate a leptophobic gauge boson to within an order of magnitude in both mass and coupling, or conversely, the failure of this specific point would rule out this specific gauge completion.

Technical Summary: Pseudo-Dirac Inelastic Dark Matter in the Leptophobic U(1)BU(1)_BU(1)B​ Model

More like this

Technical Summary: Pseudo-Dirac Inelastic Dark Matter in the Leptophobic $U(1)_B$ Model