⚛️ phenomenology

Endothermic Z'-Portal Dark Matter: LZ-LHC Complementarity

Motivated by a recent high-energy recoil event reported by the LUX-ZEPLIN collaboration, this paper proposes an endothermic $Z'$ -portal Majorana dark matter model within a gauged $U(1)_{B-L}$ framework, demonstrating how the interplay between dark matter relic abundance constraints and LHC $Z'$ resonance searches can explain the anomaly while offering a testable synergy for future experiments.

Original authors: Nobuchika Okada, Digesh Raut

Published 2026-09-21

📖 5 min read🧠 Deep dive

CC BY 4.0

Original authors: Nobuchika Okada, Digesh Raut

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 been searching for the invisible substance that makes up most of the matter in the universe. They call it dark matter. While we cannot see it, we know it is there because its gravity holds galaxies together. The leading theory suggests that dark matter consists of heavy, slow-moving particles that rarely interact with normal matter, passing through us like ghosts. To find them, scientists have built massive detectors deep underground, shielding them from cosmic rays and other noise. These detectors wait for a dark matter particle to occasionally bump into an atomic nucleus, creating a tiny flash of light or a small amount of heat. However, the signals these detectors look for are usually very faint, and the energy of the collision is expected to be low.

Recently, a major experiment called LUX-ZEPLIN, located deep in a mine in South Dakota, reported something unusual. The detector recorded a single event where a nucleus recoiled with a surprisingly high amount of energy, far stronger than what standard dark matter theories usually predict. This single event was not enough to claim a discovery, but it was strong enough to grab attention, suggesting that if dark matter exists, it might behave in a more complex way than previously thought. The question became: could this specific, high-energy bump be the first real sign of a new kind of dark matter, and if so, what does that tell us about the laws of physics?

In a new study, researchers Nobuchika Okada and Digesh Raut propose a specific explanation for this event. They suggest that the dark matter particle is not a simple, static object, but rather one that can change its state. Imagine a dark matter particle as a heavy ball that, when it hits a nucleus, absorbs some of the energy from the collision to jump into a slightly heavier version of itself. This process, known as endothermic scattering, requires a significant amount of energy to happen. Because the collision must provide this extra energy to make the jump, the resulting recoil of the nucleus is pushed to higher energies, matching the strange signal seen by the LUX-ZEPLIN team. The researchers built a mathematical model where these particles interact with normal matter through a new, heavy force-carrying particle, which they call a Z-prime boson.

The beauty of this model lies in how it connects three different areas of physics that usually operate in isolation. First, the model must explain why the universe has the right amount of dark matter today. The researchers found that for their proposed particles to exist in the correct abundance, they must be nearly half the mass of the heavy Z-prime boson. This specific relationship allows the particles to annihilate each other efficiently in the early universe, leaving behind just the right amount of dark matter we see now. Second, the model must explain the high-energy bump seen in the mine. The same heavy boson that helped create the dark matter in the past now acts as the bridge that allows the dark matter to jump to its heavier state during a collision today. Third, the model must survive the tests of our most powerful particle colliders. The Large Hadron Collider in Europe smashes protons together at incredible speeds, looking for signs of new particles like this Z-prime boson.

The researchers mapped out the possible properties of this dark matter and the Z-prime boson to see if a solution exists that satisfies all three conditions at once. They discovered a narrow window of possibility. If the Z-prime boson is too heavy or the force it carries is too weak, the dark matter would have annihilated too much in the early universe, leaving the cosmos empty. If the force is too strong, the Large Hadron Collider would have already seen the Z-prime boson. However, there is a sweet spot in the middle where the dark matter abundance is correct, the high-energy collision in the mine is possible, and the Large Hadron Collider has not yet ruled it out.

This study highlights a powerful synergy between different types of experiments. The underground detector sees the aftermath of a collision, while the particle collider looks for the creation of the force carrier itself. The researchers showed that the specific conditions needed to explain the LUX-ZEPLIN event are not random; they are tightly linked to the mass and strength of the new force. If the dark matter is indeed behaving this way, the next generation of the Large Hadron Collider, which will run with much higher intensity, should be able to find the Z-prime boson directly. Finding that particle would confirm the existence of the force that connects the dark sector to our world, turning a single, mysterious bump in a detector into a confirmed chapter of new physics. Until then, the model remains a compelling possibility, waiting for the next wave of data to either confirm the story or close the door on this particular explanation.

Technical Summary: Endothermic Z′-Portal Dark Matter: LZ-LHC Complementarity

Problem Statement
The paper addresses the interpretation of a recent high-energy nuclear recoil event reported by the LUX-ZEPLIN (LZ) Collaboration, characterized by a recoil energy of $E_R \approx 248$ keV with a global significance of $2.6\sigma$ . Conventional elastic scattering of halo dark matter (DM) struggles to accommodate such high-energy recoils. While endothermic DM scattering (where a DM particle transitions to a slightly heavier state) naturally favors high-energy recoils, a significant theoretical challenge arises: simultaneously reproducing the observed thermal relic abundance and the interaction strength required for the LZ event. Standard thermal freeze-out typically requires an annihilation cross-section of $\sim 1$ pb, whereas direct detection constraints often limit the scattering cross-section. If the same interaction mediates both processes, satisfying both conditions simultaneously is nontrivial without additional mechanisms.

Methodology
The authors propose a simple $Z'$ -portal framework for endothermic Majorana dark matter, realized concretely within a gauged $U(1)_{B-L}$ extension of the Standard Model. The model introduces:

Dark Sector: Two nearly degenerate Majorana fermions, $\psi_1$ (the DM candidate) and $\psi_2$ (the excited state), formed from a pseudo-Dirac limit of $Z_2$ -odd singlet fermions ( $\eta_L, \xi_L$ ).
Mediator: A $Z'$ boson arising from the spontaneous breaking of $U(1)_{B-L}$ symmetry.
Interaction Structure: The $Z'$ couples to the dark sector via off-diagonal vector-like interactions ( $\psi_1 \leftrightarrow \psi_2$ ) and diagonal axial-vector interactions. The SM fermions couple via standard $B-L$ charges.

The phenomenology is controlled by two primary free parameters: the $U(1)_{B-L}$ gauge coupling ( $g_{BL}$ ) and the $Z'$ boson mass ( $m_{Z'}$ ). The mass splitting $\Delta m = m_2 - m_1$ is fixed at $\mathcal{O}(10^2)$ keV to match the LZ recoil kinematics.

The analysis proceeds through three main calculations:

Relic Abundance: The authors solve the coupled Boltzmann equations for the nearly degenerate states $\psi_1$ and $\psi_2$ . They focus on the coannihilation process $\psi_1 \psi_2 \to f\bar{f}$ (mediated by an off-shell $Z'$ ), which is $s$ -wave unsuppressed, unlike the $p$ -wave suppressed diagonal annihilations. They require the calculated relic density to match the observed value $\Omega_{DM}h^2 \simeq 0.12$ .
Direct Detection: They calculate the spin-independent inelastic scattering cross-section ( $\sigma_{SI}$ ) for $\psi_1 N \to \psi_2 N$ . This is mediated by $Z'$ exchange in the limit where momentum transfer is much smaller than $m_{Z'}$ .
Collider Constraints: They evaluate the resonant dilepton production cross-section ( $pp \to Z' \to \ell^+\ell^-$ ) at the LHC ( $\sqrt{s}=13$ TeV) using the narrow-width approximation. These results are compared against ATLAS Run-2 exclusion limits and projected High-Luminosity LHC (HL-LHC) sensitivities.

Key Results
The study identifies a specific region in the $(m_{Z'}, g_{BL})$ parameter space where the model is viable:

Resonant Enhancement: For a fixed $m_{Z'}$ , the observed relic abundance is achieved when the DM mass is near the resonance, $m_{DM} \approx m_{Z'}/2$ . This resonant enhancement allows the coannihilation cross-section to be sufficiently large to deplete the DM abundance even for relatively small couplings.
Complementary Bounds:
- Lower Bound: The requirement to reproduce the relic abundance imposes a lower bound on $g_{BL}$ for a given $m_{Z'}$ . If $g_{BL}$ is too small, even resonant enhancement cannot reduce the relic density to the observed level.
- Upper Bound: LHC searches for $Z'$ resonances in the dilepton channel impose a strict upper bound on $g_{BL}$ .
LZ Compatibility: The parameter space allowed between these lower (relic) and upper (LHC) bounds successfully accommodates the spin-independent scattering cross-sections ( $\sigma_{SI} \sim 10^{-48} - 10^{-46}$ cm $^2$ ) required to explain the LZ event, given the specific mass splitting.
Theoretical Consistency: The allowed region also satisfies the theoretical requirement that the gauge coupling remains perturbative up to the Planck scale (avoiding a Landau pole).

Significance and Claims
The paper claims that the interplay between the LZ event, thermal relic density constraints, and LHC $Z'$ searches provides a powerful, self-consistent test of the endothermic $Z'$ -portal framework. Specifically:

The model demonstrates that the tension between the high interaction strength needed for the LZ event and the annihilation requirements for thermal freeze-out can be resolved via resonant coannihilation near the $Z'$ pole.
The framework predicts a "sweet spot" in parameter space where the DM explanation for the LZ event is simultaneously consistent with current LHC null results and future HL-LHC sensitivity.
The authors conclude that the synergy between future $Z'$ resonance searches at the HL-LHC and the LZ experiment offers a direct pathway to test this specific interpretation of the LZ anomaly.

The paper does not propose new experimental setups but rather highlights how existing and planned data from the LHC and LZ can jointly validate or rule out this specific class of endothermic dark matter models.

More like this