⚛️ phenomenology

Mono-Z signal for dark matter searches at future lepton colliders and cosmological interpretation

This paper investigates the mono-Z signature for dark matter searches at future electron-positron colliders within the dimension-six dark matter effective field theory framework, identifying viable parameter spaces through comprehensive constraints and demonstrating robust discovery potential for specific dark matter candidates using advanced kinematic variables and beam polarization.

Original authors: Anupam Ghosh, Partha Kumar Paul, Abhik Sarkar, Rituparna Ghosh, Rachit Sharma, and, Subhaditya Bhattacharya

Published 2026-09-29

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CC BY 4.0

Original authors: Anupam Ghosh, Partha Kumar Paul, Abhik Sarkar, Rituparna Ghosh, Rachit Sharma, and, Subhaditya Bhattacharya

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

Dark matter is the invisible scaffolding of the universe. It makes up most of the matter in existence, yet it refuses to interact with light or ordinary matter in any way we can easily detect. We know it is there only because its gravity pulls on stars and galaxies, holding them together. For decades, physicists have tried to catch a glimpse of these elusive particles using massive underground detectors or by looking for the faint glow of their collisions in deep space. While these methods have narrowed the search, they have not yet found the particle. This leaves a crucial gap in our understanding: if dark matter exists, how does it talk to the rest of the universe?

To answer this, scientists are looking toward the future of particle physics: the next generation of particle colliders. Unlike the current Large Hadron Collider, which smashes protons together in a chaotic storm of debris, future machines will collide electrons and positrons. These are the fundamental building blocks of matter and antimatter, and their collisions are remarkably clean and precise. In this controlled environment, physicists can look for a specific, tell-tale sign of dark matter: a single particle of light or a heavy carrier of the weak force, known as a Z boson, flying off alone while the rest of the energy vanishes. This "mono-Z" signal would be the recoil of an invisible dark matter pair, much like a cue ball striking a hidden object and stopping short while the visible ball rolls away.

A team of researchers has now mapped out exactly how to find this signal. They focused on a theoretical framework that treats dark matter not as a single specific particle, but as a category of possibilities, including particles that behave like spinning tops, like waves, or like heavy vectors. Using powerful computer simulations, they tested how these different types of dark matter would behave if they were produced at a future electron-positron collider operating at a energy of one trillion electron volts. The team did not just look for the signal; they built a comprehensive filter to separate it from the background noise of known physics. They accounted for the fact that the Standard Model of particle physics also produces invisible particles—neutrinos—that could mimic a dark matter signal. By carefully analyzing the energy, direction, and momentum of the visible Z boson, and by using the unique ability of future colliders to polarize their beams—essentially spinning the electrons in a specific direction to suppress background noise—they identified which types of dark matter could be discovered.

The results of this study reveal a landscape where discovery is possible, but highly dependent on the nature of the dark matter itself. The researchers found that if dark matter consists of certain types of fermions, specifically those with a dipole moment, or if it is a scalar particle that prefers to interact with leptons, the future collider has a strong chance of finding it. These scenarios allow the machine to probe energy scales far beyond what current experiments can reach. However, the study also rules out several possibilities. If dark matter interacts with ordinary matter in a way that allows it to be easily detected by current underground sensors, those models are already excluded by existing data. Furthermore, if dark matter is a specific type of fermion that interacts through a Higgs portal, the signal is so faint at the planned energy levels that it would likely remain invisible, even with the most advanced detectors.

One of the most striking findings is how the spin and structure of the dark matter particle change the strategy for finding it. For some types of dark matter, the best way to see them is to use a beam of electrons that are mostly right-handed, while for others, a left-handed beam is far more effective. This sensitivity to the "handedness" of the beam allows physicists to distinguish between different theories of dark matter, a capability that current colliders lack. The study also highlighted that the energy of the collision matters immensely. For certain types of dark matter linked to the Higgs boson, a lower-energy machine operating at 250 billion electron volts would be far more effective than the higher-energy one, because the production rate drops sharply as energy increases for these specific interactions.

The researchers concluded that the mono-Z channel is a powerful and complementary tool for the search. It offers a way to probe the weak and hypercharge forces that govern how dark matter might interact with the universe, forces that are often invisible to other search methods. While the study confirms that a significant portion of the theoretical landscape remains out of reach due to existing constraints from other experiments, it provides a clear roadmap for the future. By tuning the beam polarization and carefully selecting the collision energy, the next generation of colliders could finally reveal the particle nature of the dark matter that holds our universe together. The path forward is not a single shot in the dark, but a series of precise, calculated steps designed to catch the invisible in the act of disappearing.

Technical Summary: Mono-Z Signal for Dark Matter Searches at Future Lepton Colliders and Cosmological Interpretation

Problem Statement
The existence of Dark Matter (DM) remains a primary mystery in modern physics, with the Standard Model (SM) failing to provide a viable particle candidate. While gravitational evidence is robust, non-gravitational interactions must be probed through direct detection (DD), indirect detection (ID), and collider searches. Current Large Hadron Collider (LHC) searches, primarily relying on QCD-driven processes, have placed stringent constraints on many DM models but have been less effective at constraining Electroweak extensions of the SM. Furthermore, mono-photon ( $\gamma$ ) searches at future lepton colliders, while sensitive to electromagnetic couplings, are largely blind to the $SU(2)_L$ structure of DM interactions. This work addresses the need to probe the Electroweak structure of DM interactions using the mono-Z signature ( $e^+e^- \to Z + \text{missing energy}$ ) within the Dark Matter Effective Field Theory (DMEFT) framework, considering scalar, fermionic, and vector DM candidates up to dimension-six operators.

Methodology
The authors employ a systematic DMEFT approach where DM-SM interactions are parametrized by gauge-invariant higher-dimensional operators suppressed by an effective scale $\Lambda$ . The study focuses on operators up to dimension six for scalar ( $\phi$ ), Dirac fermion ( $\chi$ ), Majorana fermion ( $\psi$ ), and vector ( $X_\mu$ ) DM candidates.

Operator Classification: Operators are classified by their production topologies: Higgsstrahlung ( $e^+e^- \to Zh \to Z + \text{DM}$ ), initial-state radiation (ISR) from leptonic contact interactions, final-state emission (FS) via gauge-field strength tensors, and mixed ISR/FS mechanisms for dipole operators.
Cosmological and Experimental Constraints: The viable parameter space ( $m_{DM}$ $m_{D M}$ vs. $\Lambda$ $Λ$ ) is determined by imposing:
- Observed DM relic abundance ( $\Omega_{DM}h^2 \approx 0.12$ ) calculated via micrOMEGAs.
- Direct detection limits from the LZ experiment (and projected DARWIN sensitivity).
- Indirect detection constraints from Fermi-LAT, HAWC, HESS, MAGIC, and VERITAS.
- Higgs invisible decay limits ( $\mathcal{B}(h \to \text{inv}) < 10.7\%$ ).
- Recast LHC mono-Z limits based on ATLAS data (139 fb $^{-1}$ at 13 TeV).
Collider Analysis: The study simulates the mono-Z signal at a future International Linear Collider (ILC) with center-of-mass energies $\sqrt{s} = 1$ $s = 1$ TeV (for most operators) and $\sqrt{s} = 250$ $s = 250$ GeV (for Higgs-portal operators).
- Simulation: Signal and SM backgrounds ( $e^+e^- \to Z\nu\bar{\nu}$ ) are generated using MadGraph5_aMC@NLO, showered with Pythia 8, and passed through a Delphes 3 detector simulation.
- Backgrounds: The dominant SM background arises from $Z\nu\bar{\nu}$ production, including $ZZ$ production with invisible decay, non-resonant $Z\nu\bar{\nu}$ , and $t$ -channel $W$ -exchange topologies.
- Optimization: The analysis exploits beam polarization to suppress the $t$ -channel $W$ -exchange background (which couples to left-handed electrons) and to enhance signal rates based on the specific Electroweak structure of each operator. Kinematic variables such as missing energy ( $\not{E}$ ), missing transverse momentum ( $p_T^{miss}$ ), recoil mass ( $m_{rec}$ ), and $Z$ -boson pseudorapidity ( $\eta_Z$ ) are used for discrimination.

Key Contributions and Results

Operator Viability:
- Excluded: The Dirac operators $O_{D\chi}^{(6)}$ and $O_{e\chi}^{(6)}$ are fully excluded by current spin-independent direct detection limits. The leptophilic fermion operator $O_{\ell\chi}^{(6)}$ is only viable for $m_\chi \gtrsim 520$ GeV, placing it beyond the kinematic reach of a 1 TeV collider.
- Viable: The study focuses on the fermion dipole operator ( $O_{B\chi}^{(5)}$ ), scalar leptophilic operator ( $O_{L\phi}^{(6)}$ ), and gauge-portal operators ( $O_{W\phi}^{(6)}$ , $O_{B\phi}^{(6)}$ ).
Discovery Prospects at $\sqrt{s} = 1$ TeV:
- Fermion Dipole ( $O_{B\chi}^{(5)}$ ): With right-handed electron polarization ( $P_{e^-} = +80\%$ ), the background is suppressed, yielding a statistical significance of $Z \approx 1.14$ for a benchmark point ( $m_\chi=100$ GeV, $\Lambda=7.3$ TeV). While 5 $\sigma$ discovery is not reachable for the cosmologically preferred high- $\Lambda$ values, the ILC offers significantly improved sensitivity over LHC recasting (probing multi-TeV scales vs. $\sim 400$ GeV at LHC).
- Scalar Leptophilic ( $O_{L\phi}^{(6)}$ ): Using a beam configuration with enhanced positron polarization and right-handed electrons ( $P_{e^+}, P_{e^-} = +20\%, +80\%$ ), the analysis achieves a statistical significance of $Z \approx 4.39$ for the benchmark point ( $m_\phi=100$ GeV, $\Lambda=2.0$ TeV), corresponding to evidence rather than discovery. However, the projected 5 $\sigma$ discovery reach for scalar DM with $m_\phi \lesssim 300$ GeV extends up to $\Lambda \approx 1.84$ TeV.
- Gauge Portals ( $O_{W\phi}^{(6)}$ , $O_{B\phi}^{(6)}$ ): These operators show robust discovery potential. $O_{W\phi}^{(6)}$ (left-handed enhanced) and $O_{B\phi}^{(6)}$ (right-handed enhanced) both achieve $Z > 6$ for their respective benchmarks. The 5 $\sigma$ reach extends to $\Lambda \approx 1.35$ TeV for $O_{B\phi}^{(6)}$ and $\Lambda \approx 1.30$ TeV for $O_{W\phi}^{(6)}$ .
Discovery Prospects at $\sqrt{s} = 250$ GeV (Higgs-Portal):
- For Higgs-portal operators ( $O_{D\phi}^{(6)}$ and $O_{DX}^{(6)}$ ), the viable parameter space is restricted to the Higgs resonance region ( $m_{DM} \approx 59$ GeV).
- The vector DM operator ( $O_{DX}^{(6)}$ ) is readily discoverable with $Z \approx 7.3$ at the nominal luminosity ($8$ ab $^{-1}$ ).
- The scalar counterpart ( $O_{D\phi}^{(6)}$ ) has a significantly lower cross-section, resulting in $Z \approx 0.71$ , rendering it inaccessible at the first ILC stage.

Significance and Claims
The paper claims that the mono-Z channel at future lepton colliders provides a powerful and complementary probe to the mono- $\gamma$ channel, specifically because it is sensitive to the $SU(2)_L$ structure and hypercharge components of DM interactions. The study emphasizes that:

Beam Polarization is Critical: The ability to polarize beams allows for the selective suppression of the dominant $t$ -channel $W$ -exchange SM background and the optimization of signal rates based on the chiral nature of the effective operators.
Cosmological Constraints Shape Reach: The discovery potential is not solely a function of collider energy but is fundamentally shaped by the interplay between operator structure and cosmological constraints (relic density, DD, ID). For instance, stringent DD limits push the dipole operator's scale beyond realistic collider reach, while gauge portals remain accessible.
Complementarity to LHC: The ILC offers a sensitivity to effective scales ( $\Lambda$ ) well beyond the reach of current LHC mono-Z recast analyses, particularly for Electroweak-coupled operators.
Spin and Structure Dependence: The results highlight that collider sensitivity depends significantly on the spin of the DM candidate and the Lorentz/Electroweak structure of the operators, as demonstrated by the stark difference in discovery prospects between scalar and vector Higgs-portal operators.

The authors conclude that while the analysis relies on standard thermal freeze-out assumptions and treats operators individually, the mono-Z channel serves as a robust guideline for future DM searches, capable of probing viable DMEFT interactions at multi-TeV scales.

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