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Search for dark matter produced in association with a low-multiplicity jet in proton-proton collisions at $\sqrt{s}$ = 13 TeV

Using 138 fb $^{-1}$ of 13 TeV proton-proton collision data from the CMS experiment, this study presents the first LHC search for dark matter produced with a low-multiplicity jet, employing machine learning to set 95% confidence level upper limits on production cross sections within simplified vector and axial-vector mediator models.

Original authors: CMS Collaboration

Published 2026-10-02

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CC BY 4.0

Original authors: CMS Collaboration

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

The universe is filled with things we can see: stars, gas clouds, and the vast, dark voids between them. Yet, astronomers know that the visible matter accounts for only a small fraction of what exists. The rest is an invisible substance called dark matter, which exerts gravity but does not emit or reflect light. We know it is there because its gravitational pull holds galaxies together, but we have never directly caught a glimpse of a dark matter particle. It remains one of the biggest mysteries in physics, a ghostly presence that shapes the cosmos while hiding from our most powerful telescopes. To find it, scientists must look for the subtle footprints it might leave behind when it interacts with ordinary matter, or perhaps when it is created in the violent collisions of high-energy particles.

At the Large Hadron Collider, a massive ring of magnets buried beneath the border of France and Switzerland, physicists smash protons together at nearly the speed of light. These collisions recreate the extreme conditions of the early universe, potentially spawning new, heavy particles that vanish almost instantly. In a recent study, the CMS collaboration, a team of thousands of scientists working with one of the collider's giant detectors, searched for a very specific and unusual signature of dark matter. Instead of looking for the usual spray of debris, they hunted for a scenario where dark matter is produced alongside a single, narrow jet of energy. This jet is not the messy spray of particles typical of high-energy crashes, but a tight, focused beam containing very few constituents, resembling a pencil in its narrowness.

The researchers analyzed data corresponding to an integrated luminosity of 138 fb⁻¹, recorded between 2016 and 2018. They were looking for events where this narrow jet recoiled against a large amount of missing energy, which would indicate that invisible dark matter particles had escaped the detector. Because the signal is so faint and easily hidden by the background noise of ordinary particle interactions, the team employed advanced machine learning tools. These computer programs were trained to distinguish the subtle differences between the rare dark matter signature and the common background events, acting as a highly sensitive filter to sift through the billions of collisions.

The search yielded no evidence of dark matter. The number of events observed matched the predictions for standard physics perfectly, with no unexpected excesses to suggest the presence of new particles. While this might sound like a null result, it is a powerful finding because it allows scientists to rule out specific theories about how dark matter might behave. By not finding the signal, the team was able to exclude a wide range of possibilities. They determined that if dark matter particles have a mass around 150 billion electron volts, the particles that might carry the force between them (called mediators) cannot be lighter than about 4.25 trillion electron volts. For heavier dark matter particles, around 550 billion electron volts, the mediators are excluded up to masses of 3.5 trillion electron volts.

This work represents the first time the Large Hadron Collider has specifically targeted this low-multiplicity jet signature, a strategy that had not been explored before. The fact that the search came up empty tells us that if dark matter exists in this particular form, it is even more elusive than previously thought, hiding behind a higher wall of energy than scientists had hoped to penetrate with current data. The results provide a clear boundary for future searches, guiding theorists to look in different directions or at higher energy scales. The search continues, but for now, the dark sector remains hidden, and the universe keeps its most fundamental secret safe from the eyes of the detector.

Technical Summary: Search for Dark Matter Produced in Association with a Low-Multiplicity Jet

Problem and Motivation
While the Standard Model (SM) of particle physics is highly successful, it does not account for dark matter (DM). Direct detection of DM particles remains elusive. This paper presents a search for DM production in proton-proton ($pp$) collisions at a center-of-mass energy of $\sqrt{s} = 13$ TeV, utilizing a novel signature distinct from traditional "mono-X" searches. The analysis targets a simplified model featuring an Abelian dark sector with a light GeV-scale $Z'$ boson. In this scenario, a pair of DM particles is produced, with one radiating a $Z'$ boson via final-state radiation (FSR). The $Z'$ boson, assumed to be leptophobic and light ( $0.3 < m_{Z'} < 3$ GeV), decays primarily into light quark pairs ( $u\bar{u}, d\bar{d}, s\bar{s}$ ). Due to the small mass and large Lorentz boost of the $Z'$ , its decay products are highly collimated, forming a narrow cone of radiation. This results in a distinctive "pencil-jet" signature: a single jet with low charged-particle multiplicity and a narrow angular size, resembling hadronically decaying $\tau$ leptons. This topology offers a potential sensitivity extension beyond conventional mono-jet searches, particularly in regions where FSR contributions are comparable to or exceed initial-state radiation (ISR) contributions.

Methodology
The analysis utilizes the full dataset recorded by the CMS experiment during the 2016–2018 LHC data-taking periods, corresponding to an integrated luminosity of 138 fb $^{-1}$ .

Event Selection: Events are selected requiring large missing transverse momentum ( $p_{\text{T}}^{\text{miss}} > 250$ GeV) and a single energetic "pencil-jet" with transverse momentum $p_{\text{T}} > 140$ GeV and pseudorapidity $|\eta| < 2.3$ . The pencil-jet is reconstructed using the "hadrons-plus-strips" algorithm, originally developed for $\tau$ lepton reconstruction, and is defined as an object with at most three tracks, charged hadrons, and electromagnetic clusters within a cone of $\Delta R < 0.1$ . To suppress backgrounds, events containing electrons, muons, photons, or $b$ -tagged jets are vetoed.
Background Estimation: The dominant backgrounds are $Z(\nu\nu) + \text{jets}$ and $W(\ell\nu) + \text{jets}$ , where the neutrino or undetected lepton generates genuine missing transverse momentum. Other contributions include $Z(\ell\ell) + \text{jets}$ , top quark production, diboson processes, and QCD multijets (where $p_{\text{T}}^{\text{miss}}$ arises from mismeasurement). Background yields are estimated using Monte Carlo (MC) simulations generated with MADGRAPH5 aMC@NLO and POWHEG, normalized to next-to-leading order (NLO) cross sections where available.
Signal Extraction Strategy: Given the subtle differences between signal and background kinematics and jet substructure, a supervised machine learning (ML) approach is employed. A two-stage architecture is used: a feed-forward neural network (NN) implemented in TensorFlow is trained on 14 input variables (including pencil-jet kinematics, associated jet properties, and global event variables like recoil), followed by a boosted decision tree (BDT) using XGBoost. The BDT output serves as the primary discriminant. The model is trained on a combined signal class (varying DM and mediator masses) and a background class, with hyperparameters optimized via randomized search.
Systematic Uncertainties: Major uncertainties include the pencil-jet reconstruction efficiency and misidentification rates (derived from $\tau$ lepton control samples), jet energy scale and resolution (JES/JER), and theoretical uncertainties in $Z/W + \text{jets}$ production (scale variations, parton distribution functions, and electroweak corrections). These are incorporated as nuisance parameters in the final statistical fit.

Key Contributions

Novel Signature: This work represents the first search at the LHC specifically targeting the "pencil-jet" signature associated with dark matter production via a light $Z'$ mediator.
Machine Learning Application: The analysis demonstrates the effectiveness of a hybrid NN-BDT approach in distinguishing low-multiplicity, collimated jets from generic QCD jets and standard background processes in a challenging final state.
Scale Factor Derivation: The study utilizes hadronic $\tau$ decays as a proxy to derive scale factors and uncertainties for the pencil-jet reconstruction, addressing the lack of a well-established SM object with identical two-prong jet characteristics.

Results
No statistically significant excess of events over the SM background prediction is observed in the signal region. The observed data distributions for the ML output and key kinematic variables (recoil, jet substructure) are consistent with background expectations within uncertainties.

Upper limits on the DM production cross section are set at the 95% confidence level (CL) within simplified models featuring vector and axial-vector mediators. The results are interpreted in the plane of DM mass ( $m_{\text{DM}}$ ) versus mediator mass ( $m_{\text{med}}$ ), assuming a fixed $Z'$ mass of 1 GeV.

For a DM mass of approximately 150 GeV, mediator masses up to 4.25 TeV are excluded at 95% CL.
For a DM mass of approximately 550 GeV, mediator masses up to 3.5 TeV are excluded at 95% CL.
The exclusion reach diminishes at higher masses due to the rapidly decreasing signal production cross section.

Significance
The paper claims that these results provide the first constraints on this specific final state, significantly extending the sensitivity of DM searches at the LHC. By employing a dedicated search for low-multiplicity jets and leveraging ML techniques, the analysis probes a region of parameter space that complements traditional mono-jet searches. The derived limits place stringent constraints on simplified DM models with spin-1 mediators, offering important guidance for future searches, particularly in phase space regions where improvements in luminosity and analysis techniques could further extend sensitivity. The analysis confirms that the ML-based approach is robust against detector condition variations and simulation mismodeling, validating its use for future high-precision searches.

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