⚛️ high-energy experiments

Search for nonresonant production of strongly coupled dark matter in proton-proton collisions at $\sqrt{s}$ = 13 TeV

Using 138 fb $^{-1}$ of proton-proton collision data at $\sqrt{s}$ = 13 TeV collected by the CMS detector, this study presents a search for nonresonant semivisible jets indicative of strongly coupled dark matter using both supervised and unsupervised machine learning techniques, finding no significant excess and setting exclusion limits on mediator masses up to 2.4 TeV.

Original authors: CMS Collaboration

Published 2026-10-27

📖 5 min read🧠 Deep dive

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

For decades, the most powerful machines on Earth have been smashing protons together at nearly the speed of light, revealing a universe built from a specific set of fundamental particles. This standard model of physics has been remarkably successful, predicting the behavior of everything from the lightest atoms to the heaviest known particles. Yet, astronomers have long known that this model is incomplete. Observations of how galaxies spin and how light bends around massive clusters of stars suggest that most of the matter in the universe is invisible. This missing mass, known as dark matter, does not emit light, reflect it, or interact with the forces that hold atoms together, making it impossible to see directly. While scientists have spent years searching for a simple, heavy particle that might explain this darkness, they have found nothing. This silence has led researchers to consider more complex possibilities: perhaps dark matter is not a single lonely particle, but a whole hidden sector of particles that interact with each other through their own forces, much like the visible matter we know, but remain hidden from our view.

In a recent study, the CMS collaboration at the Large Hadron Collider in Switzerland put one of these complex ideas to the test. They looked for evidence of a "dark sector" where particles are created in pairs, with one part of the pair being visible and the other part invisible. In this scenario, a heavy particle would decay into a spray of new particles. Some of these new particles would be stable and invisible, escaping the detector without a trace, while others would be unstable and decay immediately into ordinary particles that the detector can see. The result would be a jet of particles that looks like a normal spray of debris, but with a significant portion of its energy missing. The researchers called these strange objects "semivisible jets." Unlike typical dark matter searches that look for a single jet recoiling against a large gap of missing energy, this search looked for the missing energy to be aligned right alongside the visible jet, hidden within the spray itself.

To find these elusive signals, the team analyzed a massive dataset of proton-proton collisions collected between 2016 and 2018, corresponding to an integrated luminosity of 138 inverse femtobarns. This amount of data represents a vast number of collisions, providing a deep well of information to sift through. The challenge was distinguishing these hypothetical semivisible jets from the overwhelming background of ordinary particle sprays produced by standard physics processes. To do this, the researchers employed two distinct machine-learning strategies. The first was a supervised approach, where a computer program was trained on simulations of the specific dark matter model to recognize the unique patterns of a semivisible jet. The second was an unsupervised approach, where a different computer program learned what a normal jet looks like by studying real data, and then flagged any jet that looked unusual or "anomalous" compared to that norm. This second method was designed to be more flexible, capable of spotting signals even if they didn't perfectly match the specific simulations used in the first method.

The analysis focused on events where the missing energy was aligned with a jet, a signature that would be a smoking gun for this type of dark sector. The researchers carefully filtered out events caused by detector errors or known background processes, such as the production of top quarks or the decay of W and Z bosons. They then examined the distribution of missing energy across all the events they had collected. Despite the sophisticated tools and the sheer volume of data, the search came up empty. The researchers found no significant excess of events that could be attributed to semivisible jets. The data matched the predictions of the standard model perfectly, with no signs of the hidden sector particles they were hunting.

Because no signal was found, the team used their results to rule out specific versions of the dark matter model they were testing. They determined that if these semivisible jets exist, the heavy particle that creates them cannot have a mass between 0.5 and 2.4 trillion electronvolts, depending on the other properties of the model. For the unsupervised search, which is better at spotting signals where the invisible part of the jet is larger, they were able to exclude masses up to 2.1 trillion electronvolts. These limits are significant because they close the door on a wide range of theoretical possibilities that had not been tested before. The study demonstrates that even when dark matter is hidden inside a jet, mixed with ordinary particles, it leaves a distinct fingerprint that modern detectors and advanced computer algorithms can search for. While the search did not find the dark matter, it successfully mapped out the territory where it is not, guiding future experiments toward new possibilities.

Technical Summary: Search for Nonresonant Production of Strongly Coupled Dark Matter in Proton-Proton Collisions at $\sqrt{s} = 13$ TeV

Problem and Motivation
While the Standard Model (SM) of particle physics successfully describes known elementary particles, astronomical observations—such as galaxy rotation curves and gravitational lensing—strongly indicate the existence of dark matter (DM) unexplained by current theory. Traditional collider searches have focused on Weakly Interacting Massive Particles (WIMPs), which typically produce signatures of missing transverse momentum ( $p^{\text{miss}}_T$ ) recoiling against visible SM particles. However, no evidence for WIMP DM has been found.

This paper investigates an alternative class of models involving "hidden valleys" or dark sectors (DS) governed by a confining interaction similar to SM quantum chromodynamics (QCD), often termed "dark QCD." In these scenarios, dark quarks shower and hadronize into dark hadrons. Stable dark hadrons escape the detector as DM, while unstable ones decay promptly into SM quarks. This process results in "semivisible jets" (SVJs)—collimated sprays containing both visible particles and invisible DM candidates. Unlike conventional DM searches where $p^{\text{miss}}_T$ is recoiling against a jet, SVJ events feature $p^{\text{miss}}_T$ aligned with the jet itself. This paper presents the first CMS search for the nonresonant production of such strongly coupled dark matter.

Methodology
The analysis utilizes proton-proton collision data collected by the CMS detector at $\sqrt{s} = 13$ TeV during the 2016–2018 data-taking period, corresponding to an integrated luminosity of 138 fb $^{-1}$ .

Signal Model: The signal is mediated by a massive bifundamental scalar $\Phi$ that couples simultaneously to SM quarks and dark quarks. The model is defined by four parameters: the mediator mass ( $m_\Phi$ ), the Yukawa coupling ( $\lambda$ ), the fraction of stable dark hadrons ( $r_{\text{inv}}$ ), and the dark-hadron mass scale ( $m_{\text{dark}}$ ).
Event Selection: Events are selected requiring high scalar sum of transverse momenta ( $S_T > 1300$ GeV), at least two wide jets ( $R=0.8$ ), and significant $p^{\text{miss}}_T$ ( $> 200$ GeV). A key selection criterion requires the minimum angle between any jet and the $p^{\text{miss}}_T$ vector ( $\Delta\phi_{\text{min}}$ ) to be less than 1.5, reflecting the expected alignment in SVJ events.
Machine Learning Strategies: Two complementary taggers are employed to distinguish SVJs from SM jets:
1. Supervised Tagger (PARTICLENET): A graph neural network (GNN) trained on simulated signal and background samples. It utilizes particle-level information (constituent four-vectors) to learn specific dark-shower dynamics. It is highly sensitive to the specific model parameters used in training but less model-agnostic.
2. Unsupervised Tagger (Wasserstein Normalized Autoencoder - WNAE): An anomaly detection algorithm trained on SM data (QCD and $t\bar{t}$ enriched regions) to learn the probability distribution of SM jet substructure. It identifies SVJs as jets with anomalous substructure without prior knowledge of the signal model, offering broader sensitivity to untested signal hypotheses.
Background Estimation: The dominant background arises from QCD multijet events with mismeasured jets inducing artificial $p^{\text{miss}}_T$ . This is estimated using the ABCDisCoTEC method, a machine-learning-enhanced ABCD technique. A neural network classifier is trained to be decorrelated from $p^{\text{miss}}_T$ to partition events into four regions (A, B, C, D), allowing the background in the signal region (A) to be predicted from control regions (B, C, D) using data.
Systematic Uncertainties: Uncertainties include detector effects (jet energy scale/resolution, pileup), theoretical modeling (PDFs, renormalization scales), and specific corrections for jet substructure mismodeling using Lund jet plane densities.

Key Contributions

Dual-Strategy Approach: The paper introduces and compares a model-dependent supervised GNN and a model-agnostic unsupervised autoencoder for SVJ identification, demonstrating the trade-offs between specific sensitivity and model independence.
Substructure Correction: A novel correction method is applied to signal simulations to account for mismodeling of jet substructure. This involves reclustering signal jets into subjets corresponding to SM quarks and reweighting them based on the Lund jet plane density observed in data control regions.
ABCD Method Enhancement: The application of the ABCDisCoTEC method allows for robust background estimation in a regime dominated by instrumental backgrounds (mismeasured jets) where traditional simulation-based estimates are unreliable.

Results
No significant excess of events was observed over the expected SM background in the $p^{\text{miss}}_T$ distribution for either tagger strategy. Consequently, upper limits at 95% confidence level (CL) on the production cross-section of the bifundamental mediator $\Phi$ were set.

Supervised Search: Excludes mediator masses between 0.5 and 2.4 TeV, depending on other signal parameters. For signal models with $r_{\text{inv}} = 0.3$ and $\lambda = 1.0$ , all considered dark-hadron masses are excluded for $m_\Phi < 1.7$ TeV.
Unsupervised Search: Excludes mediator masses between 0.5 and 2.1 TeV. Notably, for signal models with higher fractions of stable dark matter ( $r_{\text{inv}} \approx 0.6\text{--}0.9$ ), the unsupervised search demonstrates increased sensitivity, excluding mediator masses up to 2.1 TeV, whereas the supervised search (trained on lower $r_{\text{inv}}$ values) only excludes up to 1.7 TeV.
Parameter Space: The results exclude specific regions in the $(m_\Phi, r_{\text{inv}})$ , $(m_\Phi, m_{\text{dark}})$ , and $(m_\Phi, \lambda)$ planes. For instance, for $m_\Phi < 1.6$ TeV, all considered variations of $\lambda$ are excluded in the supervised search, while $\lambda > 2$ is excluded for all $m_\Phi$ in the same strategy.

Significance
This work represents the first CMS search for nonresonant production of strongly coupled dark matter. By employing machine learning techniques to exploit both jet-level substructure and event-level kinematics, the analysis extends the reach of dark sector searches beyond traditional WIMP paradigms. The paper highlights that while supervised methods offer high sensitivity to specific benchmark models, unsupervised anomaly detection provides crucial robustness against the vast uncertainty in dark sector parameters, successfully excluding regions of parameter space that would otherwise remain unprobed. These results complement existing searches for composite dark matter and constrain the production of bifundamental scalar mediators in strongly coupled dark sectors.

More like this