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Search for resonant production of lepton-enriched semivisible jets in proton-proton collisions at $\sqrt{s}$ = 13 TeV

Using 138 fb $^{-1}$ of 13 TeV proton-proton collision data, the CMS collaboration performed the first search for resonant lepton-enriched semivisible jets, employing a dual machine-learning strategy to exclude mediator masses up to 4.7 TeV in the all-lepton scenario and between 1.8 and 3.5 TeV in the tau-enriched scenario.

Original authors: CMS Collaboration

Published 2026-08-07

📖 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

The Invisible Shadow and the Glowing Clue

Imagine the universe as a giant, bustling city. We can see the buildings, the cars, and the people—the stars, planets, and atoms that make up everything we touch. But astronomers know that most of the city is actually made of "dark matter," an invisible substance that holds the galaxy together with its gravity but refuses to show up on our cameras. It's like a ghost that pushes on walls but never leaves a footprint. For decades, scientists have been trying to catch this ghost by smashing particles together at super-fast speeds, hoping the collision will knock a piece of the ghost loose so we can see it.

Usually, when scientists look for this dark matter, they expect it to be shy and quiet, like a ninja that disappears instantly, leaving behind only a "missing" amount of energy. This is the standard search: look for a crash where something vanishes. But what if the dark matter isn't a ninja? What if it's a party animal? Some theories suggest that dark matter lives in a "dark sector" with its own rules, its own forces, and even its own version of light. In this wilder scenario, when dark matter is created, it might not just vanish. Instead, it could form a messy spray of particles—a "jet"—that is mostly invisible but has a few glowing, visible parts mixed in, like a dark cloud that occasionally flashes with lightning. This paper is about hunting for that specific kind of messy, glowing cloud.

The Hunt for the "Semi-Visible" Party

The scientists at the CMS experiment, a massive detector at the Large Hadron Collider (CERN) in Switzerland, decided to play detective with a new strategy. They used data from 138 billion billion proton-proton collisions (that's 138 fb⁻¹ of data) collected at an energy of 13 TeV. Their goal was to find a specific type of event called a "semivisible jet" (SVJ).

Think of a normal jet of particles like a stream of water from a hose. A "semivisible" jet is like a stream of water that has been mixed with a bunch of invisible bubbles. Most of the stream is there, but some of it is missing, and the missing part is perfectly aligned with the stream itself. In this specific search, the scientists were looking for jets that were "enriched" with leptons—particles like electrons, muons, and tau particles. It's as if they were looking for a dark cloud that, instead of just being dark, was sprinkled with glittering stars.

To find these rare events, the team used a clever two-step machine-learning strategy. First, they used a "Graph Neural Network" (GNN), which acts like a super-smart jet scanner. Instead of just looking at the jet as a blob, this scanner looks at the jet like a tree, analyzing how the particles branch out and interact. It was trained to spot the unique "fingerprint" of a dark jet, distinguishing it from the billions of ordinary jets created by standard physics.

Second, they used a "Fully Connected Neural Network" (DNN) to act as a referee. This network looked at the whole event, checking if the missing energy (the invisible bubbles) was lined up perfectly with the jet (the stream). They also split their search into two categories: one looking for jets with any kind of lepton (the "SVJℓ" scenario) and another looking specifically for jets heavy with tau leptons (the "SVJτ" scenario), because tau particles behave differently and might hide in the mess differently.

The Results: A Clean Sweep

After running their complex algorithms through the mountain of data, the scientists found something very important, even though it wasn't the "glittering cloud" they were hoping to see. They found no evidence of these lepton-enriched semivisible jets. The data matched the predictions of the Standard Model perfectly, meaning the "dark party" didn't happen in the way they predicted.

However, "not finding it" is still a huge scientific victory because it tells us where not to look. By not seeing these jets, the team was able to set strict limits on how heavy the "mediator" particle (the heavy Z′ boson that would create the dark jets) could be.

Here is what they ruled out:

For the "all-lepton" scenario (SVJℓ): They can now say with 95% confidence that if these particles exist, the heavy mediator creating them cannot be lighter than 4.7 TeV. They have effectively scanned the mass range from 1.5 TeV up to 4.7 TeV and found nothing.
For the "tau-lepton" scenario (SVJτ): They ruled out mediator masses between 1.8 TeV and 3.5 TeV.

In simpler terms, if the dark sector exists and creates these specific types of jets, the "key" to unlocking it (the Z′ boson) must be heavier than the heaviest things the scientists have been able to test so far. The paper explicitly states that these are the first experimental constraints ever placed on this specific type of lepton-enriched semivisible jet.

The team was very careful with their confidence. They didn't just guess; they simulated millions of events to understand what the background noise looked like and used advanced statistical methods to ensure their "no signal" result was solid. They even checked for a tiny, interesting blip in the data that looked like a 2.4-sigma deviation (a small hint of something unusual), but after checking for statistical flukes, it turned out to be just a random fluctuation with a global significance of only 1.6 sigma—nowhere near enough to claim a discovery.

So, the story ends with the scientists holding up a sign that says, "We looked for the glittering dark clouds, and we didn't find them in this size range." This doesn't mean dark matter doesn't exist, but it does mean that if it does, it's hiding in a way that is even more elusive than this specific "lepton-enriched" theory predicted. The hunt continues, but the map just got a little clearer.

Technical Summary: Search for Resonant Production of Lepton-Enriched Semivisible Jets

Problem and Motivation
While collider searches for dark matter (DM) have predominantly focused on Weakly Interacting Massive Particles (WIMPs) yielding "mono-X" signatures (large missing transverse momentum, $p^{\text{miss}}_T$ , recoiling against visible Standard Model particles), these approaches often lack sensitivity to Hidden Valley (HV) scenarios. In HV models, a dark sector (DS) with QCD-like dynamics produces dark hadrons. If a fraction of these hadrons are stable, they escape detection, while unstable ones decay to Standard Model (SM) particles. This can result in "semivisible jets" (SVJs), where $p^{\text{miss}}_T$ is aligned with a jet.

Previous searches by ATLAS and CMS have targeted fully hadronic SVJ signatures. However, recent theoretical studies suggest that existing searches are insensitive to scenarios where SVJs are enriched with leptons. This paper addresses this gap by presenting the first search for resonant production of SVJs enriched in leptonic content, specifically targeting two distinct scenarios: jets enriched in all lepton flavors ( $\text{SVJ}_\ell$ ) and jets predominantly enriched in tau leptons ( $\text{SVJ}_\tau$ ).

Methodology
The analysis utilizes 138 fb $^{-1}$ of proton-proton collision data at $\sqrt{s} = 13$ TeV collected by the CMS detector during 2016–2018. The signal model assumes a heavy $Z'$ mediator decaying to dark quarks ( $\chi$ ), which hadronize via a dark QCD force into stable and unstable dark hadrons. The unstable hadrons decay promptly to SM quarks and leptons.

Signal Scenarios:
- $\text{SVJ}_\ell$ : Mediated by a $Z'$ and a dark photon $A'$ . Dark vector mesons ( $\rho_{\text{dark}}$ ) decay democratically to all SM lepton flavors and quarks.
- $\text{SVJ}_\tau$ : Mediated by a $Z'$ coupled to tau leptons. Dark pions ( $\pi_{\text{dark}}$ ) decay to the heaviest kinematically accessible up-type quarks and tau leptons. The resulting electrons and muons (from $\tau$ decays) are softer and accompanied by neutrinos compared to the $\text{SVJ}_\ell$ case.
Event Selection and Categorization:
Events are selected based on high transverse mass ( $m_T$ ) of the dijet system and alignment between $p^{\text{miss}}_T$ and the leading jets. A key innovation is the categorization based on lepton isolation within jets using a "mini-isolation" variable ( $I_{\text{mini}}$ ).
- $\text{SVJ}_\ell$ : Primarily analyzed in a "multilepton" category where leptons pass isolation cuts.
- $\text{SVJ}_\tau$ : Analyzed in both "0-lepton" (no isolated leptons) and "multilepton" categories, as the softer lepton spectrum and higher neutrino content lead to different isolation efficiencies.
Machine Learning Strategy:
A dual machine-learning approach is employed to enhance signal sensitivity and background estimation:
1. Jet Tagging (LUNDNET): An extension of the LUNDNET algorithm, utilizing a Graph Neural Network (GNN) operating on a "Lund tree" representation of jet constituents. This architecture captures the distinct radiation patterns of SVJs (arising from double parton showering in dark and SM sectors) compared to SM jets. The network is trained separately for $\text{SVJ}_\ell$ and $\text{SVJ}_\tau$ signals in their respective lepton categories.
2. Background Estimation (MD-ABCDISCOTEC): A fully connected Deep Neural Network (DNN) is used to estimate backgrounds in the signal region (SR) using an ABCD method. To ensure the validity of the ABCD method, two discriminant variables ( $D_1, D_2$ ) are trained to be statistically independent of each other and of the search variable ( $m_T$ ). This is achieved using a "mass-decorrelated ABCDISCOTEC" (MD-ABCDISCOTEC) technique, which minimizes distance correlation losses (DisCo) and enforces a closure relation.

Key Contributions

First Experimental Constraints: This work provides the first experimental limits on lepton-enriched semivisible jets, a class of signatures previously unexplored by collider experiments.
Novel ML Integration: The paper introduces the first application of an extended LUNDNET GNN for distinguishing lepton-enriched SVJs from SM backgrounds.
Advanced Background Estimation: It demonstrates the use of the MD-ABCDISCOTEC method for resonant searches, successfully decorrelating discriminants from the search mass variable ( $m_T$ ) to enable robust background estimation in bins of $m_T$ .
Dual-Scenario Analysis: The analysis uniquely handles two distinct signal topologies ( $\text{SVJ}_\ell$ and $\text{SVJ}_\tau$ ) with tailored selection strategies (lepton isolation vs. 0-lepton) and specific ML training configurations.

Results
No significant excess of events over the Standard Model prediction was observed in the data. The results are interpreted as 95% confidence level (CL) upper limits on the production cross-section times branching fraction ( $\sigma_{Z'} \mathcal{B}_{\text{dark}}$ ).

$\text{SVJ}_\ell$ Scenario: Mediator masses ( $m_{Z'}$ ) are excluded in the range 1.5 to 4.7 TeV for benchmark invisible fractions ( $r_{\text{inv}}$ ) of 0.3 and dark hadron masses ( $m_{\text{dark}}$ ) of 16 GeV. The exclusion range is most sensitive for moderate $r_{\text{inv}}$ values where selection efficiency and background rejection are optimal.
$\text{SVJ}_\tau$ Scenario: Mediator masses are excluded in the range 1.8 to 3.5 TeV for $r_{\text{inv}} = 0.3$ , $B_\tau = 0.3$ , and $m_{\text{dark}} = 8$ GeV. The 0-lepton category contributes significantly to excluding high-mass signals ( $>3$ TeV), while the multilepton category enhances sensitivity at lower masses by suppressing QCD background.
Local Fluctuation: A small discrepancy between observed and expected limits was noted at $m_{Z'} = 3$ TeV and $r_{\text{inv}} = 0.7$ for the $\text{SVJ}_\tau$ search, with a local significance of 2.4 $\sigma$ . However, after accounting for the look-elsewhere effect, the global significance reduces to 1.6 $\sigma$ , consistent with a statistical fluctuation.

Significance
The paper claims to complement existing searches for dijet resonances, dark matter with initial-state radiation, and fully hadronic semivisible jets by exploring a new parameter space characterized by lepton enrichment. By establishing the first constraints on these specific HV scenarios, the analysis demonstrates the capability of modern machine-learning techniques (GNNs for jet substructure and decorrelated DNNs for background estimation) to probe complex dark sector signatures that were previously inaccessible to standard trigger and selection strategies. The results constrain models where the dark sector communicates with the SM via portals that preferentially produce leptons, thereby narrowing the viable parameter space for strongly coupled dark matter models.

The Invisible Shadow and the Glowing Clue

The Hunt for the "Semi-Visible" Party

The Results: A Clean Sweep

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