Soft Unclustered Energy Pattern (SUEP)

• SUEP is a collider signature characterized by a high multiplicity of low-momentum particles distributed nearly isotropically, emerging from hidden-sector dynamics.
• It contrasts with standard QCD jets by exhibiting a democratic energy distribution without clear jet-like structures, underscoring unique event morphologies.
• Experimental strategies employ advanced triggering and machine learning methods to effectively isolate SUEP events, offering insights into hidden valley physics.

Searching arXiv for recent and foundational SUEP papers to ground the article. {"query":"SUEP Soft Unclustered Energy Pattern arXiv", "max_results": 10} Soft Unclustered Energy Patterns (SUEPs) are collider final states characterized by a very large multiplicity of low-momentum particles distributed broadly in angle rather than organized into a small number of narrow jets. In the LHC context, SUEPs are motivated primarily by Hidden Valley or dark-QCD-like sectors with strong, approximately pseudo-conformal or quasi-conformal dynamics, in which a mediator produces dark quarks or related hidden-sector states that shower, hadronize into many dark hadrons, and then decay to Standard Model particles. The resulting signature is anomalous relative to ordinary QCD because it is “soft” at the level of individual particles, “unclustered” at the level of event morphology, and best recognized as a global pattern rather than as a resonance, missing-energy excess, or isolated hard object (Chhibra et al., 2023).

1. Hidden-sector origin and theoretical definition

In the benchmark constructions used in the SUEP literature, the hidden sector is a confining non-Abelian theory connected to the Standard Model through a mediator, often a scalar portal state or a Higgs-related interaction. The defining dynamical ingredient is large hidden-sector coupling, typically expressed through a ’t Hooft parameter such as

$\lambda_D \equiv \alpha_D N_{C_D},$

with the SUEP regime corresponding to large coupling and approximately isotropic dark-meson emission in the mediator rest frame (Petrillo et al., 2022).

The theoretical contrast with QCD is central. In QCD, asymptotic freedom enhances soft and collinear radiation, so visible energy flow is concentrated into jetty structures. In the strongly coupled pseudo-conformal picture used for SUEP, large-angle emissions are not strongly suppressed, the original parton directions are effectively forgotten, and the shower becomes “democratic,” distributing energy among many hadrons rather than a few hard partons. This is the basis for the standard SUEP description as a soft, spherical, high-multiplicity hidden shower (Barron et al., 2021).

Several papers use thermalized or Boltzmann-like toy models for the hidden hadrons. One representative form is

$$\frac{dN}{d^{3}\mathbf{p}} \propto \exp\!\left(-\frac{\sqrt{\mathbf{p}^{2}+m_D^2}}{T_D}\right),$$

where $m_D$ is the dark-hadron mass and $T_D\sim \Lambda$ is an effective Hagedorn temperature. In the same framework, multiplicity is motivated by strong-coupling scaling relations such as

$$\langle n \rangle \sim \left(\frac{Q}{\Lambda}\right)^{2\gamma_T(1)}, \qquad \langle n \rangle \sim \left(\frac{Q}{\Lambda}\right)^{1+\mathcal{O}(1/\sqrt{\lambda})}$$

in the strong-coupling limit (Barron et al., 2021). This suggests that the hallmark observables of SUEP—high multiplicity, soft momentum spectra, and isotropy—are not ad hoc analysis choices but direct consequences of the hidden-shower dynamics.

2. Event morphology and discriminating observables

At detector level, SUEP is defined operationally through global event structure. One CMS trigger study summarizes the experimental picture as “spherically-symmetric energy deposits by an anomalously large number of soft Standard Model particles” with transverse energies of order few $\times 100$ MeV, emphasizing that the signature is atypical because the energy is not organized into jet-like structures (Chhibra et al., 2023). Ordinary QCD background instead produces a small number of hard, collimated jets with localized energy flow in the $\eta$-$\phi$ plane.

The visible topology depends on the frame and reconstruction strategy. In some descriptions SUEP is approximately spherical in azimuth and pseudorapidity, while the track-trigger study stresses that at the LHC it is approximately isotropic in $\phi$ but localized in $\eta$, producing a “belt of fire” (Petrillo et al., 2022). This suggests that practical analyses often reconstruct isotropy either in the candidate rest frame or in transverse projections rather than relying on naive lab-frame spherical symmetry.

The dominant observables used across the literature are charged-particle or charged-track multiplicity, event-shape variables, and geometric track-distribution descriptors. CMS and ATLAS searches use variants of sphericity defined from eigenvalues of a generalized momentum tensor,

$$\frac{dN}{d^{3}\mathbf{p}} \propto \exp\!\left(-\frac{\sqrt{\mathbf{p}^{2}+m_D^2}}{T_D}\right),$$0

with $$\frac{dN}{d^{3}\mathbf{p}} \propto \exp\!\left(-\frac{\sqrt{\mathbf{p}^{2}+m_D^2}}{T_D}\right),$$1 corresponding to maximally jet-like configurations and $$\frac{dN}{d^{3}\mathbf{p}} \propto \exp\!\left(-\frac{\sqrt{\mathbf{p}^{2}+m_D^2}}{T_D}\right),$$2 to perfectly spherical ones (Collaboration, 2024). Earlier methodology work identified three especially useful observables: charged-particle multiplicity, event ring isotropy, and the matrix of pairwise geometric distances $$\frac{dN}{d^{3}\mathbf{p}} \propto \exp\!\left(-\frac{\sqrt{\mathbf{p}^{2}+m_D^2}}{T_D}\right),$$3 between charged tracks, with $$\frac{dN}{d^{3}\mathbf{p}} \propto \exp\!\left(-\frac{\sqrt{\mathbf{p}^{2}+m_D^2}}{T_D}\right),$$4 as a scalar summary (Barron et al., 2021).

Reconstruction choices are adapted to the expected large angular size of the shower. In CMS searches based on tracks, charged particles from the primary vertex are clustered with anti-$$\frac{dN}{d^{3}\mathbf{p}} \propto \exp\!\left(-\frac{\sqrt{\mathbf{p}^{2}+m_D^2}}{T_D}\right),$$5 using a large radius $$\frac{dN}{d^{3}\mathbf{p}} \propto \exp\!\left(-\frac{\sqrt{\mathbf{p}^{2}+m_D^2}}{T_D}\right),$$6, and the candidate is analyzed in its rest frame to recover isotropy more faithfully (Collaboration, 2024). In the $$\frac{dN}{d^{3}\mathbf{p}} \propto \exp\!\left(-\frac{\sqrt{\mathbf{p}^{2}+m_D^2}}{T_D}\right),$$7-associated search, the SUEP candidate is similarly built from charged PF candidates from the primary vertex with $$\frac{dN}{d^{3}\mathbf{p}} \propto \exp\!\left(-\frac{\sqrt{\mathbf{p}^{2}+m_D^2}}{T_D}\right),$$8 GeV and $$\frac{dN}{d^{3}\mathbf{p}} \propto \exp\!\left(-\frac{\sqrt{\mathbf{p}^{2}+m_D^2}}{T_D}\right),$$9, clustered with anti-$m_D$0 and $m_D$1, then characterized by multiplicity and rest-frame sphericity (Collaboration, 7 Apr 2026).

3. Trigger problem and real-time detection

SUEP is widely described as a worst-case trigger scenario. The difficulty is not the presence of an unusual hard object but the absence of one: no energetic jets, photons, or leptons are guaranteed, while the visible tracks are numerous but soft. The track-trigger study states explicitly that SUEPs are “a worst case scenario for triggers at hadron colliders” because the signature can resemble pile-up unless many soft tracks are reconstructed and associated to the same hard-scatter vertex (Petrillo et al., 2022).

That study quantifies the dependence on track-threshold design. For a simple high-multiplicity soft-track trigger with $m_D$2, thresholds of $m_D$3, $m_D$4, and $m_D$5 GeV were examined. With $m_D$6 GeV, $m_D$7 efficiency is reached for mediator masses above $m_D$8 GeV with $m_D$9, and above $T_D\sim \Lambda$0 GeV with $T_D\sim \Lambda$1. With $T_D\sim \Lambda$2 GeV, $T_D\sim \Lambda$3 efficiency is only possible above roughly $T_D\sim \Lambda$4 GeV, while a CMS-like $T_D\sim \Lambda$5 GeV track trigger is effectively unusable, giving negligible efficiency for all signal points (Petrillo et al., 2022). A common misconception is that heavier mediators help because the tracks become harder; the paper states instead that the $T_D\sim \Lambda$6 shape is largely independent of mediator mass, and the efficiency rise comes from larger multiplicity.

A complementary strategy is online anomaly detection. A CMS High-Level Trigger study represents each event as a three-channel $T_D\sim \Lambda$7-$T_D\sim \Lambda$8 image using the inner tracker, ECAL, and HCAL, with final tensor shape $T_D\sim \Lambda$9. The images are extremely sparse: only about $$\langle n \rangle \sim \left(\frac{Q}{\Lambda}\right)^{2\gamma_T(1)}, \qquad \langle n \rangle \sim \left(\frac{Q}{\Lambda}\right)^{1+\mathcal{O}(1/\sqrt{\lambda})}$$0 of the total $$\langle n \rangle \sim \left(\frac{Q}{\Lambda}\right)^{2\gamma_T(1)}, \qquad \langle n \rangle \sim \left(\frac{Q}{\Lambda}\right)^{1+\mathcal{O}(1/\sqrt{\lambda})}$$1k pixels are non-zero, so the authors replace standard losses with the inverse of the Dice loss to emphasize overlap on active pixels rather than “learning the zeros.” The model is a symmetric deep convolutional autoencoder with five convolutional layers down to a $$\langle n \rangle \sim \left(\frac{Q}{\Lambda}\right)^{2\gamma_T(1)}, \qquad \langle n \rangle \sim \left(\frac{Q}{\Lambda}\right)^{1+\mathcal{O}(1/\sqrt{\lambda})}$$2 bottleneck and five transposed-convolution layers back up, totaling $$\langle n \rangle \sim \left(\frac{Q}{\Lambda}\right)^{2\gamma_T(1)}, \qquad \langle n \rangle \sim \left(\frac{Q}{\Lambda}\right)^{1+\mathcal{O}(1/\sqrt{\lambda})}$$3 trainable parameters (Chhibra et al., 2023).

Performance in that trigger study is benchmark-dependent. Using the inverse of reconstructed $$\langle n \rangle \sim \left(\frac{Q}{\Lambda}\right)^{2\gamma_T(1)}, \qquad \langle n \rangle \sim \left(\frac{Q}{\Lambda}\right)^{1+\mathcal{O}(1/\sqrt{\lambda})}$$4 as anomaly proxy, the reported AUC ranges from $$\langle n \rangle \sim \left(\frac{Q}{\Lambda}\right)^{2\gamma_T(1)}, \qquad \langle n \rangle \sim \left(\frac{Q}{\Lambda}\right)^{1+\mathcal{O}(1/\sqrt{\lambda})}$$5 for SUEP(125) to $$\langle n \rangle \sim \left(\frac{Q}{\Lambda}\right)^{2\gamma_T(1)}, \qquad \langle n \rangle \sim \left(\frac{Q}{\Lambda}\right)^{1+\mathcal{O}(1/\sqrt{\lambda})}$$6 for SUEP(1000). At $$\langle n \rangle \sim \left(\frac{Q}{\Lambda}\right)^{2\gamma_T(1)}, \qquad \langle n \rangle \sim \left(\frac{Q}{\Lambda}\right)^{1+\mathcal{O}(1/\sqrt{\lambda})}$$7 SUEP signal efficiency, the QCD mistag rate improves to $$\langle n \rangle \sim \left(\frac{Q}{\Lambda}\right)^{2\gamma_T(1)}, \qquad \langle n \rangle \sim \left(\frac{Q}{\Lambda}\right)^{1+\mathcal{O}(1/\sqrt{\lambda})}$$8 for SUEP(125) and to as low as $$\langle n \rangle \sim \left(\frac{Q}{\Lambda}\right)^{2\gamma_T(1)}, \qquad \langle n \rangle \sim \left(\frac{Q}{\Lambda}\right)^{1+\mathcal{O}(1/\sqrt{\lambda})}$$9 for SUEP(1000). Inference on an Intel Core i5-9600KF CPU takes about $\times 100$0 ms, below the CMS HLT latency scale of $\times 100$1 ms, which makes the approach compatible with real-time deployment (Chhibra et al., 2023).

4. Dedicated collider searches

The first dedicated experimental SUEP search was performed by CMS in Run 2 data at $\times 100$2 TeV with integrated luminosity $\times 100$3. That analysis targeted gluon-fusion production of a scalar mediator and exploited boosted topologies selected by high-threshold hadronic triggers. Tracks from the primary vertex with $\times 100$4 GeV and $\times 100$5 were clustered into anti-$\times 100$6 wide jets with $\times 100$7; the jet with larger track multiplicity was taken as the SUEP candidate, and the signal region required $\times 100$8 and $\times 100$9. Background from QCD multijet production was estimated with an extended ABCD method. No significant excess was observed, and CMS set $\eta$0 confidence level limits on gluon-fusion scalar-mediator production with SUEP-like decays (Collaboration, 2024).

CMS later reported the first search for SUEP produced in association with a $\eta$1 or $\eta$2 boson, again at $\eta$3 TeV with the full $\eta$4 Run 2 dataset. Here the trigger handle is leptonic $\eta$5 or $\eta$6 decay, and the SUEP candidate is reconstructed from charged PF candidates from the primary vertex with $\eta$7 GeV and $\eta$8, clustered with anti-$\eta$9 and $\phi$0. The $\phi$1 channel explicitly uses rest-frame sphericity, with a signal region requiring $\phi$2 and a signal-enriched region defined by $\phi$3 and $\phi$4. Backgrounds are estimated entirely from data using an extended ABCD method. No significant deviation from the background-only prediction is found, and the search improves previous CMS gluon-fusion SUEP limits by up to two orders of magnitude in production-rate sensitivity (Collaboration, 7 Apr 2026).

ATLAS has also performed a Run 2 SUEP search, targeting final states that contain muons. Using $\phi$5 of $\phi$6 TeV proton-proton data collected in 2015–2018, the analysis selects events with multi-muon triggers, low average muon $\phi$7, promptness requirements, and at least five muons. The main discriminants are muon-system sphericity $\phi$8, computed in the reconstructed muon-system rest frame, and a pile-up-corrected charged-track multiplicity. The dominant background is QCD multijet production, modeled with a likelihood-based ABCD method in the $\phi$9 plane. No significant excess is observed; the best observed $\phi$0 CL upper limits on $\phi$1 reach approximately $\phi$2 fb for $\phi$3 GeV, $\phi$4 fb for $\phi$5 GeV, and $\phi$6 fb for $\phi$7 GeV. If the $\phi$8 GeV mediator is identified with the Standard Model Higgs boson, this corresponds to an upper limit on $\phi$9 of around $\eta$0 (Collaboration, 19 May 2026).

5. Analysis paradigms and machine-learning formulations

SUEP has become a testing ground for several search paradigms because the signal is defined primarily by morphology. One influential HL-LHC study of prompt hadronic SUEP in exotic Higgs decays compared cut-and-count methods, supervised machine learning, and unsupervised anomaly detection. The baseline preselection used

$\eta$1

where $\eta$2 is ring isotropy and $\eta$3 is the mean pairwise track separation. The supervised approach used a dynamic graph convolutional neural network acting on a modified distance-matrix representation

$\eta$4

while the unsupervised approach used a fully connected autoencoder trained only on background. The study found that the HL-LHC can probe exotic Higgs branching ratios to SUEP at the percent level even in the prompt, purely hadronic scenario, and emphasized the practical robustness of unsupervised methods when signal simulation is uncertain (Barron et al., 2021).

The methodological scope has broadened beyond inclusive SUEP. “Quirk SUEP” considers a hybrid topology in which a hard dijet resonance is accompanied by many soft, nearly isotropic tracks from quirk de-excitation. The analysis uses four soft-activity observables—track multiplicity, polar-angle centrality $\eta$5, transverse sphericity, and average track-pair separation $\eta$6—and compares three strategies: a simple cut on track multiplicity, a supervised neural classifier, and weakly supervised anomaly detection with CATHODE. For $\eta$7 at $\eta$8 TeV, the inclusive resonance search alone excludes none of the benchmark parameter space studied, whereas all track-assisted strategies improve sensitivity substantially; the supervised classifier performs best, the tight track-multiplicity cut is close behind, and CATHODE is competitive when multiplicity dominates the anomaly (Curtin et al., 12 Jun 2025).

A plausible implication is that SUEP methodology is less a single search recipe than a family of morphology-based analyses. Across the literature, the recurring ingredients are low-$\eta$9 track reconstruction, large-radius clustering or explicit pairwise geometry, event-shape observables computed in an approximately relevant rest frame, and either data-driven control regions or unsupervised learning to avoid excessive dependence on a precise signal model.

6. Variants, limitations, and broader significance

Although SUEP was developed as a collider concept, the underlying hidden-sector dynamics have been exported to other contexts. A recent dark-matter study considers annihilation into a confining dark sector that produces SUEP showers of many soft dark mesons $$\frac{dN}{d^{3}\mathbf{p}} \propto \exp\!\left(-\frac{\sqrt{\mathbf{p}^{2}+m_D^2}}{T_D}\right),$$00. The key point is that prompt $$\frac{dN}{d^{3}\mathbf{p}} \propto \exp\!\left(-\frac{\sqrt{\mathbf{p}^{2}+m_D^2}}{T_D}\right),$$01 decays to SM quarks within a hadronization length can greatly enhance antinucleus coalescence relative to ordinary QCD-like showers. For benchmark choices such as $$\frac{dN}{d^{3}\mathbf{p}} \propto \exp\!\left(-\frac{\sqrt{\mathbf{p}^{2}+m_D^2}}{T_D}\right),$$02, $$\frac{dN}{d^{3}\mathbf{p}} \propto \exp\!\left(-\frac{\sqrt{\mathbf{p}^{2}+m_D^2}}{T_D}\right),$$03, and $$\frac{dN}{d^{3}\mathbf{p}} \propto \exp\!\left(-\frac{\sqrt{\mathbf{p}^{2}+m_D^2}}{T_D}\right),$$04, the paper finds source-level antideuteron and antihelium yields far above standard WIMP expectations and predicts potentially observable event counts at AMS-02 and GAPS (Mauro et al., 16 Feb 2026).

The experimental meaning of SUEP is therefore broader than a single benchmark decay chain, but present limits remain analysis-specific. Collider searches differ in production mode—gluon fusion, $$\frac{dN}{d^{3}\mathbf{p}} \propto \exp\!\left(-\frac{\sqrt{\mathbf{p}^{2}+m_D^2}}{T_D}\right),$$05 associated production, or resonance-assisted topologies—in visible final state—fully hadronic, track-dominated, or muon-containing—and in trigger handle. They also differ in reconstruction frame and threshold choices: for example, SUEP sensitivity in track triggers depends critically on whether prompt tracks can be reconstructed at $$\frac{dN}{d^{3}\mathbf{p}} \propto \exp\!\left(-\frac{\sqrt{\mathbf{p}^{2}+m_D^2}}{T_D}\right),$$06 GeV rather than at $$\frac{dN}{d^{3}\mathbf{p}} \propto \exp\!\left(-\frac{\sqrt{\mathbf{p}^{2}+m_D^2}}{T_D}\right),$$07 GeV (Petrillo et al., 2022). ATLAS explicitly optimizes for prompt muons (Collaboration, 19 May 2026), while the CMS $$\frac{dN}{d^{3}\mathbf{p}} \propto \exp\!\left(-\frac{\sqrt{\mathbf{p}^{2}+m_D^2}}{T_D}\right),$$08 search is most sensitive to low dark-photon mass and low temperature because those parameters produce more particles with lower momenta (Collaboration, 7 Apr 2026).

These differences undercut a common misconception that SUEP is defined by perfect spherical symmetry alone. The consistent core across the literature is instead a hidden shower whose visible final state is unusually high-multiplicity, soft, and non-jet-like. How that structure appears experimentally depends on boosts, detector acceptance, decay composition, and trigger strategy. Within that more precise definition, SUEP has become a standard benchmark for hidden-sector phenomenology, for trigger-design studies, and for anomaly-detection methods aimed at signatures that are anomalous chiefly because they fail to resemble QCD.