Search for soft unclustered energy patterns produced in association with a W or Z boson in proton-proton collisions at $\sqrt{s}$ = 13 TeV

Abstract: A search for a Higgs boson produced in association with a W or Z boson and decaying via a soft unclustered energy pattern (SUEP) is presented. The analysis is based on proton-proton collision data corresponding to an integrated luminosity of 138 fb$^{-1}$ collected between 2016 and 2018 at the LHC. Final states with a leptonic W or Z boson decay associated with a high multiplicity of low-momentum charged particles are explored for the first time. The results show no significant excess over the standard model background expectation. Limits are set on the production cross section of a Higgs boson that decays to a SUEP, for a range of parameters of the SUEP model. Material is provided to facilitate further interpretation of the results.

• The paper presents a search for SUEP production in association with W/Z bosons using 13 TeV proton-proton collision data from the CMS detector.
• The paper employs advanced lepton triggering and a data-driven extended ABCD method to isolate low-pT SUEP signals from significant background noise.
• The paper sets stringent upper limits on the cross section for hidden-valley models, significantly improving constraints compared to previous gluon-fusion strategies.

Search for Soft Unclustered Energy Patterns Produced in Association with a W or Z Boson in Proton-Proton Collisions at $\sqrt{s} = 13$ TeV

Introduction and Physics Motivation

This study presents a search for soft unclustered energy patterns (SUEP) produced in association with a W or Z boson in proton-proton collisions at $\sqrt{s} = 13$ TeV, employing the CMS detector. SUEP signatures, predicted in hidden-valley (HV) scenarios with strong dark-QCD-like dynamics, manifest as high-multiplicity, low-momentum, isotropically distributed final states. Such signals represent compelling targets for beyond-the-Standard-Model (BSM) physics, particularly addressing elusive new sectors connected via a Higgs portal.

The analysis is differentiated from prior SUEP searches by exploiting associated production modes ($VH$) with leptonic decays of the vector boson, as opposed to the previously-studied gluon-fusion channel. This strategy enables more efficient trigger strategies while reducing the overwhelming QCD multijet background. Triggering on leptons from on-shell W or Z decays sharply increases the signal sensitivity, especially for SUEP models with low dark-meson mass and Boltzmann temperature, which enhance the typical multiplicity and spherical topology of the event.

Figure 1: Schematic diagram of the 125 GeV Higgs boson decaying to a SUEP shower, produced in association with a leptonically decaying vector boson.

Experimental Methodology and Data Analysis

Detector Overview and Reconstruction Algorithms

The CMS detector provides efficient reconstruction of electrons, muons, and jets with sub-GeV tracking precision and comprehensive calorimetry, essential for discriminating low-momentum SUEP constituents from SM processes. Global particle flow (PF) and advanced isolation, impact parameter, and identification criteria are employed to minimize the background from fake leptons and jets.

Signal and Background Modeling

Signal samples are generated for the $pp \to VH$ production (with $V=W$ or $Z$, $H\to$ SUEP) and various SUEP parameter configurations. Decays proceed via Higgs to a dense dark sector shower of dark mesons, each decaying to pairs of dark photons, themselves visible in the detector only via kinetic mixing. Multiple signal scenarios are considered:

• Dominantly leptonic or hadronic dark photon decay modes,
• Dark meson mass $m_{dark}$ between 1–8 GeV,
• Boltzmann temperature $T_{dark}$ spanning $m_{dark}/4$ to $\sqrt{s} = 13$0.

Backgrounds are modeled via both full simulation and data-driven techniques, with the dominant sources arising from Drell–Yan, $\sqrt{s} = 13$1+jets, $\sqrt{s} = 13$2, and multijet production.

Event Selection and Signal Regions

Two orthogonal channels are defined:

• $\sqrt{s} = 13$3 channel: Exactly one tight lepton (electron or muon) and a SUEP candidate clustered using anti-$\sqrt{s} = 13$4 with $\sqrt{s} = 13$5, alongside missing $\sqrt{s} = 13$6.
• $\sqrt{s} = 13$7 channel: Exactly two opposite-sign, same-flavor leptons and a SUEP candidate, with further requirements on dilepton invariant and $\sqrt{s} = 13$8.

Backgrounds are suppressed with stringent lepton identification, sphericity requirements on the SUEP candidate, and $\sqrt{s} = 13$9-jet vetoes. Control regions with real photons (PR-WH, PR-ZH) and $VH$0-enriched/diluted selections allow validation of background estimates.

Data-Driven Background Estimation

The extended ABCD method is adopted using $VH$1 (the multiplicity of SUEP candidate charged tracks) and another decorrelated variable as axes, dividing the sample into nine subregions. This methodology allows an essentially simulation-independent estimate of the SM background, including systematic evaluation of closure and non-closure effects, as established in real and signal-free control samples.

Figure 2: Distributions of $VH$2 in extended ABCD subregions for validation regions, illustrating agreement between data and background estimation with uncertainties.

Systematic uncertainties arising from lepton selection, jet calibration, tracking, $VH$3-tagging, pileup, initial/final state radiation, and luminosity are included as nuisance parameters in the likelihood fits. Cross-checks confirm that the omission of possible small signal leakage in background-dominated regions negligibly impacts the sensitivity.

Results

No statistically significant excess is observed beyond the SM expectation in either the $VH$4 or $VH$5 channel. The observed $VH$6 distributions are compatible with the post-fit SM backgrounds, and upper limits are set on the cross section times branching fraction to SUEP as a function of model parameters.

Figure 3: Distributions of $VH$7 in the signal regions for the $VH$8 (upper) and $VH$9 (lower) channels, post-fit, along with representative signal hypotheses.

The analysis provides strong bounds, with the most stringent limits for low $pp \to VH$0 and $pp \to VH$1 due to their higher multiplicity of low-$pp \to VH$2 particles. These limits improve upon previous gluon-fusion-based SUEP searches by up to two orders of magnitude for some parameter regimes.

Figure 4: Observed upper limits at 95\% CL on the $pp \to VH$3 for hadronic dark photon decays as a function of $pp \to VH$4 and $pp \to VH$5.

Figure 5: Observed upper limits for models with dominantly leptonic dark photon decays.

Figure 6: Upper limits for scenarios where all dark photons decay hadronically ($pp \to VH$6 hadrons) = 100%).

Model-agnostic, single-bin fits are also provided to facilitate reinterpretation, yielding absolute limits on excess events as a function of minimum observed track multiplicity.

Figure 7: 95\% CL upper limits on the signal yield for varying $pp \to VH$7 in the two channels.

Implications and Outlook

The analysis demonstrates that associated Higgs production channels provide greatly enhanced sensitivity to SUEP final states compared to gluon-fusion production, particularly when leveraging leptonically decaying vector bosons for triggering and background rejection. No evidence for dark Higgs portal scenarios with large hidden sectors is observed in the probed parameter space, but substantial swaths of previously unexcluded territory in HV/SUEP models are now probed at the percent-level branching sensitivity.

The provided detailed statistical models and reinterpretation tools (e.g., via DELPHES+MADANALYSIS) significantly widen accessibility for future theoretical reinterpretations and alternate BSM model testing. The methodology and the model-agnostic approach could set the standard for future exotic, low-$pp \to VH$8, high-multiplicity searches, applicable to next-generation LHC runs and other future hadron collider experiments.

Conclusion

This search provides a comprehensive, state-of-the-art approach to probing SUEP signatures in Higgs-associated production with vector bosons decaying to leptons. No evidence of hidden-sector SUEP production is found, and stringent upper bounds—improved by up to two orders of magnitude compared with previous strategies—are placed on such phenomena. Future work may exploit similar concepts across additional production topologies and with larger datasets, further enhancing the discovery potential for non-QCD-like or high-multiplicity BSM final states.

(2604.05996)