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| CMS-PAS-EXO-24-010 | ||
| Search for nonresonant production of strongly coupled dark matter in proton-proton collisions at $ \sqrt{s}= $ 13 TeV | ||
| CMS Collaboration | ||
| 2026-07-30 | ||
| Abstract: A search is presented for strongly coupled dark matter in the form of semivisible jets---containing both visible matter and invisible dark matter---produced in nonresonant processes, using 138 fb$ ^{-1} $ of proton-proton collision data at $ \sqrt{s}= $ 13 TeV collected with the CMS detector at the CERN LHC. The signal model includes a bifundamental scalar, $ \Phi $, that couples simultaneously to standard model quarks and dark sector quarks, the latter forming semivisible jets. The final state therefore includes moderate missing energy aligned with a jet, a signature rejected by most dark matter searches. Two separate strategies are employed to identify semivisible jets: a supervised graph neural network and an unsupervised autoencoder. No significant excess corresponding to the dark sector signal hypotheses is observed. Upper limits at 95% confidence level on signal model parameters are determined for each strategy. The supervised search excludes mediator masses of 0.5--2.4 TeV, depending on the other signal model parameters. For signal models with semivisible jets containing higher fractions of invisible dark matter, the unsupervised search demonstrates increased sensitivity and excludes mediator masses up to 2.2 TeV, whereas the supervised analysis excludes the same models up to mediator masses of 1.7--2.0 TeV. | ||
| Links: CDS record (PDF) ; CADI line (restricted) ; | ||
| Figures | |
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Figure 1:
Representative Feynman diagrams of leading-order production of dark quarks $ \chi $ through a bifundamental mediator $ \Phi $. Left: direct $ t $-channel production. Middle: associated production. Right: pair production. |
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Figure 1-a:
Representative Feynman diagrams of leading-order production of dark quarks $ \chi $ through a bifundamental mediator $ \Phi $. Left: direct $ t $-channel production. Middle: associated production. Right: pair production. |
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Figure 1-b:
Representative Feynman diagrams of leading-order production of dark quarks $ \chi $ through a bifundamental mediator $ \Phi $. Left: direct $ t $-channel production. Middle: associated production. Right: pair production. |
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Figure 1-c:
Representative Feynman diagrams of leading-order production of dark quarks $ \chi $ through a bifundamental mediator $ \Phi $. Left: direct $ t $-channel production. Middle: associated production. Right: pair production. |
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Figure 2:
Normalized distributions of the characteristic variables $ S_{\mathrm{T}} $, $ \Delta\phi_{\text{min}} $, and $ p_{\mathrm{T}}^\text{miss} $ for the simulated SM backgrounds and several signal models. For each variable, the selection on that variable is omitted, but all other preselection criteria are applied. The vertical black dotted line indicates the preselection requirement on the variable, with the arrow indicating the region of the distribution included in the analysis. |
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Figure 2-a:
Normalized distributions of the characteristic variables $ S_{\mathrm{T}} $, $ \Delta\phi_{\text{min}} $, and $ p_{\mathrm{T}}^\text{miss} $ for the simulated SM backgrounds and several signal models. For each variable, the selection on that variable is omitted, but all other preselection criteria are applied. The vertical black dotted line indicates the preselection requirement on the variable, with the arrow indicating the region of the distribution included in the analysis. |
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Figure 2-b:
Normalized distributions of the characteristic variables $ S_{\mathrm{T}} $, $ \Delta\phi_{\text{min}} $, and $ p_{\mathrm{T}}^\text{miss} $ for the simulated SM backgrounds and several signal models. For each variable, the selection on that variable is omitted, but all other preselection criteria are applied. The vertical black dotted line indicates the preselection requirement on the variable, with the arrow indicating the region of the distribution included in the analysis. |
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Figure 2-c:
Normalized distributions of the characteristic variables $ S_{\mathrm{T}} $, $ \Delta\phi_{\text{min}} $, and $ p_{\mathrm{T}}^\text{miss} $ for the simulated SM backgrounds and several signal models. For each variable, the selection on that variable is omitted, but all other preselection criteria are applied. The vertical black dotted line indicates the preselection requirement on the variable, with the arrow indicating the region of the distribution included in the analysis. |
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Figure 3:
The PARTICLENET score distribution for data, background simulation, and a selection of signal models (left), and the performance discriminating between the simulated QCD background and signal models with varying $ m_{\Phi} $ and $ r_{\mathrm{inv}} $ values with $ m_{\mathrm{dark}} = $ 20 GeV, $ \lambda = $ 1 (right). The signal models used for training PARTICLENET are marked with a star. The simulated background score distributions are shown for illustration purposes only; they are not used to predict the SM background in the statistical interpretation. The signal jets are corrected for substructure-related mismodeling using their Lund jet plane density, as described in Section 7. The background simulation has no substructure correction applied. The statistical uncertainty in the background simulation from the limited number of simulated events is included but is generally small. |
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Figure 3-a:
The PARTICLENET score distribution for data, background simulation, and a selection of signal models (left), and the performance discriminating between the simulated QCD background and signal models with varying $ m_{\Phi} $ and $ r_{\mathrm{inv}} $ values with $ m_{\mathrm{dark}} = $ 20 GeV, $ \lambda = $ 1 (right). The signal models used for training PARTICLENET are marked with a star. The simulated background score distributions are shown for illustration purposes only; they are not used to predict the SM background in the statistical interpretation. The signal jets are corrected for substructure-related mismodeling using their Lund jet plane density, as described in Section 7. The background simulation has no substructure correction applied. The statistical uncertainty in the background simulation from the limited number of simulated events is included but is generally small. |
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Figure 3-b:
The PARTICLENET score distribution for data, background simulation, and a selection of signal models (left), and the performance discriminating between the simulated QCD background and signal models with varying $ m_{\Phi} $ and $ r_{\mathrm{inv}} $ values with $ m_{\mathrm{dark}} = $ 20 GeV, $ \lambda = $ 1 (right). The signal models used for training PARTICLENET are marked with a star. The simulated background score distributions are shown for illustration purposes only; they are not used to predict the SM background in the statistical interpretation. The signal jets are corrected for substructure-related mismodeling using their Lund jet plane density, as described in Section 7. The background simulation has no substructure correction applied. The statistical uncertainty in the background simulation from the limited number of simulated events is included but is generally small. |
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Figure 4:
For the WNAE model trained on jets with 200 $ < p_{\mathrm{T}} < $ 300 GeV, the score distribution for data, background simulation, and a selection of signal models (left), and the performance discriminating between the simulated QCD background and signal models with varying $ m_{\Phi} $ and $ r_{\mathrm{inv}} $ values with $ m_{\mathrm{dark}} = $ 20 GeV, $ \lambda = $ 1 (right). The fluctuations of the WNAE AUC at low $ r_{\mathrm{inv}} $ and $ m_{\Phi} $ arise from the limited number of events in this region. The simulated background score distributions are shown for illustration purposes only; they are not used to predict the SM background in the statistical interpretation. The signal jets are corrected for substructure-related mismodeling using their Lund jet plane density, as described in Section 7. The background simulation has no substructure correction applied. The statistical uncertainty in the background simulation from the limited number of simulated events is included but is generally small. |
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Figure 4-a:
For the WNAE model trained on jets with 200 $ < p_{\mathrm{T}} < $ 300 GeV, the score distribution for data, background simulation, and a selection of signal models (left), and the performance discriminating between the simulated QCD background and signal models with varying $ m_{\Phi} $ and $ r_{\mathrm{inv}} $ values with $ m_{\mathrm{dark}} = $ 20 GeV, $ \lambda = $ 1 (right). The fluctuations of the WNAE AUC at low $ r_{\mathrm{inv}} $ and $ m_{\Phi} $ arise from the limited number of events in this region. The simulated background score distributions are shown for illustration purposes only; they are not used to predict the SM background in the statistical interpretation. The signal jets are corrected for substructure-related mismodeling using their Lund jet plane density, as described in Section 7. The background simulation has no substructure correction applied. The statistical uncertainty in the background simulation from the limited number of simulated events is included but is generally small. |
png pdf |
Figure 4-b:
For the WNAE model trained on jets with 200 $ < p_{\mathrm{T}} < $ 300 GeV, the score distribution for data, background simulation, and a selection of signal models (left), and the performance discriminating between the simulated QCD background and signal models with varying $ m_{\Phi} $ and $ r_{\mathrm{inv}} $ values with $ m_{\mathrm{dark}} = $ 20 GeV, $ \lambda = $ 1 (right). The fluctuations of the WNAE AUC at low $ r_{\mathrm{inv}} $ and $ m_{\Phi} $ arise from the limited number of events in this region. The simulated background score distributions are shown for illustration purposes only; they are not used to predict the SM background in the statistical interpretation. The signal jets are corrected for substructure-related mismodeling using their Lund jet plane density, as described in Section 7. The background simulation has no substructure correction applied. The statistical uncertainty in the background simulation from the limited number of simulated events is included but is generally small. |
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Figure 5:
The event classifier output scores for data, background simulation, and a selection of signal models (left) and the event classifier performance evaluated on a range of signal hypotheses with $ m_{\mathrm{dark}}= $ 20 GeV, $ \lambda= $ 1, and varying $ r_{\mathrm{inv}} $ and $ m_{\Phi} $, against the total background (right). The signal models used for training the event classifier are marked with a star. The simulated background score distributions are shown for illustration purposes only; they are not used to predict the SM background in the statistical interpretation. The signal jets are corrected for substructure-related mismodeling using their Lund jet plane density, as described in Section 7. The background simulation has no substructure correction applied. The statistical uncertainty in the background simulation from the limited number of simulated events is included but is generally small. |
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Figure 5-a:
The event classifier output scores for data, background simulation, and a selection of signal models (left) and the event classifier performance evaluated on a range of signal hypotheses with $ m_{\mathrm{dark}}= $ 20 GeV, $ \lambda= $ 1, and varying $ r_{\mathrm{inv}} $ and $ m_{\Phi} $, against the total background (right). The signal models used for training the event classifier are marked with a star. The simulated background score distributions are shown for illustration purposes only; they are not used to predict the SM background in the statistical interpretation. The signal jets are corrected for substructure-related mismodeling using their Lund jet plane density, as described in Section 7. The background simulation has no substructure correction applied. The statistical uncertainty in the background simulation from the limited number of simulated events is included but is generally small. |
png pdf |
Figure 5-b:
The event classifier output scores for data, background simulation, and a selection of signal models (left) and the event classifier performance evaluated on a range of signal hypotheses with $ m_{\mathrm{dark}}= $ 20 GeV, $ \lambda= $ 1, and varying $ r_{\mathrm{inv}} $ and $ m_{\Phi} $, against the total background (right). The signal models used for training the event classifier are marked with a star. The simulated background score distributions are shown for illustration purposes only; they are not used to predict the SM background in the statistical interpretation. The signal jets are corrected for substructure-related mismodeling using their Lund jet plane density, as described in Section 7. The background simulation has no substructure correction applied. The statistical uncertainty in the background simulation from the limited number of simulated events is included but is generally small. |
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Figure 6:
The observed data, the postfit estimated background, and a representative signal model for the PARTICLENET supervised tagger strategy (upper) and for the WNAE unsupervised tagger strategy (lower). The plots display all three years of data taking combined, while the actual fits consider each year independently. |
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Figure 6-a:
The observed data, the postfit estimated background, and a representative signal model for the PARTICLENET supervised tagger strategy (upper) and for the WNAE unsupervised tagger strategy (lower). The plots display all three years of data taking combined, while the actual fits consider each year independently. |
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Figure 6-b:
The observed data, the postfit estimated background, and a representative signal model for the PARTICLENET supervised tagger strategy (upper) and for the WNAE unsupervised tagger strategy (lower). The plots display all three years of data taking combined, while the actual fits consider each year independently. |
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Figure 7:
The exclusion limits as a function of $ m_{\Phi} $ and $ m_{\mathrm{dark}} $ (upper left), $ m_{\Phi} $ and $ r_{\mathrm{inv}} $ (upper right), and $ m_{\Phi} $ and $ \lambda $ (lower), combining all three data-taking years and all $ n_{\text{SVJ}}^{\text{PN}} $ categories, for the PARTICLENET supervised tagger strategy. |
png pdf |
Figure 7-a:
The exclusion limits as a function of $ m_{\Phi} $ and $ m_{\mathrm{dark}} $ (upper left), $ m_{\Phi} $ and $ r_{\mathrm{inv}} $ (upper right), and $ m_{\Phi} $ and $ \lambda $ (lower), combining all three data-taking years and all $ n_{\text{SVJ}}^{\text{PN}} $ categories, for the PARTICLENET supervised tagger strategy. |
png pdf |
Figure 7-b:
The exclusion limits as a function of $ m_{\Phi} $ and $ m_{\mathrm{dark}} $ (upper left), $ m_{\Phi} $ and $ r_{\mathrm{inv}} $ (upper right), and $ m_{\Phi} $ and $ \lambda $ (lower), combining all three data-taking years and all $ n_{\text{SVJ}}^{\text{PN}} $ categories, for the PARTICLENET supervised tagger strategy. |
png pdf |
Figure 7-c:
The exclusion limits as a function of $ m_{\Phi} $ and $ m_{\mathrm{dark}} $ (upper left), $ m_{\Phi} $ and $ r_{\mathrm{inv}} $ (upper right), and $ m_{\Phi} $ and $ \lambda $ (lower), combining all three data-taking years and all $ n_{\text{SVJ}}^{\text{PN}} $ categories, for the PARTICLENET supervised tagger strategy. |
png pdf |
Figure 8:
The exclusion limits as a function of $ m_{\Phi} $ and $ m_{\mathrm{dark}} $ (upper left), $ m_{\Phi} $ and $ r_{\mathrm{inv}} $ (upper right), and $ m_{\Phi} $ and $ \lambda $ (lower), combining all three data-taking years and all $ n_{\text{SVJ}}^{\text{WNAE}} $ categories, for the WNAE unsupervised tagger strategy. |
png pdf |
Figure 8-a:
The exclusion limits as a function of $ m_{\Phi} $ and $ m_{\mathrm{dark}} $ (upper left), $ m_{\Phi} $ and $ r_{\mathrm{inv}} $ (upper right), and $ m_{\Phi} $ and $ \lambda $ (lower), combining all three data-taking years and all $ n_{\text{SVJ}}^{\text{WNAE}} $ categories, for the WNAE unsupervised tagger strategy. |
png pdf |
Figure 8-b:
The exclusion limits as a function of $ m_{\Phi} $ and $ m_{\mathrm{dark}} $ (upper left), $ m_{\Phi} $ and $ r_{\mathrm{inv}} $ (upper right), and $ m_{\Phi} $ and $ \lambda $ (lower), combining all three data-taking years and all $ n_{\text{SVJ}}^{\text{WNAE}} $ categories, for the WNAE unsupervised tagger strategy. |
png pdf |
Figure 8-c:
The exclusion limits as a function of $ m_{\Phi} $ and $ m_{\mathrm{dark}} $ (upper left), $ m_{\Phi} $ and $ r_{\mathrm{inv}} $ (upper right), and $ m_{\Phi} $ and $ \lambda $ (lower), combining all three data-taking years and all $ n_{\text{SVJ}}^{\text{WNAE}} $ categories, for the WNAE unsupervised tagger strategy. |
| Tables | |
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Table 1:
The background fractions in % after applying the preselection criteria in the different $ n_{\text{SVJ}} $ categories for the PARTICLENET and WNAE SVJ taggers. |
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Table 2:
The range of effects on the signal or background yield at the preselection level for each systematic uncertainty. Values smaller than 0.01% are rounded to 0.0%. These values are given for the baseline signal hypothesis with $ m_{\Phi} = $ 2 TeV, $ m_{\mathrm{dark}} = $ 20 GeV, $ r_{\mathrm{inv}} = $ 0.3, and $ \lambda = $ 1. The 10--90% quantile range for all signal models are also provided. |
| Summary |
| This note presents the first CMS search for nonresonant production of strongly coupled dark matter. The search uses data from proton-proton collisions recorded by the CMS detector during the 2016--2018 data-taking period, corresponding to an integrated luminosity of 138 fb$ ^{-1} $ at a center-of-mass energy of 13 TeV. The signal model consists of a strongly-coupled dark sector with several flavors of dark quarks that shower and hadronize to form stable and unstable bound states called dark hadrons. The stable dark hadrons are dark matter candidates, while the unstable dark hadrons decay promptly to standard model (SM) quarks, showering and hadronizing in the visible sector to produce semivisible jets (SVJs) composed of both visible and invisible particles. This note focuses on nonresonant production via a massive scalar bifundamental mediator $ \Phi $ with a Yukawa-like coupling between the dark and the SM sectors. The search probes variations of the mediator mass $ m_{\Phi} $, the dark hadron mass $ m_{\mathrm{dark}} $, the fraction of stable, invisible dark hadrons $ r_{\mathrm{inv}} $, and the bifundamental Yukawa coupling $ \lambda $. Two complementary strategies are employed to identify SVJs, yielding two sets of results. The first uses a supervised tagger, PARTICLENET, which is model-dependent and utilizes jet constituents to identify SVJs. The second uses an unsupervised tagger, the Wasserstein normalized autoencoder, to learn the substructure of SM jets in order to identify SVJs as anomalous. The response of these taggers is sensitive to potential mismodeling of the jet substructure in the signal simulation, which is corrected using a procedure designed for jets with high subjet multiplicity. This procedure compares the Lund jet plane of the signal subjets, each of which corresponds to one SM quark, to that of subjets from the hadronic decay of a W boson in observed data. For both the supervised and unsupervised tagger strategies, the SM background is estimated from data using a deep neural network discriminator that is trained on event-level kinematic features to be decorrelated from the $ p_{\mathrm{T}}^\text{miss} $ in order to partition events into four regions, separating signal from background. The supervised tagger strategy places 95% confidence level (CL) exclusion limits on the production cross sections for different signal models, which can be interpreted to exclude ranges of signal model parameters. These exclusions include 0.5 $ \leq m_{\Phi} \leq $ 2.4 TeV, depending on the other signal model parameters. All considered values of $ m_{\mathrm{dark}} $ are excluded for mediator masses below 1.7 TeV, depending on other signal parameters. For mediator masses less than 1.5 TeV, all variations of $ \lambda $ are excluded; for the full range of mediator masses considered, $ \lambda > $ 2 is excluded. Similarly, the unsupervised tagger strategy excludes 0.5 $ \leq m_{\Phi} \leq $ 2.0 TeV, depending on the other signal model parameters. Depending on other signal model parameters, the unsupervised tagger strategy excludes all considered $ m_{\mathrm{dark}} $ masses for mediator masses up to 1.6 TeV. For the full range of mediator masses, $ \lambda > $ 3.0 is excluded. These results complement existing searches for composite dark matter originating from strongly coupled dark sectors. A set of new signal hypotheses are are excluded by placing limits on the production cross section of the massive scalar bifundamental mediator $ \Phi $. The use of machine learning to exploit both jet- and event-level information increases the sensitivity of the search and enables the exclusion of a wide range of models in the targeted parameter space. |
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