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| CMS-EXO-24-010 ; CERN-EP-2026-260 | ||
| Search for nonresonant production of strongly coupled dark matter in proton-proton collisions at $ \sqrt{s}= $ 13 TeV | ||
| CMS Collaboration | ||
| 23 October 2026 | ||
| Submitted to the Journal of High Energy Physics | ||
| Abstract: A search is presented for semivisible jets produced in nonresonant processes, using proton-proton collision data at $ \sqrt{s}= $ 13 TeV, collected with the CMS detector at the CERN LHC and corresponding to an integrated luminosity of 138 fb$ ^{-1} $. These jets, containing both visible and invisible particles, would indicate the presence of dark matter arising from a strongly coupled hidden sector. The signal model includes a bifundamental scalar that couples simultaneously to standard model quarks and dark-sector quarks, the latter forming semivisible jets. The final state therefore includes missing transverse momentum aligned with a jet, rather than recoiling against standard model particles as typically required by conventional collider dark-matter searches. Two separate machine-learning strategies are employed to identify semivisible jets: a supervised graph neural network and an unsupervised autoencoder. No significant excess corresponding to dark-sector signal hypotheses is observed. Upper limits at 95% confidence level on the signal production cross section are determined for each strategy and interpreted as exclusions in the signal model parameter space. The supervised search excludes mediator masses between 0.5 and 2.4 TeV, depending on the other signal model parameters. For signal models with semivisible jets containing higher fractions of stable dark-matter particles, the unsupervised search demonstrates increased sensitivity with 5 (11)% higher expected (observed) mediator mass exclusions than the supervised search. | ||
| Links: e-print arXiv:2610.33140 [hep-ex] (PDF) ; CDS record ; inSPIRE record ; HepData record ; 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: $ t $-channel production of dark quarks. Middle: associated production of $ \Phi $ with a dark quark. Right: $ \Phi $ 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: $ t $-channel production of dark quarks. Middle: associated production of $ \Phi $ with a dark quark. Right: $ \Phi $ 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: $ t $-channel production of dark quarks. Middle: associated production of $ \Phi $ with a dark quark. Right: $ \Phi $ 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: $ t $-channel production of dark quarks. Middle: associated production of $ \Phi $ with a dark quark. Right: $ \Phi $ pair production. |
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Figure 2:
Unit-normalized distributions of the discriminating 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, all preselection criteria are applied except the selection on that variable. 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:
Unit-normalized distributions of the discriminating 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, all preselection criteria are applied except the selection on that variable. 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:
Unit-normalized distributions of the discriminating 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, all preselection criteria are applied except the selection on that variable. 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:
Unit-normalized distributions of the discriminating 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, all preselection criteria are applied except the selection on that variable. 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 scaled for visibility (left), and the performance discriminating between the simulated QCD background and signal models with varying $ m_{\Phi} $ and $ r_{\text{inv}} $ values with $ m_{\text{dark}} = $ 20 GeV and $ \lambda = $ 1 (right), after applying the preselection criteria. The lower panel shows the ratio between the data and the simulated background. 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 4. The background simulation has no substructure correction applied. The statistical uncertainties in the data points are smaller than the marker size. The statistical uncertainty in the background simulation from the limited number of simulated events is shown, 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 scaled for visibility (left), and the performance discriminating between the simulated QCD background and signal models with varying $ m_{\Phi} $ and $ r_{\text{inv}} $ values with $ m_{\text{dark}} = $ 20 GeV and $ \lambda = $ 1 (right), after applying the preselection criteria. The lower panel shows the ratio between the data and the simulated background. 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 4. The background simulation has no substructure correction applied. The statistical uncertainties in the data points are smaller than the marker size. The statistical uncertainty in the background simulation from the limited number of simulated events is shown, 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 scaled for visibility (left), and the performance discriminating between the simulated QCD background and signal models with varying $ m_{\Phi} $ and $ r_{\text{inv}} $ values with $ m_{\text{dark}} = $ 20 GeV and $ \lambda = $ 1 (right), after applying the preselection criteria. The lower panel shows the ratio between the data and the simulated background. 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 4. The background simulation has no substructure correction applied. The statistical uncertainties in the data points are smaller than the marker size. The statistical uncertainty in the background simulation from the limited number of simulated events is shown, but is generally small. |
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Figure 4:
The WNAE score distribution for data, background simulation, and a selection of signal models scaled for visibility (left), and the performance discriminating between the simulated QCD background and signal models with varying $ m_{\Phi} $ and $ r_{\text{inv}} $ values with $ m_{\text{dark}} = $ 20 GeV, $ \lambda = $ 1 (right), after applying the preselection criteria, for the model trained on jets with 200 $ < p_{\mathrm{T}} < $ 300 GeV. The lower panel shows the ratio between the data and the simulated background. The fluctuations of the WNAE AUC at low $ r_{\text{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 4. The background simulation has no substructure correction applied. The statistical uncertainties in the data points are smaller than the marker size. The statistical uncertainty in the background simulation from the limited number of simulated events is shown, but is generally small. |
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Figure 4-a:
The WNAE score distribution for data, background simulation, and a selection of signal models scaled for visibility (left), and the performance discriminating between the simulated QCD background and signal models with varying $ m_{\Phi} $ and $ r_{\text{inv}} $ values with $ m_{\text{dark}} = $ 20 GeV, $ \lambda = $ 1 (right), after applying the preselection criteria, for the model trained on jets with 200 $ < p_{\mathrm{T}} < $ 300 GeV. The lower panel shows the ratio between the data and the simulated background. The fluctuations of the WNAE AUC at low $ r_{\text{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 4. The background simulation has no substructure correction applied. The statistical uncertainties in the data points are smaller than the marker size. The statistical uncertainty in the background simulation from the limited number of simulated events is shown, but is generally small. |
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Figure 4-b:
The WNAE score distribution for data, background simulation, and a selection of signal models scaled for visibility (left), and the performance discriminating between the simulated QCD background and signal models with varying $ m_{\Phi} $ and $ r_{\text{inv}} $ values with $ m_{\text{dark}} = $ 20 GeV, $ \lambda = $ 1 (right), after applying the preselection criteria, for the model trained on jets with 200 $ < p_{\mathrm{T}} < $ 300 GeV. The lower panel shows the ratio between the data and the simulated background. The fluctuations of the WNAE AUC at low $ r_{\text{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 4. The background simulation has no substructure correction applied. The statistical uncertainties in the data points are smaller than the marker size. The statistical uncertainty in the background simulation from the limited number of simulated events is shown, 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 scaled for visibility (left) and the event classifier performance evaluated on a range of signal hypotheses with $ m_{\text{dark}}= $ 20 GeV, $ \lambda= $ 1, and varying $ r_{\text{inv}} $ and $ m_{\Phi} $, against the total background (right), after applying the preselection criteria. The lower panel shows the ratio between the data and the simulated background. 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 4. The background simulation has no substructure correction applied. The statistical uncertainties in the data points are smaller than the marker size. The statistical uncertainty in the background simulation from the limited number of simulated events is shown, 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 scaled for visibility (left) and the event classifier performance evaluated on a range of signal hypotheses with $ m_{\text{dark}}= $ 20 GeV, $ \lambda= $ 1, and varying $ r_{\text{inv}} $ and $ m_{\Phi} $, against the total background (right), after applying the preselection criteria. The lower panel shows the ratio between the data and the simulated background. 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 4. The background simulation has no substructure correction applied. The statistical uncertainties in the data points are smaller than the marker size. The statistical uncertainty in the background simulation from the limited number of simulated events is shown, but is generally small. |
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Figure 5-b:
The event classifier output scores for data, background simulation, and a selection of signal models scaled for visibility (left) and the event classifier performance evaluated on a range of signal hypotheses with $ m_{\text{dark}}= $ 20 GeV, $ \lambda= $ 1, and varying $ r_{\text{inv}} $ and $ m_{\Phi} $, against the total background (right), after applying the preselection criteria. The lower panel shows the ratio between the data and the simulated background. 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 4. The background simulation has no substructure correction applied. The statistical uncertainties in the data points are smaller than the marker size. The statistical uncertainty in the background simulation from the limited number of simulated events is shown, 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 background uncertainty includes both systematic and statistical components. The lower panels show the ratio of the observed data to the estimated background. 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 background uncertainty includes both systematic and statistical components. The lower panels show the ratio of the observed data to the estimated background. 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 background uncertainty includes both systematic and statistical components. The lower panels show the ratio of the observed data to the estimated background. 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_{\text{dark}} $ (upper left), $ m_{\Phi} $ and $ r_{\text{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. The dotted orange lines around the expected limit show the 68% CL interval. In the upper left plot, the $ m_{\text{dark}}^{\text{max}} $ value is obtained by combining Eqs. \eqrefeq:lambda_mass and \eqrefeq:shower_cond and rounding up to the nearest 10 GeV, with the minimum set to 20 GeV. |
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Figure 7-a:
The exclusion limits as a function of $ m_{\Phi} $ and $ m_{\text{dark}} $ (upper left), $ m_{\Phi} $ and $ r_{\text{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. The dotted orange lines around the expected limit show the 68% CL interval. In the upper left plot, the $ m_{\text{dark}}^{\text{max}} $ value is obtained by combining Eqs. \eqrefeq:lambda_mass and \eqrefeq:shower_cond and rounding up to the nearest 10 GeV, with the minimum set to 20 GeV. |
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Figure 7-b:
The exclusion limits as a function of $ m_{\Phi} $ and $ m_{\text{dark}} $ (upper left), $ m_{\Phi} $ and $ r_{\text{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. The dotted orange lines around the expected limit show the 68% CL interval. In the upper left plot, the $ m_{\text{dark}}^{\text{max}} $ value is obtained by combining Eqs. \eqrefeq:lambda_mass and \eqrefeq:shower_cond and rounding up to the nearest 10 GeV, with the minimum set to 20 GeV. |
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Figure 7-c:
The exclusion limits as a function of $ m_{\Phi} $ and $ m_{\text{dark}} $ (upper left), $ m_{\Phi} $ and $ r_{\text{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. The dotted orange lines around the expected limit show the 68% CL interval. In the upper left plot, the $ m_{\text{dark}}^{\text{max}} $ value is obtained by combining Eqs. \eqrefeq:lambda_mass and \eqrefeq:shower_cond and rounding up to the nearest 10 GeV, with the minimum set to 20 GeV. |
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Figure 8:
The exclusion limits as a function of $ m_{\Phi} $ and $ m_{\text{dark}} $ (upper left), $ m_{\Phi} $ and $ r_{\text{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. The dotted orange lines around the expected limit show the 68% CL interval. In the upper left plot, the $ m_{\text{dark}}^{\text{max}} $ value is obtained by combining Eqs. \eqrefeq:lambda_mass and \eqrefeq:shower_cond and rounding up to the nearest 10 GeV, with the minimum set to 20 GeV. |
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Figure 8-a:
The exclusion limits as a function of $ m_{\Phi} $ and $ m_{\text{dark}} $ (upper left), $ m_{\Phi} $ and $ r_{\text{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. The dotted orange lines around the expected limit show the 68% CL interval. In the upper left plot, the $ m_{\text{dark}}^{\text{max}} $ value is obtained by combining Eqs. \eqrefeq:lambda_mass and \eqrefeq:shower_cond and rounding up to the nearest 10 GeV, with the minimum set to 20 GeV. |
png pdf |
Figure 8-b:
The exclusion limits as a function of $ m_{\Phi} $ and $ m_{\text{dark}} $ (upper left), $ m_{\Phi} $ and $ r_{\text{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. The dotted orange lines around the expected limit show the 68% CL interval. In the upper left plot, the $ m_{\text{dark}}^{\text{max}} $ value is obtained by combining Eqs. \eqrefeq:lambda_mass and \eqrefeq:shower_cond and rounding up to the nearest 10 GeV, with the minimum set to 20 GeV. |
png pdf |
Figure 8-c:
The exclusion limits as a function of $ m_{\Phi} $ and $ m_{\text{dark}} $ (upper left), $ m_{\Phi} $ and $ r_{\text{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. The dotted orange lines around the expected limit show the 68% CL interval. In the upper left plot, the $ m_{\text{dark}}^{\text{max}} $ value is obtained by combining Eqs. \eqrefeq:lambda_mass and \eqrefeq:shower_cond and rounding up to the nearest 10 GeV, with the minimum set to 20 GeV. |
| Tables | |
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Table 1:
The simulated background fractions [%] 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 impacts in % on the signal yield at the preselection level or on the background yield in region A, for each corresponding systematic uncertainty. Values smaller than 0.01% are rounded to 0%. The second column shows the values for the baseline signal hypothesis with $ m_{\Phi} = $ 2 TeV, $ m_{\text{dark}} = $ 20 GeV, $ r_{\text{inv}} = $ 0.3, and $ \lambda = $ 1. The third column shows the 10--90% quantile range across all signal models. |
| Summary |
| The first CMS search for nonresonant production of strongly coupled dark matter has been presented. The search uses data from proton-proton collisions recorded with 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 paper focuses on nonresonant production via a massive bifundamental scalar 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_{\text{dark}} $, the fraction of stable dark hadrons, 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 jets. 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 an ``ABCD'' method in which a deep neural network discriminator is trained on event-level kinematic features to be decorrelated from the missing transverse momentum in order to partition events into four regions, separating signal from background. The unsupervised tagger strategy is particularly suited to searches for strongly coupled dark sectors, as many details of the signal model can subtly change the resulting jets and their substructure. Beyond the signal model parameters varied in this search, additional dark-sector parameters such as the number of dark-quark flavors and the number of dark colors, among others, may impact the visible behavior. The unsupervised tagger is trained independently from any signal model parameter choices and therefore has more consistent sensitivity in order to exclude a broader range of possible variations. The supervised tagger analysis places 95% confidence level 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 $ < m_{\Phi} < $ 2.4 TeV, depending on the other signal model parameters. All considered values of $ m_{\text{dark}} $ are excluded for mediator masses below 1.7 TeV, depending on other signal parameters. For mediator masses less than 1.6 TeV, all considered variations of $ \lambda $ are excluded; for the full range of mediator masses considered, $ \lambda > $ 2 is excluded. Similarly, the unsupervised tagger analysis excludes 0.5 $ < m_{\Phi} < $ 2.1 TeV, depending on other signal model parameters. The unsupervised tagger analysis excludes all considered $ m_{\text{dark}} $ masses for mediator masses up to 1.6 TeV. For the full range of mediator masses considered, $ \lambda > $ 3 is excluded. These results complement existing searches for composite dark matter originating from strongly coupled dark sectors. A set of new signal hypotheses is excluded by placing limits on the inclusive production cross section for signal processes mediated by a massive bifundamental scalar $ \Phi $. The use of machine-learning techniques 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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