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| CMS-SUS-23-017 ; CERN-EP-2026-161 | ||
| Search for dark matter produced in association with a low-multiplicity jet in proton-proton collisions at $ \sqrt{s} = $ 13 TeV | ||
| CMS Collaboration | ||
| 30 September 2026 | ||
| Submitted to Physical Review D | ||
| Abstract: A search for dark matter particles is presented using events with large missing transverse momentum and a single energetic jet containing few constituents. The analysis uses proton-proton collision data recorded by the CMS experiment at a center-of-mass energy of 13 TeV. This corresponds to an integrated luminosity of 138 fb$ ^{-1} $, recorded during the 2016--2018 LHC data-taking period. This is the first search at the LHC to employ the low-multiplicity jet signature. Supervised machine learning is used to maximize sensitivity to potential signals in this challenging final state. No excess of events over the standard model background prediction is observed. The results are used to set upper limits on the dark matter production cross section at 95% confidence level (CL) within simplified models featuring vector and axial-vector mediators. For a dark matter particle mass of approximately 150 (550) GeV, mediator masses up to 4250 (3500) GeV are excluded at 95% CL. | ||
| Links: e-print arXiv:2610.00995 [hep-ex] (PDF) ; CDS record ; inSPIRE record ; HepData record ; CADI line (restricted) ; | ||
| Figures | |
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Figure 1:
Representative leading order Feynman diagram of the signal process, where DM is the dark matter candidate, V/A represents the vector or axial-vector mediator, $ g_{\mathrm{q}} $ and $ g_{\mathrm{DM}} $ represents the mediator coupling to the quarks and DM respectively. Due to the low mass of the $ \mathrm{Z}^{'} $ boson ($ {\approx} $ 1 GeV), it primarily decays to a low-multiplicity final state, typically two pions, and is expected to be reconstructed in the detector as a jet with very narrow cone of radiation, called the pencil-jet. |
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Figure 2:
Comparison between observed data and simulated backgrounds in the single electron validation region for the recoil (upper-left), the charged hadron energy fraction of the associated jet (upper-right), the neutral electromagnetic energy fraction of the associated jet (lower-left), and the ratio of pencil-jet $ p_{\mathrm{T}} $ to the associated jet $ p_{\mathrm{T}} $ (lower-right). This region is orthogonal to the signal region, resulting in a negligible expected signal contribution. Total systematic uncertainties are labeled as ``Sys uncertainity" in the legend box. The ratio of data to the pre-fit background prediction is shown in the bottom pads, with the grey band indicating the total systematic uncertainty. |
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Figure 2-a:
Comparison between observed data and simulated backgrounds in the single electron validation region for the recoil (upper-left), the charged hadron energy fraction of the associated jet (upper-right), the neutral electromagnetic energy fraction of the associated jet (lower-left), and the ratio of pencil-jet $ p_{\mathrm{T}} $ to the associated jet $ p_{\mathrm{T}} $ (lower-right). This region is orthogonal to the signal region, resulting in a negligible expected signal contribution. Total systematic uncertainties are labeled as ``Sys uncertainity" in the legend box. The ratio of data to the pre-fit background prediction is shown in the bottom pads, with the grey band indicating the total systematic uncertainty. |
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Figure 2-b:
Comparison between observed data and simulated backgrounds in the single electron validation region for the recoil (upper-left), the charged hadron energy fraction of the associated jet (upper-right), the neutral electromagnetic energy fraction of the associated jet (lower-left), and the ratio of pencil-jet $ p_{\mathrm{T}} $ to the associated jet $ p_{\mathrm{T}} $ (lower-right). This region is orthogonal to the signal region, resulting in a negligible expected signal contribution. Total systematic uncertainties are labeled as ``Sys uncertainity" in the legend box. The ratio of data to the pre-fit background prediction is shown in the bottom pads, with the grey band indicating the total systematic uncertainty. |
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Figure 2-c:
Comparison between observed data and simulated backgrounds in the single electron validation region for the recoil (upper-left), the charged hadron energy fraction of the associated jet (upper-right), the neutral electromagnetic energy fraction of the associated jet (lower-left), and the ratio of pencil-jet $ p_{\mathrm{T}} $ to the associated jet $ p_{\mathrm{T}} $ (lower-right). This region is orthogonal to the signal region, resulting in a negligible expected signal contribution. Total systematic uncertainties are labeled as ``Sys uncertainity" in the legend box. The ratio of data to the pre-fit background prediction is shown in the bottom pads, with the grey band indicating the total systematic uncertainty. |
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Figure 2-d:
Comparison between observed data and simulated backgrounds in the single electron validation region for the recoil (upper-left), the charged hadron energy fraction of the associated jet (upper-right), the neutral electromagnetic energy fraction of the associated jet (lower-left), and the ratio of pencil-jet $ p_{\mathrm{T}} $ to the associated jet $ p_{\mathrm{T}} $ (lower-right). This region is orthogonal to the signal region, resulting in a negligible expected signal contribution. Total systematic uncertainties are labeled as ``Sys uncertainity" in the legend box. The ratio of data to the pre-fit background prediction is shown in the bottom pads, with the grey band indicating the total systematic uncertainty. |
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Figure 3:
Comparison between observed data and simulated backgrounds in the signal region for the recoil (upper-left), the charged hadron energy fraction of the associated jet (upper-right), the neutral electromagnetic energy fraction of the associated jet (lower-left), and the ratio of pencil-jet $ p_{\mathrm{T}} $ to the associated jet $ p_{\mathrm{T}} $ (lower-right). Total systematic uncertainties are labeled as ``Sys uncertainity" in the legend box. The ratio of data to the pre-fit background prediction is shown in the bottom pads, with the grey band indicating the total systematic uncertainty. |
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Figure 3-a:
Comparison between observed data and simulated backgrounds in the signal region for the recoil (upper-left), the charged hadron energy fraction of the associated jet (upper-right), the neutral electromagnetic energy fraction of the associated jet (lower-left), and the ratio of pencil-jet $ p_{\mathrm{T}} $ to the associated jet $ p_{\mathrm{T}} $ (lower-right). Total systematic uncertainties are labeled as ``Sys uncertainity" in the legend box. The ratio of data to the pre-fit background prediction is shown in the bottom pads, with the grey band indicating the total systematic uncertainty. |
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Figure 3-b:
Comparison between observed data and simulated backgrounds in the signal region for the recoil (upper-left), the charged hadron energy fraction of the associated jet (upper-right), the neutral electromagnetic energy fraction of the associated jet (lower-left), and the ratio of pencil-jet $ p_{\mathrm{T}} $ to the associated jet $ p_{\mathrm{T}} $ (lower-right). Total systematic uncertainties are labeled as ``Sys uncertainity" in the legend box. The ratio of data to the pre-fit background prediction is shown in the bottom pads, with the grey band indicating the total systematic uncertainty. |
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Figure 3-c:
Comparison between observed data and simulated backgrounds in the signal region for the recoil (upper-left), the charged hadron energy fraction of the associated jet (upper-right), the neutral electromagnetic energy fraction of the associated jet (lower-left), and the ratio of pencil-jet $ p_{\mathrm{T}} $ to the associated jet $ p_{\mathrm{T}} $ (lower-right). Total systematic uncertainties are labeled as ``Sys uncertainity" in the legend box. The ratio of data to the pre-fit background prediction is shown in the bottom pads, with the grey band indicating the total systematic uncertainty. |
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Figure 3-d:
Comparison between observed data and simulated backgrounds in the signal region for the recoil (upper-left), the charged hadron energy fraction of the associated jet (upper-right), the neutral electromagnetic energy fraction of the associated jet (lower-left), and the ratio of pencil-jet $ p_{\mathrm{T}} $ to the associated jet $ p_{\mathrm{T}} $ (lower-right). Total systematic uncertainties are labeled as ``Sys uncertainity" in the legend box. The ratio of data to the pre-fit background prediction is shown in the bottom pads, with the grey band indicating the total systematic uncertainty. |
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Figure 4:
Percentage of events in the validation regions: single electron (upper-left), single muon (upper-right), double electron (lower-left), and double muon (lower-right), with low and high ML scores. The lighter shading represents the fraction of events with low scores (as expected for these background-enriched regions), while the darker shading corresponds to the fraction with high scores ($ > $ 0.71), indicative of signal-like behavior. Colored markers denote simulated samples for 2016 (blue), 2017 (red), and 2018 (green), while data are shown in grey. |
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Figure 5:
Pre-fit distributions of the ML output after full unblinding for the three data-taking periods: 2016 (upper-left), 2017 (upper-right), and 2018 (lower), comparing data with the total expected background. Distributions for two representative signal samples are overlaid, normalized to their expected theoretical cross sections. In the legend, ``Sys uncertainty" denotes total systematic uncertainties. The bottom pad in each plot shows the ratio of data to the predicted background, with the gray band indicating the pre-fit uncertainty. |
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Figure 5-a:
Pre-fit distributions of the ML output after full unblinding for the three data-taking periods: 2016 (upper-left), 2017 (upper-right), and 2018 (lower), comparing data with the total expected background. Distributions for two representative signal samples are overlaid, normalized to their expected theoretical cross sections. In the legend, ``Sys uncertainty" denotes total systematic uncertainties. The bottom pad in each plot shows the ratio of data to the predicted background, with the gray band indicating the pre-fit uncertainty. |
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Figure 5-b:
Pre-fit distributions of the ML output after full unblinding for the three data-taking periods: 2016 (upper-left), 2017 (upper-right), and 2018 (lower), comparing data with the total expected background. Distributions for two representative signal samples are overlaid, normalized to their expected theoretical cross sections. In the legend, ``Sys uncertainty" denotes total systematic uncertainties. The bottom pad in each plot shows the ratio of data to the predicted background, with the gray band indicating the pre-fit uncertainty. |
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Figure 5-c:
Pre-fit distributions of the ML output after full unblinding for the three data-taking periods: 2016 (upper-left), 2017 (upper-right), and 2018 (lower), comparing data with the total expected background. Distributions for two representative signal samples are overlaid, normalized to their expected theoretical cross sections. In the legend, ``Sys uncertainty" denotes total systematic uncertainties. The bottom pad in each plot shows the ratio of data to the predicted background, with the gray band indicating the pre-fit uncertainty. |
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Figure 6:
Post-fit distributions of the ML output for the three data-taking periods: 2016 (upper-left), 2017 (upper-right), and 2018 (lower), comparing data with the total expected background. Distributions for two representative signal samples are overlaid, normalized to their expected theoretical cross sections. In the legend, ``Sys uncertainty" denotes total systematic uncertainties. The bottom pad in each plot shows the ratio of data to the predicted background, with the gray band indicating the post-fit uncertainty. |
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Figure 6-a:
Post-fit distributions of the ML output for the three data-taking periods: 2016 (upper-left), 2017 (upper-right), and 2018 (lower), comparing data with the total expected background. Distributions for two representative signal samples are overlaid, normalized to their expected theoretical cross sections. In the legend, ``Sys uncertainty" denotes total systematic uncertainties. The bottom pad in each plot shows the ratio of data to the predicted background, with the gray band indicating the post-fit uncertainty. |
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Figure 6-b:
Post-fit distributions of the ML output for the three data-taking periods: 2016 (upper-left), 2017 (upper-right), and 2018 (lower), comparing data with the total expected background. Distributions for two representative signal samples are overlaid, normalized to their expected theoretical cross sections. In the legend, ``Sys uncertainty" denotes total systematic uncertainties. The bottom pad in each plot shows the ratio of data to the predicted background, with the gray band indicating the post-fit uncertainty. |
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Figure 6-c:
Post-fit distributions of the ML output for the three data-taking periods: 2016 (upper-left), 2017 (upper-right), and 2018 (lower), comparing data with the total expected background. Distributions for two representative signal samples are overlaid, normalized to their expected theoretical cross sections. In the legend, ``Sys uncertainty" denotes total systematic uncertainties. The bottom pad in each plot shows the ratio of data to the predicted background, with the gray band indicating the post-fit uncertainty. |
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Figure 7:
The 95% CL upper limits on $ \mu = {\sigma}/{\sigma_{\text{theory}}} $ for the vector mediator with $ m_{\mathrm{Z}^{'}} = $ 1 GeV. The left panel shows the limits as a function of the mediator mass, $ m_{\mathrm{med}} $ for a fixed dark matter mass of $ m_{\mathrm{DM}}= $ 150 GeV, while the right panel shows the limits as a function of the dark matter mass, $ m_{\mathrm{DM}} $ for a fixed mediator mass of $ m_{\mathrm{med}} = $ 4 TeV. A linear interpolation is applied between the available mass points. The inner (green) and outer (yellow) bands correspond to the 1 and 2 standard deviations (s.d.), respectively, of the expected limits under the background-only hypothesis. |
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Figure 7-a:
The 95% CL upper limits on $ \mu = {\sigma}/{\sigma_{\text{theory}}} $ for the vector mediator with $ m_{\mathrm{Z}^{'}} = $ 1 GeV. The left panel shows the limits as a function of the mediator mass, $ m_{\mathrm{med}} $ for a fixed dark matter mass of $ m_{\mathrm{DM}}= $ 150 GeV, while the right panel shows the limits as a function of the dark matter mass, $ m_{\mathrm{DM}} $ for a fixed mediator mass of $ m_{\mathrm{med}} = $ 4 TeV. A linear interpolation is applied between the available mass points. The inner (green) and outer (yellow) bands correspond to the 1 and 2 standard deviations (s.d.), respectively, of the expected limits under the background-only hypothesis. |
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Figure 7-b:
The 95% CL upper limits on $ \mu = {\sigma}/{\sigma_{\text{theory}}} $ for the vector mediator with $ m_{\mathrm{Z}^{'}} = $ 1 GeV. The left panel shows the limits as a function of the mediator mass, $ m_{\mathrm{med}} $ for a fixed dark matter mass of $ m_{\mathrm{DM}}= $ 150 GeV, while the right panel shows the limits as a function of the dark matter mass, $ m_{\mathrm{DM}} $ for a fixed mediator mass of $ m_{\mathrm{med}} = $ 4 TeV. A linear interpolation is applied between the available mass points. The inner (green) and outer (yellow) bands correspond to the 1 and 2 standard deviations (s.d.), respectively, of the expected limits under the background-only hypothesis. |
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Figure 8:
The 95% CL upper limits on $ \mu = {\sigma}/{\sigma_{\text{theory}}} $ for the axial vector mediator with $ m_{\mathrm{Z}^{'}} = $ 1 GeV. The left panel shows the limits as a function of the mediator mass, $ m_{\mathrm{med}} $ for a fixed dark matter mass of $ m_{\mathrm{DM}}= $ 150 GeV, while the right panel shows the limits as a function of the dark matter mass, $ m_{\mathrm{DM}} $ for a fixed mediator mass of $ m_{\mathrm{med}} = $ 4 TeV. A linear interpolation is applied between the available mass points. The inner (green) and outer (yellow) bands correspond to the 1 and 2 standard deviations (s.d.), respectively, of the expected limits under the background-only hypothesis. |
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Figure 8-a:
The 95% CL upper limits on $ \mu = {\sigma}/{\sigma_{\text{theory}}} $ for the axial vector mediator with $ m_{\mathrm{Z}^{'}} = $ 1 GeV. The left panel shows the limits as a function of the mediator mass, $ m_{\mathrm{med}} $ for a fixed dark matter mass of $ m_{\mathrm{DM}}= $ 150 GeV, while the right panel shows the limits as a function of the dark matter mass, $ m_{\mathrm{DM}} $ for a fixed mediator mass of $ m_{\mathrm{med}} = $ 4 TeV. A linear interpolation is applied between the available mass points. The inner (green) and outer (yellow) bands correspond to the 1 and 2 standard deviations (s.d.), respectively, of the expected limits under the background-only hypothesis. |
png pdf |
Figure 8-b:
The 95% CL upper limits on $ \mu = {\sigma}/{\sigma_{\text{theory}}} $ for the axial vector mediator with $ m_{\mathrm{Z}^{'}} = $ 1 GeV. The left panel shows the limits as a function of the mediator mass, $ m_{\mathrm{med}} $ for a fixed dark matter mass of $ m_{\mathrm{DM}}= $ 150 GeV, while the right panel shows the limits as a function of the dark matter mass, $ m_{\mathrm{DM}} $ for a fixed mediator mass of $ m_{\mathrm{med}} = $ 4 TeV. A linear interpolation is applied between the available mass points. The inner (green) and outer (yellow) bands correspond to the 1 and 2 standard deviations (s.d.), respectively, of the expected limits under the background-only hypothesis. |
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Figure 9:
Expected and observed exclusion regions in the $ m_{\mathrm{DM}}-m_{\mathrm{med}} $ plane for the axial vector mediator (left) and vector mediator (right), assuming $ m_{\mathrm{Z}^{'}}= $ 1 GeV. The parameter space in the lower-left region of each panels is excluded at the 95% CL level. The color scale indicates the theoretical cross section of the signal process. |
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Figure 9-a:
Expected and observed exclusion regions in the $ m_{\mathrm{DM}}-m_{\mathrm{med}} $ plane for the axial vector mediator (left) and vector mediator (right), assuming $ m_{\mathrm{Z}^{'}}= $ 1 GeV. The parameter space in the lower-left region of each panels is excluded at the 95% CL level. The color scale indicates the theoretical cross section of the signal process. |
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Figure 9-b:
Expected and observed exclusion regions in the $ m_{\mathrm{DM}}-m_{\mathrm{med}} $ plane for the axial vector mediator (left) and vector mediator (right), assuming $ m_{\mathrm{Z}^{'}}= $ 1 GeV. The parameter space in the lower-left region of each panels is excluded at the 95% CL level. The color scale indicates the theoretical cross section of the signal process. |
| Tables | |
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Table 1:
Simulated datasets used to model the background processes. The table summarizes the expected yields of each background contribution in the signal region for the corresponding data-taking years, as obtained from the background-only fit. Total systematic uncertainties are reported including both upward and downward variations. The production cross sections for each process, along with their references, are also provided. |
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Table 2:
List of the input variables used in the ML model along with brief descriptions of their physical meaning. |
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Table 3:
Major sources of systematic uncertainty. All listed uncertainties affect the shapes of the input variables. The ``Value" column indicates the impact of each uncertainty, expressed as a percentage of the event yield. Most uncertainties are correlated across processes and data-taking eras, except for the pencil-jet scale factors and misidentification rates, which are treated as uncorrelated across decay modes and eras. In addition, misidentification uncertainties are taken to be correlated among non-QCD processes. The labels ``QCD" and ``EW" denote uncertainties associated with higher-order QCD and electroweak effects, respectively. They affect the $ \mathrm{Z}+\text{jets} $ and $ \mathrm{W}+\text{jets} $ processes. |
| Summary |
| A novel search for dark matter (DM) particles is presented using 138 fb$ ^{-1} $ of proton-proton collision data recorded by the CMS detector at a center-of-mass energy of 13 TeV. The analysis targets a distinctive final state characterized by a large transverse momentum imbalance and an energetic low-multiplicity jet. This topology provides a distinctive and potentially more sensitive probe of dark-sector dynamics than traditional mono-jet searches. To enhance sensitivity to the signal, supervised machine learning techniques are employed. No significant deviation from the standard model predictions is observed. Upper limits at 95% confidence level are set on the DM production cross section within the framework of simplified models with vector and axial-vector mediators. Mediator masses up to approximately 4.25 TeV are excluded for a DM mass of 150 GeV, while for a DM mass of 550 GeV, mediator masses up to approximately 3.5 TeV are excluded in both scenarios. These results provide the first constraints on this novel final state and significantly extend the sensitivity of DM searches at the LHC. |
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