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| CMS-PAS-EXO-24-036 | ||
| Search for inelastic dark matter with low-momentum displaced electrons in proton-proton collisions at $ \sqrt{s} = $ 13 TeV | ||
| CMS Collaboration | ||
| 2026-07-15 | ||
| Abstract: A search for inelastic dark matter in events with missing transverse momentum and a nonresonant pair of low-momentum, displaced electrons is presented. The analysis is performed using a sample of proton-proton (pp) collision data collected by the CMS experiment at the CERN LHC corresponding to an integrated luminosity of 138 fb$ ^{-1} $ recorded in 2016--2018 at a center-of-mass energy of 13 TeV. A dedicated algorithm for reconstructing low-$ p_{\mathrm{T}} $ electrons is used to improve the search sensitivity, marking its first application to displaced electrons in CMS. No significant deviation from the standard model expectation is observed, and upper limits at 95% confidence level are set on the product of the inelastic dark matter production cross section $ \sigma(\mathrm{pp} \to A^{'} \to \chi_{1}\chi_{2}) $ and the decay branching fraction $ \mathcal{B}(\chi_{2} \to \chi_{1}\mathrm{e}^{+}\mathrm{e}^{-}) $, where $ A^{'} $ is a dark photon and $ \chi_{1} $ and $ \chi_{2} $ are states in the dark sector with small mass splitting, the lightest of which is the stable dark matter. Stringent constraints are placed on benchmark inelastic dark matter scenarios with mass splitting of 10% and 20% of the dark matter particle over the range from 3 to 100 GeV, providing the first collider constraints on inelastic dark matter in the electron final state. | ||
| Links: CDS record (PDF) ; CADI line (restricted) ; | ||
| Figures | |
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Figure 1:
Feynman diagram for the IDM collider signature, showing the cascade decay of a dark photon A' into a pair of charged leptons and DM particles $ \chi_{1} $ and $ \chi_{2} $. |
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Figure 2:
Fraction of reconstructed IDM signal electrons compared across different electron reconstruction algorithms, as a function of generator-level electron $ p_{\mathrm{T}} $ (left) and $ L_{xy} $ (right), derived from simulated IDM samples with selected signal benchmarks. The different signal benchmarks are labeled by the mass $m_{1}$ of the stable DM state, the proper decay length $ c\tau $ of the heavier state $ \chi_{2} $, and the mass splitting $ \Delta \equiv m_2 - m_1 $ between the two states. |
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Figure 2-a:
Fraction of reconstructed IDM signal electrons compared across different electron reconstruction algorithms, as a function of generator-level electron $ p_{\mathrm{T}} $ (left) and $ L_{xy} $ (right), derived from simulated IDM samples with selected signal benchmarks. The different signal benchmarks are labeled by the mass $m_{1}$ of the stable DM state, the proper decay length $ c\tau $ of the heavier state $ \chi_{2} $, and the mass splitting $ \Delta \equiv m_2 - m_1 $ between the two states. |
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Figure 2-b:
Fraction of reconstructed IDM signal electrons compared across different electron reconstruction algorithms, as a function of generator-level electron $ p_{\mathrm{T}} $ (left) and $ L_{xy} $ (right), derived from simulated IDM samples with selected signal benchmarks. The different signal benchmarks are labeled by the mass $m_{1}$ of the stable DM state, the proper decay length $ c\tau $ of the heavier state $ \chi_{2} $, and the mass splitting $ \Delta \equiv m_2 - m_1 $ between the two states. |
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Figure 3:
Electron transverse momentum resolution compared across different electron reconstruction algorithms, as a function of generator-level electron $ p_{\mathrm{T}} $ (left) and $ L_{xy} $ (right). The values plotted are the averages of results obtained from the full set of IDM samples simulated for this analysis. The resolution shown in the upper panels is quantified by a fit of the relative residual $ (p_{\mathrm{T}}^{\mathrm{reco}}-p_{\mathrm{T}}^{\mathrm{gen}})/p_{\mathrm{T}}^{\mathrm{gen}} $ using a Double Side Crystal Ball (DSCB) function [27,28], which has a width parameter $ \sigma $. The median residual shown in the lower panels demonstrates that the reconstructed $ p_{\mathrm{T}} $ has minimal bias. |
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Figure 3-a:
Electron transverse momentum resolution compared across different electron reconstruction algorithms, as a function of generator-level electron $ p_{\mathrm{T}} $ (left) and $ L_{xy} $ (right). The values plotted are the averages of results obtained from the full set of IDM samples simulated for this analysis. The resolution shown in the upper panels is quantified by a fit of the relative residual $ (p_{\mathrm{T}}^{\mathrm{reco}}-p_{\mathrm{T}}^{\mathrm{gen}})/p_{\mathrm{T}}^{\mathrm{gen}} $ using a Double Side Crystal Ball (DSCB) function [27,28], which has a width parameter $ \sigma $. The median residual shown in the lower panels demonstrates that the reconstructed $ p_{\mathrm{T}} $ has minimal bias. |
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Figure 3-b:
Electron transverse momentum resolution compared across different electron reconstruction algorithms, as a function of generator-level electron $ p_{\mathrm{T}} $ (left) and $ L_{xy} $ (right). The values plotted are the averages of results obtained from the full set of IDM samples simulated for this analysis. The resolution shown in the upper panels is quantified by a fit of the relative residual $ (p_{\mathrm{T}}^{\mathrm{reco}}-p_{\mathrm{T}}^{\mathrm{gen}})/p_{\mathrm{T}}^{\mathrm{gen}} $ using a Double Side Crystal Ball (DSCB) function [27,28], which has a width parameter $ \sigma $. The median residual shown in the lower panels demonstrates that the reconstructed $ p_{\mathrm{T}} $ has minimal bias. |
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Figure 4:
Illustration of the expected signal event topology and definition of $ \theta_\text{coll} $. |
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Figure 5:
Illustration of the ABCD plane in which region A is the SR. |
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Figure 6:
Distribution of the BDT score in data and simulation in the SS validation region $ \mathrm{VR^{SS}} $. |
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Figure 7:
Shown in the left panel are observed data yields in the ABCD regions, with region A corresponding to the signal region. The background prediction is obtained from the post-fit ABCD background estimate. The panel on the right shows the distribution of the BDT score for the observed data and the predicted background. The background template is constructed from data events normalized to the post-fit background prediction. Representative signal benchmarks are overlaid for comparison. |
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Figure 7-a:
Shown in the left panel are observed data yields in the ABCD regions, with region A corresponding to the signal region. The background prediction is obtained from the post-fit ABCD background estimate. The panel on the right shows the distribution of the BDT score for the observed data and the predicted background. The background template is constructed from data events normalized to the post-fit background prediction. Representative signal benchmarks are overlaid for comparison. |
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Figure 7-b:
Shown in the left panel are observed data yields in the ABCD regions, with region A corresponding to the signal region. The background prediction is obtained from the post-fit ABCD background estimate. The panel on the right shows the distribution of the BDT score for the observed data and the predicted background. The background template is constructed from data events normalized to the post-fit background prediction. Representative signal benchmarks are overlaid for comparison. |
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Figure 8:
Expected and observed limits on the product of the cross section $ \sigma(\mathrm{p}\mathrm{p} \to A' \to \chi_{1} \chi_{2} ) $ and the branching ratio, where $ \mathcal{B}( \chi_{2} \to \chi_{1} \mathrm{e}^+\mathrm{e}^-) $ is assumed to be 100%. We plot the limits as a function of $ m_1 $ for IDM signals with 10% (left) and 20% (right) mass splittings and 1mm (top), 10 mm (middle), and 100 mm (bottom) $ \chi_{2} $ mean lifetimes. The expected theoretical cross section is overlaid. The peaking structure near $ m_1 = $ 30 GeV is due to resonant effects when the A' mass is near that of the SM Z boson. |
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Figure 8-a:
Expected and observed limits on the product of the cross section $ \sigma(\mathrm{p}\mathrm{p} \to A' \to \chi_{1} \chi_{2} ) $ and the branching ratio, where $ \mathcal{B}( \chi_{2} \to \chi_{1} \mathrm{e}^+\mathrm{e}^-) $ is assumed to be 100%. We plot the limits as a function of $ m_1 $ for IDM signals with 10% (left) and 20% (right) mass splittings and 1mm (top), 10 mm (middle), and 100 mm (bottom) $ \chi_{2} $ mean lifetimes. The expected theoretical cross section is overlaid. The peaking structure near $ m_1 = $ 30 GeV is due to resonant effects when the A' mass is near that of the SM Z boson. |
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Figure 8-b:
Expected and observed limits on the product of the cross section $ \sigma(\mathrm{p}\mathrm{p} \to A' \to \chi_{1} \chi_{2} ) $ and the branching ratio, where $ \mathcal{B}( \chi_{2} \to \chi_{1} \mathrm{e}^+\mathrm{e}^-) $ is assumed to be 100%. We plot the limits as a function of $ m_1 $ for IDM signals with 10% (left) and 20% (right) mass splittings and 1mm (top), 10 mm (middle), and 100 mm (bottom) $ \chi_{2} $ mean lifetimes. The expected theoretical cross section is overlaid. The peaking structure near $ m_1 = $ 30 GeV is due to resonant effects when the A' mass is near that of the SM Z boson. |
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Figure 8-c:
Expected and observed limits on the product of the cross section $ \sigma(\mathrm{p}\mathrm{p} \to A' \to \chi_{1} \chi_{2} ) $ and the branching ratio, where $ \mathcal{B}( \chi_{2} \to \chi_{1} \mathrm{e}^+\mathrm{e}^-) $ is assumed to be 100%. We plot the limits as a function of $ m_1 $ for IDM signals with 10% (left) and 20% (right) mass splittings and 1mm (top), 10 mm (middle), and 100 mm (bottom) $ \chi_{2} $ mean lifetimes. The expected theoretical cross section is overlaid. The peaking structure near $ m_1 = $ 30 GeV is due to resonant effects when the A' mass is near that of the SM Z boson. |
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Figure 8-d:
Expected and observed limits on the product of the cross section $ \sigma(\mathrm{p}\mathrm{p} \to A' \to \chi_{1} \chi_{2} ) $ and the branching ratio, where $ \mathcal{B}( \chi_{2} \to \chi_{1} \mathrm{e}^+\mathrm{e}^-) $ is assumed to be 100%. We plot the limits as a function of $ m_1 $ for IDM signals with 10% (left) and 20% (right) mass splittings and 1mm (top), 10 mm (middle), and 100 mm (bottom) $ \chi_{2} $ mean lifetimes. The expected theoretical cross section is overlaid. The peaking structure near $ m_1 = $ 30 GeV is due to resonant effects when the A' mass is near that of the SM Z boson. |
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Figure 8-e:
Expected and observed limits on the product of the cross section $ \sigma(\mathrm{p}\mathrm{p} \to A' \to \chi_{1} \chi_{2} ) $ and the branching ratio, where $ \mathcal{B}( \chi_{2} \to \chi_{1} \mathrm{e}^+\mathrm{e}^-) $ is assumed to be 100%. We plot the limits as a function of $ m_1 $ for IDM signals with 10% (left) and 20% (right) mass splittings and 1mm (top), 10 mm (middle), and 100 mm (bottom) $ \chi_{2} $ mean lifetimes. The expected theoretical cross section is overlaid. The peaking structure near $ m_1 = $ 30 GeV is due to resonant effects when the A' mass is near that of the SM Z boson. |
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Figure 8-f:
Expected and observed limits on the product of the cross section $ \sigma(\mathrm{p}\mathrm{p} \to A' \to \chi_{1} \chi_{2} ) $ and the branching ratio, where $ \mathcal{B}( \chi_{2} \to \chi_{1} \mathrm{e}^+\mathrm{e}^-) $ is assumed to be 100%. We plot the limits as a function of $ m_1 $ for IDM signals with 10% (left) and 20% (right) mass splittings and 1mm (top), 10 mm (middle), and 100 mm (bottom) $ \chi_{2} $ mean lifetimes. The expected theoretical cross section is overlaid. The peaking structure near $ m_1 = $ 30 GeV is due to resonant effects when the A' mass is near that of the SM Z boson. |
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Figure 9:
Observed two-dimensional exclusion contours in the $ ( m_{1} ,y) $ plane for the 10% (left) and 20% (right) mass splitting scenarios, where $ y \equiv \epsilon^2 \alpha_D ( m_{1} /m_{A'})^4 $. The color fill denotes the upper limit on the product of the production cross section and branching fraction, with $ \mathcal{B}( \chi_{2} \to \chi_{1} \mathrm{e}^+\mathrm{e}^-) $ assumed to be 100%. The exclusion contours trace the signal strength $ \mu = $ 1 boundary, excluding the region of parameter space above them. The increased sensitivity near $ m_{1} = $ 30 GeV is due to resonant effects when the A' mass is near that of the SM Z boson. |
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Figure 9-a:
Observed two-dimensional exclusion contours in the $ ( m_{1} ,y) $ plane for the 10% (left) and 20% (right) mass splitting scenarios, where $ y \equiv \epsilon^2 \alpha_D ( m_{1} /m_{A'})^4 $. The color fill denotes the upper limit on the product of the production cross section and branching fraction, with $ \mathcal{B}( \chi_{2} \to \chi_{1} \mathrm{e}^+\mathrm{e}^-) $ assumed to be 100%. The exclusion contours trace the signal strength $ \mu = $ 1 boundary, excluding the region of parameter space above them. The increased sensitivity near $ m_{1} = $ 30 GeV is due to resonant effects when the A' mass is near that of the SM Z boson. |
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Figure 9-b:
Observed two-dimensional exclusion contours in the $ ( m_{1} ,y) $ plane for the 10% (left) and 20% (right) mass splitting scenarios, where $ y \equiv \epsilon^2 \alpha_D ( m_{1} /m_{A'})^4 $. The color fill denotes the upper limit on the product of the production cross section and branching fraction, with $ \mathcal{B}( \chi_{2} \to \chi_{1} \mathrm{e}^+\mathrm{e}^-) $ assumed to be 100%. The exclusion contours trace the signal strength $ \mu = $ 1 boundary, excluding the region of parameter space above them. The increased sensitivity near $ m_{1} = $ 30 GeV is due to resonant effects when the A' mass is near that of the SM Z boson. |
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Figure 10:
Leading electron $ p_{\mathrm{T}} $ at generator level, highlighting the $ p_{\mathrm{T}} $ cutoff differences between the previous muon analysis [5] and this electron analysis. |
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Figure 11:
(Left) Electron reconstruction efficiency as a function of $ p_{\mathrm{T}} $ for a fixed $ L_{xy} $ bin. (Right) Electron reconstruction efficiency as a function of $ L_{xy} $ for a fixed $ p_{\mathrm{T}} $ bin. In both panels, the efficiencies are averaged over signal samples with mean proper lifetimes ranging from 1 to 100 mm and dark matter masses between 5 and 100 GeV. The performance of the low-$ p_{\mathrm{T}} $ electron reconstruction is compared with that of the GED electron reconstruction. |
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Figure 11-a:
(Left) Electron reconstruction efficiency as a function of $ p_{\mathrm{T}} $ for a fixed $ L_{xy} $ bin. (Right) Electron reconstruction efficiency as a function of $ L_{xy} $ for a fixed $ p_{\mathrm{T}} $ bin. In both panels, the efficiencies are averaged over signal samples with mean proper lifetimes ranging from 1 to 100 mm and dark matter masses between 5 and 100 GeV. The performance of the low-$ p_{\mathrm{T}} $ electron reconstruction is compared with that of the GED electron reconstruction. |
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Figure 11-b:
(Left) Electron reconstruction efficiency as a function of $ p_{\mathrm{T}} $ for a fixed $ L_{xy} $ bin. (Right) Electron reconstruction efficiency as a function of $ L_{xy} $ for a fixed $ p_{\mathrm{T}} $ bin. In both panels, the efficiencies are averaged over signal samples with mean proper lifetimes ranging from 1 to 100 mm and dark matter masses between 5 and 100 GeV. The performance of the low-$ p_{\mathrm{T}} $ electron reconstruction is compared with that of the GED electron reconstruction. |
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Figure 12:
Two-dimensional distribution of the di-electron invariant mass $ m_{ee} $ and $ L_{xy} $ for background events, before the dedicated conversion rejection cuts are applied with $ m_{ee} > $ 0.1 GeV. |
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Figure 13:
Distribution of $ L_{xy} $ for simulated background events, after the dedicated conversion rejection cuts are applied with $ m_{ee}> $ 0.1 GeV. |
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Figure 14:
Subset of input variables for the BDT model, in both data and simulation, in the phase space with OS electron pair vertices. |
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Figure 14-a:
Subset of input variables for the BDT model, in both data and simulation, in the phase space with OS electron pair vertices. |
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Figure 14-b:
Subset of input variables for the BDT model, in both data and simulation, in the phase space with OS electron pair vertices. |
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Figure 15:
Feature importance ranking of BDT input variables after the training. |
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Figure 16:
BDT output score distribution in signal and background simulation, in the phase space with OS electron pair vertices. |
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Figure 17:
Closure test for ABCD background estimation in OS SR with MC simulation, as well as in SS VR with data and simulation, with varying BDT thresholds. |
| Tables | |
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Table 1:
Background prediction validation tests in $ \mathrm{VR^{SS}} $, the region containing events with a pair of same-sign electrons. Only statistical uncertainties are considered. |
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Table 2:
Background prediction validation tests in $ \mathrm{VR^{OS}} $, defined as the subset of events with opposite-sign electron pairs with ``medium'' BDT score. Only statistical uncertainties are considered. |
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Table 3:
Summary of pre-fit background prediction in SR from the ABCD method. Only statistical uncertainties are considered. |
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Table 4:
Summary of systematic uncertainties, shown as the average variation in the yield of simulated signal events during each data-taking period. Note that the estimated background and observation are derived solely from data and are not subject to systematic uncertainties. Uncertainty sources noted with an * are treated as fully correlated across data-taking periods, while all others are treated as fully uncorrelated. |
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Table 5:
Summary of post-fit background prediction and observed data yield in SR. |
| Summary |
| The first collider search for inelastic dark matter with low-momentum, displaced electrons in the final state has been performed, using proton-proton (pp) collision data collected by the CMS experiment at $ \sqrt{s} = $ 13 TeV corresponding to an integrated luminosity of 138 fb$ ^{-1} $. A dedicated electron reconstruction algorithm, developed for the flavor physics program in CMS, was employed to enhance the sensitivity of the search in the low-momentum and displaced regime. A machine learning algorithm is trained to optimally separate signal and background events, using collimated and displaced electron pair vertex distributions. No significant deviation from the standard model predictions is observed. Upper limits at 95% confidence level are set on the product of the inelastic dark matter production cross section $ \sigma(\mathrm{p}\mathrm{p} \to A' \to $ \chi_{1} $$ \chi_{2} $) $ and the decay branching fraction $ \mathcal{B}($ \chi_{2} $ \to $ \chi_{1} $\mathrm{e}^+\mathrm{e}^-) $, where A' is a dark photon and $ \chi_{1} $ and $ \chi_{2} $ are states in the dark sector with small mass splitting, the lightest of which is the stable dark matter. Stringent constraints are placed on benchmark scenarios with 10% and 20% mass splitting of the dark matter mass range of 3 to 100 GeV, extending the sensitivity of collider searches to inelastic dark matter models. |
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