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CMS-EXO-23-005 ; CERN-EP-2024-106

Dark sector searches with the CMS experiment

CMS Collaboration

22 May 2024

Submitted to Physics Reports

Abstract: Astrophysical observations provide compelling evidence for gravitationally interacting dark matter in the universe that cannot be explained by the standard model of particle physics. The extraordinary amount of data from the CERN LHC presents a unique opportunity to shed light on the nature of dark matter at unprecedented collision energies. This Report comprehensively reviews the most recent searches with the CMS experiment for particles and interactions belonging to a dark sector and for dark-sector mediators. Models with invisible massive particles are probed by searches for signatures of missing transverse momentum recoiling against visible standard model particles. Searches for mediators are also conducted via fully visible final states. The results of these searches are compared with those obtained from direct-detection experiments. Searches for alternative scenarios predicting more complex dark sectors with multiple new particles and new forces are also presented. Many of these models include long-lived particles, which could manifest themselves with striking unconventional signatures with relatively small amounts of background. Searches for such particles are discussed and their impact on dark-sector scenarios is evaluated. Many results and interpretations have been newly obtained for this Report.

Links: e-print arXiv:2405.13778 [hep-ex] (PDF) ; CDS record ; inSPIRE record ; CADI line (restricted) ;

Figures
png pdf	Figure 1: An outline of the paper organization in terms of theoretical models and observable final states and how the two perspectives are related.
png pdf	Figure 2: Map of the models probed in CMS searches for dark sectors.
png pdf	Figure 3: Example Feynman diagrams in the taxonomy of dark sector models.
png pdf	Figure 4: Representative Feynman diagrams for simplified model processes of DM pair production via different mediators. First row left: $ \mathrm{Z}^{'} $ mediator, with $ g_{\mathrm{q}} $ and $ g_{\text{DM}} $ couplings to the quarks and the DM candidate $ \chi $, respectively, discussed in Section 2.1.1.1. In this diagram, we also show the initial-state radiation that is regularly used as an additional component in the searches. First row right: $ \mathrm{Z}^{'} $ mediator, with $ g_{\mathrm{q}} $ couplings to the quarks, also discussed in Section 2.1.1.1. Second row: dark-photon mediator $ \text{A}^{\prime} $, via mixing with the SM photon, discussed in Section 2.1.1.2. Third row left: generic scalar mediator $ \text{S} $, with Yukawa couplings $ y_\mathrm{q} = m_\mathrm{q} g_\mathrm{q}/v $, and $ y_\textrm{DM} $ and gluon coupling induced primarily via the top quark loop, discussed in Section 2.1.2.1. Third row right: dark Higgs mediator $ \mathrm{H}_{\mathrm{D}} $, produced via mixing $ \theta_{\text{h}} $ with the SM Higgs boson, discussed in Section 2.1.2.2. As discussed in Section 2.1.2.3, the Higgs portal scenario can be seen as a subcase of the dark-Higgs portal. Fourth row left: pseudoscalar and ALP ($ \text{P} $/$ \mathrm{a} $) mediators, either with Yukawa-like coupling $ y_\mathrm{t} $ or effective coupling $ \Lambda^{-1} $, as described in Sections 2.1.2.4 and 2.1.2.5, respectively. Fourth row right: the fermion portal via the bifundamental mediator $ \Phi $, discussed in Section 2.1.4.
png pdf	Figure 4-a: Representative Feynman diagrams for simplified model processes of DM pair production via different mediators. First row left: $ \mathrm{Z}^{'} $ mediator, with $ g_{\mathrm{q}} $ and $ g_{\text{DM}} $ couplings to the quarks and the DM candidate $ \chi $, respectively, discussed in Section 2.1.1.1. In this diagram, we also show the initial-state radiation that is regularly used as an additional component in the searches. First row right: $ \mathrm{Z}^{'} $ mediator, with $ g_{\mathrm{q}} $ couplings to the quarks, also discussed in Section 2.1.1.1. Second row: dark-photon mediator $ \text{A}^{\prime} $, via mixing with the SM photon, discussed in Section 2.1.1.2. Third row left: generic scalar mediator $ \text{S} $, with Yukawa couplings $ y_\mathrm{q} = m_\mathrm{q} g_\mathrm{q}/v $, and $ y_\textrm{DM} $ and gluon coupling induced primarily via the top quark loop, discussed in Section 2.1.2.1. Third row right: dark Higgs mediator $ \mathrm{H}_{\mathrm{D}} $, produced via mixing $ \theta_{\text{h}} $ with the SM Higgs boson, discussed in Section 2.1.2.2. As discussed in Section 2.1.2.3, the Higgs portal scenario can be seen as a subcase of the dark-Higgs portal. Fourth row left: pseudoscalar and ALP ($ \text{P} $/$ \mathrm{a} $) mediators, either with Yukawa-like coupling $ y_\mathrm{t} $ or effective coupling $ \Lambda^{-1} $, as described in Sections 2.1.2.4 and 2.1.2.5, respectively. Fourth row right: the fermion portal via the bifundamental mediator $ \Phi $, discussed in Section 2.1.4.
png pdf	Figure 4-b: Representative Feynman diagrams for simplified model processes of DM pair production via different mediators. First row left: $ \mathrm{Z}^{'} $ mediator, with $ g_{\mathrm{q}} $ and $ g_{\text{DM}} $ couplings to the quarks and the DM candidate $ \chi $, respectively, discussed in Section 2.1.1.1. In this diagram, we also show the initial-state radiation that is regularly used as an additional component in the searches. First row right: $ \mathrm{Z}^{'} $ mediator, with $ g_{\mathrm{q}} $ couplings to the quarks, also discussed in Section 2.1.1.1. Second row: dark-photon mediator $ \text{A}^{\prime} $, via mixing with the SM photon, discussed in Section 2.1.1.2. Third row left: generic scalar mediator $ \text{S} $, with Yukawa couplings $ y_\mathrm{q} = m_\mathrm{q} g_\mathrm{q}/v $, and $ y_\textrm{DM} $ and gluon coupling induced primarily via the top quark loop, discussed in Section 2.1.2.1. Third row right: dark Higgs mediator $ \mathrm{H}_{\mathrm{D}} $, produced via mixing $ \theta_{\text{h}} $ with the SM Higgs boson, discussed in Section 2.1.2.2. As discussed in Section 2.1.2.3, the Higgs portal scenario can be seen as a subcase of the dark-Higgs portal. Fourth row left: pseudoscalar and ALP ($ \text{P} $/$ \mathrm{a} $) mediators, either with Yukawa-like coupling $ y_\mathrm{t} $ or effective coupling $ \Lambda^{-1} $, as described in Sections 2.1.2.4 and 2.1.2.5, respectively. Fourth row right: the fermion portal via the bifundamental mediator $ \Phi $, discussed in Section 2.1.4.
png pdf	Figure 4-c: Representative Feynman diagrams for simplified model processes of DM pair production via different mediators. First row left: $ \mathrm{Z}^{'} $ mediator, with $ g_{\mathrm{q}} $ and $ g_{\text{DM}} $ couplings to the quarks and the DM candidate $ \chi $, respectively, discussed in Section 2.1.1.1. In this diagram, we also show the initial-state radiation that is regularly used as an additional component in the searches. First row right: $ \mathrm{Z}^{'} $ mediator, with $ g_{\mathrm{q}} $ couplings to the quarks, also discussed in Section 2.1.1.1. Second row: dark-photon mediator $ \text{A}^{\prime} $, via mixing with the SM photon, discussed in Section 2.1.1.2. Third row left: generic scalar mediator $ \text{S} $, with Yukawa couplings $ y_\mathrm{q} = m_\mathrm{q} g_\mathrm{q}/v $, and $ y_\textrm{DM} $ and gluon coupling induced primarily via the top quark loop, discussed in Section 2.1.2.1. Third row right: dark Higgs mediator $ \mathrm{H}_{\mathrm{D}} $, produced via mixing $ \theta_{\text{h}} $ with the SM Higgs boson, discussed in Section 2.1.2.2. As discussed in Section 2.1.2.3, the Higgs portal scenario can be seen as a subcase of the dark-Higgs portal. Fourth row left: pseudoscalar and ALP ($ \text{P} $/$ \mathrm{a} $) mediators, either with Yukawa-like coupling $ y_\mathrm{t} $ or effective coupling $ \Lambda^{-1} $, as described in Sections 2.1.2.4 and 2.1.2.5, respectively. Fourth row right: the fermion portal via the bifundamental mediator $ \Phi $, discussed in Section 2.1.4.
png pdf	Figure 4-d: Representative Feynman diagrams for simplified model processes of DM pair production via different mediators. First row left: $ \mathrm{Z}^{'} $ mediator, with $ g_{\mathrm{q}} $ and $ g_{\text{DM}} $ couplings to the quarks and the DM candidate $ \chi $, respectively, discussed in Section 2.1.1.1. In this diagram, we also show the initial-state radiation that is regularly used as an additional component in the searches. First row right: $ \mathrm{Z}^{'} $ mediator, with $ g_{\mathrm{q}} $ couplings to the quarks, also discussed in Section 2.1.1.1. Second row: dark-photon mediator $ \text{A}^{\prime} $, via mixing with the SM photon, discussed in Section 2.1.1.2. Third row left: generic scalar mediator $ \text{S} $, with Yukawa couplings $ y_\mathrm{q} = m_\mathrm{q} g_\mathrm{q}/v $, and $ y_\textrm{DM} $ and gluon coupling induced primarily via the top quark loop, discussed in Section 2.1.2.1. Third row right: dark Higgs mediator $ \mathrm{H}_{\mathrm{D}} $, produced via mixing $ \theta_{\text{h}} $ with the SM Higgs boson, discussed in Section 2.1.2.2. As discussed in Section 2.1.2.3, the Higgs portal scenario can be seen as a subcase of the dark-Higgs portal. Fourth row left: pseudoscalar and ALP ($ \text{P} $/$ \mathrm{a} $) mediators, either with Yukawa-like coupling $ y_\mathrm{t} $ or effective coupling $ \Lambda^{-1} $, as described in Sections 2.1.2.4 and 2.1.2.5, respectively. Fourth row right: the fermion portal via the bifundamental mediator $ \Phi $, discussed in Section 2.1.4.
png pdf	Figure 4-e: Representative Feynman diagrams for simplified model processes of DM pair production via different mediators. First row left: $ \mathrm{Z}^{'} $ mediator, with $ g_{\mathrm{q}} $ and $ g_{\text{DM}} $ couplings to the quarks and the DM candidate $ \chi $, respectively, discussed in Section 2.1.1.1. In this diagram, we also show the initial-state radiation that is regularly used as an additional component in the searches. First row right: $ \mathrm{Z}^{'} $ mediator, with $ g_{\mathrm{q}} $ couplings to the quarks, also discussed in Section 2.1.1.1. Second row: dark-photon mediator $ \text{A}^{\prime} $, via mixing with the SM photon, discussed in Section 2.1.1.2. Third row left: generic scalar mediator $ \text{S} $, with Yukawa couplings $ y_\mathrm{q} = m_\mathrm{q} g_\mathrm{q}/v $, and $ y_\textrm{DM} $ and gluon coupling induced primarily via the top quark loop, discussed in Section 2.1.2.1. Third row right: dark Higgs mediator $ \mathrm{H}_{\mathrm{D}} $, produced via mixing $ \theta_{\text{h}} $ with the SM Higgs boson, discussed in Section 2.1.2.2. As discussed in Section 2.1.2.3, the Higgs portal scenario can be seen as a subcase of the dark-Higgs portal. Fourth row left: pseudoscalar and ALP ($ \text{P} $/$ \mathrm{a} $) mediators, either with Yukawa-like coupling $ y_\mathrm{t} $ or effective coupling $ \Lambda^{-1} $, as described in Sections 2.1.2.4 and 2.1.2.5, respectively. Fourth row right: the fermion portal via the bifundamental mediator $ \Phi $, discussed in Section 2.1.4.
png pdf	Figure 4-f: Representative Feynman diagrams for simplified model processes of DM pair production via different mediators. First row left: $ \mathrm{Z}^{'} $ mediator, with $ g_{\mathrm{q}} $ and $ g_{\text{DM}} $ couplings to the quarks and the DM candidate $ \chi $, respectively, discussed in Section 2.1.1.1. In this diagram, we also show the initial-state radiation that is regularly used as an additional component in the searches. First row right: $ \mathrm{Z}^{'} $ mediator, with $ g_{\mathrm{q}} $ couplings to the quarks, also discussed in Section 2.1.1.1. Second row: dark-photon mediator $ \text{A}^{\prime} $, via mixing with the SM photon, discussed in Section 2.1.1.2. Third row left: generic scalar mediator $ \text{S} $, with Yukawa couplings $ y_\mathrm{q} = m_\mathrm{q} g_\mathrm{q}/v $, and $ y_\textrm{DM} $ and gluon coupling induced primarily via the top quark loop, discussed in Section 2.1.2.1. Third row right: dark Higgs mediator $ \mathrm{H}_{\mathrm{D}} $, produced via mixing $ \theta_{\text{h}} $ with the SM Higgs boson, discussed in Section 2.1.2.2. As discussed in Section 2.1.2.3, the Higgs portal scenario can be seen as a subcase of the dark-Higgs portal. Fourth row left: pseudoscalar and ALP ($ \text{P} $/$ \mathrm{a} $) mediators, either with Yukawa-like coupling $ y_\mathrm{t} $ or effective coupling $ \Lambda^{-1} $, as described in Sections 2.1.2.4 and 2.1.2.5, respectively. Fourth row right: the fermion portal via the bifundamental mediator $ \Phi $, discussed in Section 2.1.4.
png pdf	Figure 4-g: Representative Feynman diagrams for simplified model processes of DM pair production via different mediators. First row left: $ \mathrm{Z}^{'} $ mediator, with $ g_{\mathrm{q}} $ and $ g_{\text{DM}} $ couplings to the quarks and the DM candidate $ \chi $, respectively, discussed in Section 2.1.1.1. In this diagram, we also show the initial-state radiation that is regularly used as an additional component in the searches. First row right: $ \mathrm{Z}^{'} $ mediator, with $ g_{\mathrm{q}} $ couplings to the quarks, also discussed in Section 2.1.1.1. Second row: dark-photon mediator $ \text{A}^{\prime} $, via mixing with the SM photon, discussed in Section 2.1.1.2. Third row left: generic scalar mediator $ \text{S} $, with Yukawa couplings $ y_\mathrm{q} = m_\mathrm{q} g_\mathrm{q}/v $, and $ y_\textrm{DM} $ and gluon coupling induced primarily via the top quark loop, discussed in Section 2.1.2.1. Third row right: dark Higgs mediator $ \mathrm{H}_{\mathrm{D}} $, produced via mixing $ \theta_{\text{h}} $ with the SM Higgs boson, discussed in Section 2.1.2.2. As discussed in Section 2.1.2.3, the Higgs portal scenario can be seen as a subcase of the dark-Higgs portal. Fourth row left: pseudoscalar and ALP ($ \text{P} $/$ \mathrm{a} $) mediators, either with Yukawa-like coupling $ y_\mathrm{t} $ or effective coupling $ \Lambda^{-1} $, as described in Sections 2.1.2.4 and 2.1.2.5, respectively. Fourth row right: the fermion portal via the bifundamental mediator $ \Phi $, discussed in Section 2.1.4.
png pdf	Figure 5: Feynman diagrams of the VBF, $ \mathrm{g}\mathrm{g}\mathrm{H} $, $ \mathrm{t}\overline{\mathrm{t}}\mathrm{H} $, and VH Higgs boson production modes analyzed in the $ \mathrm{H} \to \text{inv} $ searches.
png pdf	Figure 5-a: Feynman diagrams of the VBF, $ \mathrm{g}\mathrm{g}\mathrm{H} $, $ \mathrm{t}\overline{\mathrm{t}}\mathrm{H} $, and VH Higgs boson production modes analyzed in the $ \mathrm{H} \to \text{inv} $ searches.
png pdf	Figure 5-b: Feynman diagrams of the VBF, $ \mathrm{g}\mathrm{g}\mathrm{H} $, $ \mathrm{t}\overline{\mathrm{t}}\mathrm{H} $, and VH Higgs boson production modes analyzed in the $ \mathrm{H} \to \text{inv} $ searches.
png pdf	Figure 5-c: Feynman diagrams of the VBF, $ \mathrm{g}\mathrm{g}\mathrm{H} $, $ \mathrm{t}\overline{\mathrm{t}}\mathrm{H} $, and VH Higgs boson production modes analyzed in the $ \mathrm{H} \to \text{inv} $ searches.
png pdf	Figure 5-d: Feynman diagrams of the VBF, $ \mathrm{g}\mathrm{g}\mathrm{H} $, $ \mathrm{t}\overline{\mathrm{t}}\mathrm{H} $, and VH Higgs boson production modes analyzed in the $ \mathrm{H} \to \text{inv} $ searches.
png pdf	Figure 6: Feynman diagrams for production channels involving the bifundamental mediator $ \Phi $: pair production via gluon-gluon fusion (upper left), pair production via quark-antiquark annihilation (upper right), single production in association with a DM particle $ \chi $ (lower left), and $ t $-channel nonresonant DM production (lower right).
png pdf	Figure 6-a: Feynman diagrams for production channels involving the bifundamental mediator $ \Phi $: pair production via gluon-gluon fusion (upper left), pair production via quark-antiquark annihilation (upper right), single production in association with a DM particle $ \chi $ (lower left), and $ t $-channel nonresonant DM production (lower right).
png pdf	Figure 6-b: Feynman diagrams for production channels involving the bifundamental mediator $ \Phi $: pair production via gluon-gluon fusion (upper left), pair production via quark-antiquark annihilation (upper right), single production in association with a DM particle $ \chi $ (lower left), and $ t $-channel nonresonant DM production (lower right).
png pdf	Figure 6-c: Feynman diagrams for production channels involving the bifundamental mediator $ \Phi $: pair production via gluon-gluon fusion (upper left), pair production via quark-antiquark annihilation (upper right), single production in association with a DM particle $ \chi $ (lower left), and $ t $-channel nonresonant DM production (lower right).
png pdf	Figure 6-d: Feynman diagrams for production channels involving the bifundamental mediator $ \Phi $: pair production via gluon-gluon fusion (upper left), pair production via quark-antiquark annihilation (upper right), single production in association with a DM particle $ \chi $ (lower left), and $ t $-channel nonresonant DM production (lower right).
png pdf	Figure 7: Feynman diagrams for 2HDM+a signatures. Left: a mono-Higgs signature, mediated by the heavy pseudoscalar $ \text{A} $. Center: $ {\mathrm{t}\overline{\mathrm{t}}} $ resonant production, mediated by the heavy scalar H. Similar processes involve $ \mathrm{H}^\pm $ particles, $ \mbox{e.g.} \mathrm{H}^\pm \to \mathrm{t}\mathrm{b} $. Right: exotic decay of the SM-like Higgs boson $ \mathrm{h} $.
png pdf	Figure 7-a: Feynman diagrams for 2HDM+a signatures. Left: a mono-Higgs signature, mediated by the heavy pseudoscalar $ \text{A} $. Center: $ {\mathrm{t}\overline{\mathrm{t}}} $ resonant production, mediated by the heavy scalar H. Similar processes involve $ \mathrm{H}^\pm $ particles, $ \mbox{e.g.} \mathrm{H}^\pm \to \mathrm{t}\mathrm{b} $. Right: exotic decay of the SM-like Higgs boson $ \mathrm{h} $.
png pdf	Figure 7-b: Feynman diagrams for 2HDM+a signatures. Left: a mono-Higgs signature, mediated by the heavy pseudoscalar $ \text{A} $. Center: $ {\mathrm{t}\overline{\mathrm{t}}} $ resonant production, mediated by the heavy scalar H. Similar processes involve $ \mathrm{H}^\pm $ particles, $ \mbox{e.g.} \mathrm{H}^\pm \to \mathrm{t}\mathrm{b} $. Right: exotic decay of the SM-like Higgs boson $ \mathrm{h} $.
png pdf	Figure 7-c: Feynman diagrams for 2HDM+a signatures. Left: a mono-Higgs signature, mediated by the heavy pseudoscalar $ \text{A} $. Center: $ {\mathrm{t}\overline{\mathrm{t}}} $ resonant production, mediated by the heavy scalar H. Similar processes involve $ \mathrm{H}^\pm $ particles, $ \mbox{e.g.} \mathrm{H}^\pm \to \mathrm{t}\mathrm{b} $. Right: exotic decay of the SM-like Higgs boson $ \mathrm{h} $.
png pdf	Figure 8: Feynman diagrams for pair production of top squarks under the stealth SYY (left) and stealth $\mathrm{SHH}$ (right) models. In these models, the signature is a pair of SM top quarks, with additional jets originating from gluons (SYY) or b quarks ($\mathrm{SHH}$).
png pdf	Figure 8-a: Feynman diagrams for pair production of top squarks under the stealth SYY (left) and stealth $\mathrm{SHH}$ (right) models. In these models, the signature is a pair of SM top quarks, with additional jets originating from gluons (SYY) or b quarks ($\mathrm{SHH}$).
png pdf	Figure 8-b: Feynman diagrams for pair production of top squarks under the stealth SYY (left) and stealth $\mathrm{SHH}$ (right) models. In these models, the signature is a pair of SM top quarks, with additional jets originating from gluons (SYY) or b quarks ($\mathrm{SHH}$).
png pdf	Figure 9: Feynman diagram of inelastic dark matter production and decay processes in pp collisions, for fermionic DM states. The heavier DM state $ \chi_2 $ can be long-lived, and decays into $ \chi_1 $ and to a muon pair via an off-shell dark photon $ \text{A}^{\prime} $.
png pdf	Figure 10: A qualitative depiction of the phenomenological behavior of dark QCD models depending on the fraction of invisible particles within a jet $ r_{\text{inv}} $ and the proper decay length of dark hadrons c$ \tau_{\text{dark}} $. The $ r_{\text{inv}} $ parameter is defined in Section 2.2.4.1.
png pdf	Figure 11: Illustrative Feynman diagrams showing example production modes for different hidden valley phenomena: semivisible jets (left), emerging jets (center), and soft unclustered energy patterns (right). Dotted lines indicate invisible particles.
png pdf	Figure 11-a: Illustrative Feynman diagrams showing example production modes for different hidden valley phenomena: semivisible jets (left), emerging jets (center), and soft unclustered energy patterns (right). Dotted lines indicate invisible particles.
png pdf	Figure 11-b: Illustrative Feynman diagrams showing example production modes for different hidden valley phenomena: semivisible jets (left), emerging jets (center), and soft unclustered energy patterns (right). Dotted lines indicate invisible particles.
png pdf	Figure 11-c: Illustrative Feynman diagrams showing example production modes for different hidden valley phenomena: semivisible jets (left), emerging jets (center), and soft unclustered energy patterns (right). Dotted lines indicate invisible particles.
png pdf	Figure 12: The event selection efficiency for requiring HLT thresholds of 120 GeV in both $ p_{\mathrm{T}}^\text{miss} $ and $ H_{\mathrm{T}}^\text{miss} $ as a function of the offline corrected $ p_{\mathrm{T}}^\text{miss} $, which takes into account jet energy scale corrections.
png pdf	Figure 14: Illustration of the appearance of a secondary vertex (SV) from the decay of a long-lived particle resulting in charged-particle tracks that are displaced with respect to the primary interaction vertex (PV), and hence can have large impact parameter (IP) values. In BSM searches, LLPs have very long lifetimes compared to SM particles, leading to large displacements of the secondary vertices. Figure adapted from Ref. [175].
png pdf	Figure 15: The ROC curves illustrating the displaced jet tagger performance for the split SUSY (solid line), GMSB SUSY (dashed line), and RPV SUSY (dot-dashed line) benchmark models, assuming $ c\tau_0 $ values of 1 mm (left) and 1\unitm (right). The thin line with hatched shading indicates the performance obtained with a DNN training using split SUSY samples but without domain adaptation (DA). Figure taken from Ref. [192].
png pdf	Figure 16: Illustration of contributions to the delay of particles that originate from LLP decays. For prompt decays, the path length to reach a particular location on the timing detector ($ l_{\text{prompt}} $) is smaller than the path length for a deposit originating from an LLP decay ($ l_{\mathrm{LLP}} $+$ l_{\mathrm{SM'}} $). In addition, the velocity of the light SM particles ($ \rm{v}_{\text{prompt}} $) will be close to that of light while the velocity of the LLP ($ \rm{v}_{\rm{LLP}} $) can be significantly lower. These factors lead to substantial delays for the decay products of LLPs, which can be exploited to improve sensitivity.
png pdf	Figure 17: Simulated muon reconstruction efficiency of standard global muon (blue squares) and DSA (red circles) track reconstruction algorithms as a function of transverse vertex displacement $ v_{xy} $, for the IDM model discussed in Section 2.2.3. The two dashed vertical gray lines denote the ends of the fiducial tracker and muon detector regions, respectively. Figure taken from Ref. [207].
png pdf	Figure 18: Distribution of the $ I_{\text{h}} $ estimator, computed using \ddinlineE{x} measurements in the silicon strip tracker, versus the track momentum, using the data recorded in 2017 during the LHC Run 2. Expected \ddinlineE{x} losses for pion, kaon, proton, and deuteron particles are shown as black lines. Tracks with $ p_{\mathrm{T}} < $ 0.5 GeV are not included in this plot.
png pdf	Figure 19: A diagram of the ABCD method, shown for illustration on simulated background events in a search for LLPs that decay to displaced leptons. The CRs are regions A, B, and C. There are four SRs, labeled I--IV, in this search. Figure taken from Ref. [243].
png pdf	Figure 20: Comparison of $ p_{\mathrm{T}}^\text{miss} $ between data and the background prediction in the monojet SR after the simultaneous fit for the full Run 2 data set. The upper panel shows the $ p_{\mathrm{T}}^\text{miss} $ distribution, the middle panel shows the ratio of the data to the prediction, and the lower panel shows the ratio of the data minus the prediction, all divided by the uncertainty. The axial vector signal and $ {\mathrm{H} $ (inv) $ } $ signal are shown, the second of which is described in Section 6.1.2. Figure taken from Ref. [81].
png pdf	Figure 21: The $ p_{\mathrm{T}}^\text{miss} $ (left) and $ m_{\mathrm{T}} $ (right) distributions for events in the SR in the 0-jet final state, in the search for new physics in leptonically decaying Z boson events. The uncertainty band includes both statistical and systematic components. Figures adapted from Ref. [86].
png pdf	Figure 21-a: The $ p_{\mathrm{T}}^\text{miss} $ (left) and $ m_{\mathrm{T}} $ (right) distributions for events in the SR in the 0-jet final state, in the search for new physics in leptonically decaying Z boson events. The uncertainty band includes both statistical and systematic components. Figures adapted from Ref. [86].
png pdf	Figure 21-b: The $ p_{\mathrm{T}}^\text{miss} $ (left) and $ m_{\mathrm{T}} $ (right) distributions for events in the SR in the 0-jet final state, in the search for new physics in leptonically decaying Z boson events. The uncertainty band includes both statistical and systematic components. Figures adapted from Ref. [86].
png pdf	Figure 22: Distribution of $ p_{\mathrm{T}}^\text{miss} $ from SM backgrounds and data in the SR after simultaneously fitting the SR and all CRs, in the search for mono-t events. Each bin shows the event yields divided by the width of the bin. The figure corresponds to the tight category of the SR. The stacked histograms show the individual fitted SM background contributions. The blue solid (red dashed) line represents the sum of the SM background contributions normalized to their fitted yields (to the prediction). The lower panel shows the ratio of data to fitted prediction. The gray band on the ratio indicates the one standard deviation uncertainty on the prediction after propagating all the systematic uncertainties and their correlations in the fit. Figure taken from Ref. [263].
png pdf	Figure 23: Observed $ E_{\mathrm{T}}^\gamma $ distribution in a SR compared with the post-fit background expectations for various SM processes, in the search for mono-photon events. The last bin of the distribution includes all events with $ E_{\mathrm{T}}^\gamma > $ 1000 GeV. The expected background distributions are evaluated after performing a combined fit to the data in all the control samples and the SR. The ratios of data with the pre-fit background prediction (red dashed line) and post-fit background prediction (blue solid line) are shown in the lower panel. The bands in the lower panel show the post-fit uncertainty after combining all the systematic uncertainties. The expected signal distribution from a 1 TeV vector mediator decaying into 1 GeV DM particles is overlaid. Figure adapted from Ref. [268].
png pdf	Figure 24: The $ p_{\mathrm{T}}^\text{miss} $ distribution for the expected background and observed events in data in the $ \mathrm{H}\to\mathrm{Z}\mathrm{Z} $ analysis. Two signal benchmarks, corresponding to the $ \mathrm{Z}^{'} $-2HDM (dotted orange line) and baryonic $ \mathrm{Z}^{'} $ (solid black line) model are superimposed. The signal is normalized to the product of cross section and branching fraction, where $ \mathcal{B} $ represents the $ \mathrm{H}\to\mathrm{Z}\mathrm{Z} $ branching fraction. The systematic uncertainties are shown by the hatched band. The ratios of the data and the sum of all the SM backgrounds are shown in the bottom panels. Figure taken from Ref. [269].
png pdf	Figure 25: Normalized distribution of the transverse mass of the trailing lepton plus missing transverse momentum system in the dilepton channel of the dark Higgs+$ p_{\mathrm{T}}^\text{miss} $ search, for a signal with $ m_{\mathrm{H}_{\mathrm{D}}} = $ 160 GeV (denoted as $ m_{\text{S}} $ in the figure), $ m_{\text{DM}} = $ 100 GeV (denoted as $ m_\chi $ in the figure), and $ m_{\mathrm{Z}^{'}} = $ 500 GeV (black), after the event selection criteria are applied. Predictions for the two main backgrounds of the analysis, nonresonant WW and top quark production, are shown as blue and orange solid lines, respectively. The last bin includes the overflow. Figure taken from Ref. [271].
png pdf	Figure 26: Distributions of the dijet pair invariant mass in the SRs of the search for $ \mathrm{H} \to \text{inv} $ produced via vector boson fusion, for the high missing transverse momentum category (left) and for the dijet-based category (right). The signal processes are scaled by the fitted value of $ {\mathcal{B}(\mathrm{H} \to \text{inv})} $, shown in the legend. The background contributions are estimated from the fit to the data (S+B fit). The total background estimated from a fit assuming $ {\mathcal{B}(\mathrm{H} \to \text{inv})} $ = 0 (B-only fit) is also shown. The yields from the 2017 and 2018 samples are summed and the correlations between their uncertainties are neglected. The last bin of each distribution integrates events above the bin threshold divided by the bin width. Figures adapted from Ref. [80].
png pdf	Figure 26-a: Distributions of the dijet pair invariant mass in the SRs of the search for $ \mathrm{H} \to \text{inv} $ produced via vector boson fusion, for the high missing transverse momentum category (left) and for the dijet-based category (right). The signal processes are scaled by the fitted value of $ {\mathcal{B}(\mathrm{H} \to \text{inv})} $, shown in the legend. The background contributions are estimated from the fit to the data (S+B fit). The total background estimated from a fit assuming $ {\mathcal{B}(\mathrm{H} \to \text{inv})} $ = 0 (B-only fit) is also shown. The yields from the 2017 and 2018 samples are summed and the correlations between their uncertainties are neglected. The last bin of each distribution integrates events above the bin threshold divided by the bin width. Figures adapted from Ref. [80].
png pdf	Figure 26-b: Distributions of the dijet pair invariant mass in the SRs of the search for $ \mathrm{H} \to \text{inv} $ produced via vector boson fusion, for the high missing transverse momentum category (left) and for the dijet-based category (right). The signal processes are scaled by the fitted value of $ {\mathcal{B}(\mathrm{H} \to \text{inv})} $, shown in the legend. The background contributions are estimated from the fit to the data (S+B fit). The total background estimated from a fit assuming $ {\mathcal{B}(\mathrm{H} \to \text{inv})} $ = 0 (B-only fit) is also shown. The yields from the 2017 and 2018 samples are summed and the correlations between their uncertainties are neglected. The last bin of each distribution integrates events above the bin threshold divided by the bin width. Figures adapted from Ref. [80].
png pdf	Figure 27: The $ m_{\mathrm{T}} $ distribution from the simultaneous fit for events with $ m_{jj} < $ 1500 GeV in the SRs of the search for dark photons in Higgs boson decays. The category other background includes contributions from Z+jets, nonprompt, top quark, VV, and VVV processes. Overflow events are included in the last bin. The shaded bands represent the combination of the statistical and systematic uncertainties in the predicted yields. The light green line, illustrating the possible contribution expected from inclusive SM Higgs boson production, assumes a branching fraction of 5% for $ \mathrm{H} \to \text{inv} $+$ \gamma $ decays. The lower panel shows a per-bin ratio of the data yield and the background expectation. The shaded band corresponds to the combined systematic and statistical uncertainty in the background expectation. Figure taken from Ref. [273].
png pdf	Figure 28: The normalized distribution of the minimum azimuthal angle between the $ {\vec p}_{\mathrm{T}}^{\kern1pt\text{miss}} $ and each of the two leading jets ($ \Delta\phi_{\text{min}} $) for simulated SM backgrounds and several SVJ signal models. The red vertical dotted line indicates the selection requirement on this variable. Figure taken from Ref. [148].
png pdf	Figure 29: The dijet mass distributions for the combination of $ \mathrm{Z}^{'} \to \mathrm{q}_{\text{dark}}\overline{\mathrm{q}}_{\text{dark}} $ and $ \mathrm{Z}^{'} \to \mathrm{q}\overline{\mathrm{q}} $ events, for $ r_{\text{inv}}= $ 0.3 (left) and $ r_{\text{inv}}= $ 0.0 (right), in SVJ signal models.
png pdf	Figure 29-a: The dijet mass distributions for the combination of $ \mathrm{Z}^{'} \to \mathrm{q}_{\text{dark}}\overline{\mathrm{q}}_{\text{dark}} $ and $ \mathrm{Z}^{'} \to \mathrm{q}\overline{\mathrm{q}} $ events, for $ r_{\text{inv}}= $ 0.3 (left) and $ r_{\text{inv}}= $ 0.0 (right), in SVJ signal models.
png pdf	Figure 29-b: The dijet mass distributions for the combination of $ \mathrm{Z}^{'} \to \mathrm{q}_{\text{dark}}\overline{\mathrm{q}}_{\text{dark}} $ and $ \mathrm{Z}^{'} \to \mathrm{q}\overline{\mathrm{q}} $ events, for $ r_{\text{inv}}= $ 0.3 (left) and $ r_{\text{inv}}= $ 0.0 (right), in SVJ signal models.
png pdf	Figure 30: The relative efficiencies of several selection criteria from the monojet search for SVJ signals. The efficiencies of the $ \Delta\phi({\vec p}_{\mathrm{T}}^{\,\text{jet}},{\vec p}_{\mathrm{T}}^{\kern1pt\text{miss}}) $ and $ N_{{\mathrm{b}}\text{-jet}} $ requirements are evaluated after the $ p_{\mathrm{T}}^\text{miss} > $ 250 GeV requirement. The uncertainty in the simulation is negligible.
png pdf	Figure 31: Jet $ m_{\mathrm{SD}} $ distribution in data for CA15 jets for a $ p_{\mathrm{T}} $ range of the fit from 575 to 625 GeV, in the search for low-mass vector resonances decaying into quark-antiquark pairs. Data are shown as black points. The QCD multijet background prediction, including uncertainties, is shown by the shaded bands. Smaller contributions from the W and Z bosons, and top quark background processes are shown as well. A hypothetical $ \mathrm{Z}^{'} $ boson signal with a mass of 210 GeV is also indicated. In the bottom panel, the ratio of the data to its statistical uncertainty, after subtracting the nonresonant backgrounds, is shown. Figure taken from Ref. [281].
png pdf	Figure 32: The soft drop jet mass distribution of the SR in the search for low-mass quark-antiquark resonances produced in association with a photon, after the main background estimation fit is performed. The nonresonant background is indicated by a dashed line, while the total background composed of the sum of this nonresonant background and the resonant backgrounds is shown by the solid line. Representative signals are plotted for comparison. The bottom panel shows the difference between the data and the final background estimate, divided by the statistical uncertainty of the data in each bin. The shaded region represents the total uncertainty in the background estimate in each bin. Figure taken from Ref. [283].
png pdf	Figure 33: The observed and fitted background $ m_{\mathrm{SD}} $ distributions in the 800 $ < p_{\mathrm{T}} < $ 1000 GeV category for the AK8 selection in the passing regions, in the search for low-mass resonances decaying into bottom quark-antiquark pairs. The fit is performed under the background-only hypothesis. A hypothetical signal at a mass of 140 GeV is also indicated. The shaded blue band shows the systematic uncertainty in the total background prediction. The bottom panel shows the difference between the data and the nonresonant background prediction, divided by the statistical uncertainty in the data. Figure taken from Ref. [282].
png pdf	Figure 34: The dimuon invariant mass distributions of events selected with the standard muon triggers (brown, darker), and the scouting dimuon triggers (green, lighter), in the search for a prompt dark photon resonance decaying into two muons. Events are required to pass all the selection requirements. The inset shows the data (black points), the signal model (blue line), and the background-only fit (orange line), and it is restricted to events in the barrel category in the mass range 23.9--26.1 GeV. A function describing the background is fit to these data. The bottom panel of the inset shows the bin-by-bin difference between the number of events in data and the prediction from the background fit, divided by the statistical uncertainty. Figure taken from Ref. [178].
png pdf	Figure 35: The dimuon invariant mass distribution obtained with the muon scouting data collected during 2017--2018 with two sets of selections: the $ \Upsilon{\textrm{(1S)}} $-trained muon MVA identification (blue solid line), and the $ \mathrm{J}/\psi $-trained muon MVA identification (red dashed line). Figure taken from Ref. [177].
png pdf	Figure 36: Dijet mass spectrum (points) compared to a fitted parameterization of the background (solid curve) in the search for dijet resonances using events with three jets, where the fit is performed in the range 290 $ < m_{jj} < $ 1000 GeV. The horizontal bars show the widths of each bin in dijet mass. The dashed lines represent the dijet mass distribution from 400, 550, and 700 GeV resonance signals expected to be excluded at 95% CL by this analysis. The lower panel shows the difference between the data and the fitted parametrization, divided by the statistical uncertainty of the data. Figure taken from Ref. [179].
png pdf	Figure 37: Dijet mass spectrum in the SR (points) compared to a fitted parameterization of the background (solid line) and the one obtained from the CR (green squares), in the search for high-mass dijet resonances. The lower panel shows the difference between the data and the fitted parametrization (red, solid), and the data and the prediction obtained from the CR (green, hatched), divided by the statistical uncertainty in the data, which for the ratio method includes the statistical uncertainty in the data in the CR. Examples of predicted signals from narrow gluon-gluon, quark-gluon, and quark-quark resonances are shown (dashed colored lines) with cross sections equal to the observed upper limits at 95% CL. Figure taken from Ref. [277].
png pdf	Figure 38: The invariant mass distribution of pairs of (left) electrons and (right) muons observed in data (black dots with statistical uncertainties) and expected from the SM processes (stacked histograms), in the high-mass dilepton search. For the dimuon channel, a prescaled trigger with a $ p_{\mathrm{T}} $ threshold of 27 GeV was used to collect events in the normalization region (NR) with dimuon mass less than 120 GeV. The corresponding offline threshold is 30 GeV. Events in the SR corresponding to masses greater than 120 GeV are collected using an unprescaled single-muon trigger. The bin width gradually increases with mass. The ratios of the data yields after background subtraction to the expected background yields are shown in the lower plots. The blue shaded band represents the combined statistical and systematic uncertainties in the background. Signal contributions expected from simulated resonances are shown. Figures adapted from Ref. [65].
png pdf	Figure 39: Distribution of $ N_{\text{hits}}^{\text{low \ddinline{E}{x} }} $ in the search and CRs for the early 2018 data set, in the search for fractionally charged particles. The middle (lower) panels show the ratio of the number of tracks observed in the CR (SR) and the fit function. Figure taken from Ref. [215].
png pdf	Figure 40: An example SUEP event from a representative model with a scalar mediator of mass 800 GeV shown in the lab frame (left) and the generator-level S mediator frame (right). The jets are clustered from charged particle tracks associated with the primary vertex using the anti-$ k_{\mathrm{T}} $ algorithm with a distance parameter of 1.5. The size of each dot is scaled based on the $ p_{\mathrm{T}} $ of the corresponding track.
png pdf	Figure 41: The neural network score ($ S_{\mathrm{NN}} $) distribution for 2017--2018 shows the data in the SR (black points); simulated background normalized to the number of data events (filled histograms); RPV signal model with a top squark mass of 450 GeV (red short dashed line); and stealth SYY signal model with a top squark mass of 850 GeV (cyan long dashed line), in the search for stealth top squarks. The band on the total background histogram denotes the dominant systematic uncertainties, as well as the statistical uncertainty for the non-$ {\mathrm{t}\overline{\mathrm{t}}} $ components. The lower panel shows the ratio of the number of data events to the number of normalized simulated events with the band representing the difference between the nominal ratio and the ratio obtained when varying the total background by its uncertainty. Figure taken from Ref. [290].
png pdf	Figure 42: Diphoton acoplanarity distribution in the search for axion-like particles in ultraperipheral PbPb collisions, for exclusive events measured in the data after selection criteria (squares), compared to the expected light-by-light scattering signal (orange histogram), quantum electrodynamics $ \mathrm{e}^{+} \mathrm{e}^{-} $ (yellow histogram), and the CEP+other (purple histogram) backgrounds. Signal and quantum electrodynamics $ \mathrm{e}^{+} \mathrm{e}^{-} $ MC samples are scaled according to their theoretical cross sections and integrated luminosity. The error bars around the data points indicate statistical uncertainties. The horizontal bars around the data symbols indicate the bin size. Figure taken from Ref. [219].
png pdf	Figure 43: Missing-mass distributions in the $ \mathrm{Z}\to\mu\mu $ final state of the CMS and CMS-TOTEM search using the missing-mass technique. The distributions are shown for protons reconstructed with (from left to right) the multi-multi, multi-single, single-multi, and single-single methods, respectively. The background distributions are shown after the fit. The lower panels display the ratio between the data and the background model, with the arrows indicating values lying outside the displayed range. The expectations for a signal with $ m_X= $ 1000 GeV are superimposed and normalized to 1\unitpb. Figure taken from Ref. [291].
png pdf	Figure 44: A diagram of a simulated signal event in the inclusive displaced-leptons search, from a transverse view of the interaction point, in the analysis presented in Ref. [243]. The black arrows indicate the lepton transverse impact parameter vectors.
png pdf	Figure 45: Comparison of the number of events observed in 2018 data with the expected number of background events, as a function of the smaller of the two $ d_0 $ significance values ($ \text{min}(d_0/{\sigma_{d_0}}) $) for pairs of muons that are globally reconstructed in the tracker and muon system (TMS), in the search for displaced muon pairs. The black points with error bars show the number of observed events; the green and yellow components of the stacked histograms represent the estimated numbers of DY and QCD events, respectively. The last bin includes events in the overflow. The uncertainties in the total expected background (shaded area) are statistical only. Signal contributions expected from simulated decays of exotic Higgs bosons to dark Z bosons, with Z boson masses of 20 and 50 GeV are shown in red and blue, respectively. Their yields are set to the corresponding combined median expected exclusion limits at 95% CL, scaled up as indicated in the legend to improve visibility. Figure taken from Ref. [132].
png pdf	Figure 46: Distribution of the invariant masses $ m_{(\mu\mu)1} $ vs. $ m_{(\mu\mu)2} $ of the isolated dimuon systems, in the search for displaced dimuons in final states with 4 $ \mu $+X. Triangles represent data events passing all the selection criteria and falling in the SR $ m_{(\mu\mu)1} \approx m_{(\mu\mu)2} $ (outlined by dashed lines), and white bullets represent data events that pass all selection criteria but fall outside the SR. Figure taken from Ref. [293].
png pdf	Figure 47: The dimuon invariant mass distribution from the search for displaced dimuon resonances with data scouting, shown in bins of $ l_{xy} $ as obtained from all selected dimuon events. Figure taken from Ref. [176].
png pdf	Figure 48: Distribution of the vertex track multiplicity, for data, simulated QCD multijet events, and simulated signal events, in the displaced-jets search. For a given event, if there is more than one SV candidate being reconstructed, the one with the largest vertex track multiplicity is chosen. If the track multiplicities are the same, the one with the smallest $ \chi^{2} $/ndof is chosen, where ndof is the number of degrees of freedom. The lower panel shows the ratios between the data and the simulated QCD multijet events. The blue shaded error bands and vertical bars represent the statistical uncertainties. Three benchmark signal distributions are shown (dashed lines). For visualization purposes, each signal process is given a cross section that yields 106 events produced in the analyzed data sample. Figure taken from Ref. [187].
png pdf	Figure 49: The distribution of distances between vertices in the $ x-y $ plane, $ d_{\mathrm{VV}} $, for the displaced-vertices search, for three simulated multijet signals each with a mass of 1600 GeV, with the background template distribution overlaid. The production cross section for each signal model is assumed to be the lower limit excluded by Ref. [295], corresponding to values of 0.8, 0.25, and 0.15\unitfb for the samples with $ c\tau_0 = $ 0.3, 1.0, and 10 mm, respectively. The last bin includes the overflow events. The two vertical pink dashed lines separate the regions used in the fit. Figure taken from Ref. [184].
png pdf	Figure 50: Distributions of the GNN output score for the data (points with error bars), SM multijet simulation (dark gray line), and signal simulation (colored lines), for the search for emerging jets. Separate GNNs are trained for the unflavored model (uGNN, left) and the flavor-aligned model (aGNN, right). Bins are chosen to correspond to the jet selection criteria applied in the analysis. The sums of the entries are normalized to unity. Figure taken from Ref. [297].
png pdf	Figure 51: The muon timing distribution in the DTs for 2016 data, simulated cosmic ray muon events, and simulated signal events, for the muon channel of the stopped-LLPs search. The gray bands indicate the statistical uncertainty in the simulation. The histograms are normalized to unit area. Figure taken from Ref. [206].
png pdf	Figure 52: The cluster reconstruction efficiency as a function of the simulated $ r $ and $ |z| $ decay positions of an LLP with a mass of 40 GeV and a range of $ c\tau_0 $ values between 1 and 10\unitm, for the search for neutral LLPs decaying in the muon system. Figure taken from Ref. [301].
png pdf	Figure 53: Measured min-$ d_{xy} $ distribution in the 2-match category of the IDM search, after requiring the min-$ d_{xy} $ muon to pass the isolation requirement $ I^{\text{rel}}_{\text{PF}} < $ 0.25. Overlaid with a red histogram is the background predicted from the region of the ABCD plane failing the same requirement, as well as three signal benchmark hypotheses (as defined in the legends), assuming $ \alpha_{\mathrm{D}} = \alpha_{\mathrm{EM}} $ (the fine-structure constant). The red hatched bands correspond to the background prediction uncertainty. The last bin includes the overflow. Figure taken from Ref. [207].
png pdf	Figure 54: The contributions to the delay of the LLP from the path length and the lower velocity of the parent particle, in the delayed-jets search [199]. For this model, which features LLPs with proper decay lengths of 10\unitm and masses of 3 TeV, the lower velocity dominates the contribution to the delay.
png pdf	Figure 55: The efficiency of the jet tagger working point used in the trackless and OOT jets and $ p_{\mathrm{T}}^\text{miss} $ analysis shown as a function of the lab frame LLP transverse decay length. The uncertainties shown account for lifetime dependence and statistical uncertainty. Figure taken from Ref. [200].
png pdf	Figure 56: Distributions of the output score of the interaction network ($ S_{\mathrm{ML}} $) for data, simulated background, and signal, for the displaced vertex plus $ p_{\mathrm{T}}^\text{miss} $ search. Events with at least five tracks are shown. The distributions are shown for split-SUSY signals with a gluino mass of 2000 GeV and a neutralino mass of 1800 GeV. Different gluino proper decay lengths are shown. All distributions are normalized to unity. Figure taken from Ref. [185].
png pdf	Figure 57: Observed and expected 95% CL exclusion regions in the $ m_{\text{med}}-m_{\text{DM}} $ plane for dijet searches [281,279,179,278,277] and different $ p_{\mathrm{T}}^\text{miss} $-based DM searches [81,268,86] from CMS in the leptophobic vector mediator model (upper) and the axial-vector mediator model (lower). Following the recommendation of the LHC DM Working Group [24,25], the exclusions are computed for a universal quark coupling of $ g_{\mathrm{q}} = $ 0.25 and for a DM coupling of $ g_{\text{DM}} = $ 1.0. The perturbative unitarity constraint $ m_{\text{DM}} = 0.5m_{\text{med}} $ is plotted as the gray dashed line, while the constraint from the relic density ($ \Omega \mathrm{h}^2 > $ 0.12), obtained from WMAP [303] and Planck [304], is plotted as the gray solid line. It should also be noted that the absolute exclusion of the different searches as well as their relative importance, will strongly depend on the chosen coupling and model scenario. Therefore, the exclusion regions, relic density contours, and unitarity curve shown in this plot are not applicable to other choices of coupling values or models.
png pdf	Figure 57-a: Observed and expected 95% CL exclusion regions in the $ m_{\text{med}}-m_{\text{DM}} $ plane for dijet searches [281,279,179,278,277] and different $ p_{\mathrm{T}}^\text{miss} $-based DM searches [81,268,86] from CMS in the leptophobic vector mediator model (upper) and the axial-vector mediator model (lower). Following the recommendation of the LHC DM Working Group [24,25], the exclusions are computed for a universal quark coupling of $ g_{\mathrm{q}} = $ 0.25 and for a DM coupling of $ g_{\text{DM}} = $ 1.0. The perturbative unitarity constraint $ m_{\text{DM}} = 0.5m_{\text{med}} $ is plotted as the gray dashed line, while the constraint from the relic density ($ \Omega \mathrm{h}^2 > $ 0.12), obtained from WMAP [303] and Planck [304], is plotted as the gray solid line. It should also be noted that the absolute exclusion of the different searches as well as their relative importance, will strongly depend on the chosen coupling and model scenario. Therefore, the exclusion regions, relic density contours, and unitarity curve shown in this plot are not applicable to other choices of coupling values or models.
png pdf	Figure 57-b: Observed and expected 95% CL exclusion regions in the $ m_{\text{med}}-m_{\text{DM}} $ plane for dijet searches [281,279,179,278,277] and different $ p_{\mathrm{T}}^\text{miss} $-based DM searches [81,268,86] from CMS in the leptophobic vector mediator model (upper) and the axial-vector mediator model (lower). Following the recommendation of the LHC DM Working Group [24,25], the exclusions are computed for a universal quark coupling of $ g_{\mathrm{q}} = $ 0.25 and for a DM coupling of $ g_{\text{DM}} = $ 1.0. The perturbative unitarity constraint $ m_{\text{DM}} = 0.5m_{\text{med}} $ is plotted as the gray dashed line, while the constraint from the relic density ($ \Omega \mathrm{h}^2 > $ 0.12), obtained from WMAP [303] and Planck [304], is plotted as the gray solid line. It should also be noted that the absolute exclusion of the different searches as well as their relative importance, will strongly depend on the chosen coupling and model scenario. Therefore, the exclusion regions, relic density contours, and unitarity curve shown in this plot are not applicable to other choices of coupling values or models.
png pdf	Figure 58: Observed and expected 95% CL exclusion regions in the $ m_{\text{med}}-m_{\text{DM}} $ plane for dijet [278,277,280] and dilepton [65] searches from CMS in the vector mediator model (upper) and the axial-vector mediator model (lower). Following the recommendation of the LHC DM Working Group [24,25], the exclusions are computed for a universal quark coupling of $ g_{\mathrm{q}} = $ 0.1, lepton coupling $ g_{\ell} = $ 0.01 (upper) and $ g_{\ell} = $ 0.1 (lower), and for a DM coupling of $ g_{\text{DM}} = $ 1.0. The perturbative unitarity constraint $ m_{\text{DM}} = 0.5m_{\text{med}} $ is plotted as the gray dashed line, while the constraint from the relic density ($ \Omega \mathrm{h}^2 > $ 0.12), obtained from WMAP [303] and Planck [304], is plotted as the gray solid line. It should also be noted that the absolute exclusion of the different searches as well as their relative importance, will strongly depend on the chosen coupling and model scenario. Therefore, the exclusion regions, relic density contours, and unitarity curve shown in this plot are not applicable to other choices of coupling values or models.
png pdf	Figure 58-a: Observed and expected 95% CL exclusion regions in the $ m_{\text{med}}-m_{\text{DM}} $ plane for dijet [278,277,280] and dilepton [65] searches from CMS in the vector mediator model (upper) and the axial-vector mediator model (lower). Following the recommendation of the LHC DM Working Group [24,25], the exclusions are computed for a universal quark coupling of $ g_{\mathrm{q}} = $ 0.1, lepton coupling $ g_{\ell} = $ 0.01 (upper) and $ g_{\ell} = $ 0.1 (lower), and for a DM coupling of $ g_{\text{DM}} = $ 1.0. The perturbative unitarity constraint $ m_{\text{DM}} = 0.5m_{\text{med}} $ is plotted as the gray dashed line, while the constraint from the relic density ($ \Omega \mathrm{h}^2 > $ 0.12), obtained from WMAP [303] and Planck [304], is plotted as the gray solid line. It should also be noted that the absolute exclusion of the different searches as well as their relative importance, will strongly depend on the chosen coupling and model scenario. Therefore, the exclusion regions, relic density contours, and unitarity curve shown in this plot are not applicable to other choices of coupling values or models.
png pdf	Figure 58-b: Observed and expected 95% CL exclusion regions in the $ m_{\text{med}}-m_{\text{DM}} $ plane for dijet [278,277,280] and dilepton [65] searches from CMS in the vector mediator model (upper) and the axial-vector mediator model (lower). Following the recommendation of the LHC DM Working Group [24,25], the exclusions are computed for a universal quark coupling of $ g_{\mathrm{q}} = $ 0.1, lepton coupling $ g_{\ell} = $ 0.01 (upper) and $ g_{\ell} = $ 0.1 (lower), and for a DM coupling of $ g_{\text{DM}} = $ 1.0. The perturbative unitarity constraint $ m_{\text{DM}} = 0.5m_{\text{med}} $ is plotted as the gray dashed line, while the constraint from the relic density ($ \Omega \mathrm{h}^2 > $ 0.12), obtained from WMAP [303] and Planck [304], is plotted as the gray solid line. It should also be noted that the absolute exclusion of the different searches as well as their relative importance, will strongly depend on the chosen coupling and model scenario. Therefore, the exclusion regions, relic density contours, and unitarity curve shown in this plot are not applicable to other choices of coupling values or models.
png pdf	Figure 59: A comparison of CMS exclusions in the $ m_{\text{DM}}-\sigma_\mathrm{SI} $ plane (upper) and the $ m_{\text{DM}}-\sigma_\mathrm{SD} $ plane (lower). The exclusions are derived from the model with a vector mediator, Dirac DM, and couplings of $ g_{\mathrm{q}}= $ 0.25 and $ g_{\text{DM}}= $ 1.0. Unlike for the $ m_{\text{DM}}-m_{\text{med}} $ plane, the limits are shown at 90% CL. The CMS SI exclusion contour is compared with limits from the CRESST-III [305], DarkSide-50 [306], PandaX-4T [307], XENONnT [13], and LZ [14] experiments. The CMS SD exclusion contour is compared with limits from the PICASSO [308] and PICO [309] experiments, as well as the IceCube limit for the $ \mathrm{t} \overline{\mathrm{t}} $ annihilation channel [310,311]. The CMS limits do not include a constraint on the relic density, and the absolute exclusion of the different CMS searches as well as their relative importance will strongly depend on the chosen coupling and model scenario. Therefore, the shown CMS exclusion regions in this plot are not applicable to other choices of coupling values or models.
png pdf	Figure 59-a: A comparison of CMS exclusions in the $ m_{\text{DM}}-\sigma_\mathrm{SI} $ plane (upper) and the $ m_{\text{DM}}-\sigma_\mathrm{SD} $ plane (lower). The exclusions are derived from the model with a vector mediator, Dirac DM, and couplings of $ g_{\mathrm{q}}= $ 0.25 and $ g_{\text{DM}}= $ 1.0. Unlike for the $ m_{\text{DM}}-m_{\text{med}} $ plane, the limits are shown at 90% CL. The CMS SI exclusion contour is compared with limits from the CRESST-III [305], DarkSide-50 [306], PandaX-4T [307], XENONnT [13], and LZ [14] experiments. The CMS SD exclusion contour is compared with limits from the PICASSO [308] and PICO [309] experiments, as well as the IceCube limit for the $ \mathrm{t} \overline{\mathrm{t}} $ annihilation channel [310,311]. The CMS limits do not include a constraint on the relic density, and the absolute exclusion of the different CMS searches as well as their relative importance will strongly depend on the chosen coupling and model scenario. Therefore, the shown CMS exclusion regions in this plot are not applicable to other choices of coupling values or models.
png pdf	Figure 59-b: A comparison of CMS exclusions in the $ m_{\text{DM}}-\sigma_\mathrm{SI} $ plane (upper) and the $ m_{\text{DM}}-\sigma_\mathrm{SD} $ plane (lower). The exclusions are derived from the model with a vector mediator, Dirac DM, and couplings of $ g_{\mathrm{q}}= $ 0.25 and $ g_{\text{DM}}= $ 1.0. Unlike for the $ m_{\text{DM}}-m_{\text{med}} $ plane, the limits are shown at 90% CL. The CMS SI exclusion contour is compared with limits from the CRESST-III [305], DarkSide-50 [306], PandaX-4T [307], XENONnT [13], and LZ [14] experiments. The CMS SD exclusion contour is compared with limits from the PICASSO [308] and PICO [309] experiments, as well as the IceCube limit for the $ \mathrm{t} \overline{\mathrm{t}} $ annihilation channel [310,311]. The CMS limits do not include a constraint on the relic density, and the absolute exclusion of the different CMS searches as well as their relative importance will strongly depend on the chosen coupling and model scenario. Therefore, the shown CMS exclusion regions in this plot are not applicable to other choices of coupling values or models.
png pdf	Figure 60: Observed and expected 95% CL exclusion regions for the universal quark coupling $ g_{\mathrm{q}} $, assuming a DM coupling $ g_{\text{DM}} = $ 1.0, for varying $ \mathrm{Z}^{'} $ mediator mass [283,281,179,279,278,81,277,285]. The hashed areas indicate the direction of the excluded area from the observed limits. The gray dashed lines show the $ g_{\mathrm{q}} $ values at fixed values of the relative width $ \Gamma_{\mathrm{Z}^{'}}/m_{\mathrm{Z}^{'}} $. Most searches assume that the intrinsic $ \mathrm{Z}^{'} $ width is negligible compared to the experimental resolution and hence are valid for $ \Gamma_{\mathrm{Z}^{'}}/m_{\mathrm{Z}^{'}} \lesssim 10% $. The dijet search is valid for $ \Gamma_{\mathrm{Z}^{'}}/m_{\mathrm{Z}^{'}} \lesssim 50% $, and the dijet angular analysis is valid for $ \Gamma_{\mathrm{Z}^{'}}/m_{\mathrm{Z}^{'}} \lesssim 100% $. The observed DM relic density is also shown; it drops to 2.17 $ \times10^{-4} $ for $ m_{\mathrm{Z}^{'}} = $ 5 GeV.
png pdf	Figure 61: Limits at 95% CL from the monojet search [81] interpreted via MADANALYSIS [DVN/IRF7ZL_2021] for a dark-photon model with a DM coupling. The limits are presented in terms of the mixing parameter $ \epsilon^{2} $ with $ g_{\text{DM}} = $ 1.0 and $ \alpha_{\text{dark}} = g_{\text{DM}}^{2}/(4\pi) $. The constraint from the relic density ($ \Omega_{c} \mathrm{h}^2 \geq $ 0.12), obtained from WMAP [303] and Planck [304], is plotted in magenta.
png pdf	Figure 62: Observed upper limits at 90% CL on the square of the kinetic mixing coefficient $ \epsilon $ in the minimal model of a dark photon from a CMS dimuon search [177] in the mass ranges of 1.1--2.6 GeV and 4.2--7.9 GeV (pink) and from another CMS dimuon search [178] at larger masses (green). The limits are compared with the existing limits at 90% CL provided by LHCb (blue) [314,315] and BaBar (gray) [316].
png pdf	Figure 63: Observed (solid lines) and expected (dashed lines) 95% CL exclusion limits for the scalar model as a function of $ m_{\text{med}} $ for different $ p_{\mathrm{T}}^\text{miss} $-based DM searches from CMS [81,86,84]. The hashed areas indicate the direction of the excluded area from the observed limits. Following the recommendation of the LHC DM Working Group [24,25], the exclusions are computed for a universal quark coupling of $ g_{\mathrm{q}} = $ 1.0 and for a DM coupling of $ g_{\text{DM}} = $ 1.0. The exclusion away from $ \sigma / \sigma_{\text{theory}} = $ 1 only applies to coupling combinations that yield the same kinematic distributions as the benchmark model considered here.
png pdf	Figure 64: Observed (red lines) and expected (black lines) 95% CL exclusion limits for the dark-Higgs boson model in terms of $ m_{\mathrm{H}_{\mathrm{D}}} $ (written as s in the figure) and $ m_{\mathrm{Z}^{'}} $ for $ m_{\text{DM}}= $ 150 GeV (upper) and 200 GeV (lower) (where $ m_{\text{DM}} $ is written as $ m_\chi $ in the figure). The gray line indicates where the model parameters produce exactly the observed relic density. Figure taken from Ref. [271].
png pdf	Figure 64-a: Observed (red lines) and expected (black lines) 95% CL exclusion limits for the dark-Higgs boson model in terms of $ m_{\mathrm{H}_{\mathrm{D}}} $ (written as s in the figure) and $ m_{\mathrm{Z}^{'}} $ for $ m_{\text{DM}}= $ 150 GeV (upper) and 200 GeV (lower) (where $ m_{\text{DM}} $ is written as $ m_\chi $ in the figure). The gray line indicates where the model parameters produce exactly the observed relic density. Figure taken from Ref. [271].
png pdf	Figure 64-b: Observed (red lines) and expected (black lines) 95% CL exclusion limits for the dark-Higgs boson model in terms of $ m_{\mathrm{H}_{\mathrm{D}}} $ (written as s in the figure) and $ m_{\mathrm{Z}^{'}} $ for $ m_{\text{DM}}= $ 150 GeV (upper) and 200 GeV (lower) (where $ m_{\text{DM}} $ is written as $ m_\chi $ in the figure). The gray line indicates where the model parameters produce exactly the observed relic density. Figure taken from Ref. [271].
png pdf	Figure 65: 95% CL upper limits on the mixing parameter $ \theta_{\text{h}}^{2} $ from the $ \mathrm{H} \to \text{inv} $ analysis [85] (Section 6.1.2) interpreted with a dark-Higgs boson model.
png pdf	Figure 66: Results on $ {\mathcal{B}(\mathrm{H} \to \text{inv})} $, shown separately for each Higgs boson production mode as tagged by the input analyses, as well as combined across modes. Left: observed and expected upper limits on $ {\mathcal{B}(\mathrm{H} \to \text{inv})} $ at 95% CL. Right: best-fit estimates of $ {\mathcal{B}(\mathrm{H} \to \text{inv})} $. Figure adapted from Ref. [85].
png pdf	Figure 66-a: Results on $ {\mathcal{B}(\mathrm{H} \to \text{inv})} $, shown separately for each Higgs boson production mode as tagged by the input analyses, as well as combined across modes. Left: observed and expected upper limits on $ {\mathcal{B}(\mathrm{H} \to \text{inv})} $ at 95% CL. Right: best-fit estimates of $ {\mathcal{B}(\mathrm{H} \to \text{inv})} $. Figure adapted from Ref. [85].
png pdf	Figure 66-b: Results on $ {\mathcal{B}(\mathrm{H} \to \text{inv})} $, shown separately for each Higgs boson production mode as tagged by the input analyses, as well as combined across modes. Left: observed and expected upper limits on $ {\mathcal{B}(\mathrm{H} \to \text{inv})} $ at 95% CL. Right: best-fit estimates of $ {\mathcal{B}(\mathrm{H} \to \text{inv})} $. Figure adapted from Ref. [85].
png pdf	Figure 67: Translation of the exclusion limits on $ {\mathcal{B}(\mathrm{H} \to \text{inv})} $ into 90% CL upper limits on the spin-independent DM-nucleon scattering cross section [85], and comparison with results from the CRESST-III [305], DarkSide-50 [306], PandaX-4T [307], and LUX-ZEPLIN [14] experiments. Figure adapted from Ref. [85].
png pdf	Figure 68: Observed (solid lines) and expected (dashed lines) 95% CL exclusion limits for the pseudoscalar model in terms of $ m_{\text{med}} $ for different $ p_{\mathrm{T}}^\text{miss} $-based DM searches from CMS [81,86,84]. The hashed areas indicate the direction of the excluded area from the observed limits. Following the recommendation of the LHC DM Working Group [24,25], the exclusions are computed for a universal quark coupling of $ g_{\mathrm{q}} = $ 1.0 and for a DM coupling of $ g_{\text{DM}} = $ 1.0. The exclusion away from $ \sigma / \sigma_{\text{theory}} = $ 1 only applies to coupling combinations that yield the same kinematic distributions as the benchmark model considered here.
png pdf	Figure 69: Observed (solid line) and expected (dashed lines) exclusions at 95% CL in the $ m_{\Phi}-m_{\text{DM}} $ plane for the fermion portal model scenario obtained from the monojet search performed using data collected in 2016--2018. Figure adapted from Ref. [81].
png pdf	Figure 70: Observed (solid lines) and expected (dashed lines) exclusion regions at 95% CL in the $ m_{\mathrm{a}}-m_{\text{A}} $ plane for the 2HDM+a scenario arising from various ``mono-X'' searches performed using data collected in 2016--2018 [86,81,270]. Following the recommendation of the LHC DM Working Group [24,25], the projection is performed for values of the other parameters as follows: $ m_{\mathrm{H}}=m_{\text{A}}=m_{\mathrm{H}^{\pm}} $, $ \sin\theta= $ 0.35, $ \tan\beta= $ 1, $ m_{\text{DM}}= $ 10 GeV, and $ y_{\text{DM}}= $ 1.
png pdf	Figure 71: Exclusion regions at 95% CL in the $ m_{\mathrm{a}}-m_{\text{DM}} $ plane for the 2HDM+a scenario arising from searches for exotic and invisible decays of the 125 GeV Higgs boson performed using data collected in 2016--2018 [318,319,320,321,85]. Following the recommendation of the LHC DM Working Group [24,25], the projection is performed for values of the other parameters as follows: $ m_{\mathrm{H}}=m_{\text{A}}=m_{\mathrm{H}^{\pm}}= $ 1 TeV, $ \sin\theta= $ 0.35, $ \tan\beta= $ 1, and $ y_{\text{DM}}= $ 1. The branching fractions of the pseudoscalar boson to SM and DM particles are computed using the MADWIDTH [322] functionality within MadGraph-5\_aMC@NLO.
png pdf	Figure 72: Observed 95% CL exclusion contours in the plane defined by the kinetic mixing parameter ($ \epsilon $) and the mass of the new dark boson. A summary of Run 2 CMS searches focusing on displaced signatures is presented. Two of those searches, namely Refs. [132] (red) and [294] (blue), consider the HAHM signal and use a final state with at least two muons $ (2\mu+X) $, and the latter one uses data scouting. The third search (orange) [293] uses a final state with at least four muons $ (4\mu+X) $ and a dark SUSY signal scenario.
png pdf	Figure 73: Expected and observed 95% CL upper limit on the product of the top squark pair production cross section and branching fraction in terms of the top squark mass for the stealth SYY SUSY model (upper) and stealth $\mathrm{SHH}$ SUSY model (lower). Particle masses and branching fractions assumed for the model are included. The expected cross section is computed at NNLO accuracy, improved by using the summation of soft gluons at next-to-next-to-leading logarithmic (NNLL) order, and is shown in the red curve. Upper figure adapted from Ref. [290].
png pdf	Figure 73-a: Expected and observed 95% CL upper limit on the product of the top squark pair production cross section and branching fraction in terms of the top squark mass for the stealth SYY SUSY model (upper) and stealth $\mathrm{SHH}$ SUSY model (lower). Particle masses and branching fractions assumed for the model are included. The expected cross section is computed at NNLO accuracy, improved by using the summation of soft gluons at next-to-next-to-leading logarithmic (NNLL) order, and is shown in the red curve. Upper figure adapted from Ref. [290].
png pdf	Figure 73-b: Expected and observed 95% CL upper limit on the product of the top squark pair production cross section and branching fraction in terms of the top squark mass for the stealth SYY SUSY model (upper) and stealth $\mathrm{SHH}$ SUSY model (lower). Particle masses and branching fractions assumed for the model are included. The expected cross section is computed at NNLO accuracy, improved by using the summation of soft gluons at next-to-next-to-leading logarithmic (NNLL) order, and is shown in the red curve. Upper figure adapted from Ref. [290].
png pdf	Figure 74: Observed 95% CL exclusions of the product of the top squark pair production cross section and branching fraction as functions of the top squark mass and proper decay length of the singlino for the stealth $\mathrm{SY\overline{Y}}$ (left) and stealth $\mathrm{SHH}$ (right) SUSY model where the mass of the singlino is 100 GeV (upper) and $ m_{\tilde{\mathrm{t}}}- $ 225 GeV (lower). Exclusions are for the stealth SUSY search [290] (dark green), the displaced vertices search [184] (gray), the displaced-jets search [187] (red), the trackless- and OOT-jets search [200] (blue), and muon system showers search (MS clusters) [301] (orange). The hatching direction on each contour denotes the region of excluded 2D phase space that is bounded by the respective contour. Note that the displaced-jets search has no sensitivity less than $ c\tau_{\widetilde{\text{S}}}=$ 0.1 mm, the DVs search has no sensitivity less than $ c\tau_{\widetilde{\text{S}}}= $ 0.1 (0.3) mm for the $\mathrm{SY\overline{Y}}$ ($\mathrm{SHH}$) model, and the stealth SUSY search has no sensitivity to either stealth SUSY model when $ m_{\widetilde{\text{S}}} - m_{\tilde{\mathrm{t}}} = $ 225 GeV. Additionally, for the specific result here, the muon system showers search only uses the CSCs component of the muon system.
png pdf	Figure 74-a: Observed 95% CL exclusions of the product of the top squark pair production cross section and branching fraction as functions of the top squark mass and proper decay length of the singlino for the stealth $\mathrm{SY\overline{Y}}$ (left) and stealth $\mathrm{SHH}$ (right) SUSY model where the mass of the singlino is 100 GeV (upper) and $ m_{\tilde{\mathrm{t}}}- $ 225 GeV (lower). Exclusions are for the stealth SUSY search [290] (dark green), the displaced vertices search [184] (gray), the displaced-jets search [187] (red), the trackless- and OOT-jets search [200] (blue), and muon system showers search (MS clusters) [301] (orange). The hatching direction on each contour denotes the region of excluded 2D phase space that is bounded by the respective contour. Note that the displaced-jets search has no sensitivity less than $ c\tau_{\widetilde{\text{S}}}=$ 0.1 mm, the DVs search has no sensitivity less than $ c\tau_{\widetilde{\text{S}}}= $ 0.1 (0.3) mm for the $\mathrm{SY\overline{Y}}$ ($\mathrm{SHH}$) model, and the stealth SUSY search has no sensitivity to either stealth SUSY model when $ m_{\widetilde{\text{S}}} - m_{\tilde{\mathrm{t}}} = $ 225 GeV. Additionally, for the specific result here, the muon system showers search only uses the CSCs component of the muon system.
png pdf	Figure 74-b: Observed 95% CL exclusions of the product of the top squark pair production cross section and branching fraction as functions of the top squark mass and proper decay length of the singlino for the stealth $\mathrm{SY\overline{Y}}$ (left) and stealth $\mathrm{SHH}$ (right) SUSY model where the mass of the singlino is 100 GeV (upper) and $ m_{\tilde{\mathrm{t}}}- $ 225 GeV (lower). Exclusions are for the stealth SUSY search [290] (dark green), the displaced vertices search [184] (gray), the displaced-jets search [187] (red), the trackless- and OOT-jets search [200] (blue), and muon system showers search (MS clusters) [301] (orange). The hatching direction on each contour denotes the region of excluded 2D phase space that is bounded by the respective contour. Note that the displaced-jets search has no sensitivity less than $ c\tau_{\widetilde{\text{S}}}=$ 0.1 mm, the DVs search has no sensitivity less than $ c\tau_{\widetilde{\text{S}}}= $ 0.1 (0.3) mm for the $\mathrm{SY\overline{Y}}$ ($\mathrm{SHH}$) model, and the stealth SUSY search has no sensitivity to either stealth SUSY model when $ m_{\widetilde{\text{S}}} - m_{\tilde{\mathrm{t}}} = $ 225 GeV. Additionally, for the specific result here, the muon system showers search only uses the CSCs component of the muon system.
png pdf	Figure 74-c: Observed 95% CL exclusions of the product of the top squark pair production cross section and branching fraction as functions of the top squark mass and proper decay length of the singlino for the stealth $\mathrm{SY\overline{Y}}$ (left) and stealth $\mathrm{SHH}$ (right) SUSY model where the mass of the singlino is 100 GeV (upper) and $ m_{\tilde{\mathrm{t}}}- $ 225 GeV (lower). Exclusions are for the stealth SUSY search [290] (dark green), the displaced vertices search [184] (gray), the displaced-jets search [187] (red), the trackless- and OOT-jets search [200] (blue), and muon system showers search (MS clusters) [301] (orange). The hatching direction on each contour denotes the region of excluded 2D phase space that is bounded by the respective contour. Note that the displaced-jets search has no sensitivity less than $ c\tau_{\widetilde{\text{S}}}=$ 0.1 mm, the DVs search has no sensitivity less than $ c\tau_{\widetilde{\text{S}}}= $ 0.1 (0.3) mm for the $\mathrm{SY\overline{Y}}$ ($\mathrm{SHH}$) model, and the stealth SUSY search has no sensitivity to either stealth SUSY model when $ m_{\widetilde{\text{S}}} - m_{\tilde{\mathrm{t}}} = $ 225 GeV. Additionally, for the specific result here, the muon system showers search only uses the CSCs component of the muon system.
png pdf	Figure 74-d: Observed 95% CL exclusions of the product of the top squark pair production cross section and branching fraction as functions of the top squark mass and proper decay length of the singlino for the stealth $\mathrm{SY\overline{Y}}$ (left) and stealth $\mathrm{SHH}$ (right) SUSY model where the mass of the singlino is 100 GeV (upper) and $ m_{\tilde{\mathrm{t}}}- $ 225 GeV (lower). Exclusions are for the stealth SUSY search [290] (dark green), the displaced vertices search [184] (gray), the displaced-jets search [187] (red), the trackless- and OOT-jets search [200] (blue), and muon system showers search (MS clusters) [301] (orange). The hatching direction on each contour denotes the region of excluded 2D phase space that is bounded by the respective contour. Note that the displaced-jets search has no sensitivity less than $ c\tau_{\widetilde{\text{S}}}=$ 0.1 mm, the DVs search has no sensitivity less than $ c\tau_{\widetilde{\text{S}}}= $ 0.1 (0.3) mm for the $\mathrm{SY\overline{Y}}$ ($\mathrm{SHH}$) model, and the stealth SUSY search has no sensitivity to either stealth SUSY model when $ m_{\widetilde{\text{S}}} - m_{\tilde{\mathrm{t}}} = $ 225 GeV. Additionally, for the specific result here, the muon system showers search only uses the CSCs component of the muon system.
png pdf	Figure 75: Two-dimensional exclusion surface in the search for IDM, assuming $ \Delta = 0.1 \, m_{\text{DM}} $, in terms of the DM mass $ m_{\text{DM}} $ and the signal strength $ y $, with $ m_{\text{med}} = 3 \, m_{\text{DM}} $. Filled histograms denote observed limits on $ \sigma(\mathrm{p}\mathrm{p} \to \text{A}^{\prime} \to \chi_2 \chi_1) \, \mathcal{B}(\chi_2 \to \chi_1 \mu^{+} \mu^{-}) $. Solid (dashed) curves denote the observed (expected) exclusion limits at 95% CL, with 68% CL uncertainty bands around the expectation. Regions above the curves are excluded, depending on the $ \alpha_{\text{dark}} $ hypothesis: $ \alpha_{\text{dark}} = \alpha_{\text{EM}} $ (dark blue) or 0.1 (light magenta). The sensitivity is higher in the region near $ m_{\text{DM}} \approx $ 30 GeV or $ m_{\text{med}} \approx $ 90 GeV because of the $ \text{A}^{\prime} $ mixing with the Z boson in that mass range. Figure adapted from Ref. [207].
png pdf	Figure 76: Observed and expected 95% CL excluded regions of the $ m_{\mathrm{Z}^{'}}-r_{\text{inv}} $ plane from the dedicated SVJ search [148], the dijet search [277] (Section 6.2.2.2), and the monojet search [81] (Section 6.1.1.1). The hashed areas indicate the direction of the excluded area from the observed limits.
png pdf	Figure 77: Observed and expected 95% CL exclusion limits on $ g_{\mathrm{q}} $ for SVJ signals from the dedicated SVJ search [148], the dijet search [277], and the monojet search [81], for $ r_{\text{inv}}= $ 0.3 (upper) and $ r_{\text{inv}}= $ 0.6 (lower). The hashed areas indicate the direction of the excluded area from the observed limits. The observed limits from the monojet search in the upper plot and the inclusive SVJ search in the lower plot are outside the range of validity of the narrow-width approximation, so they are not shown.
png pdf	Figure 77-a: Observed and expected 95% CL exclusion limits on $ g_{\mathrm{q}} $ for SVJ signals from the dedicated SVJ search [148], the dijet search [277], and the monojet search [81], for $ r_{\text{inv}}= $ 0.3 (upper) and $ r_{\text{inv}}= $ 0.6 (lower). The hashed areas indicate the direction of the excluded area from the observed limits. The observed limits from the monojet search in the upper plot and the inclusive SVJ search in the lower plot are outside the range of validity of the narrow-width approximation, so they are not shown.
png pdf	Figure 77-b: Observed and expected 95% CL exclusion limits on $ g_{\mathrm{q}} $ for SVJ signals from the dedicated SVJ search [148], the dijet search [277], and the monojet search [81], for $ r_{\text{inv}}= $ 0.3 (upper) and $ r_{\text{inv}}= $ 0.6 (lower). The hashed areas indicate the direction of the excluded area from the observed limits. The observed limits from the monojet search in the upper plot and the inclusive SVJ search in the lower plot are outside the range of validity of the narrow-width approximation, so they are not shown.
png pdf	Figure 78: Observed and expected 95% CL exclusion limits from the track-based [297] and muon detector shower-based [301] searches for pair production of a bifundamental mediator that decays into a jet and an emerging jet, for $ m_{\text{dark}}= $ 10 GeV and various choices of $ \Phi $ masses and $ \pi_{\text{dark}} $ proper decay lengths, in the unflavored model (upper) and the flavor-aligned model (lower).
png pdf	Figure 78-a: Observed and expected 95% CL exclusion limits from the track-based [297] and muon detector shower-based [301] searches for pair production of a bifundamental mediator that decays into a jet and an emerging jet, for $ m_{\text{dark}}= $ 10 GeV and various choices of $ \Phi $ masses and $ \pi_{\text{dark}} $ proper decay lengths, in the unflavored model (upper) and the flavor-aligned model (lower).
png pdf	Figure 78-b: Observed and expected 95% CL exclusion limits from the track-based [297] and muon detector shower-based [301] searches for pair production of a bifundamental mediator that decays into a jet and an emerging jet, for $ m_{\text{dark}}= $ 10 GeV and various choices of $ \Phi $ masses and $ \pi_{\text{dark}} $ proper decay lengths, in the unflavored model (upper) and the flavor-aligned model (lower).
png pdf	Figure 79: Observed 95% CL exclusion limits on the branching fraction of the Higgs boson decay into DS hadrons, $ \Psi $, for the search for neutral decays in the muon system (Section 6.3.3.1). Sensitivity for the gluon (left) and Higgs boson (right) DS decay portals are shown. The model parameters considered here are $ m_{\omega_{\text{dark}}}=2.5m_{\eta_{\text{dark}}} $, $ \Lambda_{\text{dark}} =m_{\eta_{\text{dark}}} $. Figure adapted from Ref. [301].
png pdf	Figure 79-a: Observed 95% CL exclusion limits on the branching fraction of the Higgs boson decay into DS hadrons, $ \Psi $, for the search for neutral decays in the muon system (Section 6.3.3.1). Sensitivity for the gluon (left) and Higgs boson (right) DS decay portals are shown. The model parameters considered here are $ m_{\omega_{\text{dark}}}=2.5m_{\eta_{\text{dark}}} $, $ \Lambda_{\text{dark}} =m_{\eta_{\text{dark}}} $. Figure adapted from Ref. [301].
png pdf	Figure 79-b: Observed 95% CL exclusion limits on the branching fraction of the Higgs boson decay into DS hadrons, $ \Psi $, for the search for neutral decays in the muon system (Section 6.3.3.1). Sensitivity for the gluon (left) and Higgs boson (right) DS decay portals are shown. The model parameters considered here are $ m_{\omega_{\text{dark}}}=2.5m_{\eta_{\text{dark}}} $, $ \Lambda_{\text{dark}} =m_{\eta_{\text{dark}}} $. Figure adapted from Ref. [301].
png pdf	Figure 80: Observed and expected 95% CL excluded regions in the SUEP search (Section 6.2.3.2) in $ m_{\text{dark}} $--$ T_{\text{dark}} $ for each $ m_{\text{S}} $ value, considering the case with $ m_{\text{A}^{\prime}}= $ 1.0 GeV ($ \text{A}^{\prime} \to \pi^{+}\pi^{-} $ with $ \mathcal{B}=100% $). The regions below the lines are excluded. Figure taken from Ref. [289].
png pdf	Figure 81: Observed 95% CL upper limits on the branching fraction of Higgs bosons decaying into LLPs with masses between 40 and 55 GeV [243,294,292,323,187,301,85].
png pdf	Figure 82: Observed 95% CL upper limits on the branching fraction of Higgs bosons decaying into LLPs with masses between 15 and 30 GeV [243,294,292,323,187,301,85].
png pdf	Figure 83: Observed 95% CL upper limits on the branching fraction of Higgs bosons decaying into LLPs with masses between 0.4 and 7 GeV [294,301].
png pdf	Figure 84: Observed 95% CL exclusion limits for $ \mathrm{Z}^{'} $ bosons decaying into LLPs with fully hadronic final states, for a $ \mathrm{Z}^{'} $ boson mass of 3000 GeV (upper) and 4500 GeV (lower). Analyses employing different strategies are shown to have complementary lifetime sensitivity [184,199,200,187]. The theoretical cross section assumes the Z' has SM-like couplings to SM quarks [66].
png pdf	Figure 84-a: Observed 95% CL exclusion limits for $ \mathrm{Z}^{'} $ bosons decaying into LLPs with fully hadronic final states, for a $ \mathrm{Z}^{'} $ boson mass of 3000 GeV (upper) and 4500 GeV (lower). Analyses employing different strategies are shown to have complementary lifetime sensitivity [184,199,200,187]. The theoretical cross section assumes the Z' has SM-like couplings to SM quarks [66].
png pdf	Figure 84-b: Observed 95% CL exclusion limits for $ \mathrm{Z}^{'} $ bosons decaying into LLPs with fully hadronic final states, for a $ \mathrm{Z}^{'} $ boson mass of 3000 GeV (upper) and 4500 GeV (lower). Analyses employing different strategies are shown to have complementary lifetime sensitivity [184,199,200,187]. The theoretical cross section assumes the Z' has SM-like couplings to SM quarks [66].
png pdf	Figure 85: Observed 95% CL exclusion limits for $ \mathrm{Z}^{'} $ bosons decaying into LLPs with hadronic plus $ p_{\mathrm{T}}^\text{miss} $ final states, for a $ \mathrm{Z}^{'} $ boson mass of 3000 GeV (upper) and 4500 GeV (lower). Analyses employing different strategies are shown to have complementary lifetime sensitivity [199,200,187]. The theoretical cross section assumes the Z' has SM-like couplings to SM quarks [66].
png pdf	Figure 85-a: Observed 95% CL exclusion limits for $ \mathrm{Z}^{'} $ bosons decaying into LLPs with hadronic plus $ p_{\mathrm{T}}^\text{miss} $ final states, for a $ \mathrm{Z}^{'} $ boson mass of 3000 GeV (upper) and 4500 GeV (lower). Analyses employing different strategies are shown to have complementary lifetime sensitivity [199,200,187]. The theoretical cross section assumes the Z' has SM-like couplings to SM quarks [66].
png pdf	Figure 85-b: Observed 95% CL exclusion limits for $ \mathrm{Z}^{'} $ bosons decaying into LLPs with hadronic plus $ p_{\mathrm{T}}^\text{miss} $ final states, for a $ \mathrm{Z}^{'} $ boson mass of 3000 GeV (upper) and 4500 GeV (lower). Analyses employing different strategies are shown to have complementary lifetime sensitivity [199,200,187]. The theoretical cross section assumes the Z' has SM-like couplings to SM quarks [66].
png pdf	Figure 86: Observed 95% CL exclusion limits for $ \mathrm{H}_{\mathrm{D}} $ decaying into LLPs with a fully hadronic final state, for a $ \mathrm{H}_{\mathrm{D}} $ mass of 400 GeV (upper) and 800 GeV (lower). The $ \mathrm{H}_{\mathrm{D}} $ production cross section assumes point-like effective theory [274]. Analyses employing different strategies are shown to have complementary lifetime sensitivity [184,301,187,200].
png pdf	Figure 86-a: Observed 95% CL exclusion limits for $ \mathrm{H}_{\mathrm{D}} $ decaying into LLPs with a fully hadronic final state, for a $ \mathrm{H}_{\mathrm{D}} $ mass of 400 GeV (upper) and 800 GeV (lower). The $ \mathrm{H}_{\mathrm{D}} $ production cross section assumes point-like effective theory [274]. Analyses employing different strategies are shown to have complementary lifetime sensitivity [184,301,187,200].
png pdf	Figure 86-b: Observed 95% CL exclusion limits for $ \mathrm{H}_{\mathrm{D}} $ decaying into LLPs with a fully hadronic final state, for a $ \mathrm{H}_{\mathrm{D}} $ mass of 400 GeV (upper) and 800 GeV (lower). The $ \mathrm{H}_{\mathrm{D}} $ production cross section assumes point-like effective theory [274]. Analyses employing different strategies are shown to have complementary lifetime sensitivity [184,301,187,200].
png pdf	Figure 87: Observed 95% CL exclusion limits for $ \mathrm{H}_{\mathrm{D}} $ decaying into LLPs with a hadronic plus $ p_{\mathrm{T}}^\text{miss} $ final state, for a $ \mathrm{H}_{\mathrm{D}} $ mass of 400 GeV (upper) and 800 GeV (lower). The $ \mathrm{H}_{\mathrm{D}} $ production cross section assumes point-like effective theory [274]. Analyses employing different strategies are shown to have complementary lifetime sensitivity [187,200].
png pdf	Figure 87-a: Observed 95% CL exclusion limits for $ \mathrm{H}_{\mathrm{D}} $ decaying into LLPs with a hadronic plus $ p_{\mathrm{T}}^\text{miss} $ final state, for a $ \mathrm{H}_{\mathrm{D}} $ mass of 400 GeV (upper) and 800 GeV (lower). The $ \mathrm{H}_{\mathrm{D}} $ production cross section assumes point-like effective theory [274]. Analyses employing different strategies are shown to have complementary lifetime sensitivity [187,200].
png pdf	Figure 87-b: Observed 95% CL exclusion limits for $ \mathrm{H}_{\mathrm{D}} $ decaying into LLPs with a hadronic plus $ p_{\mathrm{T}}^\text{miss} $ final state, for a $ \mathrm{H}_{\mathrm{D}} $ mass of 400 GeV (upper) and 800 GeV (lower). The $ \mathrm{H}_{\mathrm{D}} $ production cross section assumes point-like effective theory [274]. Analyses employing different strategies are shown to have complementary lifetime sensitivity [187,200].
png pdf	Figure 88: A qualitative depiction of how the results in this Report map onto the models probed in CMS searches for dark sectors.

Tables
png pdf	Table 1: Summary of $ p_{\mathrm{T}} $ (or $ E_{\mathrm{T}} $) requirements (in GeV) of a subset of the HLT algorithms deployed in CMS during 2018, for trigger paths based on one or two physics objects. One $ p_{\mathrm{T}} $ threshold value is given for the single-object triggers, and two $ p_{\mathrm{T}} $ threshold values are given for the di-object triggers. Triggers with isolated leptons are labeled ``iso.'', and have generally lower kinematical thresholds than the corresponding algorithms that do not impose isolation requirements on leptons. The ``1-prong'' note for the tau lepton trigger refers to a selection targeting the $ \tau $ decay into a single charged particle + neutrals. The ``barrel'' note for the photon trigger refers to a photon reconstructed solely within the barrel section of the ECAL. The ``AK4'' and ``AK8'' notes refer to jets reconstructed with the anti-$ k_\text{T} $ algorithm and a distance parameter of 0.4 and 0.8, respectively [165]; the mass threshold is applied to $ m_\text{trim} $, the trimmed jet mass [172]. The ``b tags'' note refers to the number of jets that are b-tagged with the DEEPCSV algorithm [175].
png pdf	Table 2: Data sets, respective integrated luminosities, and relevant publications for each $ \mathrm{H} \to \text{inv} $ production mode across Run 1 and Run 2. For some data-taking periods, no $ \mathrm{H} \to \text{inv} $ searches have been performed for the given production mode. Table adapted from Ref. [85].
png pdf	Table 3: Trigger thresholds for various jet-based triggers in Run 2. All values are in GeVns.
png pdf	Table 4: Summary of 95% CL observed exclusion limits on $ m_{\text{med}} = m_{\mathrm{Z}^{'}} $ for $p_{\mathrm{T}}^\text{miss}-based$ DM searches in the leptophobic vector and axial-vector model. Following the recommendation of the LHC DM Working Group [24,25], the exclusions are computed for a universal quark coupling of $ g_{\mathrm{q}} = $ 0.25 and for a DM coupling of $ g_{\text{DM}} = $ 1.0.
png pdf	Table 5: Summary of 95% CL observed exclusion limits on $ m_{\text{med}} = m_{\text{S}} $ for $p_{\mathrm{T}}^\text{miss}-based$ DM searches from CMS in the scalar model. Following the recommendation of the LHC DM Working Group [24,25], the exclusions are computed for a universal quark coupling of $ g_{\mathrm{q}} = $ 1.0 and for a DM coupling of $ g_{\text{DM}} = $ 1.0. Each search listed here used data corresponding to $ \mathcal{L}_{\mathrm{int}} = $ 137 fb$^{-1} $.
png pdf	Table 6: The observed best-fit estimates of $ {\mathcal{B}(\mathrm{H} \to \text{inv})} $, for each analysis channel in the combination, and the 95% CL observed and expected (exp) upper limits on $ {\mathcal{B}(\mathrm{H} \to \text{inv})} $. Table adapted from Ref. [85].

Summary

A comprehensive review of dark sector (DS) searches with the CMS experiment at the LHC has been presented, using proton-proton and heavy ion collision data collected in Run 2, from 2016 to 2018, or, in some cases, from Run 1 (2011--2012) or Run 3 (2022). These searches have been interpreted in simplified and extended DS models. Figure 88 qualitatively illustrates how the results map into this theoretical framework. The broad DS search program spans many different signatures, including those with invisible particles, those with particles promptly decaying into fully visible final states, and those with long-lived particles (LLPs). A number of searches have been newly reinterpreted with DS benchmark scenarios for this Report. In order to perform these searches, several unique techniques of data collection and reconstruction were employed, and they are also described in this Report. The broad variety of searches provides sensitivity across a wide range of models and parameter space, and the results represent the most complete set of constraints on DS models obtained by the CMS Collaboration to date. In particular, this Report has presented the latest constraints from the CMS experiment on a comprehensive set of simplified dark matter models, and it has compared these constraints with those from direct-detection experiments. New reinterpretations have been shown for extended DS scenarios, including semivisible jets, emerging jets, dark supersymmetry, hidden Abelian Higgs models, and two-Higgs-doublet plus a pseudoscalar models. Several scenarios involving LLPs have been presented, including models with heavy LLPs, stealth supersymmetry, and Higgs boson decays to LLPs. In addition, future improvements will provide increased DS sensitivity. For Run 3 of the LHC [324], new triggers are available [183], as well as improvements to unique data-collection strategies, such as data scouting and data parking [176]. These strategies have already been exploited by some of the searches presented in this Report, and more analyses in the future will also benefit from them. Finally, the High-Luminosity LHC will provide even further DS sensitivity, owing to both the increased performance of the accelerator and the substantial upgrades of the CMS detector [160,325,326,327,328,329,330,331]. The impressive extension in sensitivity that will be achieved for DS models has been shown in several studies of the physics performance at the High-Luminosity LHC [332,333,334].

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176	CMS Collaboration	Enriching the physics program of the CMS experiment via data scouting and data parking	Submitted to Phys. Rept., 2024	CMS-EXO-23-007 2403.16134
177	CMS Collaboration	Search for direct production of GeV-scale resonances decaying to a pair of muons in proton-proton collisions at $ \sqrt{s} = $ 13 TeV	JHEP 12 (2023) 070	CMS-EXO-21-005 2309.16003
178	CMS Collaboration	Search for a narrow resonance lighter than 200 GeV decaying to a pair of muons in proton-proton collisions at $ \sqrt{s} = $ 13 TeV	PRL 124 (2020) 131802	CMS-EXO-19-018 1912.04776
179	CMS Collaboration	Search for dijet resonances using events with three jets in proton-proton collisions at $ \sqrt{s}= $ 13 TeV	PLB 805 (2020) 135448	CMS-EXO-19-004 1911.03761
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280	CMS Collaboration	Search for low mass vector resonances decaying into quark-antiquark pairs in proton-proton collisions at $ \sqrt{s}= $ 13 TeV	JHEP 01 (2018) 097	CMS-EXO-17-001 1710.00159
281	CMS Collaboration	Search for low mass vector resonances decaying into quark-antiquark pairs in proton-proton collisions at $ \sqrt{s}= $ 13 TeV	PRD 100 (2019) 112007	CMS-EXO-18-012 1909.04114
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319	CMS Collaboration	Search for light pseudoscalar boson pairs produced from decays of the 125 GeV Higgs boson in final states with two muons and two nearby tracks in pp collisions at $ \sqrt{s}= $ 13 TeV	PLB 800 (2020) 135087	CMS-HIG-18-006 1907.07235
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