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CMS-PAS-EXO-23-016

Long-lived particle triggers at CMS: Strategy and performance in proton-proton collisions at $ \sqrt{s}= $ 13.6 TeV

CMS Collaboration

2025-07-01

Abstract: The CMS Run 3 (2022-2026) physics program expands the scope of the search for long-lived particles at the CERN LHC with the addition of dedicated triggers and the improvement of the existing triggers. These customized triggers are described in this note, along with their performance using several models of new physics and the proton-proton collision data collected by the CMS detector during 2022-2024 at a center-of-mass energy of 13.6 TeV.

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Figures
png pdf	Figure 1: Schematic view in the $ R-z $ plane of a CMS detector quadrant at the start of Run 3, with the axis parallel to the beam ($ z $) running horizontally and the radius ($ R $) increasing upward. The interaction point is in the lower left corner. The locations of the various muon stations and the steel flux-return disks (dark areas) are shown, along with the silicon tracker, the electromagnetic calorimeter (ECAL), and the hadronic calorimeter (HCAL). The locations of the various muon stations are shown in color: drift tubes (DTs) with labels MB, cathode strip chambers (CSCs) with labels ME, resistive plate chambers (RPCs) with labels RB and RE, and gas electron multipliers (GEMs) with labels GE. The M denotes muon, B stands for barrel, and E for endcap. Figure taken from Ref. [16].
png pdf	Figure 2: Standard tracking efficiency offline during Run 3 for different tracking iterations, as a function of simulated radial position of the track production vertex (left). Overall standard tracking efficiency at the HLT during Run 3, as a function of the simulated radial position of the track production vertex (right). In both figures, $ \mathrm{t} \overline{\mathrm{t}} $ simulation in 2025 conditions and an average PU of 62 is used, and the tracks are required to have $ p_{\mathrm{T}} > $ 0.9 GeV and $ |\eta| < $ 2.5.
png pdf	Figure 2-a: Standard tracking efficiency offline during Run 3 for different tracking iterations, as a function of simulated radial position of the track production vertex (left). Overall standard tracking efficiency at the HLT during Run 3, as a function of the simulated radial position of the track production vertex (right). In both figures, $ \mathrm{t} \overline{\mathrm{t}} $ simulation in 2025 conditions and an average PU of 62 is used, and the tracks are required to have $ p_{\mathrm{T}} > $ 0.9 GeV and $ |\eta| < $ 2.5.
png pdf	Figure 2-b: Standard tracking efficiency offline during Run 3 for different tracking iterations, as a function of simulated radial position of the track production vertex (left). Overall standard tracking efficiency at the HLT during Run 3, as a function of the simulated radial position of the track production vertex (right). In both figures, $ \mathrm{t} \overline{\mathrm{t}} $ simulation in 2025 conditions and an average PU of 62 is used, and the tracks are required to have $ p_{\mathrm{T}} > $ 0.9 GeV and $ |\eta| < $ 2.5.
png pdf	Figure 3: Feynman diagrams for the AMSB $ \tilde{\chi}_{1}^{\pm} \to \tilde{\chi}_{1}^{0} $+X process.
png pdf	Figure 3-a: Feynman diagrams for the AMSB $ \tilde{\chi}_{1}^{\pm} \to \tilde{\chi}_{1}^{0} $+X process.
png pdf	Figure 3-b: Feynman diagrams for the AMSB $ \tilde{\chi}_{1}^{\pm} \to \tilde{\chi}_{1}^{0} $+X process.
png pdf	Figure 3-c: Feynman diagrams for the AMSB $ \tilde{\chi}_{1}^{\pm} \to \tilde{\chi}_{1}^{0} $+X process.
png pdf	Figure 4: Feynman diagram for the $ \mathrm{H} \to \mathrm{X}\mathrm{X} $ process.
png pdf	Figure 5: Feynman diagram for the $ \mathrm{H} \to \mathrm{Z}_\text{D}\mathrm{Z}_\text{D} $ process.
png pdf	Figure 6: Feynman diagram for the direct $ \tilde{\tau} $ pair production, followed by decay of each $ \tilde{\tau} $ to a $ \tau $ lepton and a neutralino $ \tilde{\chi}_{1}^{0} $ (or a gravitino $ \tilde{\mathrm{G}} $).
png pdf	Figure 7: Feynman diagram for the GMSB SPS8 benchmark model, where pair-produced squarks and gluinos undergo cascade decays and eventually produce a gravitino $ \tilde{\mathrm{G}} $.
png pdf	Figure 8: Feynman diagram for the singlet-triplet Higgs portal dark matter benchmark model, where a charged dark partner particle $ \chi^{\pm} $ in a compressed dark sector decays via an off-shell W boson and produces a stable neutral dark matter candidate $ \chi^{0} $.
png pdf	Figure 9: Event display of a simulated disappearing track. The $ \tilde{\chi}_{1}^{\pm} $ (red line) is the LLP that decays in the tracker and recoils off an ISR jet (green lines), while $ \tilde{\chi}_{1}^{0} $ (yellow line) is undetected by the detector, and $ \pi^{\pm} $ (blue curve) is not reconstructed because of its low $ p_{\mathrm{T}} $. The yellow and red arrows represent the calo and PF $ p_{\mathrm{T}}^\text{miss} $, respectively.
png pdf	Figure 10: L1T+HLT efficiency of the disappearing-track trigger: Efficiency as a function of the number of tracker layers with valid measurements of the track that pass the offline requirements, in $ \tilde{\chi}_{1}^{\pm} \to \tilde{\chi}_{1}^{0} $+X simulated events in 2022 conditions, where $ m_{\tilde{\chi}_{1}^{\pm}}= $ 900 GeV and $ \tilde{\chi}_{1}^{0} $ is nearly mass-degenerate with $ \tilde{\chi}_{1}^{\pm} $ (left). The efficiency is shown for LLPs with $ c\tau= $ 10, 100, and 1000 cm in black, blue, and red, respectively. Comparison of efficiencies calculated with 2022 data (black), 2023 data (blue), and $ \mathrm{W} \to \ell\nu $ simulation (red), as a function of offline reconstructed PF $ p_{\mathrm{T}}^{\text{miss},\,\mu} $ (right). The efficiency follows the turn-on shape but does not reach 100% because of the isolated track leg of the algorithm.
png pdf	Figure 10-a: L1T+HLT efficiency of the disappearing-track trigger: Efficiency as a function of the number of tracker layers with valid measurements of the track that pass the offline requirements, in $ \tilde{\chi}_{1}^{\pm} \to \tilde{\chi}_{1}^{0} $+X simulated events in 2022 conditions, where $ m_{\tilde{\chi}_{1}^{\pm}}= $ 900 GeV and $ \tilde{\chi}_{1}^{0} $ is nearly mass-degenerate with $ \tilde{\chi}_{1}^{\pm} $ (left). The efficiency is shown for LLPs with $ c\tau= $ 10, 100, and 1000 cm in black, blue, and red, respectively. Comparison of efficiencies calculated with 2022 data (black), 2023 data (blue), and $ \mathrm{W} \to \ell\nu $ simulation (red), as a function of offline reconstructed PF $ p_{\mathrm{T}}^{\text{miss},\,\mu} $ (right). The efficiency follows the turn-on shape but does not reach 100% because of the isolated track leg of the algorithm.
png pdf	Figure 10-b: L1T+HLT efficiency of the disappearing-track trigger: Efficiency as a function of the number of tracker layers with valid measurements of the track that pass the offline requirements, in $ \tilde{\chi}_{1}^{\pm} \to \tilde{\chi}_{1}^{0} $+X simulated events in 2022 conditions, where $ m_{\tilde{\chi}_{1}^{\pm}}= $ 900 GeV and $ \tilde{\chi}_{1}^{0} $ is nearly mass-degenerate with $ \tilde{\chi}_{1}^{\pm} $ (left). The efficiency is shown for LLPs with $ c\tau= $ 10, 100, and 1000 cm in black, blue, and red, respectively. Comparison of efficiencies calculated with 2022 data (black), 2023 data (blue), and $ \mathrm{W} \to \ell\nu $ simulation (red), as a function of offline reconstructed PF $ p_{\mathrm{T}}^{\text{miss},\,\mu} $ (right). The efficiency follows the turn-on shape but does not reach 100% because of the isolated track leg of the algorithm.
png pdf	Figure 11: L1T+HLT efficiency of each leg of the disappearing-track trigger in 2022 data (black), 2023 data (blue), and $ \mathrm{W} \to \ell\nu $ simulation (red). Efficiency of the L1T + HLT $ p_{\mathrm{T}}^\text{miss} $ leg as a function of offline reconstructed PF $ p_{\mathrm{T}}^{\text{miss},\,\mu} $ (left). Efficiency of the full HLT path, taking into account only events that already passed through the $ p_{\mathrm{T}}^\text{miss} $ leg, as a function of the selected muon $ p_{\mathrm{T}} $ (right).
png pdf	Figure 11-a: L1T+HLT efficiency of each leg of the disappearing-track trigger in 2022 data (black), 2023 data (blue), and $ \mathrm{W} \to \ell\nu $ simulation (red). Efficiency of the L1T + HLT $ p_{\mathrm{T}}^\text{miss} $ leg as a function of offline reconstructed PF $ p_{\mathrm{T}}^{\text{miss},\,\mu} $ (left). Efficiency of the full HLT path, taking into account only events that already passed through the $ p_{\mathrm{T}}^\text{miss} $ leg, as a function of the selected muon $ p_{\mathrm{T}} $ (right).
png pdf	Figure 11-b: L1T+HLT efficiency of each leg of the disappearing-track trigger in 2022 data (black), 2023 data (blue), and $ \mathrm{W} \to \ell\nu $ simulation (red). Efficiency of the L1T + HLT $ p_{\mathrm{T}}^\text{miss} $ leg as a function of offline reconstructed PF $ p_{\mathrm{T}}^{\text{miss},\,\mu} $ (left). Efficiency of the full HLT path, taking into account only events that already passed through the $ p_{\mathrm{T}}^\text{miss} $ leg, as a function of the selected muon $ p_{\mathrm{T}} $ (right).
png pdf	Figure 12: Event display of simulated $ \tilde{\tau} $ pair production in a GMSB benchmark model, followed by the decay of each $ \tilde{\tau} $ to a $ \tau $ lepton and a neutralino $ \tilde{\chi}_{1}^{0} $, with the $ \tau $ leptons decaying hadronically. The magenta lines indicate the $ \tilde{\tau} $ particles, the light blue lines indicate the neutralinos, and the dark orange lines indicate the $ \tau $ leptons. The shaded dark yellow cones show the two reconstructed jets, and the orange lines inside the jets are the hadrons from the $ \tau $ decay.
png pdf	Figure 13: L1T+HLT efficiency of the displaced $ \tau_\mathrm{h} $ trigger, for simulated $ \mathrm{p}\mathrm{p} \to \tilde{\tau}\tilde{\tau} (\tilde{\tau} \to \tau\tilde{\chi}_{1}^{0}) $ events, where each $ \tau $ decays hadronically and the $ \tilde{\tau} $ has a simulated $ c\tau $ of 10 cm. The efficiency is shown for the displaced di-$ \tau_\mathrm{h} $ trigger path (blue filled triangles), the previously available $ p_{\mathrm{T}}^\text{miss} $-based paths (orange open circles), the previously available prompt di-$ \tau_\mathrm{h} $ paths (purple open squares), the combination of the $ p_{\mathrm{T}}^\text{miss} $-based and prompt di-$ \tau_\mathrm{h} $ paths (gray open triangles), and the combination of the $ p_{\mathrm{T}}^\text{miss} $-based, prompt di-$ \tau_\mathrm{h} $, and displaced di-$ \tau_\mathrm{h} $ paths (red filled circles), using 2022 data-taking conditions. The efficiency is evaluated with respect to truth-level quantities. Efficiency of the highest-$ p_{\mathrm{T}} \tau $ of the event as a function of the $ d_{\text{0}} $ (left). Efficiency as a function of $ p_{\mathrm{T}}^\text{miss} $ (right). A selection on the visible component of the truth-level tau lepton $ p_{\mathrm{T}} > $ 30 GeV and its pseudorapidity $ |\eta| < $ 2.1 is applied. The lower panels show the ratio (gain in %) of the trigger efficiency given by the combination of the displaced di-$ \tau_\mathrm{h} $ trigger path with the $ p_{\mathrm{T}}^\text{miss} $-based and prompt di-$ \tau_\mathrm{h} $ paths, divided by that of the combination of the previously available $ p_{\mathrm{T}}^\text{miss} $-based and prompt di-$ \tau_\mathrm{h} $ paths.
png pdf	Figure 13-a: L1T+HLT efficiency of the displaced $ \tau_\mathrm{h} $ trigger, for simulated $ \mathrm{p}\mathrm{p} \to \tilde{\tau}\tilde{\tau} (\tilde{\tau} \to \tau\tilde{\chi}_{1}^{0}) $ events, where each $ \tau $ decays hadronically and the $ \tilde{\tau} $ has a simulated $ c\tau $ of 10 cm. The efficiency is shown for the displaced di-$ \tau_\mathrm{h} $ trigger path (blue filled triangles), the previously available $ p_{\mathrm{T}}^\text{miss} $-based paths (orange open circles), the previously available prompt di-$ \tau_\mathrm{h} $ paths (purple open squares), the combination of the $ p_{\mathrm{T}}^\text{miss} $-based and prompt di-$ \tau_\mathrm{h} $ paths (gray open triangles), and the combination of the $ p_{\mathrm{T}}^\text{miss} $-based, prompt di-$ \tau_\mathrm{h} $, and displaced di-$ \tau_\mathrm{h} $ paths (red filled circles), using 2022 data-taking conditions. The efficiency is evaluated with respect to truth-level quantities. Efficiency of the highest-$ p_{\mathrm{T}} \tau $ of the event as a function of the $ d_{\text{0}} $ (left). Efficiency as a function of $ p_{\mathrm{T}}^\text{miss} $ (right). A selection on the visible component of the truth-level tau lepton $ p_{\mathrm{T}} > $ 30 GeV and its pseudorapidity $ |\eta| < $ 2.1 is applied. The lower panels show the ratio (gain in %) of the trigger efficiency given by the combination of the displaced di-$ \tau_\mathrm{h} $ trigger path with the $ p_{\mathrm{T}}^\text{miss} $-based and prompt di-$ \tau_\mathrm{h} $ paths, divided by that of the combination of the previously available $ p_{\mathrm{T}}^\text{miss} $-based and prompt di-$ \tau_\mathrm{h} $ paths.
png pdf	Figure 13-b: L1T+HLT efficiency of the displaced $ \tau_\mathrm{h} $ trigger, for simulated $ \mathrm{p}\mathrm{p} \to \tilde{\tau}\tilde{\tau} (\tilde{\tau} \to \tau\tilde{\chi}_{1}^{0}) $ events, where each $ \tau $ decays hadronically and the $ \tilde{\tau} $ has a simulated $ c\tau $ of 10 cm. The efficiency is shown for the displaced di-$ \tau_\mathrm{h} $ trigger path (blue filled triangles), the previously available $ p_{\mathrm{T}}^\text{miss} $-based paths (orange open circles), the previously available prompt di-$ \tau_\mathrm{h} $ paths (purple open squares), the combination of the $ p_{\mathrm{T}}^\text{miss} $-based and prompt di-$ \tau_\mathrm{h} $ paths (gray open triangles), and the combination of the $ p_{\mathrm{T}}^\text{miss} $-based, prompt di-$ \tau_\mathrm{h} $, and displaced di-$ \tau_\mathrm{h} $ paths (red filled circles), using 2022 data-taking conditions. The efficiency is evaluated with respect to truth-level quantities. Efficiency of the highest-$ p_{\mathrm{T}} \tau $ of the event as a function of the $ d_{\text{0}} $ (left). Efficiency as a function of $ p_{\mathrm{T}}^\text{miss} $ (right). A selection on the visible component of the truth-level tau lepton $ p_{\mathrm{T}} > $ 30 GeV and its pseudorapidity $ |\eta| < $ 2.1 is applied. The lower panels show the ratio (gain in %) of the trigger efficiency given by the combination of the displaced di-$ \tau_\mathrm{h} $ trigger path with the $ p_{\mathrm{T}}^\text{miss} $-based and prompt di-$ \tau_\mathrm{h} $ paths, divided by that of the combination of the previously available $ p_{\mathrm{T}}^\text{miss} $-based and prompt di-$ \tau_\mathrm{h} $ paths.
png pdf	Figure 14: Total rate of the displaced $ \tau_\mathrm{h} $ trigger in 2022 (left) and 2023 (right) data, as a function of PU.
png pdf	Figure 14-a: Total rate of the displaced $ \tau_\mathrm{h} $ trigger in 2022 (left) and 2023 (right) data, as a function of PU.
png pdf	Figure 14-b: Total rate of the displaced $ \tau_\mathrm{h} $ trigger in 2022 (left) and 2023 (right) data, as a function of PU.
png pdf	Figure 15: Event display of a pair of displaced jets arising from an LLP decay, producing displaced vertices and tracks. The simulated process is $ \mathrm{H} \to \text{S}\text{S} \to \mathrm{q}\overline{\mathrm{q}}\mathrm{q}\overline{\mathrm{q}} $. The blue curves indicate the reconstructed tracks. The yellow cones indicate two reconstructed jets, with a number of associated displaced tracks. The blue point indicates the displaced vertex induced by the LLP decay.
png pdf	Figure 16: HLT efficiency for a given event passing the main displaced-jets trigger to satisfy HLT calorimeter $ H_{\mathrm{T}} > $ 430 GeV (left) and $ H_{\mathrm{T}} > $ 390 GeV (right) as a function of the offline calorimeter $ H_{\mathrm{T}} $. For this trigger, the minimum calorimeter $ H_{\mathrm{T}} $ threshold was 430 (390) GeV in 2022 (2023 and later). The measurements are performed in data collected in 2022 (green circles), in 2023 before an update of the HCAL gains and energy response corrections (black squares), and in 2023 after the update (blue triangles).
png pdf	Figure 16-a: HLT efficiency for a given event passing the main displaced-jets trigger to satisfy HLT calorimeter $ H_{\mathrm{T}} > $ 430 GeV (left) and $ H_{\mathrm{T}} > $ 390 GeV (right) as a function of the offline calorimeter $ H_{\mathrm{T}} $. For this trigger, the minimum calorimeter $ H_{\mathrm{T}} $ threshold was 430 (390) GeV in 2022 (2023 and later). The measurements are performed in data collected in 2022 (green circles), in 2023 before an update of the HCAL gains and energy response corrections (black squares), and in 2023 after the update (blue triangles).
png pdf	Figure 16-b: HLT efficiency for a given event passing the main displaced-jets trigger to satisfy HLT calorimeter $ H_{\mathrm{T}} > $ 430 GeV (left) and $ H_{\mathrm{T}} > $ 390 GeV (right) as a function of the offline calorimeter $ H_{\mathrm{T}} $. For this trigger, the minimum calorimeter $ H_{\mathrm{T}} $ threshold was 430 (390) GeV in 2022 (2023 and later). The measurements are performed in data collected in 2022 (green circles), in 2023 before an update of the HCAL gains and energy response corrections (black squares), and in 2023 after the update (blue triangles).
png pdf	Figure 17: HLT efficiency of the main displaced-jets trigger: Efficiency of an offline calorimeter jet to pass the online $ p_{\mathrm{T}} $ requirement in displaced-jets triggers (left), which require $ p_{\mathrm{T}} > $ 40 GeV, in data collected in 2022 (green squares), in 2023 before an update of the HCAL gains and energy response corrections (black filled circles), and in 2023 after the update (blue open circles). The efficiencies measured with QCD multijet simulation are also shown, with 2022 conditions (red triangles) and 2023 conditions (purple triangles). These measurements are performed using events collected with a prescaled trigger that requires $ H_{\mathrm{T}} > $ 425 GeV at the HLT. An offline $ H_{\mathrm{T}} > $ 450 GeV selection is also applied to ensure the prescaled trigger reaches its plateau. The efficiency is $ {>} 96% $ when the offline jet $ p_{\mathrm{T}} $ is $ {>} $ 40 GeV. The efficiency has a broader turn-on in the later 2023 data because of the update of the HCAL conditions. Efficiency of an offline calorimeter jet to have at most one HLT prompt track in 2022 conditions, as a function of the number of offline prompt tracks, in simulated $ \mathrm{H}\to\text{S}\text{S} $, $ \text{S}\to\mathrm{b}\overline{\mathrm{b}} $ signal events where $ m_{\mathrm{H}}= $ 125 GeV and $ m_{\text{S}}= $ 40 GeV (right). Two proper decay lengths of the $ \text{S} $ particle are shown: $ c\tau=$ 10 mm (green circles) and $ c\tau=$ 100 mm (blue squares). For jets in signal events, when the number of offline prompt tracks is $ {<} $ 4, the tagging efficiency is larger than 70%.
png pdf	Figure 17-a: HLT efficiency of the main displaced-jets trigger: Efficiency of an offline calorimeter jet to pass the online $ p_{\mathrm{T}} $ requirement in displaced-jets triggers (left), which require $ p_{\mathrm{T}} > $ 40 GeV, in data collected in 2022 (green squares), in 2023 before an update of the HCAL gains and energy response corrections (black filled circles), and in 2023 after the update (blue open circles). The efficiencies measured with QCD multijet simulation are also shown, with 2022 conditions (red triangles) and 2023 conditions (purple triangles). These measurements are performed using events collected with a prescaled trigger that requires $ H_{\mathrm{T}} > $ 425 GeV at the HLT. An offline $ H_{\mathrm{T}} > $ 450 GeV selection is also applied to ensure the prescaled trigger reaches its plateau. The efficiency is $ {>} 96% $ when the offline jet $ p_{\mathrm{T}} $ is $ {>} $ 40 GeV. The efficiency has a broader turn-on in the later 2023 data because of the update of the HCAL conditions. Efficiency of an offline calorimeter jet to have at most one HLT prompt track in 2022 conditions, as a function of the number of offline prompt tracks, in simulated $ \mathrm{H}\to\text{S}\text{S} $, $ \text{S}\to\mathrm{b}\overline{\mathrm{b}} $ signal events where $ m_{\mathrm{H}}= $ 125 GeV and $ m_{\text{S}}= $ 40 GeV (right). Two proper decay lengths of the $ \text{S} $ particle are shown: $ c\tau=$ 10 mm (green circles) and $ c\tau=$ 100 mm (blue squares). For jets in signal events, when the number of offline prompt tracks is $ {<} $ 4, the tagging efficiency is larger than 70%.
png pdf	Figure 17-b: HLT efficiency of the main displaced-jets trigger: Efficiency of an offline calorimeter jet to pass the online $ p_{\mathrm{T}} $ requirement in displaced-jets triggers (left), which require $ p_{\mathrm{T}} > $ 40 GeV, in data collected in 2022 (green squares), in 2023 before an update of the HCAL gains and energy response corrections (black filled circles), and in 2023 after the update (blue open circles). The efficiencies measured with QCD multijet simulation are also shown, with 2022 conditions (red triangles) and 2023 conditions (purple triangles). These measurements are performed using events collected with a prescaled trigger that requires $ H_{\mathrm{T}} > $ 425 GeV at the HLT. An offline $ H_{\mathrm{T}} > $ 450 GeV selection is also applied to ensure the prescaled trigger reaches its plateau. The efficiency is $ {>} 96% $ when the offline jet $ p_{\mathrm{T}} $ is $ {>} $ 40 GeV. The efficiency has a broader turn-on in the later 2023 data because of the update of the HCAL conditions. Efficiency of an offline calorimeter jet to have at most one HLT prompt track in 2022 conditions, as a function of the number of offline prompt tracks, in simulated $ \mathrm{H}\to\text{S}\text{S} $, $ \text{S}\to\mathrm{b}\overline{\mathrm{b}} $ signal events where $ m_{\mathrm{H}}= $ 125 GeV and $ m_{\text{S}}= $ 40 GeV (right). Two proper decay lengths of the $ \text{S} $ particle are shown: $ c\tau=$ 10 mm (green circles) and $ c\tau=$ 100 mm (blue squares). For jets in signal events, when the number of offline prompt tracks is $ {<} $ 4, the tagging efficiency is larger than 70%.
png pdf	Figure 18: HLT efficiency of the main displaced-jets trigger in 2022 conditions, for $ \mathrm{H}\to\text{S}\text{S} $ signal events where $ m_{\mathrm{H}}= $ 125 GeV and $ m_{\text{S}}= $ 40 GeV. The per-parton (quark or lepton) HLT displaced-jet tagging efficiency as a function of the truth-level $ L_{\text{xy}} $ of the parton is shown for displaced b quarks (blue circles), d quarks (purple triangles), and $ \tau $ leptons (green squares) with $ p_{\mathrm{T}} > $ 40 GeV and $ |\eta| < $ 2.0.
png pdf	Figure 19: The ratio between the Run 3 displaced-jets trigger efficiency and the Run 2 displaced-jets trigger efficiency as a function of LLP $ c\tau $, in simulated $ \mathrm{H}\to\text{S}\text{S} $, $ \text{S}\to\mathrm{b}\overline{\mathrm{b}} $ signal events where $ m_{\mathrm{H}}= $ 125 GeV and $ m_{\text{S}}= $ 15 (blue triangles), 40 (green squares), or 55 (red circles) GeV. The Run-3 displaced-jets trigger efficiencies are measured in 2022 conditions.
png pdf	Figure 20: Diagram showing the lateral view of the CMS HCAL barrel and endcap in Run 3. The distinct depth segmentation is indicated by the different colors, where the HCAL barrel consists of 4 depth layers and the HCAL endcaps contain up to 7 depth layers. A delayed jet signature (left), where the time delay results from a combination of the low LLP velocity due to its relatively high mass and the path length difference with respect to a promptly produced particle, is shown. A displaced jet signature (right) resulting from LLPs decaying within the HCAL volume, producing significant energy deposits deeper in the HCAL with minimal energy deposits in shallower calorimeter layers, is also depicted.
png pdf	Figure 20-a: Diagram showing the lateral view of the CMS HCAL barrel and endcap in Run 3. The distinct depth segmentation is indicated by the different colors, where the HCAL barrel consists of 4 depth layers and the HCAL endcaps contain up to 7 depth layers. A delayed jet signature (left), where the time delay results from a combination of the low LLP velocity due to its relatively high mass and the path length difference with respect to a promptly produced particle, is shown. A displaced jet signature (right) resulting from LLPs decaying within the HCAL volume, producing significant energy deposits deeper in the HCAL with minimal energy deposits in shallower calorimeter layers, is also depicted.
png pdf	Figure 20-b: Diagram showing the lateral view of the CMS HCAL barrel and endcap in Run 3. The distinct depth segmentation is indicated by the different colors, where the HCAL barrel consists of 4 depth layers and the HCAL endcaps contain up to 7 depth layers. A delayed jet signature (left), where the time delay results from a combination of the low LLP velocity due to its relatively high mass and the path length difference with respect to a promptly produced particle, is shown. A displaced jet signature (right) resulting from LLPs decaying within the HCAL volume, producing significant energy deposits deeper in the HCAL with minimal energy deposits in shallower calorimeter layers, is also depicted.
png pdf	Figure 21: L1T HCAL tower efficiency of the timing-flagged towers in 2023 data: HCAL delayed timing tower efficiency during an HCAL timing phase scan during 2023, with efficiencies split by trigger towers centered at $ \eta\approx $ 0 (blue circles), 0.65 (red squares), 1.26 (black triangles) and with width $ \Delta \eta = $ 0.087. The sharp turn-on between timing delays of 0-6 ns is expected with the prompt timing range set at $ t_{\text{pulse}}\leq $ 6 ns, demonstrating the timing trigger performance. The timing-flagged towers must have at least one delayed cell, no prompt cells, and energy over 4 GeV. The efficiency is calculated relative to towers with any valid timing code, meaning the tower contains at least one cell with energy $ \geq $ 4 GeV and a TDC code of prompt, slightly delayed, or very delayed. Multiple flagged towers are required for the HCAL-based displaced and delayed jet L1T to be set, and this shows the turn-on at a per-tower level relative to incoming pulse timing.
png pdf	Figure 22: L1T efficiency of the LLP jet trigger in 2023 data: The HCAL LLP-flagged L1T trigger delayed jet fraction versus jet $ E_{\mathrm{T}} $ during the 2023 HCAL phase scan demonstrates that the delayed jet fraction approaches unity as the timing shift, with units in ns, is increased. The figure shows results inclusive in pseudorapidity for the HCAL barrel, corresponding to $ |\eta| \leq $ 1.35. The fraction of LLP-flagged L1 jets is compared to all L1 jets from a dataset of events enriched with jets or $ p_{\mathrm{T}}^\text{miss} $. No explicit selection criterion is applied on the jet $ E_{\mathrm{T}} $, though the implicit requirement for a jet to have at least two cells with $ E_{\mathrm{T}}\geq $ 4 GeV shapes the resulting jet turn-on curve.
png pdf	Figure 23: L1T efficiency of the HCAL-based LLP jet triggers, as a function of event $ H_{\mathrm{T}} $ (left) and jet $ p_{\mathrm{T}} $ (right), for $ \mathrm{H} \to \text{S}\text{S} \to \mathrm{b}\overline{\mathrm{b}}\mathrm{b}\overline{\mathrm{b}} $ events with $ m_{\mathrm{H}}= $ 350 GeV, $ m_{\text{S}}= $ 80 GeV, and $ c\tau_{\text{S}}= $ 0.5 m (light blue circles) and $ m_{\mathrm{H}}= $ 125 GeV, $ m_{\text{S}}= $ 50 GeV, and $ c\tau_{\text{S}}= $ 3 m (purple triangles), in 2023 conditions. The trigger efficiency is evaluated for LLPs decaying in HB depths 3 or 4, corresponding to 214.2 $ \leq R < 295\,\text{cm} $ and $ |\eta|\leq $ 1.26. These LLPs are also required to match to an offline jet in HB.
png pdf	Figure 23-a: L1T efficiency of the HCAL-based LLP jet triggers, as a function of event $ H_{\mathrm{T}} $ (left) and jet $ p_{\mathrm{T}} $ (right), for $ \mathrm{H} \to \text{S}\text{S} \to \mathrm{b}\overline{\mathrm{b}}\mathrm{b}\overline{\mathrm{b}} $ events with $ m_{\mathrm{H}}= $ 350 GeV, $ m_{\text{S}}= $ 80 GeV, and $ c\tau_{\text{S}}= $ 0.5 m (light blue circles) and $ m_{\mathrm{H}}= $ 125 GeV, $ m_{\text{S}}= $ 50 GeV, and $ c\tau_{\text{S}}= $ 3 m (purple triangles), in 2023 conditions. The trigger efficiency is evaluated for LLPs decaying in HB depths 3 or 4, corresponding to 214.2 $ \leq R < 295\,\text{cm} $ and $ |\eta|\leq $ 1.26. These LLPs are also required to match to an offline jet in HB.
png pdf	Figure 23-b: L1T efficiency of the HCAL-based LLP jet triggers, as a function of event $ H_{\mathrm{T}} $ (left) and jet $ p_{\mathrm{T}} $ (right), for $ \mathrm{H} \to \text{S}\text{S} \to \mathrm{b}\overline{\mathrm{b}}\mathrm{b}\overline{\mathrm{b}} $ events with $ m_{\mathrm{H}}= $ 350 GeV, $ m_{\text{S}}= $ 80 GeV, and $ c\tau_{\text{S}}= $ 0.5 m (light blue circles) and $ m_{\mathrm{H}}= $ 125 GeV, $ m_{\text{S}}= $ 50 GeV, and $ c\tau_{\text{S}}= $ 3 m (purple triangles), in 2023 conditions. The trigger efficiency is evaluated for LLPs decaying in HB depths 3 or 4, corresponding to 214.2 $ \leq R < 295\,\text{cm} $ and $ |\eta|\leq $ 1.26. These LLPs are also required to match to an offline jet in HB.
png pdf	Figure 24: L1T efficiency of the HCAL-based LLP jet triggers as a function of LLP decay radius $ R $ for $ \mathrm{H} \to \text{S}\text{S} \to \mathrm{b}\overline{\mathrm{b}}\mathrm{b}\overline{\mathrm{b}} $ events with $ m_{\mathrm{H}}= $ 350 GeV, $ m_{\text{S}}= $ 80 GeV, and $ c\tau_{\text{S}}= $ 0.5 m (light blue circles) and $ m_{\mathrm{H}}= $ 125 GeV, $ m_{\text{S}}= $ 50 GeV, and $ c\tau_{\text{S}}= $ 3 m (purple triangles), in 2023 conditions. The trigger efficiency is evaluated for LLPs within $ |\eta|\leq $ 1.26 where either the LLP or its decay products are matched to an offline jet in HB with $ p_{\mathrm{T}} > $ 100 GeV.
png pdf	Figure 25: HLT efficiency of the CalRatio trigger as a function of the leading PF jet NHF in 2024 data, measured with respect to a logical OR of the HCAL-based LLP L1 jet triggers (left). Distribution of the leading PF jet NHF (right) in 2024 data (black circles), $ \mathrm{W} \to \ell\nu $ background simulation in 2024 conditions (red squares), and $ \mathrm{H} \to \text{S}\text{S} \to \mathrm{b}\overline{\mathrm{b}}\mathrm{b}\overline{\mathrm{b}} $ signal simulation in 2023 conditions (blue and purple triangles). Events are required to have $ H_{\mathrm{T}} > $ 200 GeV and the leading jet is required to have $ p_{\mathrm{T}} > $ 60 GeV and $ |\eta| \leq $ 1.5, which are equivalent to the respective HLT jet object selections. The signal distributions additionally require the leading jet to be matched to an LLP decaying anywhere inside the barrel calorimeter volume (129 $ \leq R < 295\,\text{cm} $). The clear separation between the displaced signal and the prompt background in the right plot motivates the development of the CalRatio trigger.
png pdf	Figure 25-a: HLT efficiency of the CalRatio trigger as a function of the leading PF jet NHF in 2024 data, measured with respect to a logical OR of the HCAL-based LLP L1 jet triggers (left). Distribution of the leading PF jet NHF (right) in 2024 data (black circles), $ \mathrm{W} \to \ell\nu $ background simulation in 2024 conditions (red squares), and $ \mathrm{H} \to \text{S}\text{S} \to \mathrm{b}\overline{\mathrm{b}}\mathrm{b}\overline{\mathrm{b}} $ signal simulation in 2023 conditions (blue and purple triangles). Events are required to have $ H_{\mathrm{T}} > $ 200 GeV and the leading jet is required to have $ p_{\mathrm{T}} > $ 60 GeV and $ |\eta| \leq $ 1.5, which are equivalent to the respective HLT jet object selections. The signal distributions additionally require the leading jet to be matched to an LLP decaying anywhere inside the barrel calorimeter volume (129 $ \leq R < 295\,\text{cm} $). The clear separation between the displaced signal and the prompt background in the right plot motivates the development of the CalRatio trigger.
png pdf	Figure 25-b: HLT efficiency of the CalRatio trigger as a function of the leading PF jet NHF in 2024 data, measured with respect to a logical OR of the HCAL-based LLP L1 jet triggers (left). Distribution of the leading PF jet NHF (right) in 2024 data (black circles), $ \mathrm{W} \to \ell\nu $ background simulation in 2024 conditions (red squares), and $ \mathrm{H} \to \text{S}\text{S} \to \mathrm{b}\overline{\mathrm{b}}\mathrm{b}\overline{\mathrm{b}} $ signal simulation in 2023 conditions (blue and purple triangles). Events are required to have $ H_{\mathrm{T}} > $ 200 GeV and the leading jet is required to have $ p_{\mathrm{T}} > $ 60 GeV and $ |\eta| \leq $ 1.5, which are equivalent to the respective HLT jet object selections. The signal distributions additionally require the leading jet to be matched to an LLP decaying anywhere inside the barrel calorimeter volume (129 $ \leq R < 295\,\text{cm} $). The clear separation between the displaced signal and the prompt background in the right plot motivates the development of the CalRatio trigger.
png pdf	Figure 26: Diagram of a typical delayed-jet signal event.
png pdf	Figure 27: L1T+HLT efficiency of the inclusive (trackless) delayed-jet triggers introduced in Run 3 in red squares (blue triangles), in 2022 conditions, and the $ H_{\mathrm{T}} $ trigger (black circles), which was all that was available in Run 2, for a $ \mathrm{H} \to \mathrm{X}\mathrm{X} \to \mathrm{b}\overline{\mathrm{b}}\mathrm{b}\overline{\mathrm{b}} $ signal with $ m_{\mathrm{H}}= $ 1000 GeV, $ m_{\mathrm{X}}= $ 450 GeV, and $ c\tau= $ 10 m. The addition of these delayed jet triggers results in a significant improvement in the efficiency of the signal for 430 $ < H_{\mathrm{T}} < $ 1050 GeV.
png pdf	Figure 28: L1T+HLT efficiency of the delayed-jets triggers for signal models with $ \mathrm{H} \to \mathrm{X}\mathrm{X} \to \mathrm{b}\overline{\mathrm{b}}\mathrm{b}\overline{\mathrm{b}} $ (left) and $ \mathrm{H} \to \mathrm{X}\mathrm{X} \to 4\tau $ (right), with $ m_{\mathrm{H}}= $ 1000 GeV, $ m_{\mathrm{X}}= $ 450 GeV and $ c\tau= $ 10 m, in 2022 conditions. The improvement from the tau triggers (blue and green triangles) can be seen in the $ H_{\mathrm{T}} < $ 430 GeV region compared to the $ H_{\mathrm{T}} $-seeded triggers (black circles and red squares). These plots include events with jets with $ p_{\mathrm{T}} > $ 40 GeV, number of ECAL cells $ {>} $ 5, barrel region with $ |\eta| < $ 1.48 and jet timing $ {>} $ 2 ns.
png pdf	Figure 28-a: L1T+HLT efficiency of the delayed-jets triggers for signal models with $ \mathrm{H} \to \mathrm{X}\mathrm{X} \to \mathrm{b}\overline{\mathrm{b}}\mathrm{b}\overline{\mathrm{b}} $ (left) and $ \mathrm{H} \to \mathrm{X}\mathrm{X} \to 4\tau $ (right), with $ m_{\mathrm{H}}= $ 1000 GeV, $ m_{\mathrm{X}}= $ 450 GeV and $ c\tau= $ 10 m, in 2022 conditions. The improvement from the tau triggers (blue and green triangles) can be seen in the $ H_{\mathrm{T}} < $ 430 GeV region compared to the $ H_{\mathrm{T}} $-seeded triggers (black circles and red squares). These plots include events with jets with $ p_{\mathrm{T}} > $ 40 GeV, number of ECAL cells $ {>} $ 5, barrel region with $ |\eta| < $ 1.48 and jet timing $ {>} $ 2 ns.
png pdf	Figure 28-b: L1T+HLT efficiency of the delayed-jets triggers for signal models with $ \mathrm{H} \to \mathrm{X}\mathrm{X} \to \mathrm{b}\overline{\mathrm{b}}\mathrm{b}\overline{\mathrm{b}} $ (left) and $ \mathrm{H} \to \mathrm{X}\mathrm{X} \to 4\tau $ (right), with $ m_{\mathrm{H}}= $ 1000 GeV, $ m_{\mathrm{X}}= $ 450 GeV and $ c\tau= $ 10 m, in 2022 conditions. The improvement from the tau triggers (blue and green triangles) can be seen in the $ H_{\mathrm{T}} < $ 430 GeV region compared to the $ H_{\mathrm{T}} $-seeded triggers (black circles and red squares). These plots include events with jets with $ p_{\mathrm{T}} > $ 40 GeV, number of ECAL cells $ {>} $ 5, barrel region with $ |\eta| < $ 1.48 and jet timing $ {>} $ 2 ns.
png pdf	Figure 29: L1T+HLT efficiency of the delayed-jets triggers as a function of jet timing for 2022 and 2023 data-taking periods for the $ H_{\mathrm{T}} $-seeded trigger (left) and the $ \tau $-seeded trigger (right). A clear turn-on feature can be seen around the threshold values. The plots include events that pass the $ p_{\mathrm{T}}^\text{miss} > $ 200 GeV trigger and have at least one barrel jet with $ p_{\mathrm{T}} > $ 50 GeV, number of ECAL cells $ {>} $ 8, and ECAL energy $ {>} $ 25 GeV. The $ H_{\mathrm{T}} $ is calculated using the scalar sum of jets with offline $ p_{\mathrm{T}} > $ 40 GeV, and this is different from the $ H_{\mathrm{T}} $ calculation used at the HLT level, which can cause trigger inefficiencies. The maximum triggerable jet time is 12.5 ns.
png pdf	Figure 30: Diagram of a prompt (orange dotted line) and displaced (red solid line) electron, which comes from the decay of a chargino, reaching the ECAL in the $ x-z $ plane. The ECAL crystal clocks are shifted so that a prompt electron arrives at the same time stamp for any crystal. An electron produced at a displaced vertex thus arrives delayed compared to a prompt particle. This is diagrammatically shown in the clocks above the ECAL crystals in blue.
png pdf	Figure 31: ECAL time delay of the $ \mathrm{e}/\gamma $ L1 seeds in the barrel (left) and endcap (right). The distributions are shown for 2023 $ \mathrm{Z} \to \mathrm{e}\mathrm{e} $ data (black points) and $ \chi^{0} c\tau $ values of 3 (light red circles), 30 (darker red circles), and 300 cm (bright red circles), assuming the singlet-triplet Higgs dark portal model ($ \chi^{\pm} \to \chi^{0} \ell \nu $, where the $ \chi^{\pm} $ has a mass of 220 GeV and the $ \chi^{0} $ has a mass of 200 GeV). The distributions are normalized to unity.
png pdf	Figure 31-a: ECAL time delay of the $ \mathrm{e}/\gamma $ L1 seeds in the barrel (left) and endcap (right). The distributions are shown for 2023 $ \mathrm{Z} \to \mathrm{e}\mathrm{e} $ data (black points) and $ \chi^{0} c\tau $ values of 3 (light red circles), 30 (darker red circles), and 300 cm (bright red circles), assuming the singlet-triplet Higgs dark portal model ($ \chi^{\pm} \to \chi^{0} \ell \nu $, where the $ \chi^{\pm} $ has a mass of 220 GeV and the $ \chi^{0} $ has a mass of 200 GeV). The distributions are normalized to unity.
png pdf	Figure 31-b: ECAL time delay of the $ \mathrm{e}/\gamma $ L1 seeds in the barrel (left) and endcap (right). The distributions are shown for 2023 $ \mathrm{Z} \to \mathrm{e}\mathrm{e} $ data (black points) and $ \chi^{0} c\tau $ values of 3 (light red circles), 30 (darker red circles), and 300 cm (bright red circles), assuming the singlet-triplet Higgs dark portal model ($ \chi^{\pm} \to \chi^{0} \ell \nu $, where the $ \chi^{\pm} $ has a mass of 220 GeV and the $ \chi^{0} $ has a mass of 200 GeV). The distributions are normalized to unity.
png pdf	Figure 32: HLT rate (blue points) of the delayed-diphoton trigger in the first data collected in 2023, corresponding to an integrated luminosity of 4.2 fb$ ^{-1} $, compared with the PU during the same data-taking period(red points), as a function of integrated luminosity (left). The rate decreases nonlinearly, and then changes to linear asymptotically through a single collision fill. It recovers by the start of the next fill with $ {<}1% $ reduction in rate between the fills. The rate generally increased throughout the year because of periodic online calibrations to mitigate the loss in trigger efficiency due to radiation damage of the ECAL crystals. The delayed-diphoton trigger rate shows a linear dependency on PU in 2024 data, at an instantaneous luminosity of approximately 1.8 $ \times$ 10$^{34} $ cm$^{-2}$s$^{-1}$ (right).
png pdf	Figure 32-a: HLT rate (blue points) of the delayed-diphoton trigger in the first data collected in 2023, corresponding to an integrated luminosity of 4.2 fb$ ^{-1} $, compared with the PU during the same data-taking period(red points), as a function of integrated luminosity (left). The rate decreases nonlinearly, and then changes to linear asymptotically through a single collision fill. It recovers by the start of the next fill with $ {<}1% $ reduction in rate between the fills. The rate generally increased throughout the year because of periodic online calibrations to mitigate the loss in trigger efficiency due to radiation damage of the ECAL crystals. The delayed-diphoton trigger rate shows a linear dependency on PU in 2024 data, at an instantaneous luminosity of approximately 1.8 $ \times$ 10$^{34} $ cm$^{-2}$s$^{-1}$ (right).
png pdf	Figure 32-b: HLT rate (blue points) of the delayed-diphoton trigger in the first data collected in 2023, corresponding to an integrated luminosity of 4.2 fb$ ^{-1} $, compared with the PU during the same data-taking period(red points), as a function of integrated luminosity (left). The rate decreases nonlinearly, and then changes to linear asymptotically through a single collision fill. It recovers by the start of the next fill with $ {<}1% $ reduction in rate between the fills. The rate generally increased throughout the year because of periodic online calibrations to mitigate the loss in trigger efficiency due to radiation damage of the ECAL crystals. The delayed-diphoton trigger rate shows a linear dependency on PU in 2024 data, at an instantaneous luminosity of approximately 1.8 $ \times$ 10$^{34} $ cm$^{-2}$s$^{-1}$ (right).
png pdf	Figure 33: L1T+HLT efficiency of the delayed-diphoton trigger as a function of the subleading probe electron ($ \mathrm{e}_2 $) supercluster seed time, measured with data collected in 2023. At the HLT, the subleading $ \mathrm{e}/\gamma $ supercluster ($ \mathrm{e}/\gamma_2 $) is required to have $ p_{\mathrm{T}} > $ 12 GeV, $ |\eta| < $ 2.1, and a seed time $ {>} $ 1 ns. The trigger is fully efficient above 1 ns.
png pdf	Figure 34: L1T+HLT efficiency of the delayed-diphoton trigger as a function of subleading probe electron ($ \mathrm{e}_2 $) $ p_{\mathrm{T}} $ (left) and $ \eta $ (right), measured with data collected in 2023. At the HLT, the subleading $ \mathrm{e}/\gamma $ supercluster ($ \mathrm{e}/\gamma_2 $) is required to have $ p_{\mathrm{T}} > $ 12 GeV, $ |\eta| < $ 2.1, and a seed time $ {>} $ 1 ns. The efficiency rises sharply for $ p_{\mathrm{T}} > $ 12 GeV and plateaus for $ p_{\mathrm{T}} > $ 35 GeV. The slow rise in between is from additional L1 $ H_{\mathrm{T}} $ requirements. The trigger is efficient in the region $ |\eta| < $ 2.1.
png pdf	Figure 34-a: L1T+HLT efficiency of the delayed-diphoton trigger as a function of subleading probe electron ($ \mathrm{e}_2 $) $ p_{\mathrm{T}} $ (left) and $ \eta $ (right), measured with data collected in 2023. At the HLT, the subleading $ \mathrm{e}/\gamma $ supercluster ($ \mathrm{e}/\gamma_2 $) is required to have $ p_{\mathrm{T}} > $ 12 GeV, $ |\eta| < $ 2.1, and a seed time $ {>} $ 1 ns. The efficiency rises sharply for $ p_{\mathrm{T}} > $ 12 GeV and plateaus for $ p_{\mathrm{T}} > $ 35 GeV. The slow rise in between is from additional L1 $ H_{\mathrm{T}} $ requirements. The trigger is efficient in the region $ |\eta| < $ 2.1.
png pdf	Figure 34-b: L1T+HLT efficiency of the delayed-diphoton trigger as a function of subleading probe electron ($ \mathrm{e}_2 $) $ p_{\mathrm{T}} $ (left) and $ \eta $ (right), measured with data collected in 2023. At the HLT, the subleading $ \mathrm{e}/\gamma $ supercluster ($ \mathrm{e}/\gamma_2 $) is required to have $ p_{\mathrm{T}} > $ 12 GeV, $ |\eta| < $ 2.1, and a seed time $ {>} $ 1 ns. The efficiency rises sharply for $ p_{\mathrm{T}} > $ 12 GeV and plateaus for $ p_{\mathrm{T}} > $ 35 GeV. The slow rise in between is from additional L1 $ H_{\mathrm{T}} $ requirements. The trigger is efficient in the region $ |\eta| < $ 2.1.
png pdf	Figure 35: Diagrams of a promptly-produced photon in the $ x-y $ plane showering in the ECAL (left), a delayed photon produced from a long-lived neutralino $ \tilde{\chi}^{0} $ in the $ x-y $ plane and showering later in the ECAL (middle), and an elliptical shower in the $ \eta-\phi $ plane produced from a delayed photon (right). The lengths of the major ($ S_{\text{major}} $) and minor ($ S_{\text{minor}} $) axes of the shower and the reconstructed hits (RecHits) that compose the shower are labeled.
png pdf	Figure 36: L1T+HLT efficiency of the displaced photon$ +H_{\mathrm{T}} $ trigger as a function of photon $ p_{\mathrm{T}} $ (left) and event $ H_{\mathrm{T}} $ (right), for 2017 data (black points) and a GMSB signal with $ \Lambda = $ 100 TeV and $ c\tau=10\,\text{cm} $ (blue triangles) and $ c\tau=1000\,\text{cm} $ (red squares). Left: The efficiency to obtain a photon at the HLT passing the trigger requirements is shown. This includes the L1T component. Right: The efficiency to pass the $ H_{\mathrm{T}} $ trigger requirement is shown.
png pdf	Figure 36-a: L1T+HLT efficiency of the displaced photon$ +H_{\mathrm{T}} $ trigger as a function of photon $ p_{\mathrm{T}} $ (left) and event $ H_{\mathrm{T}} $ (right), for 2017 data (black points) and a GMSB signal with $ \Lambda = $ 100 TeV and $ c\tau=10\,\text{cm} $ (blue triangles) and $ c\tau=1000\,\text{cm} $ (red squares). Left: The efficiency to obtain a photon at the HLT passing the trigger requirements is shown. This includes the L1T component. Right: The efficiency to pass the $ H_{\mathrm{T}} $ trigger requirement is shown.
png pdf	Figure 36-b: L1T+HLT efficiency of the displaced photon$ +H_{\mathrm{T}} $ trigger as a function of photon $ p_{\mathrm{T}} $ (left) and event $ H_{\mathrm{T}} $ (right), for 2017 data (black points) and a GMSB signal with $ \Lambda = $ 100 TeV and $ c\tau=10\,\text{cm} $ (blue triangles) and $ c\tau=1000\,\text{cm} $ (red squares). Left: The efficiency to obtain a photon at the HLT passing the trigger requirements is shown. This includes the L1T component. Right: The efficiency to pass the $ H_{\mathrm{T}} $ trigger requirement is shown.
png pdf	Figure 37: Total rate of the displaced photon$ +H_{\mathrm{T}} $ HLT path in 2022 data (left), at an instantaneous luminosity of approximately 1.8 $ \times$ 10$^{34} $ cm$^{-2}$s$^{-1}$, and 2023 data (right), at an instantaneous luminosity of approximately 2.0 $ \times$ 10$^{34} $ cm$^{-2}$s$^{-1}$, as a function of PU. The rate vs PU behavior was nonlinear in 2022 and fixed in time for 2023 data taking.
png pdf	Figure 37-a: Total rate of the displaced photon$ +H_{\mathrm{T}} $ HLT path in 2022 data (left), at an instantaneous luminosity of approximately 1.8 $ \times$ 10$^{34} $ cm$^{-2}$s$^{-1}$, and 2023 data (right), at an instantaneous luminosity of approximately 2.0 $ \times$ 10$^{34} $ cm$^{-2}$s$^{-1}$, as a function of PU. The rate vs PU behavior was nonlinear in 2022 and fixed in time for 2023 data taking.
png pdf	Figure 37-b: Total rate of the displaced photon$ +H_{\mathrm{T}} $ HLT path in 2022 data (left), at an instantaneous luminosity of approximately 1.8 $ \times$ 10$^{34} $ cm$^{-2}$s$^{-1}$, and 2023 data (right), at an instantaneous luminosity of approximately 2.0 $ \times$ 10$^{34} $ cm$^{-2}$s$^{-1}$, as a function of PU. The rate vs PU behavior was nonlinear in 2022 and fixed in time for 2023 data taking.
png pdf	Figure 38: A Run 3 event containing a candidate LLP decay into a pair of muons away from the interaction point, reconstructed in the CMS detector. The red lines correspond to the two muons, which are detected only in the muon system. The muon tracks are used to calculate a dimuon vertex, indicated by the white circle, where the LLP is hypothesized to have decayed.
png pdf	Figure 39: BMTF (upper left), OMTF (upper right), and EMTF (lower) L1T efficiencies for beamspot-constrained and -unconstrained $ p_{\mathrm{T}} $ assignment algorithms for L1T $ p_{\mathrm{T}} > $ 10 GeV with respect to truth-level muon track $ d_{\text{0}} $, obtained using a sample which produces LLPs that decay to dimuons. The L1T algorithms and data-taking conditions correspond to 2024. A selection on the truth-level muon track $ p_{\mathrm{T}} > $ 15 GeV is applied to show the performance at the efficiency plateau. The truth-level muon tracks are extrapolated to the second muon station to determine the $ \eta^{GEN}_{st2} $ values that are used in the plot. The solid markers show the new vertex-unconstrained algorithm performance, while the hollow markers show the default beamspot-constrained algorithm performance. In the EMTF plot, the different colors show different $ |\eta| $ regions: 1.24 $ < |\eta^{GEN}_{st2}| < $ 1.6 (blue), 1.6 $ < |\eta^{GEN}_{st2}| < $ 2.0 (red).
png pdf	Figure 39-a: BMTF (upper left), OMTF (upper right), and EMTF (lower) L1T efficiencies for beamspot-constrained and -unconstrained $ p_{\mathrm{T}} $ assignment algorithms for L1T $ p_{\mathrm{T}} > $ 10 GeV with respect to truth-level muon track $ d_{\text{0}} $, obtained using a sample which produces LLPs that decay to dimuons. The L1T algorithms and data-taking conditions correspond to 2024. A selection on the truth-level muon track $ p_{\mathrm{T}} > $ 15 GeV is applied to show the performance at the efficiency plateau. The truth-level muon tracks are extrapolated to the second muon station to determine the $ \eta^{GEN}_{st2} $ values that are used in the plot. The solid markers show the new vertex-unconstrained algorithm performance, while the hollow markers show the default beamspot-constrained algorithm performance. In the EMTF plot, the different colors show different $ |\eta| $ regions: 1.24 $ < |\eta^{GEN}_{st2}| < $ 1.6 (blue), 1.6 $ < |\eta^{GEN}_{st2}| < $ 2.0 (red).
png pdf	Figure 39-b: BMTF (upper left), OMTF (upper right), and EMTF (lower) L1T efficiencies for beamspot-constrained and -unconstrained $ p_{\mathrm{T}} $ assignment algorithms for L1T $ p_{\mathrm{T}} > $ 10 GeV with respect to truth-level muon track $ d_{\text{0}} $, obtained using a sample which produces LLPs that decay to dimuons. The L1T algorithms and data-taking conditions correspond to 2024. A selection on the truth-level muon track $ p_{\mathrm{T}} > $ 15 GeV is applied to show the performance at the efficiency plateau. The truth-level muon tracks are extrapolated to the second muon station to determine the $ \eta^{GEN}_{st2} $ values that are used in the plot. The solid markers show the new vertex-unconstrained algorithm performance, while the hollow markers show the default beamspot-constrained algorithm performance. In the EMTF plot, the different colors show different $ |\eta| $ regions: 1.24 $ < |\eta^{GEN}_{st2}| < $ 1.6 (blue), 1.6 $ < |\eta^{GEN}_{st2}| < $ 2.0 (red).
png pdf	Figure 39-c: BMTF (upper left), OMTF (upper right), and EMTF (lower) L1T efficiencies for beamspot-constrained and -unconstrained $ p_{\mathrm{T}} $ assignment algorithms for L1T $ p_{\mathrm{T}} > $ 10 GeV with respect to truth-level muon track $ d_{\text{0}} $, obtained using a sample which produces LLPs that decay to dimuons. The L1T algorithms and data-taking conditions correspond to 2024. A selection on the truth-level muon track $ p_{\mathrm{T}} > $ 15 GeV is applied to show the performance at the efficiency plateau. The truth-level muon tracks are extrapolated to the second muon station to determine the $ \eta^{GEN}_{st2} $ values that are used in the plot. The solid markers show the new vertex-unconstrained algorithm performance, while the hollow markers show the default beamspot-constrained algorithm performance. In the EMTF plot, the different colors show different $ |\eta| $ regions: 1.24 $ < |\eta^{GEN}_{st2}| < $ 1.6 (blue), 1.6 $ < |\eta^{GEN}_{st2}| < $ 2.0 (red).
png pdf	Figure 40: L1T+HLT efficiencies of the various displaced-dimuon triggers and their logical OR as a function of $ c\tau $ for the HAHM signal events with $ m_{\mathrm{H}}= $ 125 GeV and $ m_{\mathrm{Z}_\text{D}} = $ 20 GeV, in 2022 conditions. The efficiency is defined as the fraction of simulated events that satisfy the detector acceptance and the requirements of the following sets of triggers: the Run 2 (2018) triggers (dashed black); the Run 3 (2022, L3) triggers (blue); the Run 3 (2022, L2) triggers (red); and the logical OR of all these triggers (Run 3 (2022), solid black). The lower panel shows the ratio of the overall Run 3 (2022) efficiency to the Run 2 (2018) efficiency. Figure adapted from Ref. [105].
png pdf	Figure 41: L1T+HLT efficiency of the Run 3 (2022, L3) triggers in 2022 data (black), 2023 data (red), and simulation (green) as a function of $ \text{min}(p_{\mathrm{T}}) $ (upper left), $ \text{max}(p_{\mathrm{T}}) $ (upper right), and $ \text{min}(d_{\text{0}}) $ (lower) of the two muons forming TMS-TMS dimuons in events enriched in $ \mathrm{J}/\psi\to\mu\mu $ events. Efficiency in data is the fraction of $ \mathrm{J}/\psi\to\mu\mu $ events recorded by the triggers based on the information from jets and $ p_{\mathrm{T}}^\text{miss} $ that also satisfy the requirements of the Run 3 (2022, L3) triggers. It is compared to the efficiency of the Run 3 (2022, L3) triggers in a combination of simulated samples of $ \mathrm{J}/\psi\to\mu\mu $ events produced in various $ {\mathrm{B}} $ hadron decays. The lower panels show the ratio of the data to simulated events.
png pdf	Figure 41-a: L1T+HLT efficiency of the Run 3 (2022, L3) triggers in 2022 data (black), 2023 data (red), and simulation (green) as a function of $ \text{min}(p_{\mathrm{T}}) $ (upper left), $ \text{max}(p_{\mathrm{T}}) $ (upper right), and $ \text{min}(d_{\text{0}}) $ (lower) of the two muons forming TMS-TMS dimuons in events enriched in $ \mathrm{J}/\psi\to\mu\mu $ events. Efficiency in data is the fraction of $ \mathrm{J}/\psi\to\mu\mu $ events recorded by the triggers based on the information from jets and $ p_{\mathrm{T}}^\text{miss} $ that also satisfy the requirements of the Run 3 (2022, L3) triggers. It is compared to the efficiency of the Run 3 (2022, L3) triggers in a combination of simulated samples of $ \mathrm{J}/\psi\to\mu\mu $ events produced in various $ {\mathrm{B}} $ hadron decays. The lower panels show the ratio of the data to simulated events.
png pdf	Figure 41-b: L1T+HLT efficiency of the Run 3 (2022, L3) triggers in 2022 data (black), 2023 data (red), and simulation (green) as a function of $ \text{min}(p_{\mathrm{T}}) $ (upper left), $ \text{max}(p_{\mathrm{T}}) $ (upper right), and $ \text{min}(d_{\text{0}}) $ (lower) of the two muons forming TMS-TMS dimuons in events enriched in $ \mathrm{J}/\psi\to\mu\mu $ events. Efficiency in data is the fraction of $ \mathrm{J}/\psi\to\mu\mu $ events recorded by the triggers based on the information from jets and $ p_{\mathrm{T}}^\text{miss} $ that also satisfy the requirements of the Run 3 (2022, L3) triggers. It is compared to the efficiency of the Run 3 (2022, L3) triggers in a combination of simulated samples of $ \mathrm{J}/\psi\to\mu\mu $ events produced in various $ {\mathrm{B}} $ hadron decays. The lower panels show the ratio of the data to simulated events.
png pdf	Figure 41-c: L1T+HLT efficiency of the Run 3 (2022, L3) triggers in 2022 data (black), 2023 data (red), and simulation (green) as a function of $ \text{min}(p_{\mathrm{T}}) $ (upper left), $ \text{max}(p_{\mathrm{T}}) $ (upper right), and $ \text{min}(d_{\text{0}}) $ (lower) of the two muons forming TMS-TMS dimuons in events enriched in $ \mathrm{J}/\psi\to\mu\mu $ events. Efficiency in data is the fraction of $ \mathrm{J}/\psi\to\mu\mu $ events recorded by the triggers based on the information from jets and $ p_{\mathrm{T}}^\text{miss} $ that also satisfy the requirements of the Run 3 (2022, L3) triggers. It is compared to the efficiency of the Run 3 (2022, L3) triggers in a combination of simulated samples of $ \mathrm{J}/\psi\to\mu\mu $ events produced in various $ {\mathrm{B}} $ hadron decays. The lower panels show the ratio of the data to simulated events.
png pdf	Figure 42: HLT efficiency, defined as the fraction of events recorded by the Run 2 (2018) triggers that also satisfied the requirements of the Run 3 (2022, L3) triggers, as a function of offline-reconstructed $ \text{min}(d_{\text{0}}) $ of the two muons forming TMS-TMS dimuons in events enriched in $ \mathrm{J}/\psi\to\mu\mu $ (upper left). The black circles represent efficiencies during the 2022 data-taking period, and the red triangles represent the 2023 period. For dimuons with offline $ \text{min}(d_{\text{0}}) > 0.012\,\text{cm} $, the combined efficiency of the L3 muon reconstruction and the online $ \text{min}(d_{\text{0}}) $ requirement is larger than 90% in all data-taking periods. The HLT efficiency of the Run 3 (2022, L3) triggers, shown with blue triangles, and the Run 3 (2022, L3 dTks) triggers, shown with green squares, in $ \mathrm{J}/\psi\to\mu\mu $ events in the full 2022 and 2023 data set (upper right). Invariant mass distribution for TMS-TMS dimuons in events recorded by the Run 2 (2018) triggers in the combined 2022 and 2023 data set (black circles), and in the subset of events also selected by the Run 3 (2022, L3) trigger (blue triangles) and Run 3 (2022, L3 dTks) trigger (green squares), illustrating the background rejection of the L3 triggers (lower).
png pdf	Figure 42-a: HLT efficiency, defined as the fraction of events recorded by the Run 2 (2018) triggers that also satisfied the requirements of the Run 3 (2022, L3) triggers, as a function of offline-reconstructed $ \text{min}(d_{\text{0}}) $ of the two muons forming TMS-TMS dimuons in events enriched in $ \mathrm{J}/\psi\to\mu\mu $ (upper left). The black circles represent efficiencies during the 2022 data-taking period, and the red triangles represent the 2023 period. For dimuons with offline $ \text{min}(d_{\text{0}}) > 0.012\,\text{cm} $, the combined efficiency of the L3 muon reconstruction and the online $ \text{min}(d_{\text{0}}) $ requirement is larger than 90% in all data-taking periods. The HLT efficiency of the Run 3 (2022, L3) triggers, shown with blue triangles, and the Run 3 (2022, L3 dTks) triggers, shown with green squares, in $ \mathrm{J}/\psi\to\mu\mu $ events in the full 2022 and 2023 data set (upper right). Invariant mass distribution for TMS-TMS dimuons in events recorded by the Run 2 (2018) triggers in the combined 2022 and 2023 data set (black circles), and in the subset of events also selected by the Run 3 (2022, L3) trigger (blue triangles) and Run 3 (2022, L3 dTks) trigger (green squares), illustrating the background rejection of the L3 triggers (lower).
png pdf	Figure 42-b: HLT efficiency, defined as the fraction of events recorded by the Run 2 (2018) triggers that also satisfied the requirements of the Run 3 (2022, L3) triggers, as a function of offline-reconstructed $ \text{min}(d_{\text{0}}) $ of the two muons forming TMS-TMS dimuons in events enriched in $ \mathrm{J}/\psi\to\mu\mu $ (upper left). The black circles represent efficiencies during the 2022 data-taking period, and the red triangles represent the 2023 period. For dimuons with offline $ \text{min}(d_{\text{0}}) > 0.012\,\text{cm} $, the combined efficiency of the L3 muon reconstruction and the online $ \text{min}(d_{\text{0}}) $ requirement is larger than 90% in all data-taking periods. The HLT efficiency of the Run 3 (2022, L3) triggers, shown with blue triangles, and the Run 3 (2022, L3 dTks) triggers, shown with green squares, in $ \mathrm{J}/\psi\to\mu\mu $ events in the full 2022 and 2023 data set (upper right). Invariant mass distribution for TMS-TMS dimuons in events recorded by the Run 2 (2018) triggers in the combined 2022 and 2023 data set (black circles), and in the subset of events also selected by the Run 3 (2022, L3) trigger (blue triangles) and Run 3 (2022, L3 dTks) trigger (green squares), illustrating the background rejection of the L3 triggers (lower).
png pdf	Figure 42-c: HLT efficiency, defined as the fraction of events recorded by the Run 2 (2018) triggers that also satisfied the requirements of the Run 3 (2022, L3) triggers, as a function of offline-reconstructed $ \text{min}(d_{\text{0}}) $ of the two muons forming TMS-TMS dimuons in events enriched in $ \mathrm{J}/\psi\to\mu\mu $ (upper left). The black circles represent efficiencies during the 2022 data-taking period, and the red triangles represent the 2023 period. For dimuons with offline $ \text{min}(d_{\text{0}}) > 0.012\,\text{cm} $, the combined efficiency of the L3 muon reconstruction and the online $ \text{min}(d_{\text{0}}) $ requirement is larger than 90% in all data-taking periods. The HLT efficiency of the Run 3 (2022, L3) triggers, shown with blue triangles, and the Run 3 (2022, L3 dTks) triggers, shown with green squares, in $ \mathrm{J}/\psi\to\mu\mu $ events in the full 2022 and 2023 data set (upper right). Invariant mass distribution for TMS-TMS dimuons in events recorded by the Run 2 (2018) triggers in the combined 2022 and 2023 data set (black circles), and in the subset of events also selected by the Run 3 (2022, L3) trigger (blue triangles) and Run 3 (2022, L3 dTks) trigger (green squares), illustrating the background rejection of the L3 triggers (lower).
png pdf	Figure 43: HLT efficiency, defined as the fraction of events recorded by the Run 2 (2018) triggers that also satisfied the requirements of the Run 3 (2022, L2) triggers, as a function of offline-reconstructed $ \text{min}(d_{\text{0}}) $ of the two muons forming STA-STA dimuons in events enriched in cosmic ray muons (left). The black circles represent efficiencies during the 2022 data-taking period, and the red triangles represent the 2023 period. For displaced muons, the efficiency of the online $ \text{min}(d_{\text{0}}) $ requirement is larger than 95% in all data-taking periods. The invariant mass distribution for TMS-TMS dimuons in events recorded by the Run 2 (2018) triggers in the combined 2022 and 2023 data set (black circles), and in the subset of events also selected by the Run 3 (2022, L2) triggers (pink triangles), illustrating the background rejection of the Run 3 (2022, L2) triggers (right).
png pdf	Figure 43-a: HLT efficiency, defined as the fraction of events recorded by the Run 2 (2018) triggers that also satisfied the requirements of the Run 3 (2022, L2) triggers, as a function of offline-reconstructed $ \text{min}(d_{\text{0}}) $ of the two muons forming STA-STA dimuons in events enriched in cosmic ray muons (left). The black circles represent efficiencies during the 2022 data-taking period, and the red triangles represent the 2023 period. For displaced muons, the efficiency of the online $ \text{min}(d_{\text{0}}) $ requirement is larger than 95% in all data-taking periods. The invariant mass distribution for TMS-TMS dimuons in events recorded by the Run 2 (2018) triggers in the combined 2022 and 2023 data set (black circles), and in the subset of events also selected by the Run 3 (2022, L2) triggers (pink triangles), illustrating the background rejection of the Run 3 (2022, L2) triggers (right).
png pdf	Figure 43-b: HLT efficiency, defined as the fraction of events recorded by the Run 2 (2018) triggers that also satisfied the requirements of the Run 3 (2022, L2) triggers, as a function of offline-reconstructed $ \text{min}(d_{\text{0}}) $ of the two muons forming STA-STA dimuons in events enriched in cosmic ray muons (left). The black circles represent efficiencies during the 2022 data-taking period, and the red triangles represent the 2023 period. For displaced muons, the efficiency of the online $ \text{min}(d_{\text{0}}) $ requirement is larger than 95% in all data-taking periods. The invariant mass distribution for TMS-TMS dimuons in events recorded by the Run 2 (2018) triggers in the combined 2022 and 2023 data set (black circles), and in the subset of events also selected by the Run 3 (2022, L2) triggers (pink triangles), illustrating the background rejection of the Run 3 (2022, L2) triggers (right).
png pdf	Figure 44: 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. [108]. The black arrows indicate the lepton $ d_{\text{0}} $ vectors. Figure taken from Ref. [112].
png pdf	Figure 45: L1T+HLT efficiency of the double displaced L3 muon trigger as a function of $ \text{min}(p_{\mathrm{T}}) $ of the two global or tracker muons in the event. The efficiency is plotted for HAHM signal events in 2022 conditions with $ m_{\mathrm{Z}_\text{D}} = $ 50 GeV and $ \epsilon = 4 \times 10^{-9} $ (black triangles), $ m_{\mathrm{Z}_\text{D}} = $ 60 GeV and $ \epsilon = 2 \times 10^{-9} $ (red triangles), and $ m_{\mathrm{H}}= $ 125 GeV in both cases. The events are required to have at least two good global or tracker muons with $ p_{\mathrm{T}} > $ 23 GeV.
png pdf	Figure 46: Comparison between the $ L_{\text{xy}} $ distribution for dimuon scouting events, for Run 2 (orange) and Run 3 (blue) events in data that contain dimuon pairs with a common displaced vertex and a minimal selection on the vertex quality. The dashed vertical lines, placed at radii of 29, 68, 109, and 160 mm, correspond to the positions of the pixel layers where photons undergo conversion processes in the material, causing the observed peaks in the $ L_{\text{xy}} $ distribution. Figure taken from Ref. [33].
png pdf	Figure 47: L1T+HLT efficiency of the dimuon scouting trigger as a function of the subleading muon $ p_{\mathrm{T}} $, for 2024 data. The efficiency of the L1T dimuon seeds (pink squares) and the HLT dimuon scouting trigger with the vertex-unconstrained reconstruction algorithm (blue triangles) is shown. At least two scouting muons with $ \chi^2/dof < $ 3 and $ \Delta R > $ 0.1 are required.
png pdf	Figure 48: L1T+HLT efficiency of the dimuon scouting trigger as a function of the generator-level $ L_{\text{xy}} $, for HAHM signal events in 2024 conditions. The efficiency is shown for $ m_{\mathrm{Z}_\text{D}} = $ 14 GeV and $ c\tau= $ 100 mm (pink squares) and $ m_{\mathrm{Z}_\text{D}} = $ 2.5 GeV and $ c\tau=$ 100 mm (blue triangles). The muons are required to have $ p_{\mathrm{T}} > $ 15 GeV and $ |\eta| < $ 2.4 at the generator level.
png pdf	Figure 49: L1T+HLT efficiency of the dimuon scouting trigger as a function of the generator-level subleading muon $ p_{\mathrm{T}} $, for HAHM signal events in 2024 conditions. The efficiency is shown for $ \mathrm{Z}_\text{D} $ masses of 2.5 (left) and 14 GeV (right), and $ c\tau $ values of 1 (purple squares), 10 (blue triangles), and 100 mm (pink circles). The muons are required to have $ |\eta| < $ 2.4 at the generator level.
png pdf	Figure 49-a: L1T+HLT efficiency of the dimuon scouting trigger as a function of the generator-level subleading muon $ p_{\mathrm{T}} $, for HAHM signal events in 2024 conditions. The efficiency is shown for $ \mathrm{Z}_\text{D} $ masses of 2.5 (left) and 14 GeV (right), and $ c\tau $ values of 1 (purple squares), 10 (blue triangles), and 100 mm (pink circles). The muons are required to have $ |\eta| < $ 2.4 at the generator level.
png pdf	Figure 49-b: L1T+HLT efficiency of the dimuon scouting trigger as a function of the generator-level subleading muon $ p_{\mathrm{T}} $, for HAHM signal events in 2024 conditions. The efficiency is shown for $ \mathrm{Z}_\text{D} $ masses of 2.5 (left) and 14 GeV (right), and $ c\tau $ values of 1 (purple squares), 10 (blue triangles), and 100 mm (pink circles). The muons are required to have $ |\eta| < $ 2.4 at the generator level.
png pdf	Figure 50: The $ p_{\mathrm{T}} $ resolution of scouting muons with respect to offline muons, as a function of the scouting muon $ p_{\mathrm{T}} $, for 2024 data events. The dimuon $ \Delta R $ is required to be greater than 0.2, and the scouting muon $ p_{\mathrm{T}} $ is required to be greater than 3 GeV. The resolution is shown for muons in the barrel (blue filled points) and the endcaps (purple filled triangles) that are reconstructed with the unconstrained vertex reconstruction algorithm, as well as for muons in the barrel (red filled squares) and the endcaps (orange unfilled squares) that are reconstructed with the constrained vertex reconstruction algorithm. The figure is made using a special monitoring data set that collects events triggered by a mixture of HLT paths (both scouting and standard triggers) with a very high prescale, in which all information about the muon objects stored from the offline and scouting reconstruction.
png pdf	Figure 51: Event display of a collision triggered by the CSC MDS trigger. The CSC reconstructed hits are represented by blue dots in the muon end-cap region. This event features a CSC cluster of 210 hits in the ME1/3 ring. The event was recorded on October 8th, 2022.
png pdf	Figure 51-a: Event display of a collision triggered by the CSC MDS trigger. The CSC reconstructed hits are represented by blue dots in the muon end-cap region. This event features a CSC cluster of 210 hits in the ME1/3 ring. The event was recorded on October 8th, 2022.
png pdf	Figure 51-b: Event display of a collision triggered by the CSC MDS trigger. The CSC reconstructed hits are represented by blue dots in the muon end-cap region. This event features a CSC cluster of 210 hits in the ME1/3 ring. The event was recorded on October 8th, 2022.
png pdf	Figure 52: L1T efficiency of the One-Nominal CSC MDS trigger as a function of CSC hit cluster size, measured with muon bremsstrahlung-induced electromagnetic showers using data taken in 2022 and 2023 (left). L1T rate as a function of PU in a CMS run for the One-Nominal and Two-Loose seed for a 2023 data-taking run (right). The rate dependence on PU is extracted by using a linear fit.
png pdf	Figure 52-a: L1T efficiency of the One-Nominal CSC MDS trigger as a function of CSC hit cluster size, measured with muon bremsstrahlung-induced electromagnetic showers using data taken in 2022 and 2023 (left). L1T rate as a function of PU in a CMS run for the One-Nominal and Two-Loose seed for a 2023 data-taking run (right). The rate dependence on PU is extracted by using a linear fit.
png pdf	Figure 52-b: L1T efficiency of the One-Nominal CSC MDS trigger as a function of CSC hit cluster size, measured with muon bremsstrahlung-induced electromagnetic showers using data taken in 2022 and 2023 (left). L1T rate as a function of PU in a CMS run for the One-Nominal and Two-Loose seed for a 2023 data-taking run (right). The rate dependence on PU is extracted by using a linear fit.
png pdf	Figure 53: Diagram of the MDS signature in the DTs. The LLP decays in the DTs, opposite a jet from initial state radiation.
png pdf	Figure 54: HLT efficiency of the DT MDS triggers as a function of $ p_{\mathrm{T}}^\text{miss} $ (left) and cluster size (right), for $ \mathrm{H} \to \text{S}\text{S} \to \mathrm{b}\overline{\mathrm{b}}\mathrm{b}\overline{\mathrm{b}} $ events with $ m_{\mathrm{H}}= $ 125 GeV, $ m_{\text{S}} = $ 40 GeV, and $ c\tau_{\text{S}}= $ 1 m, in 2023 conditions. Events are required to have at least one cluster with more than 50 hits (left) and $ p_{\mathrm{T}}^\text{miss} > $ 250 GeV (right).
png pdf	Figure 54-a: HLT efficiency of the DT MDS triggers as a function of $ p_{\mathrm{T}}^\text{miss} $ (left) and cluster size (right), for $ \mathrm{H} \to \text{S}\text{S} \to \mathrm{b}\overline{\mathrm{b}}\mathrm{b}\overline{\mathrm{b}} $ events with $ m_{\mathrm{H}}= $ 125 GeV, $ m_{\text{S}} = $ 40 GeV, and $ c\tau_{\text{S}}= $ 1 m, in 2023 conditions. Events are required to have at least one cluster with more than 50 hits (left) and $ p_{\mathrm{T}}^\text{miss} > $ 250 GeV (right).
png pdf	Figure 54-b: HLT efficiency of the DT MDS triggers as a function of $ p_{\mathrm{T}}^\text{miss} $ (left) and cluster size (right), for $ \mathrm{H} \to \text{S}\text{S} \to \mathrm{b}\overline{\mathrm{b}}\mathrm{b}\overline{\mathrm{b}} $ events with $ m_{\mathrm{H}}= $ 125 GeV, $ m_{\text{S}} = $ 40 GeV, and $ c\tau_{\text{S}}= $ 1 m, in 2023 conditions. Events are required to have at least one cluster with more than 50 hits (left) and $ p_{\mathrm{T}}^\text{miss} > $ 250 GeV (right).
png pdf	Figure 55: Diagram of a stopped particle event, which can be selected by the jet No-BPTX triggers. The dotted black arrow indicates the LLP, such as a gluino, that travels through the detector before coming to a stop in the dense material of the HCAL. After some time, this stopped particle decays hadronically, producing a significant energy deposit in the HCAL.
png pdf	Figure 56: Rate of the main muon No-BPTX HLT path as a function of the number of colliding bunches, for different years in Run 2 and Run 3.
png pdf	Figure 57: Diagram of a stopped particle event, which can be selected by the muon No-BPTX triggers. The dotted black arrow indicates the LLP that travels through the detector before coming to a stop in the iron yoke in the muon system. After some time, this stopped particle decays to two back-to-back muons.
png pdf	Figure 58: Comparison of the acceptance in Run 2 and Run 3 for the CSC (left) and DT (right) MDS triggers at the L1T and HLT as a function of the LLP lifetime, for $ \mathrm{H} \to \text{S}\text{S} \to \mathrm{b}\overline{\mathrm{b}}\mathrm{b}\overline{\mathrm{b}} $ events with $ m_{\mathrm{H}}= $ 125 GeV and $ m_{\text{S}} = $ 40 GeV, in 2023 conditions. The acceptance is defined as the fraction of events that pass the specified selection, given an LLP decay in the fiducial region of the CSCs (left) or DTs (right). The left plot compares the acceptance of the Run 2 strategy of triggering on $ p_{\mathrm{T}}^\text{miss} $ (blue circles), which was required to be $ {>} $ 200 GeV offline, with that of the Run 3 strategy of triggering on the MDS signature in the CSCs, where the L1T (L1T+HLT) acceptance is shown with orange squares (red triangles). The right plot compares the acceptance of Run 2 strategy of triggering on $ p_{\mathrm{T}}^\text{miss} $ (blue circles) with the Run 3 strategy of triggering on the MDS signature in the DTs, where the L1T+HLT acceptance is shown with red triangles.
png pdf	Figure 58-a: Comparison of the acceptance in Run 2 and Run 3 for the CSC (left) and DT (right) MDS triggers at the L1T and HLT as a function of the LLP lifetime, for $ \mathrm{H} \to \text{S}\text{S} \to \mathrm{b}\overline{\mathrm{b}}\mathrm{b}\overline{\mathrm{b}} $ events with $ m_{\mathrm{H}}= $ 125 GeV and $ m_{\text{S}} = $ 40 GeV, in 2023 conditions. The acceptance is defined as the fraction of events that pass the specified selection, given an LLP decay in the fiducial region of the CSCs (left) or DTs (right). The left plot compares the acceptance of the Run 2 strategy of triggering on $ p_{\mathrm{T}}^\text{miss} $ (blue circles), which was required to be $ {>} $ 200 GeV offline, with that of the Run 3 strategy of triggering on the MDS signature in the CSCs, where the L1T (L1T+HLT) acceptance is shown with orange squares (red triangles). The right plot compares the acceptance of Run 2 strategy of triggering on $ p_{\mathrm{T}}^\text{miss} $ (blue circles) with the Run 3 strategy of triggering on the MDS signature in the DTs, where the L1T+HLT acceptance is shown with red triangles.
png pdf	Figure 58-b: Comparison of the acceptance in Run 2 and Run 3 for the CSC (left) and DT (right) MDS triggers at the L1T and HLT as a function of the LLP lifetime, for $ \mathrm{H} \to \text{S}\text{S} \to \mathrm{b}\overline{\mathrm{b}}\mathrm{b}\overline{\mathrm{b}} $ events with $ m_{\mathrm{H}}= $ 125 GeV and $ m_{\text{S}} = $ 40 GeV, in 2023 conditions. The acceptance is defined as the fraction of events that pass the specified selection, given an LLP decay in the fiducial region of the CSCs (left) or DTs (right). The left plot compares the acceptance of the Run 2 strategy of triggering on $ p_{\mathrm{T}}^\text{miss} $ (blue circles), which was required to be $ {>} $ 200 GeV offline, with that of the Run 3 strategy of triggering on the MDS signature in the CSCs, where the L1T (L1T+HLT) acceptance is shown with orange squares (red triangles). The right plot compares the acceptance of Run 2 strategy of triggering on $ p_{\mathrm{T}}^\text{miss} $ (blue circles) with the Run 3 strategy of triggering on the MDS signature in the DTs, where the L1T+HLT acceptance is shown with red triangles.
png pdf	Figure 59: L1T (blue circles) and L1T+HLT (orange squares) acceptance for the CSC MDS trigger as a function of LLP decay positions in the $ z $-direction, for $ \mathrm{H} \to \text{S}\text{S} \to \mathrm{b}\overline{\mathrm{b}}\mathrm{b}\overline{\mathrm{b}} $ events with $ m_{\mathrm{H}}= $ 350 GeV, $ m_{\text{S}}= $ 80 GeV, and $ c\tau_{\text{S}}= $ 1 m, in 2023 conditions.
png pdf	Figure 60: HLT (blue circles) and L1T+HLT (orange squares) acceptance for the DT MDS trigger as a function of LLP decay positions in the radial direction, for $ \mathrm{H} \to \text{S}\text{S} \to \mathrm{b}\overline{\mathrm{b}}\mathrm{b}\overline{\mathrm{b}} $ events with $ m_{\mathrm{H}}= $ 350 GeV, $ m_{\text{S}}= $ 80 GeV, and $ c\tau_{\text{S}}= $ 1 m, in 2023 conditions.
png pdf	Figure 61: L1T (left) and L1T+HLT (right) acceptance for the CSC MDS trigger as a function of LLP decay positions, for $ \mathrm{H} \to \text{S}\text{S} \to \mathrm{b}\overline{\mathrm{b}}\mathrm{b}\overline{\mathrm{b}} $ events with $ m_{\mathrm{H}}= $ 350 GeV, $ m_{\text{S}}= $ 80 GeV, and $ c\tau_{\text{S}}= $ 1 m, in 2023 conditions.
png pdf	Figure 61-a: L1T (left) and L1T+HLT (right) acceptance for the CSC MDS trigger as a function of LLP decay positions, for $ \mathrm{H} \to \text{S}\text{S} \to \mathrm{b}\overline{\mathrm{b}}\mathrm{b}\overline{\mathrm{b}} $ events with $ m_{\mathrm{H}}= $ 350 GeV, $ m_{\text{S}}= $ 80 GeV, and $ c\tau_{\text{S}}= $ 1 m, in 2023 conditions.
png pdf	Figure 61-b: L1T (left) and L1T+HLT (right) acceptance for the CSC MDS trigger as a function of LLP decay positions, for $ \mathrm{H} \to \text{S}\text{S} \to \mathrm{b}\overline{\mathrm{b}}\mathrm{b}\overline{\mathrm{b}} $ events with $ m_{\mathrm{H}}= $ 350 GeV, $ m_{\text{S}}= $ 80 GeV, and $ c\tau_{\text{S}}= $ 1 m, in 2023 conditions.
png pdf	Figure 62: HLT acceptance for the DT MDS trigger as a function of LLP decay position, for $ \mathrm{H} \to \text{S}\text{S} \to \mathrm{b}\overline{\mathrm{b}}\mathrm{b}\overline{\mathrm{b}} $ events with $ m_{\mathrm{H}}= $ 350 GeV, $ m_{\text{S}}= $ 80 GeV, and $ c\tau_{\text{S}}= $ 1 m, in 2023 conditions. The L1T acceptance that is based on $ p_{\mathrm{T}}^\text{miss} $ is not included.
png pdf	Figure 63: L1T+HLT acceptance for various LLP triggers using different subdetectors, as a function of LLP decay radius, for $ \mathrm{H} \to XX \to \mathrm{b}\overline{\mathrm{b}}\mathrm{b}\overline{\mathrm{b}} $ events in 2023 conditions. The plots correspond to different signal points with $ m_{\mathrm{H}}= $ 1000 GeV, $ m_{X}= $ 200 GeV on the upper left, $ m_{\mathrm{H}}= $ 350 GeV, $ m_{X}= $ 80 GeV on the upper right, $ m_{\mathrm{H}}= $ 350 GeV, $ m_{X}= $ 160 GeV on the lower left, and $ m_{\mathrm{H}}= $ 125 GeV and $ m_{X}= $ 25 GeV on the lower right. In each of these plots, the $ c\tau $ is 0.1 m for the displaced-jet triggers using the tracker and 1 m for the other triggers. The acceptance is shown for the displaced-jet triggers using the tracker (cyan points), for the delayed-jet triggers using ECAL timing (red circles), for the displaced-jet triggers using the HCAL (blue squares), for the MDS triggers with the DTs (green triangles), and for the MDS triggers with the CSCs (pink points). The boundaries of the tracker, ECAL, HCAL, DTs, and CSCs are also shown in the figures.
png pdf	Figure 63-a: L1T+HLT acceptance for various LLP triggers using different subdetectors, as a function of LLP decay radius, for $ \mathrm{H} \to XX \to \mathrm{b}\overline{\mathrm{b}}\mathrm{b}\overline{\mathrm{b}} $ events in 2023 conditions. The plots correspond to different signal points with $ m_{\mathrm{H}}= $ 1000 GeV, $ m_{X}= $ 200 GeV on the upper left, $ m_{\mathrm{H}}= $ 350 GeV, $ m_{X}= $ 80 GeV on the upper right, $ m_{\mathrm{H}}= $ 350 GeV, $ m_{X}= $ 160 GeV on the lower left, and $ m_{\mathrm{H}}= $ 125 GeV and $ m_{X}= $ 25 GeV on the lower right. In each of these plots, the $ c\tau $ is 0.1 m for the displaced-jet triggers using the tracker and 1 m for the other triggers. The acceptance is shown for the displaced-jet triggers using the tracker (cyan points), for the delayed-jet triggers using ECAL timing (red circles), for the displaced-jet triggers using the HCAL (blue squares), for the MDS triggers with the DTs (green triangles), and for the MDS triggers with the CSCs (pink points). The boundaries of the tracker, ECAL, HCAL, DTs, and CSCs are also shown in the figures.
png pdf	Figure 63-b: L1T+HLT acceptance for various LLP triggers using different subdetectors, as a function of LLP decay radius, for $ \mathrm{H} \to XX \to \mathrm{b}\overline{\mathrm{b}}\mathrm{b}\overline{\mathrm{b}} $ events in 2023 conditions. The plots correspond to different signal points with $ m_{\mathrm{H}}= $ 1000 GeV, $ m_{X}= $ 200 GeV on the upper left, $ m_{\mathrm{H}}= $ 350 GeV, $ m_{X}= $ 80 GeV on the upper right, $ m_{\mathrm{H}}= $ 350 GeV, $ m_{X}= $ 160 GeV on the lower left, and $ m_{\mathrm{H}}= $ 125 GeV and $ m_{X}= $ 25 GeV on the lower right. In each of these plots, the $ c\tau $ is 0.1 m for the displaced-jet triggers using the tracker and 1 m for the other triggers. The acceptance is shown for the displaced-jet triggers using the tracker (cyan points), for the delayed-jet triggers using ECAL timing (red circles), for the displaced-jet triggers using the HCAL (blue squares), for the MDS triggers with the DTs (green triangles), and for the MDS triggers with the CSCs (pink points). The boundaries of the tracker, ECAL, HCAL, DTs, and CSCs are also shown in the figures.
png pdf	Figure 63-c: L1T+HLT acceptance for various LLP triggers using different subdetectors, as a function of LLP decay radius, for $ \mathrm{H} \to XX \to \mathrm{b}\overline{\mathrm{b}}\mathrm{b}\overline{\mathrm{b}} $ events in 2023 conditions. The plots correspond to different signal points with $ m_{\mathrm{H}}= $ 1000 GeV, $ m_{X}= $ 200 GeV on the upper left, $ m_{\mathrm{H}}= $ 350 GeV, $ m_{X}= $ 80 GeV on the upper right, $ m_{\mathrm{H}}= $ 350 GeV, $ m_{X}= $ 160 GeV on the lower left, and $ m_{\mathrm{H}}= $ 125 GeV and $ m_{X}= $ 25 GeV on the lower right. In each of these plots, the $ c\tau $ is 0.1 m for the displaced-jet triggers using the tracker and 1 m for the other triggers. The acceptance is shown for the displaced-jet triggers using the tracker (cyan points), for the delayed-jet triggers using ECAL timing (red circles), for the displaced-jet triggers using the HCAL (blue squares), for the MDS triggers with the DTs (green triangles), and for the MDS triggers with the CSCs (pink points). The boundaries of the tracker, ECAL, HCAL, DTs, and CSCs are also shown in the figures.
png pdf	Figure 63-d: L1T+HLT acceptance for various LLP triggers using different subdetectors, as a function of LLP decay radius, for $ \mathrm{H} \to XX \to \mathrm{b}\overline{\mathrm{b}}\mathrm{b}\overline{\mathrm{b}} $ events in 2023 conditions. The plots correspond to different signal points with $ m_{\mathrm{H}}= $ 1000 GeV, $ m_{X}= $ 200 GeV on the upper left, $ m_{\mathrm{H}}= $ 350 GeV, $ m_{X}= $ 80 GeV on the upper right, $ m_{\mathrm{H}}= $ 350 GeV, $ m_{X}= $ 160 GeV on the lower left, and $ m_{\mathrm{H}}= $ 125 GeV and $ m_{X}= $ 25 GeV on the lower right. In each of these plots, the $ c\tau $ is 0.1 m for the displaced-jet triggers using the tracker and 1 m for the other triggers. The acceptance is shown for the displaced-jet triggers using the tracker (cyan points), for the delayed-jet triggers using ECAL timing (red circles), for the displaced-jet triggers using the HCAL (blue squares), for the MDS triggers with the DTs (green triangles), and for the MDS triggers with the CSCs (pink points). The boundaries of the tracker, ECAL, HCAL, DTs, and CSCs are also shown in the figures.
png pdf	Figure 64: The fiducial regions defined for the calculation of each trigger acceptance in Fig. 63. The text contains the exact definitions of each region.
png pdf	Figure 65: Diagram of the overlapping coverage, in the HLT muon $ p_{\mathrm{T}}-d_{\text{0}} $ plane, of the dimuon triggers that target displaced signatures. The L2 muons are shown in blue, the L3 muons are shown in red, and the scouting muons are shown in green. The displaced dimuon triggers, the double-displaced L3 muon triggers, and the dimuon scouting triggers are shown. The $ p_{\mathrm{T}} $ of the highest-$ p_{\mathrm{T}} $ muon ($ p_{\mathrm{T}}^{1} $) is shown on the $ y $-axis, and the minimum $ p_{\mathrm{T}} $ thresholds on each triggered muon ($ p_{\mathrm{T}}^{1,2} $) are indicated within the colored parts of the diagram. The value of 100 $ \,(1000)\,\text{cm} $ given on the $ x $-axis for the end of the tracker (muon system) is approximate.
png pdf	Figure 66: L1T+HLT acceptance of the displaced $ \tau_\mathrm{h} $ trigger, for simulated $ \mathrm{p}\mathrm{p} \to \tilde{\tau}\tilde{\tau} (\tilde{\tau} \to \tau\tilde{\chi}_{1}^{0}) $ events, where each $ \tau $ decays hadronically and the $ \tilde{\tau} $ has a simulated $ c\tau $ of 10 cm. The acceptance is shown for the displaced di-$ \tau_\mathrm{h} $ trigger path using 2022 data-taking conditions and is plotted with respect to the generator-level $ \tilde{\tau} $ decay radius. Selections on the visible component of the generator-level tau lepton $ p_{\mathrm{T}} $ ($ p_{\mathrm{T}}(\tau) > $ 30 GeV), its pseudorapidity ($ |\eta(\tau)| < $ 2.1), and its decay radius ($ R < 115\,\text{cm} $) are applied.

Tables
png pdf	Table 1: The total and pure HLT rate of all dedicated LLP triggers, as calculated from 2024 data for an instantaneous luminosity of 2.1 $ \times$ 10$^{34} $ cm$^{-2}$s$^{-1}$, with a mean PU of 63.6. Rates are reported for triggers in the standard, parking, and scouting data taking separately, as well as for combined standard and parking data to show the rate of all events that are fully reconstructed. The total rates include events that may or may not have been selected by other triggers, while the pure rates correspond to events that pass dedicated LLP HLT paths and do not pass non-LLP HLT paths. The pure rates are measured separately in standard and parked data. The combined rates are slightly less than the sum of the separate standard and parking rates because some events overlap. All rates shown have a statistical uncertainty of less than 1%.
png pdf	Table 2: The LLP triggers and their total rates at the HLT in Run 3, calculated from 2024 data for an instantaneous luminosity of 2.1 $ \times$ 10$^{34} $ cm$^{-2}$s$^{-1}$, with a mean PU of 63.6. Triggers implemented for the first time in Run 3 are indicated by a dagger ($ ^\dagger $). Rate values in parentheses correspond to the parked data rates; all others are standard data rates except for dimuon scouting. Nearly all rates shown have a statistical uncertainty of less than 1 Hz. ``Disp.'' is used as an abbreviation for ``displaced'' and ``req.'' is used as an abbreviation for ``requirement''. The terms used in this table are explained in the corresponding subsection within Section 6.
png pdf	Table 3: Event requirements for the disappearing-track trigger efficiency calculation, for data and $ \mathrm{W} \to \ell\nu $ simulation (left) and signal simulation (right). The selection criteria are applied sequentially over the given objects, and an event is selected if at least one object per event passes all requirements.
png pdf	Table 4: The L1T CSC MDS trigger efficiency $ \epsilon $ in $ \mathrm{H} \to \text{S}\text{S} \to \mathrm{b}\overline{\mathrm{b}}\mathrm{b}\overline{\mathrm{b}} $ events, for different choices of $ m_{\mathrm{H}} $, $ m_{\text{S}} $, and $ c\tau_{\text{S}} $, for simulated events with at least one LLP decaying in the CSC detector acceptance. The $ \epsilon_{\text{Acc}} $ refers to the percentage of events within the CSC detector acceptance. The $ \epsilon_{\text{One-Nominal}} $ ($ \epsilon_{\text{One-Tight}} $) requires the number of hits in at least one CSC chamber to pass the nominal (tight) thresholds.
png pdf	Table 5: The L1T CSC MDS trigger efficiency $ \epsilon $ in $ \mathrm{H} \to \text{S}\text{S} \to \mathrm{b}\overline{\mathrm{b}}\mathrm{b}\overline{\mathrm{b}} $ events, for different choices of $ m_{\mathrm{H}} $, $ m_{\text{S}} $, and $ c\tau_{\text{S}} $ for simulated events with two LLPs decaying in the CSC detector acceptance. The $ \epsilon_{\text{Acc}} $ refers to the percentage of events within the CSC detector acceptance. The $ \epsilon_{\text{One-Nominal}} $ ($ \epsilon_{\text{Two-Loose}} $) requires having the number of hits in at least one (two) CSC chamber(s) passing the nominal (loose) thresholds.

Summary

The CMS Run 3 (2022-2026) long-lived particle (LLP) trigger program, which includes many dedicated triggers designed to select different LLP signatures, has been presented. These dedicated LLP triggers extend the standard CMS trigger program and provide crucial access to unconventional LLP event signatures. In time for 2022 data taking, some LLP triggers, such as the tracking-based displaced-jet, displaced-muon, and dimuon-scouting triggers, have been improved. Other LLP triggers, such as the displaced-tau trigger, delayed-jet trigger using the electromagnetic calorimeter timing, displaced-jet trigger using the hadronic calorimeter, and the muon detector shower trigger, were newly added in 2022. The performance of these triggers has been shown with several new physics models and with 2022-2024 proton-proton collision data collected at $ \sqrt{s}= $ 13.6 TeV. These triggers greatly improve the CMS sensitivity to long-lived, beyond-the-standard model particles, enhancing the experiment's ability to search for new physics. At the time of writing, two CMS LLP analyses based on early Run 3 data collected with dedicated LLP triggers have been published. These analyses are a search for displaced jets [85] and a search for displaced dimuons [105]. In the next years, many more LLP analyses using these data and the trigger presented here are expected.

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