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Compact Muon Solenoid
LHC, CERN

CMS-EXO-21-008 ; CERN-EP-2024-008
Search for long-lived particles decaying in the CMS muon detectors in proton-proton collisions at $ \sqrt{s}= $ 13 TeV
Phys. Rev. D 110 (2024) 032007
Abstract: A search for long-lived particles (LLPs) decaying in the CMS muon detectors is presented. A data sample of proton-proton collisions at $ \sqrt{s}= $ 13 TeV corresponding to an integrated luminosity of 138 fb$ ^{-1} $, recorded at the LHC in 2016-2018, is used. The decays of LLPs are reconstructed as high multiplicity clusters of hits in the muon detectors. In the context of twin Higgs models, the search is sensitive to LLP masses from 0.4 to 55 GeV and a broad range of LLP decay modes, including decays to hadrons, $ \tau $ leptons, electrons, or photons. No excess of events above the standard model background is observed. The most stringent limits to date from LHC data are set on the branching fraction of the Higgs boson decay to a pair of LLPs with masses below 10 GeV. This search also provides the best limits for various intervals of LLP proper decay length and mass. Finally, this search sets the first limits at the LHC on a dark quantum chromodynamic sector whose particles couple to the Higgs boson through gluon, Higgs boson, photon, vector, and dark-photon portals, and is sensitive to branching fractions of the Higgs boson to dark quarks as low as 2 $ \times $ 10$^{-3} $.
Figures & Tables Summary References CMS Publications
Figures

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Figure 1:
Diagram representing the twin Higgs and dark-shower models. The SM Higgs boson (H) decays to a pair of neutral long-lived scalars (S) in the twin Higgs model or to a pair of dark-sector quarks (\Psi) in the dark shower model.

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Figure 2:
The cluster reconstruction efficiency, including both DT and CSC clusters, as a function of the simulated $ r $ and $ |z| $ decay positions of the particle S decaying to $ \mathrm{d}\overline{\mathrm{d}} $ in events with $ p_{\mathrm{T}}^\text{miss} > $ 200 GeV, for a mass of 40 GeV and a range of $ c\tau $ values uniformly distributed between 1 and 10 m. The cluster reconstruction efficiency appears to be nonzero beyond MB4 because the MB4 chambers are staggered so that the outer radius of the CMS detector ranges from 738 to 800 cm. The barrel and endcap muon stations are drawn as black boxes and labeled by their station names. The region between labeled sections are mostly steel return yoke.

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Figure 3:
The DT (left) and CSC (right) cluster reconstruction efficiency as a function of the simulated $ r $ or $ |z| $ decay positions of S decaying to $ \mathrm{d}\overline{\mathrm{d}} $ in events with $ p_{\mathrm{T}}^\text{miss} > $ 200 GeV, for a mass of 40 GeV and a range of $ c\tau $ values between 1 and 10 m. The DT cluster reconstruction efficiency is shown for events where the LLP decay occurs at $ |z| < $ 700 cm. The DT cluster reconstruction efficiency appears to be nonzero beyond MB4 because the MB4 chambers are staggered so that the outer radius of the CMS detector ranges from 738 to 800 cm. The CSC cluster reconstruction efficiency is shown for events where the LLP decay occurs at $ |r| < $ 700 cm and $ |\eta| < $ 2.6. The clusters are selected from signal events satisfying the $ p_{\mathrm{T}}^\text{miss} > $ 200 GeV requirement. Regions occupied by steel shielding are shaded in gray.

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Figure 3-a:
The DT (left) and CSC (right) cluster reconstruction efficiency as a function of the simulated $ r $ or $ |z| $ decay positions of S decaying to $ \mathrm{d}\overline{\mathrm{d}} $ in events with $ p_{\mathrm{T}}^\text{miss} > $ 200 GeV, for a mass of 40 GeV and a range of $ c\tau $ values between 1 and 10 m. The DT cluster reconstruction efficiency is shown for events where the LLP decay occurs at $ |z| < $ 700 cm. The DT cluster reconstruction efficiency appears to be nonzero beyond MB4 because the MB4 chambers are staggered so that the outer radius of the CMS detector ranges from 738 to 800 cm. The CSC cluster reconstruction efficiency is shown for events where the LLP decay occurs at $ |r| < $ 700 cm and $ |\eta| < $ 2.6. The clusters are selected from signal events satisfying the $ p_{\mathrm{T}}^\text{miss} > $ 200 GeV requirement. Regions occupied by steel shielding are shaded in gray.

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Figure 3-b:
The DT (left) and CSC (right) cluster reconstruction efficiency as a function of the simulated $ r $ or $ |z| $ decay positions of S decaying to $ \mathrm{d}\overline{\mathrm{d}} $ in events with $ p_{\mathrm{T}}^\text{miss} > $ 200 GeV, for a mass of 40 GeV and a range of $ c\tau $ values between 1 and 10 m. The DT cluster reconstruction efficiency is shown for events where the LLP decay occurs at $ |z| < $ 700 cm. The DT cluster reconstruction efficiency appears to be nonzero beyond MB4 because the MB4 chambers are staggered so that the outer radius of the CMS detector ranges from 738 to 800 cm. The CSC cluster reconstruction efficiency is shown for events where the LLP decay occurs at $ |r| < $ 700 cm and $ |\eta| < $ 2.6. The clusters are selected from signal events satisfying the $ p_{\mathrm{T}}^\text{miss} > $ 200 GeV requirement. Regions occupied by steel shielding are shaded in gray.

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Figure 4:
The geometric acceptance multiplied by the efficiency of the $ p_{\mathrm{T}}^\text{miss} > $ 200 GeV selection, as a function of the proper decay length $ c\tau $ for a scalar particle S with a mass of 40 GeV.

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Figure 5:
Distributions of the cluster time ($ t_\text{cluster} $) for signal, where S decays to $ \mathrm{d}\overline{\mathrm{d}} $ with a proper decay length $ c\tau $ of 1 m and mass of 40 GeV, and for a background-enriched sample in data selected by inverting the $ N_\text{hits} $ requirement.

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Figure 6:
The distributions of $ N_\text{hits} $ (left) and $ \Delta\phi{\mathrm{(}{\vec p}_{\mathrm{T}}^{\kern1pt\text{miss}}\mathrm{, cluster)}} $ (right) for single CSC clusters are shown for S decaying to $ \mathrm{d}\overline{\mathrm{d}} $ for a proper decay length of 1 m and various masses compared to the OOT background ($ t_\text{cluster} < -$ 12.5 ns). The OOT background is representative of the overall background shape, because the background passing all the selections described above is dominated by pileup and underlying events. The shaded bands show the statistical uncertainty in the background.

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Figure 6-a:
The distributions of $ N_\text{hits} $ (left) and $ \Delta\phi{\mathrm{(}{\vec p}_{\mathrm{T}}^{\kern1pt\text{miss}}\mathrm{, cluster)}} $ (right) for single CSC clusters are shown for S decaying to $ \mathrm{d}\overline{\mathrm{d}} $ for a proper decay length of 1 m and various masses compared to the OOT background ($ t_\text{cluster} < -$ 12.5 ns). The OOT background is representative of the overall background shape, because the background passing all the selections described above is dominated by pileup and underlying events. The shaded bands show the statistical uncertainty in the background.

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Figure 6-b:
The distributions of $ N_\text{hits} $ (left) and $ \Delta\phi{\mathrm{(}{\vec p}_{\mathrm{T}}^{\kern1pt\text{miss}}\mathrm{, cluster)}} $ (right) for single CSC clusters are shown for S decaying to $ \mathrm{d}\overline{\mathrm{d}} $ for a proper decay length of 1 m and various masses compared to the OOT background ($ t_\text{cluster} < -$ 12.5 ns). The OOT background is representative of the overall background shape, because the background passing all the selections described above is dominated by pileup and underlying events. The shaded bands show the statistical uncertainty in the background.

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Figure 7:
The distributions of $ N_\text{hits} $ (left) and $ \Delta\phi{\mathrm{(}{\vec p}_{\mathrm{T}}^{\kern1pt\text{miss}}\mathrm{, cluster)}} $ (right) for DT clusters are shown for S decaying to $ \mathrm{d}\overline{\mathrm{d}} $ for a proper decay length of 1 m and various masses compared to the shape of background in a selection in which the cluster is not matched to any RPC hit and passes all other selections. The background is dominated by clusters from noise and low-$ p_{\mathrm{T}} $ particles. The shaded bands show the statistical uncertainty in the background.

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Figure 7-a:
The distributions of $ N_\text{hits} $ (left) and $ \Delta\phi{\mathrm{(}{\vec p}_{\mathrm{T}}^{\kern1pt\text{miss}}\mathrm{, cluster)}} $ (right) for DT clusters are shown for S decaying to $ \mathrm{d}\overline{\mathrm{d}} $ for a proper decay length of 1 m and various masses compared to the shape of background in a selection in which the cluster is not matched to any RPC hit and passes all other selections. The background is dominated by clusters from noise and low-$ p_{\mathrm{T}} $ particles. The shaded bands show the statistical uncertainty in the background.

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Figure 7-b:
The distributions of $ N_\text{hits} $ (left) and $ \Delta\phi{\mathrm{(}{\vec p}_{\mathrm{T}}^{\kern1pt\text{miss}}\mathrm{, cluster)}} $ (right) for DT clusters are shown for S decaying to $ \mathrm{d}\overline{\mathrm{d}} $ for a proper decay length of 1 m and various masses compared to the shape of background in a selection in which the cluster is not matched to any RPC hit and passes all other selections. The background is dominated by clusters from noise and low-$ p_{\mathrm{T}} $ particles. The shaded bands show the statistical uncertainty in the background.

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Figure 8:
Diagrams illustrating the ABCD plane for the DT-CSC category (left), and for the DT-DT and CSC-CSC categories (right). The variable $ c_1 $ is the pass-fail ratio of the $ N_\text{hits} $ selection for the background clusters. Bin A is the signal region (SR) for all categories. The size of the blue boxes on the left represents the approximate size of the expected background yield in each bin.

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Figure 8-a:
Diagrams illustrating the ABCD plane for the DT-CSC category (left), and for the DT-DT and CSC-CSC categories (right). The variable $ c_1 $ is the pass-fail ratio of the $ N_\text{hits} $ selection for the background clusters. Bin A is the signal region (SR) for all categories. The size of the blue boxes on the left represents the approximate size of the expected background yield in each bin.

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Figure 8-b:
Diagrams illustrating the ABCD plane for the DT-CSC category (left), and for the DT-DT and CSC-CSC categories (right). The variable $ c_1 $ is the pass-fail ratio of the $ N_\text{hits} $ selection for the background clusters. Bin A is the signal region (SR) for all categories. The size of the blue boxes on the left represents the approximate size of the expected background yield in each bin.

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Figure 9:
Diagram illustrating the ABCD plane for the single-CSC-cluster category, where bin A is the signal region (SR).

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Figure 10:
The signal (assuming $ \mathcal{B}(\mathrm{H}\to\mathrm{S}\mathrm{S}) = 1% $, $ \mathrm{S} \to \mathrm{d}\overline{\mathrm{d}} $, and $ c\tau= $ 1 m), background, and data distributions of $ N_\text{clusters} $ passing the $ N_\text{hits} $ selection in the search region for CSC-CSC (upper left), DT-DT (upper right), and DT-CSC (lower) categories. The branching fraction $ \mathcal{B}(\mathrm{H}\to\mathrm{S}\mathrm{S}) $ has been set to a specific value purely to allow a visual comparison of the shapes of the signal and background distributions. The background prediction is obtained from the fit to the observed data assuming no signal contribution, and is shown in blue with the shaded region showing the fitted uncertainty. No events are observed in the rightmost bins of the DT-CSC and DT-DT categories, so only the associated uncertainty is shown.

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Figure 10-a:
The signal (assuming $ \mathcal{B}(\mathrm{H}\to\mathrm{S}\mathrm{S}) = 1% $, $ \mathrm{S} \to \mathrm{d}\overline{\mathrm{d}} $, and $ c\tau= $ 1 m), background, and data distributions of $ N_\text{clusters} $ passing the $ N_\text{hits} $ selection in the search region for CSC-CSC (upper left), DT-DT (upper right), and DT-CSC (lower) categories. The branching fraction $ \mathcal{B}(\mathrm{H}\to\mathrm{S}\mathrm{S}) $ has been set to a specific value purely to allow a visual comparison of the shapes of the signal and background distributions. The background prediction is obtained from the fit to the observed data assuming no signal contribution, and is shown in blue with the shaded region showing the fitted uncertainty. No events are observed in the rightmost bins of the DT-CSC and DT-DT categories, so only the associated uncertainty is shown.

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Figure 10-b:
The signal (assuming $ \mathcal{B}(\mathrm{H}\to\mathrm{S}\mathrm{S}) = 1% $, $ \mathrm{S} \to \mathrm{d}\overline{\mathrm{d}} $, and $ c\tau= $ 1 m), background, and data distributions of $ N_\text{clusters} $ passing the $ N_\text{hits} $ selection in the search region for CSC-CSC (upper left), DT-DT (upper right), and DT-CSC (lower) categories. The branching fraction $ \mathcal{B}(\mathrm{H}\to\mathrm{S}\mathrm{S}) $ has been set to a specific value purely to allow a visual comparison of the shapes of the signal and background distributions. The background prediction is obtained from the fit to the observed data assuming no signal contribution, and is shown in blue with the shaded region showing the fitted uncertainty. No events are observed in the rightmost bins of the DT-CSC and DT-DT categories, so only the associated uncertainty is shown.

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Figure 10-c:
The signal (assuming $ \mathcal{B}(\mathrm{H}\to\mathrm{S}\mathrm{S}) = 1% $, $ \mathrm{S} \to \mathrm{d}\overline{\mathrm{d}} $, and $ c\tau= $ 1 m), background, and data distributions of $ N_\text{clusters} $ passing the $ N_\text{hits} $ selection in the search region for CSC-CSC (upper left), DT-DT (upper right), and DT-CSC (lower) categories. The branching fraction $ \mathcal{B}(\mathrm{H}\to\mathrm{S}\mathrm{S}) $ has been set to a specific value purely to allow a visual comparison of the shapes of the signal and background distributions. The background prediction is obtained from the fit to the observed data assuming no signal contribution, and is shown in blue with the shaded region showing the fitted uncertainty. No events are observed in the rightmost bins of the DT-CSC and DT-DT categories, so only the associated uncertainty is shown.

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Figure 11:
Distributions of $ N_\text{hits} $ (left) and $ \Delta\phi{\mathrm{(}{\vec p}_{\mathrm{T}}^{\kern1pt\text{miss}}\mathrm{, cluster)}} $ (right) in the search region of the single-CSC-cluster category. The background prediction is obtained from the fit to the observed data assuming no signal contribution, and is shown in blue with the shaded region showing the fitted uncertainty. The expected signal with $ \mathcal{B}(\mathrm{H}\to\mathrm{S}\mathrm{S}) = 1% $, $ \mathrm{S}\to\mathrm{d}\overline{\mathrm{d}} $, and $ c\tau= $ 1 m is shown for $ m_\mathrm{S} $ of 3, 7, 15, 40, and 55 GeV in various colors and dotted lines. The $ N_\text{hits} $ distribution includes only events in bins A and D, while the $ \Delta\phi{\mathrm{(}{\vec p}_{\mathrm{T}}^{\kern1pt\text{miss}}\mathrm{, cluster)}} $ distribution includes only events in bins A and B. The rightmost bin in the $ N_\text{hits} $ distribution includes overflow events.

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Figure 11-a:
Distributions of $ N_\text{hits} $ (left) and $ \Delta\phi{\mathrm{(}{\vec p}_{\mathrm{T}}^{\kern1pt\text{miss}}\mathrm{, cluster)}} $ (right) in the search region of the single-CSC-cluster category. The background prediction is obtained from the fit to the observed data assuming no signal contribution, and is shown in blue with the shaded region showing the fitted uncertainty. The expected signal with $ \mathcal{B}(\mathrm{H}\to\mathrm{S}\mathrm{S}) = 1% $, $ \mathrm{S}\to\mathrm{d}\overline{\mathrm{d}} $, and $ c\tau= $ 1 m is shown for $ m_\mathrm{S} $ of 3, 7, 15, 40, and 55 GeV in various colors and dotted lines. The $ N_\text{hits} $ distribution includes only events in bins A and D, while the $ \Delta\phi{\mathrm{(}{\vec p}_{\mathrm{T}}^{\kern1pt\text{miss}}\mathrm{, cluster)}} $ distribution includes only events in bins A and B. The rightmost bin in the $ N_\text{hits} $ distribution includes overflow events.

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Figure 11-b:
Distributions of $ N_\text{hits} $ (left) and $ \Delta\phi{\mathrm{(}{\vec p}_{\mathrm{T}}^{\kern1pt\text{miss}}\mathrm{, cluster)}} $ (right) in the search region of the single-CSC-cluster category. The background prediction is obtained from the fit to the observed data assuming no signal contribution, and is shown in blue with the shaded region showing the fitted uncertainty. The expected signal with $ \mathcal{B}(\mathrm{H}\to\mathrm{S}\mathrm{S}) = 1% $, $ \mathrm{S}\to\mathrm{d}\overline{\mathrm{d}} $, and $ c\tau= $ 1 m is shown for $ m_\mathrm{S} $ of 3, 7, 15, 40, and 55 GeV in various colors and dotted lines. The $ N_\text{hits} $ distribution includes only events in bins A and D, while the $ \Delta\phi{\mathrm{(}{\vec p}_{\mathrm{T}}^{\kern1pt\text{miss}}\mathrm{, cluster)}} $ distribution includes only events in bins A and B. The rightmost bin in the $ N_\text{hits} $ distribution includes overflow events.

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Figure 12:
Distributions of $ N_\text{hits} $ (left) and $ \Delta\phi{\mathrm{(}{\vec p}_{\mathrm{T}}^{\kern1pt\text{miss}}\mathrm{, cluster)}} $ (right) in the search region of the single-DT-cluster category. The background prediction is obtained from the fit to the observed data assuming no signal contribution, and is shown in blue with the shaded region showing the fitted uncertainty. The expected signal with $ \mathcal{B}(\mathrm{H}\to\mathrm{S}\mathrm{S}) = 1% $, $ \mathrm{S}\to\mathrm{d}\overline{\mathrm{d}} $, and $ c\tau= $ 1 m is shown for $ m_\mathrm{S} $ of 3, 7, 15, 40, and 55 GeV in various colors and dotted lines. The $ N_\text{hits} $ distribution includes only events in bins A and D, while the $ \Delta\phi{\mathrm{(}{\vec p}_{\mathrm{T}}^{\kern1pt\text{miss}}\mathrm{, cluster)}} $ one includes only events in bins A and B. The right-hand bin in the $ N_\text{hits} $ distribution includes overflow events.

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Figure 12-a:
Distributions of $ N_\text{hits} $ (left) and $ \Delta\phi{\mathrm{(}{\vec p}_{\mathrm{T}}^{\kern1pt\text{miss}}\mathrm{, cluster)}} $ (right) in the search region of the single-DT-cluster category. The background prediction is obtained from the fit to the observed data assuming no signal contribution, and is shown in blue with the shaded region showing the fitted uncertainty. The expected signal with $ \mathcal{B}(\mathrm{H}\to\mathrm{S}\mathrm{S}) = 1% $, $ \mathrm{S}\to\mathrm{d}\overline{\mathrm{d}} $, and $ c\tau= $ 1 m is shown for $ m_\mathrm{S} $ of 3, 7, 15, 40, and 55 GeV in various colors and dotted lines. The $ N_\text{hits} $ distribution includes only events in bins A and D, while the $ \Delta\phi{\mathrm{(}{\vec p}_{\mathrm{T}}^{\kern1pt\text{miss}}\mathrm{, cluster)}} $ one includes only events in bins A and B. The right-hand bin in the $ N_\text{hits} $ distribution includes overflow events.

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Figure 12-b:
Distributions of $ N_\text{hits} $ (left) and $ \Delta\phi{\mathrm{(}{\vec p}_{\mathrm{T}}^{\kern1pt\text{miss}}\mathrm{, cluster)}} $ (right) in the search region of the single-DT-cluster category. The background prediction is obtained from the fit to the observed data assuming no signal contribution, and is shown in blue with the shaded region showing the fitted uncertainty. The expected signal with $ \mathcal{B}(\mathrm{H}\to\mathrm{S}\mathrm{S}) = 1% $, $ \mathrm{S}\to\mathrm{d}\overline{\mathrm{d}} $, and $ c\tau= $ 1 m is shown for $ m_\mathrm{S} $ of 3, 7, 15, 40, and 55 GeV in various colors and dotted lines. The $ N_\text{hits} $ distribution includes only events in bins A and D, while the $ \Delta\phi{\mathrm{(}{\vec p}_{\mathrm{T}}^{\kern1pt\text{miss}}\mathrm{, cluster)}} $ one includes only events in bins A and B. The right-hand bin in the $ N_\text{hits} $ distribution includes overflow events.

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Figure 13:
The 95% CL expected (dotted curves) and observed (solid curves) upper limits on the branching fraction $ \mathcal{B}(\mathrm{H}\to\mathrm{S}\mathrm{S}) $ as functions of $ c\tau $ for the $ \mathrm{S}\to\mathrm{d}\overline{\mathrm{d}} $ (upper left), $ \mathrm{S}\to\pi^{0}\pi^{0} $ (upper right), and $ \mathrm{S}\to\tau^{+}\tau^{-} $ (lower) decay modes. The exclusion limits are shown for different mass hypotheses.

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Figure 13-a:
The 95% CL expected (dotted curves) and observed (solid curves) upper limits on the branching fraction $ \mathcal{B}(\mathrm{H}\to\mathrm{S}\mathrm{S}) $ as functions of $ c\tau $ for the $ \mathrm{S}\to\mathrm{d}\overline{\mathrm{d}} $ (upper left), $ \mathrm{S}\to\pi^{0}\pi^{0} $ (upper right), and $ \mathrm{S}\to\tau^{+}\tau^{-} $ (lower) decay modes. The exclusion limits are shown for different mass hypotheses.

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Figure 13-b:
The 95% CL expected (dotted curves) and observed (solid curves) upper limits on the branching fraction $ \mathcal{B}(\mathrm{H}\to\mathrm{S}\mathrm{S}) $ as functions of $ c\tau $ for the $ \mathrm{S}\to\mathrm{d}\overline{\mathrm{d}} $ (upper left), $ \mathrm{S}\to\pi^{0}\pi^{0} $ (upper right), and $ \mathrm{S}\to\tau^{+}\tau^{-} $ (lower) decay modes. The exclusion limits are shown for different mass hypotheses.

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Figure 13-c:
The 95% CL expected (dotted curves) and observed (solid curves) upper limits on the branching fraction $ \mathcal{B}(\mathrm{H}\to\mathrm{S}\mathrm{S}) $ as functions of $ c\tau $ for the $ \mathrm{S}\to\mathrm{d}\overline{\mathrm{d}} $ (upper left), $ \mathrm{S}\to\pi^{0}\pi^{0} $ (upper right), and $ \mathrm{S}\to\tau^{+}\tau^{-} $ (lower) decay modes. The exclusion limits are shown for different mass hypotheses.

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Figure 14:
The 95% CL observed upper limits on the branching fraction $ \mathcal{B}(\mathrm{H}\to\mathrm{S}\mathrm{S}) $ as functions of mass and $ c\tau $ for the $ \mathrm{S}\to\mathrm{d}\overline{\mathrm{d}} $ (upper left), $ \mathrm{S}\to\pi^{0}\pi^{0} $ (upper right), and $ \mathrm{S}\to\tau^{+}\tau^{-} $ (lower) decay modes. The area inside the solid contours represents the region for which the limit is smaller than 0.01.

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Figure 14-a:
The 95% CL observed upper limits on the branching fraction $ \mathcal{B}(\mathrm{H}\to\mathrm{S}\mathrm{S}) $ as functions of mass and $ c\tau $ for the $ \mathrm{S}\to\mathrm{d}\overline{\mathrm{d}} $ (upper left), $ \mathrm{S}\to\pi^{0}\pi^{0} $ (upper right), and $ \mathrm{S}\to\tau^{+}\tau^{-} $ (lower) decay modes. The area inside the solid contours represents the region for which the limit is smaller than 0.01.

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Figure 14-b:
The 95% CL observed upper limits on the branching fraction $ \mathcal{B}(\mathrm{H}\to\mathrm{S}\mathrm{S}) $ as functions of mass and $ c\tau $ for the $ \mathrm{S}\to\mathrm{d}\overline{\mathrm{d}} $ (upper left), $ \mathrm{S}\to\pi^{0}\pi^{0} $ (upper right), and $ \mathrm{S}\to\tau^{+}\tau^{-} $ (lower) decay modes. The area inside the solid contours represents the region for which the limit is smaller than 0.01.

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Figure 14-c:
The 95% CL observed upper limits on the branching fraction $ \mathcal{B}(\mathrm{H}\to\mathrm{S}\mathrm{S}) $ as functions of mass and $ c\tau $ for the $ \mathrm{S}\to\mathrm{d}\overline{\mathrm{d}} $ (upper left), $ \mathrm{S}\to\pi^{0}\pi^{0} $ (upper right), and $ \mathrm{S}\to\tau^{+}\tau^{-} $ (lower) decay modes. The area inside the solid contours represents the region for which the limit is smaller than 0.01.

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Figure 15:
The 95% CL expected (dotted curves) and observed (solid curves) upper limits on the branching fraction $ \mathcal{B}(\mathrm{H}\to\mathrm{S}\mathrm{S}) $ as functions of $ c\tau $ for the $ \mathrm{S}\to\mathrm{b}\overline{\mathrm{b}} $ (upper left), $ \mathrm{S}\to\pi^{+}\pi^{-} $ (upper right), $ \mathrm{S}\to \mathrm{K^+}\mathrm{K^-} $ (middle left), $ \mathrm{S}\to \mathrm{K^0}\mathrm{K^0} $ (middle right), $ \mathrm{S}\to \gamma\gamma $ (lower left), and $ \mathrm{S}\to \mathrm{e}^+\mathrm{e}^- $ (lower right) decay modes. The exclusion limits are shown for different mass hypotheses.

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Figure 15-a:
The 95% CL expected (dotted curves) and observed (solid curves) upper limits on the branching fraction $ \mathcal{B}(\mathrm{H}\to\mathrm{S}\mathrm{S}) $ as functions of $ c\tau $ for the $ \mathrm{S}\to\mathrm{b}\overline{\mathrm{b}} $ (upper left), $ \mathrm{S}\to\pi^{+}\pi^{-} $ (upper right), $ \mathrm{S}\to \mathrm{K^+}\mathrm{K^-} $ (middle left), $ \mathrm{S}\to \mathrm{K^0}\mathrm{K^0} $ (middle right), $ \mathrm{S}\to \gamma\gamma $ (lower left), and $ \mathrm{S}\to \mathrm{e}^+\mathrm{e}^- $ (lower right) decay modes. The exclusion limits are shown for different mass hypotheses.

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Figure 15-b:
The 95% CL expected (dotted curves) and observed (solid curves) upper limits on the branching fraction $ \mathcal{B}(\mathrm{H}\to\mathrm{S}\mathrm{S}) $ as functions of $ c\tau $ for the $ \mathrm{S}\to\mathrm{b}\overline{\mathrm{b}} $ (upper left), $ \mathrm{S}\to\pi^{+}\pi^{-} $ (upper right), $ \mathrm{S}\to \mathrm{K^+}\mathrm{K^-} $ (middle left), $ \mathrm{S}\to \mathrm{K^0}\mathrm{K^0} $ (middle right), $ \mathrm{S}\to \gamma\gamma $ (lower left), and $ \mathrm{S}\to \mathrm{e}^+\mathrm{e}^- $ (lower right) decay modes. The exclusion limits are shown for different mass hypotheses.

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Figure 15-c:
The 95% CL expected (dotted curves) and observed (solid curves) upper limits on the branching fraction $ \mathcal{B}(\mathrm{H}\to\mathrm{S}\mathrm{S}) $ as functions of $ c\tau $ for the $ \mathrm{S}\to\mathrm{b}\overline{\mathrm{b}} $ (upper left), $ \mathrm{S}\to\pi^{+}\pi^{-} $ (upper right), $ \mathrm{S}\to \mathrm{K^+}\mathrm{K^-} $ (middle left), $ \mathrm{S}\to \mathrm{K^0}\mathrm{K^0} $ (middle right), $ \mathrm{S}\to \gamma\gamma $ (lower left), and $ \mathrm{S}\to \mathrm{e}^+\mathrm{e}^- $ (lower right) decay modes. The exclusion limits are shown for different mass hypotheses.

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Figure 15-d:
The 95% CL expected (dotted curves) and observed (solid curves) upper limits on the branching fraction $ \mathcal{B}(\mathrm{H}\to\mathrm{S}\mathrm{S}) $ as functions of $ c\tau $ for the $ \mathrm{S}\to\mathrm{b}\overline{\mathrm{b}} $ (upper left), $ \mathrm{S}\to\pi^{+}\pi^{-} $ (upper right), $ \mathrm{S}\to \mathrm{K^+}\mathrm{K^-} $ (middle left), $ \mathrm{S}\to \mathrm{K^0}\mathrm{K^0} $ (middle right), $ \mathrm{S}\to \gamma\gamma $ (lower left), and $ \mathrm{S}\to \mathrm{e}^+\mathrm{e}^- $ (lower right) decay modes. The exclusion limits are shown for different mass hypotheses.

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Figure 15-e:
The 95% CL expected (dotted curves) and observed (solid curves) upper limits on the branching fraction $ \mathcal{B}(\mathrm{H}\to\mathrm{S}\mathrm{S}) $ as functions of $ c\tau $ for the $ \mathrm{S}\to\mathrm{b}\overline{\mathrm{b}} $ (upper left), $ \mathrm{S}\to\pi^{+}\pi^{-} $ (upper right), $ \mathrm{S}\to \mathrm{K^+}\mathrm{K^-} $ (middle left), $ \mathrm{S}\to \mathrm{K^0}\mathrm{K^0} $ (middle right), $ \mathrm{S}\to \gamma\gamma $ (lower left), and $ \mathrm{S}\to \mathrm{e}^+\mathrm{e}^- $ (lower right) decay modes. The exclusion limits are shown for different mass hypotheses.

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Figure 15-f:
The 95% CL expected (dotted curves) and observed (solid curves) upper limits on the branching fraction $ \mathcal{B}(\mathrm{H}\to\mathrm{S}\mathrm{S}) $ as functions of $ c\tau $ for the $ \mathrm{S}\to\mathrm{b}\overline{\mathrm{b}} $ (upper left), $ \mathrm{S}\to\pi^{+}\pi^{-} $ (upper right), $ \mathrm{S}\to \mathrm{K^+}\mathrm{K^-} $ (middle left), $ \mathrm{S}\to \mathrm{K^0}\mathrm{K^0} $ (middle right), $ \mathrm{S}\to \gamma\gamma $ (lower left), and $ \mathrm{S}\to \mathrm{e}^+\mathrm{e}^- $ (lower right) decay modes. The exclusion limits are shown for different mass hypotheses.

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Figure 16:
The 95% CL observed upper limits on the branching fraction $ \mathcal{B}(\mathrm{H}\to\mathrm{S}\mathrm{S}) $ as functions of mass and $ c\tau $ for the $ \mathrm{S}\to\mathrm{b}\overline{\mathrm{b}} $ (upper left), $ \mathrm{S}\to\pi^{+}\pi^{-} $ (upper right), $ \mathrm{S}\to \mathrm{K^+}\mathrm{K^-} $ (middle left), $ \mathrm{S}\to \mathrm{K^0}\mathrm{K^0} $ (middle right), $ \mathrm{S}\to\gamma\gamma $ (lower left), $ \mathrm{S}\to \mathrm{e}^+\mathrm{e}^- $ (lower right) decay modes. The area inside the solid contours represents the region for which the limit is smaller than 0.01.

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Figure 16-a:
The 95% CL observed upper limits on the branching fraction $ \mathcal{B}(\mathrm{H}\to\mathrm{S}\mathrm{S}) $ as functions of mass and $ c\tau $ for the $ \mathrm{S}\to\mathrm{b}\overline{\mathrm{b}} $ (upper left), $ \mathrm{S}\to\pi^{+}\pi^{-} $ (upper right), $ \mathrm{S}\to \mathrm{K^+}\mathrm{K^-} $ (middle left), $ \mathrm{S}\to \mathrm{K^0}\mathrm{K^0} $ (middle right), $ \mathrm{S}\to\gamma\gamma $ (lower left), $ \mathrm{S}\to \mathrm{e}^+\mathrm{e}^- $ (lower right) decay modes. The area inside the solid contours represents the region for which the limit is smaller than 0.01.

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Figure 16-b:
The 95% CL observed upper limits on the branching fraction $ \mathcal{B}(\mathrm{H}\to\mathrm{S}\mathrm{S}) $ as functions of mass and $ c\tau $ for the $ \mathrm{S}\to\mathrm{b}\overline{\mathrm{b}} $ (upper left), $ \mathrm{S}\to\pi^{+}\pi^{-} $ (upper right), $ \mathrm{S}\to \mathrm{K^+}\mathrm{K^-} $ (middle left), $ \mathrm{S}\to \mathrm{K^0}\mathrm{K^0} $ (middle right), $ \mathrm{S}\to\gamma\gamma $ (lower left), $ \mathrm{S}\to \mathrm{e}^+\mathrm{e}^- $ (lower right) decay modes. The area inside the solid contours represents the region for which the limit is smaller than 0.01.

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Figure 16-c:
The 95% CL observed upper limits on the branching fraction $ \mathcal{B}(\mathrm{H}\to\mathrm{S}\mathrm{S}) $ as functions of mass and $ c\tau $ for the $ \mathrm{S}\to\mathrm{b}\overline{\mathrm{b}} $ (upper left), $ \mathrm{S}\to\pi^{+}\pi^{-} $ (upper right), $ \mathrm{S}\to \mathrm{K^+}\mathrm{K^-} $ (middle left), $ \mathrm{S}\to \mathrm{K^0}\mathrm{K^0} $ (middle right), $ \mathrm{S}\to\gamma\gamma $ (lower left), $ \mathrm{S}\to \mathrm{e}^+\mathrm{e}^- $ (lower right) decay modes. The area inside the solid contours represents the region for which the limit is smaller than 0.01.

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Figure 16-d:
The 95% CL observed upper limits on the branching fraction $ \mathcal{B}(\mathrm{H}\to\mathrm{S}\mathrm{S}) $ as functions of mass and $ c\tau $ for the $ \mathrm{S}\to\mathrm{b}\overline{\mathrm{b}} $ (upper left), $ \mathrm{S}\to\pi^{+}\pi^{-} $ (upper right), $ \mathrm{S}\to \mathrm{K^+}\mathrm{K^-} $ (middle left), $ \mathrm{S}\to \mathrm{K^0}\mathrm{K^0} $ (middle right), $ \mathrm{S}\to\gamma\gamma $ (lower left), $ \mathrm{S}\to \mathrm{e}^+\mathrm{e}^- $ (lower right) decay modes. The area inside the solid contours represents the region for which the limit is smaller than 0.01.

png pdf
Figure 16-e:
The 95% CL observed upper limits on the branching fraction $ \mathcal{B}(\mathrm{H}\to\mathrm{S}\mathrm{S}) $ as functions of mass and $ c\tau $ for the $ \mathrm{S}\to\mathrm{b}\overline{\mathrm{b}} $ (upper left), $ \mathrm{S}\to\pi^{+}\pi^{-} $ (upper right), $ \mathrm{S}\to \mathrm{K^+}\mathrm{K^-} $ (middle left), $ \mathrm{S}\to \mathrm{K^0}\mathrm{K^0} $ (middle right), $ \mathrm{S}\to\gamma\gamma $ (lower left), $ \mathrm{S}\to \mathrm{e}^+\mathrm{e}^- $ (lower right) decay modes. The area inside the solid contours represents the region for which the limit is smaller than 0.01.

png pdf
Figure 16-f:
The 95% CL observed upper limits on the branching fraction $ \mathcal{B}(\mathrm{H}\to\mathrm{S}\mathrm{S}) $ as functions of mass and $ c\tau $ for the $ \mathrm{S}\to\mathrm{b}\overline{\mathrm{b}} $ (upper left), $ \mathrm{S}\to\pi^{+}\pi^{-} $ (upper right), $ \mathrm{S}\to \mathrm{K^+}\mathrm{K^-} $ (middle left), $ \mathrm{S}\to \mathrm{K^0}\mathrm{K^0} $ (middle right), $ \mathrm{S}\to\gamma\gamma $ (lower left), $ \mathrm{S}\to \mathrm{e}^+\mathrm{e}^- $ (lower right) decay modes. The area inside the solid contours represents the region for which the limit is smaller than 0.01.

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Figure 17:
The 95% CL observed upper limits on the branching fraction $ \mathcal{B}(\mathrm{H}\to\mathrm{S}\mathrm{S}) $ as a function of mass and $ c\tau $, assuming the branching fractions for S are identical to those of a Higgs boson evaluated at $ m_\mathrm{S} $ [66]. The area inside the solid contours represents the region for which the limit is smaller than 0.01.

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Figure 18:
The 95% CL observed upper limits on the branching fraction $ \mathcal{B}(\mathrm{H}\to\Psi\Psi) $ as functions of $ c\tau $ for the dark shower vector portal assuming $ (\xi_{\omega} $, $ \xi_{\Lambda}) = (1, 1) $. The exclusion limits are shown for different LLP mass hypotheses. The limits are calculated only at the proper decay lengths indicated by the markers and the lines connecting the markers are linear interpolations. The plot is restricted to physical $ \mathcal{B}(\mathrm{H}\to\Psi\Psi) $ values of below 1.

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Figure 19:
The 95% CL observed upper limits on the branching fraction $ \mathcal{B}(\mathrm{H}\to\Psi\Psi) $ as functions of $ c\tau $ for the dark shower gluon portal, assuming $ (\xi_{\omega} $, $ \xi_{\Lambda}) = (1, 1) $ (upper left), $ (\xi_{\omega} $, $ \xi_{\Lambda}) = (2.5, 1.0) $ (upper right), and $ (\xi_{\omega} $, $ \xi_{\Lambda}) = (2.5, 2.5) $ (lower). The exclusion limits are shown for different mass hypotheses. The limits are calculated only at the proper decay lengths indicated by the markers and the lines connecting the markers are linear interpolations. The plot is restricted to physical $ \mathcal{B}(\mathrm{H}\to\Psi\Psi) $ values of below 1.

png pdf
Figure 19-a:
The 95% CL observed upper limits on the branching fraction $ \mathcal{B}(\mathrm{H}\to\Psi\Psi) $ as functions of $ c\tau $ for the dark shower gluon portal, assuming $ (\xi_{\omega} $, $ \xi_{\Lambda}) = (1, 1) $ (upper left), $ (\xi_{\omega} $, $ \xi_{\Lambda}) = (2.5, 1.0) $ (upper right), and $ (\xi_{\omega} $, $ \xi_{\Lambda}) = (2.5, 2.5) $ (lower). The exclusion limits are shown for different mass hypotheses. The limits are calculated only at the proper decay lengths indicated by the markers and the lines connecting the markers are linear interpolations. The plot is restricted to physical $ \mathcal{B}(\mathrm{H}\to\Psi\Psi) $ values of below 1.

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Figure 19-b:
The 95% CL observed upper limits on the branching fraction $ \mathcal{B}(\mathrm{H}\to\Psi\Psi) $ as functions of $ c\tau $ for the dark shower gluon portal, assuming $ (\xi_{\omega} $, $ \xi_{\Lambda}) = (1, 1) $ (upper left), $ (\xi_{\omega} $, $ \xi_{\Lambda}) = (2.5, 1.0) $ (upper right), and $ (\xi_{\omega} $, $ \xi_{\Lambda}) = (2.5, 2.5) $ (lower). The exclusion limits are shown for different mass hypotheses. The limits are calculated only at the proper decay lengths indicated by the markers and the lines connecting the markers are linear interpolations. The plot is restricted to physical $ \mathcal{B}(\mathrm{H}\to\Psi\Psi) $ values of below 1.

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Figure 19-c:
The 95% CL observed upper limits on the branching fraction $ \mathcal{B}(\mathrm{H}\to\Psi\Psi) $ as functions of $ c\tau $ for the dark shower gluon portal, assuming $ (\xi_{\omega} $, $ \xi_{\Lambda}) = (1, 1) $ (upper left), $ (\xi_{\omega} $, $ \xi_{\Lambda}) = (2.5, 1.0) $ (upper right), and $ (\xi_{\omega} $, $ \xi_{\Lambda}) = (2.5, 2.5) $ (lower). The exclusion limits are shown for different mass hypotheses. The limits are calculated only at the proper decay lengths indicated by the markers and the lines connecting the markers are linear interpolations. The plot is restricted to physical $ \mathcal{B}(\mathrm{H}\to\Psi\Psi) $ values of below 1.

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Figure 20:
The 95% CL observed upper limits on the branching fraction $ \mathcal{B}(\mathrm{H}\to\Psi\Psi) $ as functions of $ c\tau $ for the dark shower photon portal, assuming $ (\xi_{\omega} $, $ \xi_{\Lambda}) = (1, 1) $ (upper left), $ (\xi_{\omega} $, $ \xi_{\Lambda}) = (2.5, 1.0) $ (upper right), and $ (\xi_{\omega} $, $ \xi_{\Lambda}) = (2.5, 2.5) $ (lower). The exclusion limits are shown for different mass hypotheses. The limits are calculated only at the proper decay lengths indicated by the markers and the lines connecting the markers are linear interpolations. The plot is restricted to physical $ \mathcal{B}(\mathrm{H}\to\Psi\Psi) $ values of below 1.

png pdf
Figure 20-a:
The 95% CL observed upper limits on the branching fraction $ \mathcal{B}(\mathrm{H}\to\Psi\Psi) $ as functions of $ c\tau $ for the dark shower photon portal, assuming $ (\xi_{\omega} $, $ \xi_{\Lambda}) = (1, 1) $ (upper left), $ (\xi_{\omega} $, $ \xi_{\Lambda}) = (2.5, 1.0) $ (upper right), and $ (\xi_{\omega} $, $ \xi_{\Lambda}) = (2.5, 2.5) $ (lower). The exclusion limits are shown for different mass hypotheses. The limits are calculated only at the proper decay lengths indicated by the markers and the lines connecting the markers are linear interpolations. The plot is restricted to physical $ \mathcal{B}(\mathrm{H}\to\Psi\Psi) $ values of below 1.

png pdf
Figure 20-b:
The 95% CL observed upper limits on the branching fraction $ \mathcal{B}(\mathrm{H}\to\Psi\Psi) $ as functions of $ c\tau $ for the dark shower photon portal, assuming $ (\xi_{\omega} $, $ \xi_{\Lambda}) = (1, 1) $ (upper left), $ (\xi_{\omega} $, $ \xi_{\Lambda}) = (2.5, 1.0) $ (upper right), and $ (\xi_{\omega} $, $ \xi_{\Lambda}) = (2.5, 2.5) $ (lower). The exclusion limits are shown for different mass hypotheses. The limits are calculated only at the proper decay lengths indicated by the markers and the lines connecting the markers are linear interpolations. The plot is restricted to physical $ \mathcal{B}(\mathrm{H}\to\Psi\Psi) $ values of below 1.

png pdf
Figure 20-c:
The 95% CL observed upper limits on the branching fraction $ \mathcal{B}(\mathrm{H}\to\Psi\Psi) $ as functions of $ c\tau $ for the dark shower photon portal, assuming $ (\xi_{\omega} $, $ \xi_{\Lambda}) = (1, 1) $ (upper left), $ (\xi_{\omega} $, $ \xi_{\Lambda}) = (2.5, 1.0) $ (upper right), and $ (\xi_{\omega} $, $ \xi_{\Lambda}) = (2.5, 2.5) $ (lower). The exclusion limits are shown for different mass hypotheses. The limits are calculated only at the proper decay lengths indicated by the markers and the lines connecting the markers are linear interpolations. The plot is restricted to physical $ \mathcal{B}(\mathrm{H}\to\Psi\Psi) $ values of below 1.

png pdf
Figure 21:
The 95% CL observed upper limits on the branching fraction $ \mathcal{B}(\mathrm{H}\to\Psi\Psi) $ as functions of $ c\tau $ for the dark shower Higgs boson portal, assuming $ (\xi_{\omega} $, $ \xi_{\Lambda}) = (1, 1) $ (upper left), $ (\xi_{\omega} $, $ \xi_{\Lambda}) = (2.5, 1.0) $ (upper right), and $ (\xi_{\omega} $, $ \xi_{\Lambda}) = (2.5, 2.5) $ (lower). The exclusion limits are shown for different mass hypotheses. The limits are calculated only at the proper decay lengths indicated by the markers and the lines connecting the markers are linear interpolations. The plot is restricted to physical $ \mathcal{B}(\mathrm{H}\to\Psi\Psi) $ values of below 1.

png pdf
Figure 21-a:
The 95% CL observed upper limits on the branching fraction $ \mathcal{B}(\mathrm{H}\to\Psi\Psi) $ as functions of $ c\tau $ for the dark shower Higgs boson portal, assuming $ (\xi_{\omega} $, $ \xi_{\Lambda}) = (1, 1) $ (upper left), $ (\xi_{\omega} $, $ \xi_{\Lambda}) = (2.5, 1.0) $ (upper right), and $ (\xi_{\omega} $, $ \xi_{\Lambda}) = (2.5, 2.5) $ (lower). The exclusion limits are shown for different mass hypotheses. The limits are calculated only at the proper decay lengths indicated by the markers and the lines connecting the markers are linear interpolations. The plot is restricted to physical $ \mathcal{B}(\mathrm{H}\to\Psi\Psi) $ values of below 1.

png pdf
Figure 21-b:
The 95% CL observed upper limits on the branching fraction $ \mathcal{B}(\mathrm{H}\to\Psi\Psi) $ as functions of $ c\tau $ for the dark shower Higgs boson portal, assuming $ (\xi_{\omega} $, $ \xi_{\Lambda}) = (1, 1) $ (upper left), $ (\xi_{\omega} $, $ \xi_{\Lambda}) = (2.5, 1.0) $ (upper right), and $ (\xi_{\omega} $, $ \xi_{\Lambda}) = (2.5, 2.5) $ (lower). The exclusion limits are shown for different mass hypotheses. The limits are calculated only at the proper decay lengths indicated by the markers and the lines connecting the markers are linear interpolations. The plot is restricted to physical $ \mathcal{B}(\mathrm{H}\to\Psi\Psi) $ values of below 1.

png pdf
Figure 21-c:
The 95% CL observed upper limits on the branching fraction $ \mathcal{B}(\mathrm{H}\to\Psi\Psi) $ as functions of $ c\tau $ for the dark shower Higgs boson portal, assuming $ (\xi_{\omega} $, $ \xi_{\Lambda}) = (1, 1) $ (upper left), $ (\xi_{\omega} $, $ \xi_{\Lambda}) = (2.5, 1.0) $ (upper right), and $ (\xi_{\omega} $, $ \xi_{\Lambda}) = (2.5, 2.5) $ (lower). The exclusion limits are shown for different mass hypotheses. The limits are calculated only at the proper decay lengths indicated by the markers and the lines connecting the markers are linear interpolations. The plot is restricted to physical $ \mathcal{B}(\mathrm{H}\to\Psi\Psi) $ values of below 1.

png pdf
Figure 22:
The 95% CL observed upper limits on the branching fraction $ \mathcal{B}(\mathrm{H}\to\Psi\Psi) $ as functions of $ c\tau $ for the dark shower dark-photon portal, assuming $ (\xi_{\omega} $, $ \xi_{\Lambda}) = (1, 1) $ (upper left), $ (\xi_{\omega} $, $ \xi_{\Lambda}) = (2.5, 1.0) $ (upper right), and $ (\xi_{\omega} $, $ \xi_{\Lambda}) = (2.5, 2.5) $ (lower). The exclusion limits are shown for different mass hypotheses. The limits are calculated only at the proper decay lengths indicated by the markers and the lines connecting the markers are linear interpolations. The plot is restricted to physical $ \mathcal{B}(\mathrm{H}\to\Psi\Psi) $ values of below 1.

png pdf
Figure 22-a:
The 95% CL observed upper limits on the branching fraction $ \mathcal{B}(\mathrm{H}\to\Psi\Psi) $ as functions of $ c\tau $ for the dark shower dark-photon portal, assuming $ (\xi_{\omega} $, $ \xi_{\Lambda}) = (1, 1) $ (upper left), $ (\xi_{\omega} $, $ \xi_{\Lambda}) = (2.5, 1.0) $ (upper right), and $ (\xi_{\omega} $, $ \xi_{\Lambda}) = (2.5, 2.5) $ (lower). The exclusion limits are shown for different mass hypotheses. The limits are calculated only at the proper decay lengths indicated by the markers and the lines connecting the markers are linear interpolations. The plot is restricted to physical $ \mathcal{B}(\mathrm{H}\to\Psi\Psi) $ values of below 1.

png pdf
Figure 22-b:
The 95% CL observed upper limits on the branching fraction $ \mathcal{B}(\mathrm{H}\to\Psi\Psi) $ as functions of $ c\tau $ for the dark shower dark-photon portal, assuming $ (\xi_{\omega} $, $ \xi_{\Lambda}) = (1, 1) $ (upper left), $ (\xi_{\omega} $, $ \xi_{\Lambda}) = (2.5, 1.0) $ (upper right), and $ (\xi_{\omega} $, $ \xi_{\Lambda}) = (2.5, 2.5) $ (lower). The exclusion limits are shown for different mass hypotheses. The limits are calculated only at the proper decay lengths indicated by the markers and the lines connecting the markers are linear interpolations. The plot is restricted to physical $ \mathcal{B}(\mathrm{H}\to\Psi\Psi) $ values of below 1.

png pdf
Figure 22-c:
The 95% CL observed upper limits on the branching fraction $ \mathcal{B}(\mathrm{H}\to\Psi\Psi) $ as functions of $ c\tau $ for the dark shower dark-photon portal, assuming $ (\xi_{\omega} $, $ \xi_{\Lambda}) = (1, 1) $ (upper left), $ (\xi_{\omega} $, $ \xi_{\Lambda}) = (2.5, 1.0) $ (upper right), and $ (\xi_{\omega} $, $ \xi_{\Lambda}) = (2.5, 2.5) $ (lower). The exclusion limits are shown for different mass hypotheses. The limits are calculated only at the proper decay lengths indicated by the markers and the lines connecting the markers are linear interpolations. The plot is restricted to physical $ \mathcal{B}(\mathrm{H}\to\Psi\Psi) $ values of below 1.
Tables

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Table 1:
Validation of the ABCD method for the double-cluster category in both VRs. The uncertainty in the prediction is the statistical uncertainty propagated from bins B, C, and D or bins BD and C. The expected background event rate in bin A ($ \lambda_\mathrm{A} $) and the background event rate in bins B, C, D, BD, and A ($ N_\mathrm{B} $, $ N_\mathrm{C} $, $ N_\mathrm{D} $, $ N_\mathrm{BD} $, $ N_\mathrm{A} $) are shown.

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Table 2:
Validation of the ABCD method for the single-CSC-cluster category in both VRs. The uncertainty in the prediction is the statistical uncertainty propagated from bins B, C, and D. The expected background event rate in bin A ($ \lambda_\mathrm{A} $) and the background event rate in bins B, C, D, and A ($ N_\mathrm{B} $, $ N_\mathrm{C} $, $ N_\mathrm{D} $, $ N_\mathrm{A} $) are shown.

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Table 3:
Validation of the ABCD method for the single-DT-cluster category in a pileup-enriched region. The uncertainty in the prediction is the statistical uncertainty propagated from bins B, C, and D. Bins C and D for the MB3 and MB4 categories are combined to reduce the statistical uncertainty in the two regions. The final ABCD fit in the SR will also be performed with those bins combined.

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Table 4:
Validation of the punch-through jet background prediction method for the single-DT-cluster category. The uncertainty in the prediction is the statistical uncertainty propagated from the extrapolated MB1/MB2 hit veto efficiency.

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Table 5:
Number of predicted background and observed events in the double-cluster category. The background prediction is obtained from a fit to the observed data assuming no signal contribution.

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Table 6:
Number of predicted background and observed events in the single-CSC-cluster category. The background prediction is obtained from a fit to the observed data assuming no signal contribution.

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Table 7:
Number of predicted background and observed events in the single-DT-cluster category. The background prediction is obtained from a fit to the observed data assuming no signal contribution.

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Table 8:
Expected number of signal events in bin A for each category, for a few benchmark signal models assuming $ \mathcal{B}(\mathrm{H}\to\mathrm{S}\mathrm{S}) = 1% $.
Summary
Data from proton-proton collisions at $ \sqrt{s} = $ 13 TeV recorded by the CMS experiment in 2016-2018, corresponding to an integrated luminosity of 138 fb$ ^{-1} $, have been used to conduct the first search that uses both the barrel and endcap CMS muon detectors to detect hadronic and electromagnetic showers from long-lived particle (LLP) decays. Based on this unique detector signature, the search is largely model-independent, with sensitivity to a broad range of LLP decay modes and masses extending below the GeVns scale. With the excellent shielding provided by the inner CMS detector, the CMS magnet and its steel flux-return yoke, the background is suppressed to a low level and a search for both single and pairs of LLPs decays is possible. No significant deviation from the standard model background is observed. The most stringent LHC constraints to date are set on the branching fraction of the Higgs boson to LLPs with masses below 10 GeV and decaying to particles other than muons. For higher LLP masses the search provides the most stringent branching fraction limits for specific proper decay lengths: 0.04-0.40 m and above 5 m for 15 GeV LLP; 0.3-0.9 m and above 3 m for 40 GeV LLP; and above 0.9 m for 55 GeV LLP. Finally, the first LHC limits on models of dark showers produced via H decay are set, and constrain branching fractions of the H decay to dark quarks as low as 2 $ \times $ 10$^{-3} $ at 95% confidence level.
References
1 G. F. Giudice and A. Romanino Split supersymmetry NPB 699 (2004) 65 hep-ph/0406088
2 J. L. Hewett, B. Lillie, M. Masip, and T. G. Rizzo Signatures of long-lived gluinos in split supersymmetry JHEP 09 (2004) 070 hep-ph/0408248
3 N. Arkani-Hamed, S. Dimopoulos, G. F. Giudice, and A. Romanino Aspects of split supersymmetry NPB 709 (2005) 3 hep-ph/0409232
4 P. Gambino, G. F. Giudice, and P. Slavich Gluino decays in split supersymmetry NPB 726 (2005) 35 hep-ph/0506214
5 A. Arvanitaki, N. Craig, S. Dimopoulos, and G. Villadoro Mini-split JHEP 02 (2013) 126 1210.0555
6 N. Arkani-Hamed et al. Simply unnatural supersymmetry 1212.6971
7 P. Fayet Supergauge invariant extension of the Higgs mechanism and a model for the electron and its neutrino NPB 90 (1975) 104
8 G. R. Farrar and P. Fayet Phenomenology of the production, decay, and detection of new hadronic states associated with supersymmetry PLB 76 (1978) 575
9 S. Weinberg Supersymmetry at ordinary energies. Masses and conservation laws PRD 26 (1982) 287
10 R. Barbier et al. $ R $-parity violating supersymmetry Phys. Rept. 420 (2005) 1 hep-ph/0406039
11 G. F. Giudice and R. Rattazzi Theories with gauge mediated supersymmetry breaking Phys. Rept. 322 (1999) 419 hep-ph/9801271
12 P. Meade, N. Seiberg, and D. Shih General gauge mediation Prog. Theor. Phys. Suppl. 177 (2009) 143 0801.3278
13 M. Buican, P. Meade, N. Seiberg, and D. Shih Exploring general gauge mediation JHEP 03 (2009) 016 0812.3668
14 J. Fan, M. Reece, and J. T. Ruderman Stealth supersymmetry JHEP 11 (2011) 012 1105.5135
15 J. Fan, M. Reece, and J. T. Ruderman A stealth supersymmetry sampler JHEP 07 (2012) 196 1201.4875
16 M. J. Strassler and K. M. Zurek Echoes of a hidden valley at hadron colliders PLB 651 (2007) 374 hep-ph/0604261
17 M. J. Strassler and K. M. Zurek Discovering the Higgs through highly-displaced vertices PLB 661 (2008) 263 hep-ph/0605193
18 T. Han, Z. Si, K. M. Zurek, and M. J. Strassler Phenomenology of hidden valleys at hadron colliders JHEP 07 (2008) 008 0712.2041
19 D. Smith and N. Weiner Inelastic dark matter PRD 64 (2001) 043502 hep-ph/0101138
20 Z. Chacko, H.-S. Goh, and R. Harnik Natural electroweak breaking from a mirror symmetry PRL 96 (2006) 231802 hep-ph/0506256
21 D. Curtin and C. B. Verhaaren Discovering uncolored naturalness in exotic Higgs decays JHEP 12 (2015) 072 1506.06141
22 H.-C. Cheng, S. Jung, E. Salvioni, and Y. Tsai Exotic quarks in twin Higgs models JHEP 03 (2016) 074 1512.02647
23 CMS Collaboration Search for long-lived particles decaying in the CMS end cap muon detectors in proton-proton collisions at $ \sqrt{s} = $ 13 TeV PRL 127 (2021) 261804 CMS-EXO-20-015
2107.04838
24 CMS Collaboration The CMS muon project: Technical Design Report CMS Technical Design Report CERN-LHCC-97-032, 1997
CDS
25 CMS Collaboration The CMS experiment at the CERN LHC JINST 3 (2008) S08004
26 CMS Collaboration Search for long-lived particles using displaced jets in proton-proton collisions at $ \sqrt{s} = $ 13 TeV PRD 104 (2021) 012015 CMS-EXO-19-021
2012.01581
27 ATLAS Collaboration Search for long-lived particles produced in pp collisions at $ \sqrt{s}= $ 13 TeV that decay into displaced hadronic jets in the ATLAS muon spectrometer PRD 99 (2019) 052005 1811.07370
28 ATLAS Collaboration Search for events with a pair of displaced vertices from long-lived neutral particles decaying into hadronic jets in the ATLAS muon spectrometer in pp collisions at $ \sqrt{s} = $ 13 TeV PRD 106 (2022) 032005 2203.00587
29 S. Knapen, J. Shelton, and D. Xu Perturbative benchmark models for a dark shower search program PRD 103 (2021) 115013 2103.01238
30 CMS Collaboration HEPData record for this analysis link
31 CMS Collaboration Performance of the CMS drift tube chambers with cosmic rays JINST 5 (2010) T03015 CMS-CFT-09-012
0911.4855
32 CMS Collaboration Performance of the CMS muon detector and muon reconstruction with proton-proton collisions at $ \sqrt{s}= $ 13 TeV JINST 13 (2018) P06015 CMS-MUO-16-001
1804.04528
33 CMS Collaboration Performance of the CMS cathode strip chambers with cosmic rays JINST 5 (2010) T03018 CMS-CFT-09-011
0911.4992
34 CMS Collaboration Performance of the CMS Level-1 trigger in proton-proton collisions at $ \sqrt{s} = $ 13 TeV JINST 15 (2020) P10017 CMS-TRG-17-001
2006.10165
35 CMS Collaboration The CMS trigger system JINST 12 (2017) P01020 CMS-TRG-12-001
1609.02366
36 P. Nason A new method for combining NLO QCD with shower Monte Carlo algorithms JHEP 11 (2004) 040 hep-ph/0409146
37 S. Frixione, P. Nason, and C. Oleari Matching NLO QCD computations with parton shower simulations: the POWHEG method JHEP 11 (2007) 070 0709.2092
38 S. Alioli, P. Nason, C. Oleari, and E. Re A general framework for implementing NLO calculations in shower Monte Carlo programs: the POWHEG \textscbox JHEP 06 (2010) 043 1002.2581
39 E. Re Single-top $ \mathrm{W}\mathrm{t} $-channel production matched with parton showers using the POWHEG method EPJC 71 (2011) 1547 1009.2450
40 F. Bezrukov and D. Gorbunov Light inflaton after LHC8 and WMAP9 results JHEP 07 (2013) 140 1303.4395
41 M. W. Winkler Decay and detection of a light scalar boson mixing with the Higgs boson PRD 99 (2019) 015018 1809.01876
42 T. Sjöstrand et al. An introduction to PYTHIA 8.2 Comput. Phys. Commun. 191 (2015) 159 1410.3012
43 L. Carloni, J. Rathsman, and T. Sjöstrand Discerning secluded sector gauge structures JHEP 04 (2011) 091 1102.3795
44 L. Carloni and T. Sjöstrand Visible effects of invisible Hidden Valley radiation JHEP 09 (2010) 105 1006.2911
45 CMS Collaboration Event generator tunes obtained from underlying event and multiparton scattering measurements EPJC 76 (2016) 155 CMS-GEN-14-001
1512.00815
46 CMS Collaboration Extraction and validation of a new set of CMS PYTHIA8 tunes from underlying-event measurements EPJC 80 (2020) 4 CMS-GEN-17-001
1903.12179
47 NNPDF Collaboration Parton distributions for the LHC Run II JHEP 04 (2015) 040 1410.8849
48 NNPDF Collaboration Parton distributions from high-precision collider data EPJC 77 (2017) 663 1706.00428
49 GEANT4 Collaboration GEANT 4---a simulation toolkit NIM A 506 (2003) 250
50 CMS Collaboration Particle-flow reconstruction and global event description with the CMS detector JINST 12 (2017) P10003 CMS-PRF-14-001
1706.04965
51 CMS Collaboration Performance of the reconstruction and identification of high-momentum muons in proton-proton collisions at $ \sqrt{s} = $ 13 TeV JINST 15 (2020) P02027 CMS-MUO-17-001
1912.03516
52 M. Cacciari, G. P. Salam, and G. Soyez The anti-$ k_{\mathrm{T}} $ jet clustering algorithm JHEP 04 (2008) 063 0802.1189
53 M. Cacciari, G. P. Salam, and G. Soyez FASTJET user manual EPJC 72 (2012) 1896 1111.6097
54 CMS Collaboration Jet energy scale and resolution in the CMS experiment in pp collisions at 8 TeV JINST 12 (2017) P02014 CMS-JME-13-004
1607.03663
55 CMS Collaboration Missing transverse energy performance of the CMS detector JINST 6 (2011) P09001 CMS-JME-10-009
1106.5048
56 CMS Collaboration Performance of missing transverse momentum reconstruction in proton-proton collisions at $ \sqrt{s} = $ 13 TeV using the CMS detector JINST 14 (2019) P07004 CMS-JME-17-001
1903.06078
57 M. Ester, H.-P. Kriegel, J. Sander, and X. Xu A density-based algorithm for discovering clusters in large spatial databases with noise in Proceedings of the Second International Conference on Knowledge Discovery and Data Mining, 1996
link
58 CMS Collaboration CMS jet algorithms performance in 13 TeV data CMS Physics Analysis Summary, 2016
CMS-PAS-JME-16-003
CMS-PAS-JME-16-003
59 G. Kasieczka, B. Nachman, M. D. Schwartz, and D. Shih Automating the ABCD method with machine learning PRD 103 (2021) 035021 2007.14400
60 CMS Collaboration Precision luminosity measurement in proton-proton collisions at $ \sqrt{s} = $ 13 TeV in 2015 and 2016 at CMS EPJC 81 (2021) 800 CMS-LUM-17-003
2104.01927
61 CMS Collaboration CMS luminosity measurements for the 2017 data-taking period at $ \sqrt{s} = $ 13 TeV CMS Physics Analysis Summary, 2017
CMS-PAS-LUM-17-004
CMS-PAS-LUM-17-004
62 CMS Collaboration CMS luminosity measurements for the 2018 data-taking period at $ \sqrt{s} = $ 13 TeV CMS Physics Analysis Summary, 2018
CMS-PAS-LUM-18-002
CMS-PAS-LUM-18-002
63 T. Junk Confidence level computation for combining searches with small statistics NIM A 434 (1999) 435 hep-ex/9902006
64 A. L. Read Presentation of search results: the CL$ _\mathrm{s} $ technique JPG 28 (2002) 2693
65 ATLAS and CMS Collaborations, The LHC Higgs Combination Group Procedure for the LHC Higgs boson search combination in Summer 2011 Technical Report CMS-NOTE-2011-005, ATL-PHYS-PUB-2011-11, 2011
66 Y. Gershtein, S. Knapen, and D. Redigolo Probing naturally light singlets with a displaced vertex trigger PLB 823 (2021) 136758 2012.07864
Compact Muon Solenoid
LHC, CERN