CMSEXO23014 ; CERNEP2024025  
Search for longlived particles decaying to final states with a pair of muons in protonproton collisions at $ \sqrt{s} = $ 13.6 TeV  
CMS Collaboration  
22 February 2024  
JHEP 05 (2024) 047  
Abstract: An inclusive search for longlived exotic particles (LLPs) decaying to final states with a pair of muons is presented. The search uses data corresponding to an integrated luminosity of 36.6 fb$ ^{1} $ collected by the CMS experiment from the protonproton collisions at $ \sqrt{s} = $ 13.6 TeV in 2022, the first year of Run 3 of the CERN LHC. The experimental signature is a pair of oppositely charged muons originating from a common vertex spatially separated from the protonproton interaction point by distances ranging from several hundred $ \mu $m to several meters. The sensitivity of the search benefits from new triggers for displaced dimuons developed for Run 3. The results are interpreted in the framework of the hidden Abelian Higgs model, in which the Higgs boson decays to a pair of longlived dark photons, and of an $ R $parity violating supersymmetry model, in which longlived neutralinos decay to a pair of muons and a neutrino. The limits set on these models are the most stringent to date in wide regions of lifetimes for LLPs with masses larger than 10 GeV.  
Links: eprint arXiv:2402.14491 [hepex] (PDF) ; CDS record ; inSPIRE record ; HepData record ; Physics Briefing ; CADI line (restricted) ; 
Figures  Summary  Additional Figures & Material  References  CMS Publications 

Instructions for reinterpretation can be found here 
Figures  
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Figure 1:
Feynman diagrams for (left) the HAHM model, showing the production of longlived dark photons $ \mathrm{Z}_\text{D} $ via the Higgs portal, through $ \mathrm{H} $$ \mathrm{H}_\text{D} $ mixing with the parameter $ \kappa $, with subsequent decays to pairs of muons or other fermions via the vector portal; and (right) pair production of squarks followed by $ \tilde{\mathrm{q}} \to \mathrm{q} \tilde{\chi}_{1}^{0} $ decays, where the RPV neutralino is assumed to be a longlived particle that decays into a neutrino and two charged leptons. 
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Figure 1a:
Feynman diagrams for (left) the HAHM model, showing the production of longlived dark photons $ \mathrm{Z}_\text{D} $ via the Higgs portal, through $ \mathrm{H} $$ \mathrm{H}_\text{D} $ mixing with the parameter $ \kappa $, with subsequent decays to pairs of muons or other fermions via the vector portal; and (right) pair production of squarks followed by $ \tilde{\mathrm{q}} \to \mathrm{q} \tilde{\chi}_{1}^{0} $ decays, where the RPV neutralino is assumed to be a longlived particle that decays into a neutrino and two charged leptons. 
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Figure 1b:
Feynman diagrams for (left) the HAHM model, showing the production of longlived dark photons $ \mathrm{Z}_\text{D} $ via the Higgs portal, through $ \mathrm{H} $$ \mathrm{H}_\text{D} $ mixing with the parameter $ \kappa $, with subsequent decays to pairs of muons or other fermions via the vector portal; and (right) pair production of squarks followed by $ \tilde{\mathrm{q}} \to \mathrm{q} \tilde{\chi}_{1}^{0} $ decays, where the RPV neutralino is assumed to be a longlived particle that decays into a neutrino and two charged leptons. 
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Figure 2:
The $ p_{\mathrm{T}} $ and $ d_{\text{0}} $ coverage of the 2016 Run 2 triggers (light blue), 2018 Run 2 triggers (blue), and newly designed 2022 Run 3 triggers described in the text (red). The two values of the $ p_{\mathrm{T}} $ refer to the trigger thresholds for the muons. 
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Figure 3:
Efficiencies of the Run 2 and Run 3 displaced dimuon triggers as a function of $ c\tau $ for the HAHM signal events with $ m(\mathrm{Z}_\text{D}) = $ 20 GeV. The efficiency is defined as the fraction of simulated events that satisfy the detector acceptance and the requirements of the following sets of trigger paths: the Run 2 (2018) triggers (dashed black); the Run 3 (2022, L3) triggers (blue); the Run 3 (2022, L2) triggers (red); and the OR of all these triggers (Run 3 (2022), black). The lower panel shows the ratio of the overall Run 3 (2022) efficiency to the Run 2 (2018) efficiency. 
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Figure 4:
Distributions of $ \Delta\Phi $ for (left) STASTA and (right) TMSTMS dimuons in data samples obtained by inverting some of the selection criteria and enriched in DY events (black circles) and for events passing all selection criteria except for a requirement on $ \Delta\Phi $ in all HAHM (blue triangles) and RPV SUSY (orange squares) generated signal samples combined. All distributions are normalized to unit area. 
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Figure 4a:
Distributions of $ \Delta\Phi $ for (left) STASTA and (right) TMSTMS dimuons in data samples obtained by inverting some of the selection criteria and enriched in DY events (black circles) and for events passing all selection criteria except for a requirement on $ \Delta\Phi $ in all HAHM (blue triangles) and RPV SUSY (orange squares) generated signal samples combined. All distributions are normalized to unit area. 
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Figure 4b:
Distributions of $ \Delta\Phi $ for (left) STASTA and (right) TMSTMS dimuons in data samples obtained by inverting some of the selection criteria and enriched in DY events (black circles) and for events passing all selection criteria except for a requirement on $ \Delta\Phi $ in all HAHM (blue triangles) and RPV SUSY (orange squares) generated signal samples combined. All distributions are normalized to unit area. 
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Figure 5:
Overall efficiencies in the STASTA (green) and TMSTMS (red) dimuon categories, as well as their combination (black) as a function of $ c\tau $ for the HAHM signal events with $ m(\mathrm{Z}_\text{D})= $ 20 GeV. The solid curves show efficiencies achieved with the 2022 Run 3 triggers, whereas dashed curves show efficiencies for the subset of events selected by the triggers used in the 2018 Run 2 analysis. The efficiency is defined as the fraction of signal events that satisfy the criteria of the indicated trigger as well as the full set of offline selection criteria. The lower panel shows the relative improvement of the overall signal efficiency brought in by improvements in the trigger. 
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Figure 6:
Example of background prediction checks in the STASTA category: distributions of (left) $ \Delta\Phi $ and (right) $ L_{\text{xy}}/\sigma_{L_{\text{xy}}} $ for events with $ m_{\mu\mu} > $ 15 GeV in the $ L_{\text{xy}}/\sigma_{L_{\text{xy}}} < $ 6 validation region in data (black circles) compared to the background predictions (histograms). The lower panels show the ratio of the observed to predicted number of events. Hatched histograms show the statistical uncertainty in the background prediction. 
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Figure 6a:
Example of background prediction checks in the STASTA category: distributions of (left) $ \Delta\Phi $ and (right) $ L_{\text{xy}}/\sigma_{L_{\text{xy}}} $ for events with $ m_{\mu\mu} > $ 15 GeV in the $ L_{\text{xy}}/\sigma_{L_{\text{xy}}} < $ 6 validation region in data (black circles) compared to the background predictions (histograms). The lower panels show the ratio of the observed to predicted number of events. Hatched histograms show the statistical uncertainty in the background prediction. 
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Figure 6b:
Example of background prediction checks in the STASTA category: distributions of (left) $ \Delta\Phi $ and (right) $ L_{\text{xy}}/\sigma_{L_{\text{xy}}} $ for events with $ m_{\mu\mu} > $ 15 GeV in the $ L_{\text{xy}}/\sigma_{L_{\text{xy}}} < $ 6 validation region in data (black circles) compared to the background predictions (histograms). The lower panels show the ratio of the observed to predicted number of events. Hatched histograms show the statistical uncertainty in the background prediction. 
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Figure 7:
Example of background prediction checks in the TMSTMS category: $ L_{\text{xy}}/\sigma_{L_{\text{xy}}} $ distributions for events with (left) $ \Delta\Phi < \pi/ $4 and (right) $ \Delta\Phi < \pi/ $ 30 in the 2 $ < \text{min}(d_{\text{0}}/\sigma_{d_{\text{0}}}) < $ 6 validation regions compared to the background predictions. The number of observed events (black circles) is overlaid with stacked histograms showing the expected numbers of QCD (yellow) and DY (green) background events. The last bin includes events in the histogram overflow. The lower panels show the ratio of the observed to predicted number of events. Hatched histograms show the statistical uncertainty in the background prediction. 
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Figure 7a:
Example of background prediction checks in the TMSTMS category: $ L_{\text{xy}}/\sigma_{L_{\text{xy}}} $ distributions for events with (left) $ \Delta\Phi < \pi/ $4 and (right) $ \Delta\Phi < \pi/ $ 30 in the 2 $ < \text{min}(d_{\text{0}}/\sigma_{d_{\text{0}}}) < $ 6 validation regions compared to the background predictions. The number of observed events (black circles) is overlaid with stacked histograms showing the expected numbers of QCD (yellow) and DY (green) background events. The last bin includes events in the histogram overflow. The lower panels show the ratio of the observed to predicted number of events. Hatched histograms show the statistical uncertainty in the background prediction. 
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Figure 7b:
Example of background prediction checks in the TMSTMS category: $ L_{\text{xy}}/\sigma_{L_{\text{xy}}} $ distributions for events with (left) $ \Delta\Phi < \pi/ $4 and (right) $ \Delta\Phi < \pi/ $ 30 in the 2 $ < \text{min}(d_{\text{0}}/\sigma_{d_{\text{0}}}) < $ 6 validation regions compared to the background predictions. The number of observed events (black circles) is overlaid with stacked histograms showing the expected numbers of QCD (yellow) and DY (green) background events. The last bin includes events in the histogram overflow. The lower panels show the ratio of the observed to predicted number of events. Hatched histograms show the statistical uncertainty in the background prediction. 
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Figure 8:
Example of background prediction checks in the STASTA category: distributions of (left) $ \Delta\Phi $ and (right) $ m_{\mu\mu} $ for dimuons in the lowmass (6 $ < m_{\mu\mu} < $ 10 GeV) validation region in data (black circles) compared to the background predictions (histograms). The lower panels show the ratio of the observed to predicted number of events. Hatched histograms show the statistical uncertainty in the background prediction. 
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Figure 8a:
Example of background prediction checks in the STASTA category: distributions of (left) $ \Delta\Phi $ and (right) $ m_{\mu\mu} $ for dimuons in the lowmass (6 $ < m_{\mu\mu} < $ 10 GeV) validation region in data (black circles) compared to the background predictions (histograms). The lower panels show the ratio of the observed to predicted number of events. Hatched histograms show the statistical uncertainty in the background prediction. 
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Figure 8b:
Example of background prediction checks in the STASTA category: distributions of (left) $ \Delta\Phi $ and (right) $ m_{\mu\mu} $ for dimuons in the lowmass (6 $ < m_{\mu\mu} < $ 10 GeV) validation region in data (black circles) compared to the background predictions (histograms). The lower panels show the ratio of the observed to predicted number of events. Hatched histograms show the statistical uncertainty in the background prediction. 
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Figure 9:
Example of background prediction checks in the TMSTMS category: (left) distribution of min($ d_{\text{0}}/\sigma_{d_{\text{0}}} $) for events in the $ \pi/4 < \Delta\Phi < \pi/ $2 validation region; (right) distribution of $ m_{\mu\mu} $ for events in the 2 $ < \text{min}(d_{\text{0}}/\sigma_{d_{\text{0}}}) < $ 6 validation region. The number of observed events (black circles) is overlaid with stacked histograms showing the expected numbers of QCD (yellow) and DY (green) background events. The last bin includes events in the histogram overflow. The lower panels show the ratios of the observed to predicted number of events. Hatched histograms show the statistical uncertainty in the background prediction. 
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Figure 9a:
Example of background prediction checks in the TMSTMS category: (left) distribution of min($ d_{\text{0}}/\sigma_{d_{\text{0}}} $) for events in the $ \pi/4 < \Delta\Phi < \pi/ $2 validation region; (right) distribution of $ m_{\mu\mu} $ for events in the 2 $ < \text{min}(d_{\text{0}}/\sigma_{d_{\text{0}}}) < $ 6 validation region. The number of observed events (black circles) is overlaid with stacked histograms showing the expected numbers of QCD (yellow) and DY (green) background events. The last bin includes events in the histogram overflow. The lower panels show the ratios of the observed to predicted number of events. Hatched histograms show the statistical uncertainty in the background prediction. 
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Figure 9b:
Example of background prediction checks in the TMSTMS category: (left) distribution of min($ d_{\text{0}}/\sigma_{d_{\text{0}}} $) for events in the $ \pi/4 < \Delta\Phi < \pi/ $2 validation region; (right) distribution of $ m_{\mu\mu} $ for events in the 2 $ < \text{min}(d_{\text{0}}/\sigma_{d_{\text{0}}}) < $ 6 validation region. The number of observed events (black circles) is overlaid with stacked histograms showing the expected numbers of QCD (yellow) and DY (green) background events. The last bin includes events in the histogram overflow. The lower panels show the ratios of the observed to predicted number of events. Hatched histograms show the statistical uncertainty in the background prediction. 
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Figure 10:
Comparison of the observed (black points) and expected (histograms) numbers of events in nonoverlapping (left) $ m_{\mu\mu} $ and (right) $ m^\text{corr}_{\mu\mu} $ intervals in the STASTA dimuon category, in the signal regions optimized for the (left) HAHM and (right) RPV SUSY model. Yellow and green stacked filled histograms represent mean expected background contributions from QCD and DY, respectively, while statistical uncertainties in the total expected background are shown as hatched histograms. Signal contributions expected from simulated signals indicated in the legends are shown in red and blue. Their yields are set to the corresponding median expected 95% CL exclusion limits obtained from the ensemble of both dimuon categories, scaled up as indicated in the legend to improve visibility. The last bin includes events in the histogram overflow. 
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Figure 10a:
Comparison of the observed (black points) and expected (histograms) numbers of events in nonoverlapping (left) $ m_{\mu\mu} $ and (right) $ m^\text{corr}_{\mu\mu} $ intervals in the STASTA dimuon category, in the signal regions optimized for the (left) HAHM and (right) RPV SUSY model. Yellow and green stacked filled histograms represent mean expected background contributions from QCD and DY, respectively, while statistical uncertainties in the total expected background are shown as hatched histograms. Signal contributions expected from simulated signals indicated in the legends are shown in red and blue. Their yields are set to the corresponding median expected 95% CL exclusion limits obtained from the ensemble of both dimuon categories, scaled up as indicated in the legend to improve visibility. The last bin includes events in the histogram overflow. 
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Figure 10b:
Comparison of the observed (black points) and expected (histograms) numbers of events in nonoverlapping (left) $ m_{\mu\mu} $ and (right) $ m^\text{corr}_{\mu\mu} $ intervals in the STASTA dimuon category, in the signal regions optimized for the (left) HAHM and (right) RPV SUSY model. Yellow and green stacked filled histograms represent mean expected background contributions from QCD and DY, respectively, while statistical uncertainties in the total expected background are shown as hatched histograms. Signal contributions expected from simulated signals indicated in the legends are shown in red and blue. Their yields are set to the corresponding median expected 95% CL exclusion limits obtained from the ensemble of both dimuon categories, scaled up as indicated in the legend to improve visibility. The last bin includes events in the histogram overflow. 
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Figure 11:
Distributions of $ \text{min}(d_{\text{0}}/\sigma_{d_{\text{0}}}) $ for TMSTMS dimuons with (left) $ \Delta\Phi < \pi/ $ 30 and (right) $ \Delta\Phi < \pi/ $ 4, for events in all mass intervals combined. The number of observed events (black circles) is overlaid with the stacked histograms showing the expected numbers of QCD (yellow) and DY (green) background events. Statistical uncertainties in the total expected background are shown as hatched histograms. Signal contributions expected from simulated signals indicated in the legends are shown in red and blue. Their yields are set to the corresponding median expected 95% CL exclusion limits obtained from the ensemble of both dimuon categories, scaled up as indicated in the legend to improve visibility. Events are required to satisfy all nominal selection criteria with the exception of the $ d_{\text{0}}/\sigma_{d_{\text{0}}} $ requirement. The last bin includes events in the histogram overflow. 
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Figure 11a:
Distributions of $ \text{min}(d_{\text{0}}/\sigma_{d_{\text{0}}}) $ for TMSTMS dimuons with (left) $ \Delta\Phi < \pi/ $ 30 and (right) $ \Delta\Phi < \pi/ $ 4, for events in all mass intervals combined. The number of observed events (black circles) is overlaid with the stacked histograms showing the expected numbers of QCD (yellow) and DY (green) background events. Statistical uncertainties in the total expected background are shown as hatched histograms. Signal contributions expected from simulated signals indicated in the legends are shown in red and blue. Their yields are set to the corresponding median expected 95% CL exclusion limits obtained from the ensemble of both dimuon categories, scaled up as indicated in the legend to improve visibility. Events are required to satisfy all nominal selection criteria with the exception of the $ d_{\text{0}}/\sigma_{d_{\text{0}}} $ requirement. The last bin includes events in the histogram overflow. 
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Figure 11b:
Distributions of $ \text{min}(d_{\text{0}}/\sigma_{d_{\text{0}}}) $ for TMSTMS dimuons with (left) $ \Delta\Phi < \pi/ $ 30 and (right) $ \Delta\Phi < \pi/ $ 4, for events in all mass intervals combined. The number of observed events (black circles) is overlaid with the stacked histograms showing the expected numbers of QCD (yellow) and DY (green) background events. Statistical uncertainties in the total expected background are shown as hatched histograms. Signal contributions expected from simulated signals indicated in the legends are shown in red and blue. Their yields are set to the corresponding median expected 95% CL exclusion limits obtained from the ensemble of both dimuon categories, scaled up as indicated in the legend to improve visibility. Events are required to satisfy all nominal selection criteria with the exception of the $ d_{\text{0}}/\sigma_{d_{\text{0}}} $ requirement. The last bin includes events in the histogram overflow. 
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Figure 12:
Comparison of observed and expected numbers of events in the TMSTMS dimuon category, in the RPV SUSY study that requires $ \Delta\Phi < \pi/ $ 4, in bins of $ m^\text{corr}_{\mu\mu} $. The number of observed events (black circles) is overlaid with the stacked filled histograms showing the expected numbers of QCD (yellow) and DY (green) background events in bins of $ m^\text{corr}_{\mu\mu} $ in three min($ d_{\text{0}}/\sigma_{d_{\text{0}}} $) bins: (left) 610, (center) 1020, and (right) $ {>} $ 20. Hatched histograms show statistical uncertainties in the total expected background. Contributions expected from signal events predicted by the RPV SUSY model with the parameters indicated in the legends are shown as red and blue histograms. Their yields are set to the corresponding median expected 95% CL exclusion limits obtained from the ensemble of both dimuon categories, scaled up as indicated in the legend to improve visibility. The last bin includes events in the histogram overflow. 
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Figure 13:
Comparison of observed and expected numbers of events in the TMSTMS dimuon category, in the HAHM study that requires $ \Delta\Phi < \pi/ $30, in bins of $ m_{\mu\mu} $. The number of observed events (black circles) is overlaid with the stacked histograms showing the expected numbers of QCD (yellow) and DY (green) background events in bins of $ m_{\mu\mu} $ in three min($ d_{\text{0}}/\sigma_{d_{\text{0}}} $) bins: (left) 610, (center) 1020, and (right) $ {>} $ 20. Hatched histograms show statistical uncertainties in the total expected background. Signal contributions expected from simulated $ \mathrm{H} \to \mathrm{Z}_\text{D} \mathrm{Z}_\text{D} $ events with the parameters indicated in the legends are shown as red and blue histograms. Their yields are set to the corresponding median expected 95% CL exclusion limits obtained from the ensemble of both dimuon categories, scaled up as indicated in the legend to improve visibility. The last bin includes events in the histogram overflow. 
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Figure 14:
The 95% CL upper limits on $ \mathcal{B}(\mathrm{H} \to \mathrm{Z}_\text{D} \mathrm{Z}_\text{D}) $ as a function of $ c\tau(\mathrm{Z}_\text{D}) $ in the HAHM model, for $ m(\mathrm{Z}_\text{D}) $ ranging from (upper left) 10 GeV to (lower right) 60 GeV, in the STASTA and TMSTMS dimuon categories in 2022 data and their combination. The median expected limits obtained from the STASTA and TMSTMS dimuon categories are shown as dashed blue and red curves, respectively; the combined median expected limits are shown as dashed black curves; and the combined observed limits are shown as solid black curves. The green and yellow bands correspond, respectively, to the 68 and 95% quantiles for the combined expected limits. 
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Figure 14a:
The 95% CL upper limits on $ \mathcal{B}(\mathrm{H} \to \mathrm{Z}_\text{D} \mathrm{Z}_\text{D}) $ as a function of $ c\tau(\mathrm{Z}_\text{D}) $ in the HAHM model, for $ m(\mathrm{Z}_\text{D}) $ ranging from (upper left) 10 GeV to (lower right) 60 GeV, in the STASTA and TMSTMS dimuon categories in 2022 data and their combination. The median expected limits obtained from the STASTA and TMSTMS dimuon categories are shown as dashed blue and red curves, respectively; the combined median expected limits are shown as dashed black curves; and the combined observed limits are shown as solid black curves. The green and yellow bands correspond, respectively, to the 68 and 95% quantiles for the combined expected limits. 
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Figure 14b:
The 95% CL upper limits on $ \mathcal{B}(\mathrm{H} \to \mathrm{Z}_\text{D} \mathrm{Z}_\text{D}) $ as a function of $ c\tau(\mathrm{Z}_\text{D}) $ in the HAHM model, for $ m(\mathrm{Z}_\text{D}) $ ranging from (upper left) 10 GeV to (lower right) 60 GeV, in the STASTA and TMSTMS dimuon categories in 2022 data and their combination. The median expected limits obtained from the STASTA and TMSTMS dimuon categories are shown as dashed blue and red curves, respectively; the combined median expected limits are shown as dashed black curves; and the combined observed limits are shown as solid black curves. The green and yellow bands correspond, respectively, to the 68 and 95% quantiles for the combined expected limits. 
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Figure 14c:
The 95% CL upper limits on $ \mathcal{B}(\mathrm{H} \to \mathrm{Z}_\text{D} \mathrm{Z}_\text{D}) $ as a function of $ c\tau(\mathrm{Z}_\text{D}) $ in the HAHM model, for $ m(\mathrm{Z}_\text{D}) $ ranging from (upper left) 10 GeV to (lower right) 60 GeV, in the STASTA and TMSTMS dimuon categories in 2022 data and their combination. The median expected limits obtained from the STASTA and TMSTMS dimuon categories are shown as dashed blue and red curves, respectively; the combined median expected limits are shown as dashed black curves; and the combined observed limits are shown as solid black curves. The green and yellow bands correspond, respectively, to the 68 and 95% quantiles for the combined expected limits. 
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Figure 14d:
The 95% CL upper limits on $ \mathcal{B}(\mathrm{H} \to \mathrm{Z}_\text{D} \mathrm{Z}_\text{D}) $ as a function of $ c\tau(\mathrm{Z}_\text{D}) $ in the HAHM model, for $ m(\mathrm{Z}_\text{D}) $ ranging from (upper left) 10 GeV to (lower right) 60 GeV, in the STASTA and TMSTMS dimuon categories in 2022 data and their combination. The median expected limits obtained from the STASTA and TMSTMS dimuon categories are shown as dashed blue and red curves, respectively; the combined median expected limits are shown as dashed black curves; and the combined observed limits are shown as solid black curves. The green and yellow bands correspond, respectively, to the 68 and 95% quantiles for the combined expected limits. 
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Figure 14e:
The 95% CL upper limits on $ \mathcal{B}(\mathrm{H} \to \mathrm{Z}_\text{D} \mathrm{Z}_\text{D}) $ as a function of $ c\tau(\mathrm{Z}_\text{D}) $ in the HAHM model, for $ m(\mathrm{Z}_\text{D}) $ ranging from (upper left) 10 GeV to (lower right) 60 GeV, in the STASTA and TMSTMS dimuon categories in 2022 data and their combination. The median expected limits obtained from the STASTA and TMSTMS dimuon categories are shown as dashed blue and red curves, respectively; the combined median expected limits are shown as dashed black curves; and the combined observed limits are shown as solid black curves. The green and yellow bands correspond, respectively, to the 68 and 95% quantiles for the combined expected limits. 
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Figure 14f:
The 95% CL upper limits on $ \mathcal{B}(\mathrm{H} \to \mathrm{Z}_\text{D} \mathrm{Z}_\text{D}) $ as a function of $ c\tau(\mathrm{Z}_\text{D}) $ in the HAHM model, for $ m(\mathrm{Z}_\text{D}) $ ranging from (upper left) 10 GeV to (lower right) 60 GeV, in the STASTA and TMSTMS dimuon categories in 2022 data and their combination. The median expected limits obtained from the STASTA and TMSTMS dimuon categories are shown as dashed blue and red curves, respectively; the combined median expected limits are shown as dashed black curves; and the combined observed limits are shown as solid black curves. The green and yellow bands correspond, respectively, to the 68 and 95% quantiles for the combined expected limits. 
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Figure 15:
The 95% CL upper limits on $ \mathcal{B}(\mathrm{H} \to \mathrm{Z}_\text{D} \mathrm{Z}_\text{D}) $ as a function of $ c\tau(\mathrm{Z}_\text{D}) $ in the HAHM model, for $ m(\mathrm{Z}_\text{D}) $ ranging from (upper left) 10 GeV to (lower right) 60 GeV, obtained in this analysis, the Run 2 analysis [5], and their combination. The observed limits in this analysis and in the Run 2 analysis [5] are shown as blue and red curves, respectively; the median combined expected limits are shown as dashed black curves; and the combined observed limits are shown as solid black curves. The green and yellow bands correspond, respectively, to the 68 and 95% quantiles for the combined expected limits. 
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Figure 15a:
The 95% CL upper limits on $ \mathcal{B}(\mathrm{H} \to \mathrm{Z}_\text{D} \mathrm{Z}_\text{D}) $ as a function of $ c\tau(\mathrm{Z}_\text{D}) $ in the HAHM model, for $ m(\mathrm{Z}_\text{D}) $ ranging from (upper left) 10 GeV to (lower right) 60 GeV, obtained in this analysis, the Run 2 analysis [5], and their combination. The observed limits in this analysis and in the Run 2 analysis [5] are shown as blue and red curves, respectively; the median combined expected limits are shown as dashed black curves; and the combined observed limits are shown as solid black curves. The green and yellow bands correspond, respectively, to the 68 and 95% quantiles for the combined expected limits. 
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Figure 15b:
The 95% CL upper limits on $ \mathcal{B}(\mathrm{H} \to \mathrm{Z}_\text{D} \mathrm{Z}_\text{D}) $ as a function of $ c\tau(\mathrm{Z}_\text{D}) $ in the HAHM model, for $ m(\mathrm{Z}_\text{D}) $ ranging from (upper left) 10 GeV to (lower right) 60 GeV, obtained in this analysis, the Run 2 analysis [5], and their combination. The observed limits in this analysis and in the Run 2 analysis [5] are shown as blue and red curves, respectively; the median combined expected limits are shown as dashed black curves; and the combined observed limits are shown as solid black curves. The green and yellow bands correspond, respectively, to the 68 and 95% quantiles for the combined expected limits. 
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Figure 15c:
The 95% CL upper limits on $ \mathcal{B}(\mathrm{H} \to \mathrm{Z}_\text{D} \mathrm{Z}_\text{D}) $ as a function of $ c\tau(\mathrm{Z}_\text{D}) $ in the HAHM model, for $ m(\mathrm{Z}_\text{D}) $ ranging from (upper left) 10 GeV to (lower right) 60 GeV, obtained in this analysis, the Run 2 analysis [5], and their combination. The observed limits in this analysis and in the Run 2 analysis [5] are shown as blue and red curves, respectively; the median combined expected limits are shown as dashed black curves; and the combined observed limits are shown as solid black curves. The green and yellow bands correspond, respectively, to the 68 and 95% quantiles for the combined expected limits. 
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Figure 15d:
The 95% CL upper limits on $ \mathcal{B}(\mathrm{H} \to \mathrm{Z}_\text{D} \mathrm{Z}_\text{D}) $ as a function of $ c\tau(\mathrm{Z}_\text{D}) $ in the HAHM model, for $ m(\mathrm{Z}_\text{D}) $ ranging from (upper left) 10 GeV to (lower right) 60 GeV, obtained in this analysis, the Run 2 analysis [5], and their combination. The observed limits in this analysis and in the Run 2 analysis [5] are shown as blue and red curves, respectively; the median combined expected limits are shown as dashed black curves; and the combined observed limits are shown as solid black curves. The green and yellow bands correspond, respectively, to the 68 and 95% quantiles for the combined expected limits. 
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Figure 15e:
The 95% CL upper limits on $ \mathcal{B}(\mathrm{H} \to \mathrm{Z}_\text{D} \mathrm{Z}_\text{D}) $ as a function of $ c\tau(\mathrm{Z}_\text{D}) $ in the HAHM model, for $ m(\mathrm{Z}_\text{D}) $ ranging from (upper left) 10 GeV to (lower right) 60 GeV, obtained in this analysis, the Run 2 analysis [5], and their combination. The observed limits in this analysis and in the Run 2 analysis [5] are shown as blue and red curves, respectively; the median combined expected limits are shown as dashed black curves; and the combined observed limits are shown as solid black curves. The green and yellow bands correspond, respectively, to the 68 and 95% quantiles for the combined expected limits. 
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Figure 15f:
The 95% CL upper limits on $ \mathcal{B}(\mathrm{H} \to \mathrm{Z}_\text{D} \mathrm{Z}_\text{D}) $ as a function of $ c\tau(\mathrm{Z}_\text{D}) $ in the HAHM model, for $ m(\mathrm{Z}_\text{D}) $ ranging from (upper left) 10 GeV to (lower right) 60 GeV, obtained in this analysis, the Run 2 analysis [5], and their combination. The observed limits in this analysis and in the Run 2 analysis [5] are shown as blue and red curves, respectively; the median combined expected limits are shown as dashed black curves; and the combined observed limits are shown as solid black curves. The green and yellow bands correspond, respectively, to the 68 and 95% quantiles for the combined expected limits. 
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Figure 16:
The 95% CL upper limits on $ \sigma(\mathrm{p}\mathrm{p}\to{\tilde{\mathrm{q}}} \overline{\tilde{\mathrm{q}}})\mathcal{B}( \tilde{\mathrm{q}} \to \mathrm{q} \tilde{\chi}_{1}^{0} ) $ as a function of $ c\tau(\tilde{\chi}_{1}^{0}) $ in the RPV SUSY model, for $ \mathcal{B}(\tilde{\chi}_{1}^{0}\to\mu^{+}\mu^{}\nu) = $ 0.5 and $ m({\tilde{\mathrm{q}}} ) $ ranging from (upper left) 125 GeV to (lower right) 1.6 TeV. The observed limits for various combinations of $ m({\tilde{\mathrm{q}}} ) $ and $ m(\tilde{\chi}_{1}^{0}) $ indicated in the legends are shown as solid curves. The median expected limits and their 68 and 95% quantiles are shown, respectively, as dashed black curves and green and yellow bands for the case of $ m(\tilde{\chi}_{1}^{0}) = $ 50 GeV and omitted for other neutralino masses for clarity. The gray horizontal lines indicate the theoretical values of the squarkantisquark production cross sections with the uncertainties shown as gray shaded bands. The predicted cross sections for $ m({\tilde{\mathrm{q}}} ) = $ 125, 200, and 350 GeV are, respectively, 7200, 840, and 50 pb, and fall outside the $ y $axis range. 
png pdf 
Figure 16a:
The 95% CL upper limits on $ \sigma(\mathrm{p}\mathrm{p}\to{\tilde{\mathrm{q}}} \overline{\tilde{\mathrm{q}}})\mathcal{B}( \tilde{\mathrm{q}} \to \mathrm{q} \tilde{\chi}_{1}^{0} ) $ as a function of $ c\tau(\tilde{\chi}_{1}^{0}) $ in the RPV SUSY model, for $ \mathcal{B}(\tilde{\chi}_{1}^{0}\to\mu^{+}\mu^{}\nu) = $ 0.5 and $ m({\tilde{\mathrm{q}}} ) $ ranging from (upper left) 125 GeV to (lower right) 1.6 TeV. The observed limits for various combinations of $ m({\tilde{\mathrm{q}}} ) $ and $ m(\tilde{\chi}_{1}^{0}) $ indicated in the legends are shown as solid curves. The median expected limits and their 68 and 95% quantiles are shown, respectively, as dashed black curves and green and yellow bands for the case of $ m(\tilde{\chi}_{1}^{0}) = $ 50 GeV and omitted for other neutralino masses for clarity. The gray horizontal lines indicate the theoretical values of the squarkantisquark production cross sections with the uncertainties shown as gray shaded bands. The predicted cross sections for $ m({\tilde{\mathrm{q}}} ) = $ 125, 200, and 350 GeV are, respectively, 7200, 840, and 50 pb, and fall outside the $ y $axis range. 
png pdf 
Figure 16b:
The 95% CL upper limits on $ \sigma(\mathrm{p}\mathrm{p}\to{\tilde{\mathrm{q}}} \overline{\tilde{\mathrm{q}}})\mathcal{B}( \tilde{\mathrm{q}} \to \mathrm{q} \tilde{\chi}_{1}^{0} ) $ as a function of $ c\tau(\tilde{\chi}_{1}^{0}) $ in the RPV SUSY model, for $ \mathcal{B}(\tilde{\chi}_{1}^{0}\to\mu^{+}\mu^{}\nu) = $ 0.5 and $ m({\tilde{\mathrm{q}}} ) $ ranging from (upper left) 125 GeV to (lower right) 1.6 TeV. The observed limits for various combinations of $ m({\tilde{\mathrm{q}}} ) $ and $ m(\tilde{\chi}_{1}^{0}) $ indicated in the legends are shown as solid curves. The median expected limits and their 68 and 95% quantiles are shown, respectively, as dashed black curves and green and yellow bands for the case of $ m(\tilde{\chi}_{1}^{0}) = $ 50 GeV and omitted for other neutralino masses for clarity. The gray horizontal lines indicate the theoretical values of the squarkantisquark production cross sections with the uncertainties shown as gray shaded bands. The predicted cross sections for $ m({\tilde{\mathrm{q}}} ) = $ 125, 200, and 350 GeV are, respectively, 7200, 840, and 50 pb, and fall outside the $ y $axis range. 
png pdf 
Figure 16c:
The 95% CL upper limits on $ \sigma(\mathrm{p}\mathrm{p}\to{\tilde{\mathrm{q}}} \overline{\tilde{\mathrm{q}}})\mathcal{B}( \tilde{\mathrm{q}} \to \mathrm{q} \tilde{\chi}_{1}^{0} ) $ as a function of $ c\tau(\tilde{\chi}_{1}^{0}) $ in the RPV SUSY model, for $ \mathcal{B}(\tilde{\chi}_{1}^{0}\to\mu^{+}\mu^{}\nu) = $ 0.5 and $ m({\tilde{\mathrm{q}}} ) $ ranging from (upper left) 125 GeV to (lower right) 1.6 TeV. The observed limits for various combinations of $ m({\tilde{\mathrm{q}}} ) $ and $ m(\tilde{\chi}_{1}^{0}) $ indicated in the legends are shown as solid curves. The median expected limits and their 68 and 95% quantiles are shown, respectively, as dashed black curves and green and yellow bands for the case of $ m(\tilde{\chi}_{1}^{0}) = $ 50 GeV and omitted for other neutralino masses for clarity. The gray horizontal lines indicate the theoretical values of the squarkantisquark production cross sections with the uncertainties shown as gray shaded bands. The predicted cross sections for $ m({\tilde{\mathrm{q}}} ) = $ 125, 200, and 350 GeV are, respectively, 7200, 840, and 50 pb, and fall outside the $ y $axis range. 
png pdf 
Figure 16d:
The 95% CL upper limits on $ \sigma(\mathrm{p}\mathrm{p}\to{\tilde{\mathrm{q}}} \overline{\tilde{\mathrm{q}}})\mathcal{B}( \tilde{\mathrm{q}} \to \mathrm{q} \tilde{\chi}_{1}^{0} ) $ as a function of $ c\tau(\tilde{\chi}_{1}^{0}) $ in the RPV SUSY model, for $ \mathcal{B}(\tilde{\chi}_{1}^{0}\to\mu^{+}\mu^{}\nu) = $ 0.5 and $ m({\tilde{\mathrm{q}}} ) $ ranging from (upper left) 125 GeV to (lower right) 1.6 TeV. The observed limits for various combinations of $ m({\tilde{\mathrm{q}}} ) $ and $ m(\tilde{\chi}_{1}^{0}) $ indicated in the legends are shown as solid curves. The median expected limits and their 68 and 95% quantiles are shown, respectively, as dashed black curves and green and yellow bands for the case of $ m(\tilde{\chi}_{1}^{0}) = $ 50 GeV and omitted for other neutralino masses for clarity. The gray horizontal lines indicate the theoretical values of the squarkantisquark production cross sections with the uncertainties shown as gray shaded bands. The predicted cross sections for $ m({\tilde{\mathrm{q}}} ) = $ 125, 200, and 350 GeV are, respectively, 7200, 840, and 50 pb, and fall outside the $ y $axis range. 
png pdf 
Figure 16e:
The 95% CL upper limits on $ \sigma(\mathrm{p}\mathrm{p}\to{\tilde{\mathrm{q}}} \overline{\tilde{\mathrm{q}}})\mathcal{B}( \tilde{\mathrm{q}} \to \mathrm{q} \tilde{\chi}_{1}^{0} ) $ as a function of $ c\tau(\tilde{\chi}_{1}^{0}) $ in the RPV SUSY model, for $ \mathcal{B}(\tilde{\chi}_{1}^{0}\to\mu^{+}\mu^{}\nu) = $ 0.5 and $ m({\tilde{\mathrm{q}}} ) $ ranging from (upper left) 125 GeV to (lower right) 1.6 TeV. The observed limits for various combinations of $ m({\tilde{\mathrm{q}}} ) $ and $ m(\tilde{\chi}_{1}^{0}) $ indicated in the legends are shown as solid curves. The median expected limits and their 68 and 95% quantiles are shown, respectively, as dashed black curves and green and yellow bands for the case of $ m(\tilde{\chi}_{1}^{0}) = $ 50 GeV and omitted for other neutralino masses for clarity. The gray horizontal lines indicate the theoretical values of the squarkantisquark production cross sections with the uncertainties shown as gray shaded bands. The predicted cross sections for $ m({\tilde{\mathrm{q}}} ) = $ 125, 200, and 350 GeV are, respectively, 7200, 840, and 50 pb, and fall outside the $ y $axis range. 
png pdf 
Figure 16f:
The 95% CL upper limits on $ \sigma(\mathrm{p}\mathrm{p}\to{\tilde{\mathrm{q}}} \overline{\tilde{\mathrm{q}}})\mathcal{B}( \tilde{\mathrm{q}} \to \mathrm{q} \tilde{\chi}_{1}^{0} ) $ as a function of $ c\tau(\tilde{\chi}_{1}^{0}) $ in the RPV SUSY model, for $ \mathcal{B}(\tilde{\chi}_{1}^{0}\to\mu^{+}\mu^{}\nu) = $ 0.5 and $ m({\tilde{\mathrm{q}}} ) $ ranging from (upper left) 125 GeV to (lower right) 1.6 TeV. The observed limits for various combinations of $ m({\tilde{\mathrm{q}}} ) $ and $ m(\tilde{\chi}_{1}^{0}) $ indicated in the legends are shown as solid curves. The median expected limits and their 68 and 95% quantiles are shown, respectively, as dashed black curves and green and yellow bands for the case of $ m(\tilde{\chi}_{1}^{0}) = $ 50 GeV and omitted for other neutralino masses for clarity. The gray horizontal lines indicate the theoretical values of the squarkantisquark production cross sections with the uncertainties shown as gray shaded bands. The predicted cross sections for $ m({\tilde{\mathrm{q}}} ) = $ 125, 200, and 350 GeV are, respectively, 7200, 840, and 50 pb, and fall outside the $ y $axis range. 
Summary 
Data collected by the CMS experiment in protonproton collisions at $ \sqrt{s} = $ 13.6 TeV in 2022 and corresponding to an integrated luminosity of 36.6 fb$ ^{1} $ have been used to conduct an inclusive search for longlived exotic neutral particles decaying to final states with a pair of oppositely charged muons. The search strategy is largely model independent and is sensitive to a broad range of lifetimes and masses. No significant excess of events above the standard model background is observed. The results are interpreted as limits on the parameters of the hidden Abelian Higgs model, in which the Higgs boson H decays to a pair of longlived dark photons $ \mathrm{Z}_\text{D} $, and of an $ R $parity violating supersymmetry model, in which longlived neutralinos decay to a pair of muons and a neutrino. Even though the size of the data sample used by this analysis is about a factor of 2.5 smaller than that used in the previous search for displaced dimuons by the CMS experiment in pp collisions at $ \sqrt{s} = $ 13 TeV, the constraints on the parameters of the hidden Abelian Higgs model are comparable or tighter in a significant fraction of the parameter space, thanks mainly to improvements in the trigger algorithms. The combination of the results of this analysis with the results obtained at $ \sqrt{s} = $ 13 TeV improves the constraints on the branching fraction of the Higgs boson to dark photons, $ \mathcal{B}(\mathrm{H} \to \mathrm{Z}_\text{D} \mathrm{Z}_\text{D}) $, by approximately a factor of 2. In the range 1060 GeV of the $ \mathrm{Z}_\text{D} $ mass $ m(\mathrm{Z}_\text{D}) $, $ \mathcal{B}(\mathrm{H} \to \mathrm{Z}_\text{D} \mathrm{Z}_\text{D}) = $ 1% is excluded at 95% confidence level in the range of proper decay length $ c\tau(\mathrm{Z}_\text{D}) $ from a few tens of $ \mu $m to 30 m (700 m) for $ m(\mathrm{Z}_\text{D}) $ = 10 GeV (60 GeV). For $ m(\mathrm{Z}_\text{D}) $ greater than 20 GeV and less than $ m(\mathrm{H})/ $ 2, the combined limits provide the most stringent constraints to date on $ \mathcal{B}(\mathrm{H} \to \mathrm{Z}_\text{D} \mathrm{Z}_\text{D}) $ for $ c\tau(\mathrm{Z}_\text{D}) $ between 30 $ \mu $m and $ {\approx}$ 0.1 cm, and above $ {\approx}$ 10 cm. When interpreted in the framework of the $ R $parity violating supersymmetry model at a squark mass of 1.6 TeV, the results exclude mean proper neutralino decay lengths between 0.07 and 4 cm for a 50 GeV neutralino and between 70 $ \mu $m and 2 m for a 500 GeV neutralino. 
Additional Figures  
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Additional Figure 1:
Illustration showing two longlived particles with different lifetimes decaying into a pair of muons, depicting how the signals of the muons can be traced back to the longlived particle decay point using data from the tracker and muon detectors. 
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Additional Figure 2:
Run 3 event containing a candidate for a longlived particle that decays into a pair of muons away from the interaction point, reconstructed in the CMS detector. The red lines correspond to the two standalone 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 longlived particle is hypothesized to have decayed. 
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Additional Figure 3:
Fractions of signal events with zero (green), one (blue), and two (red) STA muons matched to TMS muons by the STA to TMS association procedure, as a function of generated $ L_{\text{xy}} $, in all HAHM signal samples combined. 
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Additional Figure 4:
Efficiencies of the Run 2 and Run 3 displaced dimuon triggers as a function of $ c\tau $ for the HAHM signal events with $ m(\mathrm{Z}_\text{D}) = $ 50 GeV. The efficiency is defined as the fraction of simulated events that satisfy the detector acceptance and the requirements of the following sets of trigger paths: the Run 2 (2018) triggers (dashed black); the Run 3 (2022, L3) triggers (blue); the Run 3 (2022, L2) triggers (red); and the OR of all these triggers (Run 3 (2022), black). The lower panel shows the ratio of the overall Run 3 (2022) efficiency to the Run 2 (2018) efficiency. 
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Additional Figure 5:
Efficiencies of the Run 2 (2018) (red) and Run 3 (2022) (black) sets of displaced dimuon triggers as a function of $ m(\mathrm{Z}_\text{D}) $ for the HAHM signal events with $ c\tau = $ 1 cm (left) and 10 m (right). The efficiency is defined as the fraction of simulated events that satisfy the detector acceptance and the requirements of the indicated set of trigger paths. The lower panel shows the ratio of the Run 3 (2022) efficiency to the Run 2 (2018) efficiency. 
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Additional Figure 5a:
Efficiencies of the Run 2 (2018) (red) and Run 3 (2022) (black) sets of displaced dimuon triggers as a function of $ m(\mathrm{Z}_\text{D}) $ for the HAHM signal events with $ c\tau = $ 1 cm (left) and 10 m (right). The efficiency is defined as the fraction of simulated events that satisfy the detector acceptance and the requirements of the indicated set of trigger paths. The lower panel shows the ratio of the Run 3 (2022) efficiency to the Run 2 (2018) efficiency. 
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Additional Figure 5b:
Efficiencies of the Run 2 (2018) (red) and Run 3 (2022) (black) sets of displaced dimuon triggers as a function of $ m(\mathrm{Z}_\text{D}) $ for the HAHM signal events with $ c\tau = $ 1 cm (left) and 10 m (right). The efficiency is defined as the fraction of simulated events that satisfy the detector acceptance and the requirements of the indicated set of trigger paths. The lower panel shows the ratio of the Run 3 (2022) efficiency to the Run 2 (2018) efficiency. 
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Additional Figure 6:
Efficiency of the Run 3 (2022, L3) triggers in data (black) and in simulation (yellow) as a function of min($ p_{\mathrm{T}} $) (upper left), max($ p_{\mathrm{T}} $) (upper right), and min($ d_{\text{0}} $) (lower) of the two muons forming a dimuon in events enriched in $ {\mathrm{J}/\psi} \to\mu\mu $. 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 missing transverse energy 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 B hadron decays. 
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Additional Figure 6a:
Efficiency of the Run 3 (2022, L3) triggers in data (black) and in simulation (yellow) as a function of min($ p_{\mathrm{T}} $) (upper left), max($ p_{\mathrm{T}} $) (upper right), and min($ d_{\text{0}} $) (lower) of the two muons forming a dimuon in events enriched in $ {\mathrm{J}/\psi} \to\mu\mu $. 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 missing transverse energy 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 B hadron decays. 
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Additional Figure 6b:
Efficiency of the Run 3 (2022, L3) triggers in data (black) and in simulation (yellow) as a function of min($ p_{\mathrm{T}} $) (upper left), max($ p_{\mathrm{T}} $) (upper right), and min($ d_{\text{0}} $) (lower) of the two muons forming a dimuon in events enriched in $ {\mathrm{J}/\psi} \to\mu\mu $. 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 missing transverse energy 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 B hadron decays. 
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Additional Figure 6c:
Efficiency of the Run 3 (2022, L3) triggers in data (black) and in simulation (yellow) as a function of min($ p_{\mathrm{T}} $) (upper left), max($ p_{\mathrm{T}} $) (upper right), and min($ d_{\text{0}} $) (lower) of the two muons forming a dimuon in events enriched in $ {\mathrm{J}/\psi} \to\mu\mu $. 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 missing transverse energy 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 B hadron decays. 
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Additional Figure 7:
Left: Invariant mass distribution for TMSTMS dimuons with $ L_{\text{xy}}/\sigma_{L_{\text{xy}}} < $ 1 in events recorded by the Run 2 (2018) triggers in 2022 data (black), and in the subset of events also selected by the Run 3 (2022, L3) triggers (blue), illustrating the background rejection of the Run 3 (2022, L3) triggers. Right: Trigger 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 offlinereconstructed min($ d_{\text{0}} $) of the two muons forming TMSTMS dimuons in events enriched in $ {\mathrm{J}/\psi} \to\mu\mu $. Different symbols show efficiencies in different periods of the 2022 data taking corresponding to the integrated luminosities indicated in the legend. For dimuons with offline $ \text{min}(d_{\text{0}}) > $ 0.012 cm, the combined efficiency of the L3 muon reconstruction and the online min($ d_{\text{0}} $) requirement is larger than 90% in all data taking periods. 
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Additional Figure 7a:
Left: Invariant mass distribution for TMSTMS dimuons with $ L_{\text{xy}}/\sigma_{L_{\text{xy}}} < $ 1 in events recorded by the Run 2 (2018) triggers in 2022 data (black), and in the subset of events also selected by the Run 3 (2022, L3) triggers (blue), illustrating the background rejection of the Run 3 (2022, L3) triggers. Right: Trigger 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 offlinereconstructed min($ d_{\text{0}} $) of the two muons forming TMSTMS dimuons in events enriched in $ {\mathrm{J}/\psi} \to\mu\mu $. Different symbols show efficiencies in different periods of the 2022 data taking corresponding to the integrated luminosities indicated in the legend. For dimuons with offline $ \text{min}(d_{\text{0}}) > $ 0.012 cm, the combined efficiency of the L3 muon reconstruction and the online min($ d_{\text{0}} $) requirement is larger than 90% in all data taking periods. 
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Additional Figure 7b:
Left: Invariant mass distribution for TMSTMS dimuons with $ L_{\text{xy}}/\sigma_{L_{\text{xy}}} < $ 1 in events recorded by the Run 2 (2018) triggers in 2022 data (black), and in the subset of events also selected by the Run 3 (2022, L3) triggers (blue), illustrating the background rejection of the Run 3 (2022, L3) triggers. Right: Trigger 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 offlinereconstructed min($ d_{\text{0}} $) of the two muons forming TMSTMS dimuons in events enriched in $ {\mathrm{J}/\psi} \to\mu\mu $. Different symbols show efficiencies in different periods of the 2022 data taking corresponding to the integrated luminosities indicated in the legend. For dimuons with offline $ \text{min}(d_{\text{0}}) > $ 0.012 cm, the combined efficiency of the L3 muon reconstruction and the online min($ d_{\text{0}} $) requirement is larger than 90% in all data taking periods. 
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Additional Figure 8:
Left: Invariant mass distribution for TMSTMS dimuons with $ L_{\text{xy}}/\sigma_{L_{\text{xy}}} < $ 1 in events recorded by the Run 2 (2018) triggers in 2022 data (black), and in the subset of events also selected by the Run 3 (2022, L2) triggers (pink), illustrating the background rejection of the Run 3 (2022, L2) triggers. Right: Trigger 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 offlinereconstructed min($ d_{\text{0}} $) of the two muons forming STASTA dimuons in events enriched in cosmic ray muons. Different symbols show efficiencies in different periods of the 2022 data taking corresponding to the integrated luminosities indicated in the legend. For displaced muons, the efficiency of the online min($ d_{\text{0}} $) requirement is larger than 95% in all data taking periods. 
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Additional Figure 8a:
Left: Invariant mass distribution for TMSTMS dimuons with $ L_{\text{xy}}/\sigma_{L_{\text{xy}}} < $ 1 in events recorded by the Run 2 (2018) triggers in 2022 data (black), and in the subset of events also selected by the Run 3 (2022, L2) triggers (pink), illustrating the background rejection of the Run 3 (2022, L2) triggers. Right: Trigger 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 offlinereconstructed min($ d_{\text{0}} $) of the two muons forming STASTA dimuons in events enriched in cosmic ray muons. Different symbols show efficiencies in different periods of the 2022 data taking corresponding to the integrated luminosities indicated in the legend. For displaced muons, the efficiency of the online min($ d_{\text{0}} $) requirement is larger than 95% in all data taking periods. 
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Additional Figure 8b:
Left: Invariant mass distribution for TMSTMS dimuons with $ L_{\text{xy}}/\sigma_{L_{\text{xy}}} < $ 1 in events recorded by the Run 2 (2018) triggers in 2022 data (black), and in the subset of events also selected by the Run 3 (2022, L2) triggers (pink), illustrating the background rejection of the Run 3 (2022, L2) triggers. Right: Trigger 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 offlinereconstructed min($ d_{\text{0}} $) of the two muons forming STASTA dimuons in events enriched in cosmic ray muons. Different symbols show efficiencies in different periods of the 2022 data taking corresponding to the integrated luminosities indicated in the legend. For displaced muons, the efficiency of the online min($ d_{\text{0}} $) requirement is larger than 95% in all data taking periods. 
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Additional Figure 9:
Distributions of $ m_{\mu\mu} $ (red) and $ m^\text{corr}_{\mu\mu} $ (orange) in the TMSTMS dimuon category, for simulated signal events with $ m({\tilde{\mathrm{q}}} ) = $ 125 GeV and $ m(\tilde{\chi}_{1}^{0}) = $ 50 GeV (left), and $ m({\tilde{\mathrm{q}}} ) = $ 350 GeV and $ m(\tilde{\chi}_{1}^{0}) = $ 150 GeV (right) in the RPV SUSY model. The last bin includes events in the histogram overflow. 
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Additional Figure 9a:
Distributions of $ m_{\mu\mu} $ (red) and $ m^\text{corr}_{\mu\mu} $ (orange) in the TMSTMS dimuon category, for simulated signal events with $ m({\tilde{\mathrm{q}}} ) = $ 125 GeV and $ m(\tilde{\chi}_{1}^{0}) = $ 50 GeV (left), and $ m({\tilde{\mathrm{q}}} ) = $ 350 GeV and $ m(\tilde{\chi}_{1}^{0}) = $ 150 GeV (right) in the RPV SUSY model. The last bin includes events in the histogram overflow. 
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Additional Figure 9b:
Distributions of $ m_{\mu\mu} $ (red) and $ m^\text{corr}_{\mu\mu} $ (orange) in the TMSTMS dimuon category, for simulated signal events with $ m({\tilde{\mathrm{q}}} ) = $ 125 GeV and $ m(\tilde{\chi}_{1}^{0}) = $ 50 GeV (left), and $ m({\tilde{\mathrm{q}}} ) = $ 350 GeV and $ m(\tilde{\chi}_{1}^{0}) = $ 150 GeV (right) in the RPV SUSY model. The last bin includes events in the histogram overflow. 
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Additional Figure 10:
Offline selection efficiency of TMSTMS dimuons as a function of simulated $ L_{\text{xy}} $ and $ z $ decay positions of $ \mathrm{Z}_\text{D} $, in all generated HAHM signal samples combined. Approximate locations of silicon pixel and strip tracker modules  tracker inner barrel (TIB) and disks (TID), tracker outer barrel (TOB), and tracker endcap (TEC)  are drawn superimposed as black boxes. 
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Additional Figure 11:
Offline selection efficiency of STASTA dimuons as a function of simulated $ L_{\text{xy}} $ and $ z $ decay positions of $ \mathrm{Z}_\text{D} $, in all generated HAHM signal samples combined. Approximate locations of various CMS subdetectors are drawn superimposed as black boxes. MB1MB4 denote four DT stations in the barrel, while ME followed by two indices denote CSC stations (the first index) and rings (the second index) in the endcap. 
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Additional Figure 12:
Overall selection efficiencies as a function of $ c\tau(\mathrm{Z}_\text{D}) $ for the HAHM signal with $ m(\mathrm{Z}_\text{D}) = $ 20 GeV (left) and 50 GeV (right) in different years of data taking. Efficiencies are computed as the ratios of the number of simulated signal events in which at least one dimuon candidate passes all 2016 (dashed green), 2018 (dashed red), and 2022 (solid black) trigger and offline selection criteria to the total number of simulated signal events. The lower panel shows the ratio of the 2022 efficiency to the 2018 efficiency (dashed red) and to the 2016 efficiency (dashed green). 
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Additional Figure 12a:
Overall selection efficiencies as a function of $ c\tau(\mathrm{Z}_\text{D}) $ for the HAHM signal with $ m(\mathrm{Z}_\text{D}) = $ 20 GeV (left) and 50 GeV (right) in different years of data taking. Efficiencies are computed as the ratios of the number of simulated signal events in which at least one dimuon candidate passes all 2016 (dashed green), 2018 (dashed red), and 2022 (solid black) trigger and offline selection criteria to the total number of simulated signal events. The lower panel shows the ratio of the 2022 efficiency to the 2018 efficiency (dashed red) and to the 2016 efficiency (dashed green). 
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Additional Figure 12b:
Overall selection efficiencies as a function of $ c\tau(\mathrm{Z}_\text{D}) $ for the HAHM signal with $ m(\mathrm{Z}_\text{D}) = $ 20 GeV (left) and 50 GeV (right) in different years of data taking. Efficiencies are computed as the ratios of the number of simulated signal events in which at least one dimuon candidate passes all 2016 (dashed green), 2018 (dashed red), and 2022 (solid black) trigger and offline selection criteria to the total number of simulated signal events. The lower panel shows the ratio of the 2022 efficiency to the 2018 efficiency (dashed red) and to the 2016 efficiency (dashed green). 
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Additional Figure 13:
Overall selection efficiencies as a function of $ c\tau(\mathrm{Z}_\text{D}) $ for the HAHM model with $ m(\mathrm{Z}_\text{D}) $ ranging from 10 GeV (upper left) to 60 GeV (lower right). Each plot shows efficiencies of the two dimuon categories, TMSTMS (dashed red) and STASTA (dashed green), as well as their combination (solid black). Each efficiency is computed as the ratio of the number of simulated signal events in which at least one dimuon candidate of a given type (or any type for the combined efficiency) passes all selection criteria (including the trigger) to the total number of simulated signal events. All efficiencies are corrected by the datatosimulation scale factors described in the paper. 
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Additional Figure 13a:
Overall selection efficiencies as a function of $ c\tau(\mathrm{Z}_\text{D}) $ for the HAHM model with $ m(\mathrm{Z}_\text{D}) $ ranging from 10 GeV (upper left) to 60 GeV (lower right). Each plot shows efficiencies of the two dimuon categories, TMSTMS (dashed red) and STASTA (dashed green), as well as their combination (solid black). Each efficiency is computed as the ratio of the number of simulated signal events in which at least one dimuon candidate of a given type (or any type for the combined efficiency) passes all selection criteria (including the trigger) to the total number of simulated signal events. All efficiencies are corrected by the datatosimulation scale factors described in the paper. 
png pdf root 
Additional Figure 13b:
Overall selection efficiencies as a function of $ c\tau(\mathrm{Z}_\text{D}) $ for the HAHM model with $ m(\mathrm{Z}_\text{D}) $ ranging from 10 GeV (upper left) to 60 GeV (lower right). Each plot shows efficiencies of the two dimuon categories, TMSTMS (dashed red) and STASTA (dashed green), as well as their combination (solid black). Each efficiency is computed as the ratio of the number of simulated signal events in which at least one dimuon candidate of a given type (or any type for the combined efficiency) passes all selection criteria (including the trigger) to the total number of simulated signal events. All efficiencies are corrected by the datatosimulation scale factors described in the paper. 
png pdf root 
Additional Figure 13c:
Overall selection efficiencies as a function of $ c\tau(\mathrm{Z}_\text{D}) $ for the HAHM model with $ m(\mathrm{Z}_\text{D}) $ ranging from 10 GeV (upper left) to 60 GeV (lower right). Each plot shows efficiencies of the two dimuon categories, TMSTMS (dashed red) and STASTA (dashed green), as well as their combination (solid black). Each efficiency is computed as the ratio of the number of simulated signal events in which at least one dimuon candidate of a given type (or any type for the combined efficiency) passes all selection criteria (including the trigger) to the total number of simulated signal events. All efficiencies are corrected by the datatosimulation scale factors described in the paper. 
png pdf root 
Additional Figure 13d:
Overall selection efficiencies as a function of $ c\tau(\mathrm{Z}_\text{D}) $ for the HAHM model with $ m(\mathrm{Z}_\text{D}) $ ranging from 10 GeV (upper left) to 60 GeV (lower right). Each plot shows efficiencies of the two dimuon categories, TMSTMS (dashed red) and STASTA (dashed green), as well as their combination (solid black). Each efficiency is computed as the ratio of the number of simulated signal events in which at least one dimuon candidate of a given type (or any type for the combined efficiency) passes all selection criteria (including the trigger) to the total number of simulated signal events. All efficiencies are corrected by the datatosimulation scale factors described in the paper. 
png pdf root 
Additional Figure 13e:
Overall selection efficiencies as a function of $ c\tau(\mathrm{Z}_\text{D}) $ for the HAHM model with $ m(\mathrm{Z}_\text{D}) $ ranging from 10 GeV (upper left) to 60 GeV (lower right). Each plot shows efficiencies of the two dimuon categories, TMSTMS (dashed red) and STASTA (dashed green), as well as their combination (solid black). Each efficiency is computed as the ratio of the number of simulated signal events in which at least one dimuon candidate of a given type (or any type for the combined efficiency) passes all selection criteria (including the trigger) to the total number of simulated signal events. All efficiencies are corrected by the datatosimulation scale factors described in the paper. 
png pdf root 
Additional Figure 13f:
Overall selection efficiencies as a function of $ c\tau(\mathrm{Z}_\text{D}) $ for the HAHM model with $ m(\mathrm{Z}_\text{D}) $ ranging from 10 GeV (upper left) to 60 GeV (lower right). Each plot shows efficiencies of the two dimuon categories, TMSTMS (dashed red) and STASTA (dashed green), as well as their combination (solid black). Each efficiency is computed as the ratio of the number of simulated signal events in which at least one dimuon candidate of a given type (or any type for the combined efficiency) passes all selection criteria (including the trigger) to the total number of simulated signal events. All efficiencies are corrected by the datatosimulation scale factors described in the paper. 
png pdf 
Additional Figure 14:
Overall selection efficiencies as a function of $ c\tau(\tilde{\chi}_{1}^{0}) $ for the RPV SUSY model, for events with $ m({\tilde{\mathrm{q}}} ) $ ranging from 125 GeV (upper left) to 1600 GeV (lower right) and $ m(\tilde{\chi}_{1}^{0}) = $ 50 GeV. Each plot shows efficiencies of the two dimuon categories, TMSTMS (dashed red) and STASTA (dashed green), as well as their combination (solid black). Each efficiency is computed as the ratio of the number of simulated signal events in which at least one dimuon candidate of a given type (or any type for the combined efficiency) passes all selection criteria (including the trigger) to the total number of simulated signal events. All efficiencies are corrected by the datatosimulation scale factors described in the paper. 
png pdf root 
Additional Figure 14a:
Overall selection efficiencies as a function of $ c\tau(\tilde{\chi}_{1}^{0}) $ for the RPV SUSY model, for events with $ m({\tilde{\mathrm{q}}} ) $ ranging from 125 GeV (upper left) to 1600 GeV (lower right) and $ m(\tilde{\chi}_{1}^{0}) = $ 50 GeV. Each plot shows efficiencies of the two dimuon categories, TMSTMS (dashed red) and STASTA (dashed green), as well as their combination (solid black). Each efficiency is computed as the ratio of the number of simulated signal events in which at least one dimuon candidate of a given type (or any type for the combined efficiency) passes all selection criteria (including the trigger) to the total number of simulated signal events. All efficiencies are corrected by the datatosimulation scale factors described in the paper. 
png pdf root 
Additional Figure 14b:
Overall selection efficiencies as a function of $ c\tau(\tilde{\chi}_{1}^{0}) $ for the RPV SUSY model, for events with $ m({\tilde{\mathrm{q}}} ) $ ranging from 125 GeV (upper left) to 1600 GeV (lower right) and $ m(\tilde{\chi}_{1}^{0}) = $ 50 GeV. Each plot shows efficiencies of the two dimuon categories, TMSTMS (dashed red) and STASTA (dashed green), as well as their combination (solid black). Each efficiency is computed as the ratio of the number of simulated signal events in which at least one dimuon candidate of a given type (or any type for the combined efficiency) passes all selection criteria (including the trigger) to the total number of simulated signal events. All efficiencies are corrected by the datatosimulation scale factors described in the paper. 
png pdf root 
Additional Figure 14c:
Overall selection efficiencies as a function of $ c\tau(\tilde{\chi}_{1}^{0}) $ for the RPV SUSY model, for events with $ m({\tilde{\mathrm{q}}} ) $ ranging from 125 GeV (upper left) to 1600 GeV (lower right) and $ m(\tilde{\chi}_{1}^{0}) = $ 50 GeV. Each plot shows efficiencies of the two dimuon categories, TMSTMS (dashed red) and STASTA (dashed green), as well as their combination (solid black). Each efficiency is computed as the ratio of the number of simulated signal events in which at least one dimuon candidate of a given type (or any type for the combined efficiency) passes all selection criteria (including the trigger) to the total number of simulated signal events. All efficiencies are corrected by the datatosimulation scale factors described in the paper. 
png pdf root 
Additional Figure 14d:
Overall selection efficiencies as a function of $ c\tau(\tilde{\chi}_{1}^{0}) $ for the RPV SUSY model, for events with $ m({\tilde{\mathrm{q}}} ) $ ranging from 125 GeV (upper left) to 1600 GeV (lower right) and $ m(\tilde{\chi}_{1}^{0}) = $ 50 GeV. Each plot shows efficiencies of the two dimuon categories, TMSTMS (dashed red) and STASTA (dashed green), as well as their combination (solid black). Each efficiency is computed as the ratio of the number of simulated signal events in which at least one dimuon candidate of a given type (or any type for the combined efficiency) passes all selection criteria (including the trigger) to the total number of simulated signal events. All efficiencies are corrected by the datatosimulation scale factors described in the paper. 
png pdf root 
Additional Figure 14e:
Overall selection efficiencies as a function of $ c\tau(\tilde{\chi}_{1}^{0}) $ for the RPV SUSY model, for events with $ m({\tilde{\mathrm{q}}} ) $ ranging from 125 GeV (upper left) to 1600 GeV (lower right) and $ m(\tilde{\chi}_{1}^{0}) = $ 50 GeV. Each plot shows efficiencies of the two dimuon categories, TMSTMS (dashed red) and STASTA (dashed green), as well as their combination (solid black). Each efficiency is computed as the ratio of the number of simulated signal events in which at least one dimuon candidate of a given type (or any type for the combined efficiency) passes all selection criteria (including the trigger) to the total number of simulated signal events. All efficiencies are corrected by the datatosimulation scale factors described in the paper. 
png pdf root 
Additional Figure 14f:
Overall selection efficiencies as a function of $ c\tau(\tilde{\chi}_{1}^{0}) $ for the RPV SUSY model, for events with $ m({\tilde{\mathrm{q}}} ) $ ranging from 125 GeV (upper left) to 1600 GeV (lower right) and $ m(\tilde{\chi}_{1}^{0}) = $ 50 GeV. Each plot shows efficiencies of the two dimuon categories, TMSTMS (dashed red) and STASTA (dashed green), as well as their combination (solid black). Each efficiency is computed as the ratio of the number of simulated signal events in which at least one dimuon candidate of a given type (or any type for the combined efficiency) passes all selection criteria (including the trigger) to the total number of simulated signal events. All efficiencies are corrected by the datatosimulation scale factors described in the paper. 
png pdf 
Additional Figure 15:
Overall selection efficiencies as a function of $ c\tau(\tilde{\chi}_{1}^{0}) $ for the RPV SUSY model, for events with $ m({\tilde{\mathrm{q}}} ) $ ranging from 700 GeV (upper left) to 1600 GeV (lower) and $ m(\tilde{\chi}_{1}^{0}) = $ 500 GeV. Each plot shows efficiencies of the two dimuon categories, TMSTMS (dashed red) and STASTA (dashed green), as well as their combination (solid black). Each efficiency is computed as the ratio of the number of simulated signal events in which at least one dimuon candidate of a given type (or any type for the combined efficiency) passes all selection criteria (including the trigger) to the total number of simulated signal events. All efficiencies are corrected by the datatosimulation scale factors described in the paper. 
png pdf root 
Additional Figure 15a:
Overall selection efficiencies as a function of $ c\tau(\tilde{\chi}_{1}^{0}) $ for the RPV SUSY model, for events with $ m({\tilde{\mathrm{q}}} ) $ ranging from 700 GeV (upper left) to 1600 GeV (lower) and $ m(\tilde{\chi}_{1}^{0}) = $ 500 GeV. Each plot shows efficiencies of the two dimuon categories, TMSTMS (dashed red) and STASTA (dashed green), as well as their combination (solid black). Each efficiency is computed as the ratio of the number of simulated signal events in which at least one dimuon candidate of a given type (or any type for the combined efficiency) passes all selection criteria (including the trigger) to the total number of simulated signal events. All efficiencies are corrected by the datatosimulation scale factors described in the paper. 
png pdf root 
Additional Figure 15b:
Overall selection efficiencies as a function of $ c\tau(\tilde{\chi}_{1}^{0}) $ for the RPV SUSY model, for events with $ m({\tilde{\mathrm{q}}} ) $ ranging from 700 GeV (upper left) to 1600 GeV (lower) and $ m(\tilde{\chi}_{1}^{0}) = $ 500 GeV. Each plot shows efficiencies of the two dimuon categories, TMSTMS (dashed red) and STASTA (dashed green), as well as their combination (solid black). Each efficiency is computed as the ratio of the number of simulated signal events in which at least one dimuon candidate of a given type (or any type for the combined efficiency) passes all selection criteria (including the trigger) to the total number of simulated signal events. All efficiencies are corrected by the datatosimulation scale factors described in the paper. 
png pdf root 
Additional Figure 15c:
Overall selection efficiencies as a function of $ c\tau(\tilde{\chi}_{1}^{0}) $ for the RPV SUSY model, for events with $ m({\tilde{\mathrm{q}}} ) $ ranging from 700 GeV (upper left) to 1600 GeV (lower) and $ m(\tilde{\chi}_{1}^{0}) = $ 500 GeV. Each plot shows efficiencies of the two dimuon categories, TMSTMS (dashed red) and STASTA (dashed green), as well as their combination (solid black). Each efficiency is computed as the ratio of the number of simulated signal events in which at least one dimuon candidate of a given type (or any type for the combined efficiency) passes all selection criteria (including the trigger) to the total number of simulated signal events. All efficiencies are corrected by the datatosimulation scale factors described in the paper. 
png pdf root 
Additional Figure 16:
The 95% CL observed upper limits on $ \mathcal{B}(\mathrm{H} \to \mathrm{Z}_\text{D}\mathrm{Z}_\text{D}) $ as a function of $ c\tau(\mathrm{Z}_\text{D}) $ for the HAHM model with $ m(\mathrm{Z}_\text{D}) $ ranging from 10 to 60 GeV, obtained by combining the results of this analysis with those of the Run 2 analysis (JHEP 05 (2023) 228). 
png pdf 
Additional Figure 17:
Observed 95% CL upper limits on $ \sigma(\mathrm{p}\mathrm{p}\to{\tilde{\mathrm{q}}} \overline{\tilde{\mathrm{q}}})\mathcal{B}( \tilde{\mathrm{q}} \to \mathrm{q} \tilde{\chi}_{1}^{0} ) $ as a function of $ c\tau(\tilde{\chi}_{1}^{0}) $ in the RPV SUSY model, for $ \mathcal{B}(\tilde{\chi}_{1}^{0}\to\mu^{+}\mu^{}\nu) = $ 0.5 and various combinations of $ m({\tilde{\mathrm{q}}} ) $ and $ m(\tilde{\chi}_{1}^{0}) $ indicated in the legends. The limits obtained in this analysis (solid) are compared with the corresponding limits (dashed) from the analysis of CMS Run 1 data (PRD 91, 052012) rescaled by the ratio of $ \sigma(\mathrm{p}\mathrm{p}\to{\tilde{\mathrm{q}}} \overline{\tilde{\mathrm{q}}}) $ at 13.6 TeV and 8 TeV, and from the ATLAS search for displaced vertices of oppositely charged leptons in the 2016 data set (PLB 801, 135114) rescaled by the ratio of $ \sigma(\mathrm{p}\mathrm{p}\to{\tilde{\mathrm{q}}} \overline{\tilde{\mathrm{q}}}) $ at 13.6 TeV and 13 TeV. The gray horizontal lines indicate the theoretical values of the squarkantisquark production cross sections with the uncertainties shown as gray shaded bands. The predicted cross sections for $ m({\tilde{\mathrm{q}}} ) $ = 125 and 350 GeV are, respectively, 7200 and 50 pb, and fall outside the $ y $axis range. 
png pdf root 
Additional Figure 17a:
Observed 95% CL upper limits on $ \sigma(\mathrm{p}\mathrm{p}\to{\tilde{\mathrm{q}}} \overline{\tilde{\mathrm{q}}})\mathcal{B}( \tilde{\mathrm{q}} \to \mathrm{q} \tilde{\chi}_{1}^{0} ) $ as a function of $ c\tau(\tilde{\chi}_{1}^{0}) $ in the RPV SUSY model, for $ \mathcal{B}(\tilde{\chi}_{1}^{0}\to\mu^{+}\mu^{}\nu) = $ 0.5 and various combinations of $ m({\tilde{\mathrm{q}}} ) $ and $ m(\tilde{\chi}_{1}^{0}) $ indicated in the legends. The limits obtained in this analysis (solid) are compared with the corresponding limits (dashed) from the analysis of CMS Run 1 data (PRD 91, 052012) rescaled by the ratio of $ \sigma(\mathrm{p}\mathrm{p}\to{\tilde{\mathrm{q}}} \overline{\tilde{\mathrm{q}}}) $ at 13.6 TeV and 8 TeV, and from the ATLAS search for displaced vertices of oppositely charged leptons in the 2016 data set (PLB 801, 135114) rescaled by the ratio of $ \sigma(\mathrm{p}\mathrm{p}\to{\tilde{\mathrm{q}}} \overline{\tilde{\mathrm{q}}}) $ at 13.6 TeV and 13 TeV. The gray horizontal lines indicate the theoretical values of the squarkantisquark production cross sections with the uncertainties shown as gray shaded bands. The predicted cross sections for $ m({\tilde{\mathrm{q}}} ) $ = 125 and 350 GeV are, respectively, 7200 and 50 pb, and fall outside the $ y $axis range. 
png pdf root 
Additional Figure 17b:
Observed 95% CL upper limits on $ \sigma(\mathrm{p}\mathrm{p}\to{\tilde{\mathrm{q}}} \overline{\tilde{\mathrm{q}}})\mathcal{B}( \tilde{\mathrm{q}} \to \mathrm{q} \tilde{\chi}_{1}^{0} ) $ as a function of $ c\tau(\tilde{\chi}_{1}^{0}) $ in the RPV SUSY model, for $ \mathcal{B}(\tilde{\chi}_{1}^{0}\to\mu^{+}\mu^{}\nu) = $ 0.5 and various combinations of $ m({\tilde{\mathrm{q}}} ) $ and $ m(\tilde{\chi}_{1}^{0}) $ indicated in the legends. The limits obtained in this analysis (solid) are compared with the corresponding limits (dashed) from the analysis of CMS Run 1 data (PRD 91, 052012) rescaled by the ratio of $ \sigma(\mathrm{p}\mathrm{p}\to{\tilde{\mathrm{q}}} \overline{\tilde{\mathrm{q}}}) $ at 13.6 TeV and 8 TeV, and from the ATLAS search for displaced vertices of oppositely charged leptons in the 2016 data set (PLB 801, 135114) rescaled by the ratio of $ \sigma(\mathrm{p}\mathrm{p}\to{\tilde{\mathrm{q}}} \overline{\tilde{\mathrm{q}}}) $ at 13.6 TeV and 13 TeV. The gray horizontal lines indicate the theoretical values of the squarkantisquark production cross sections with the uncertainties shown as gray shaded bands. The predicted cross sections for $ m({\tilde{\mathrm{q}}} ) $ = 125 and 350 GeV are, respectively, 7200 and 50 pb, and fall outside the $ y $axis range. 
png pdf root 
Additional Figure 17c:
Observed 95% CL upper limits on $ \sigma(\mathrm{p}\mathrm{p}\to{\tilde{\mathrm{q}}} \overline{\tilde{\mathrm{q}}})\mathcal{B}( \tilde{\mathrm{q}} \to \mathrm{q} \tilde{\chi}_{1}^{0} ) $ as a function of $ c\tau(\tilde{\chi}_{1}^{0}) $ in the RPV SUSY model, for $ \mathcal{B}(\tilde{\chi}_{1}^{0}\to\mu^{+}\mu^{}\nu) = $ 0.5 and various combinations of $ m({\tilde{\mathrm{q}}} ) $ and $ m(\tilde{\chi}_{1}^{0}) $ indicated in the legends. The limits obtained in this analysis (solid) are compared with the corresponding limits (dashed) from the analysis of CMS Run 1 data (PRD 91, 052012) rescaled by the ratio of $ \sigma(\mathrm{p}\mathrm{p}\to{\tilde{\mathrm{q}}} \overline{\tilde{\mathrm{q}}}) $ at 13.6 TeV and 8 TeV, and from the ATLAS search for displaced vertices of oppositely charged leptons in the 2016 data set (PLB 801, 135114) rescaled by the ratio of $ \sigma(\mathrm{p}\mathrm{p}\to{\tilde{\mathrm{q}}} \overline{\tilde{\mathrm{q}}}) $ at 13.6 TeV and 13 TeV. The gray horizontal lines indicate the theoretical values of the squarkantisquark production cross sections with the uncertainties shown as gray shaded bands. The predicted cross sections for $ m({\tilde{\mathrm{q}}} ) $ = 125 and 350 GeV are, respectively, 7200 and 50 pb, and fall outside the $ y $axis range. 
png pdf root 
Additional Figure 17d:
Observed 95% CL upper limits on $ \sigma(\mathrm{p}\mathrm{p}\to{\tilde{\mathrm{q}}} \overline{\tilde{\mathrm{q}}})\mathcal{B}( \tilde{\mathrm{q}} \to \mathrm{q} \tilde{\chi}_{1}^{0} ) $ as a function of $ c\tau(\tilde{\chi}_{1}^{0}) $ in the RPV SUSY model, for $ \mathcal{B}(\tilde{\chi}_{1}^{0}\to\mu^{+}\mu^{}\nu) = $ 0.5 and various combinations of $ m({\tilde{\mathrm{q}}} ) $ and $ m(\tilde{\chi}_{1}^{0}) $ indicated in the legends. The limits obtained in this analysis (solid) are compared with the corresponding limits (dashed) from the analysis of CMS Run 1 data (PRD 91, 052012) rescaled by the ratio of $ \sigma(\mathrm{p}\mathrm{p}\to{\tilde{\mathrm{q}}} \overline{\tilde{\mathrm{q}}}) $ at 13.6 TeV and 8 TeV, and from the ATLAS search for displaced vertices of oppositely charged leptons in the 2016 data set (PLB 801, 135114) rescaled by the ratio of $ \sigma(\mathrm{p}\mathrm{p}\to{\tilde{\mathrm{q}}} \overline{\tilde{\mathrm{q}}}) $ at 13.6 TeV and 13 TeV. The gray horizontal lines indicate the theoretical values of the squarkantisquark production cross sections with the uncertainties shown as gray shaded bands. The predicted cross sections for $ m({\tilde{\mathrm{q}}} ) $ = 125 and 350 GeV are, respectively, 7200 and 50 pb, and fall outside the $ y $axis range. 
png pdf 
Additional Figure 18:
Signal efficiencies in the TMSTMS (left) and STASTA (right) dimuon category as a function of the smaller of the two values of generated muon $ p_{\mathrm{T}} $ and $ d_{\text{0}} $ in dimuons with $ L_{\text{xy}}^\mathrm{true} $ smaller than 20 cm (upper), 2070 cm (middle), and 70500 cm (lower) in the HAHM signal model. The efficiency in each bin is computed as the ratio of the number of simulated signal dimuons in that bin that pass the trigger requirements and selection criteria to the total number of simulated signal dimuons in that bin and within the geometric acceptance. The geometric acceptance is defined as the generated longitudinal decay length $ L_{\text{z}}^\mathrm{true} $ smaller than 8 m and $ \eta $ of both generated muons forming the dimuon smaller than 2.0. The efficiencies obtained from simulation are corrected by the datatosimulation scale factors described in the paper. Efficiency in the TMSTMS dimuon category for dimuons with $ L_{\text{xy}}^\mathrm{true} > $ 70 cm is zero and is not shown. 
png pdf 
Additional Figure 18a:
Signal efficiencies in the TMSTMS (left) and STASTA (right) dimuon category as a function of the smaller of the two values of generated muon $ p_{\mathrm{T}} $ and $ d_{\text{0}} $ in dimuons with $ L_{\text{xy}}^\mathrm{true} $ smaller than 20 cm (upper), 2070 cm (middle), and 70500 cm (lower) in the HAHM signal model. The efficiency in each bin is computed as the ratio of the number of simulated signal dimuons in that bin that pass the trigger requirements and selection criteria to the total number of simulated signal dimuons in that bin and within the geometric acceptance. The geometric acceptance is defined as the generated longitudinal decay length $ L_{\text{z}}^\mathrm{true} $ smaller than 8 m and $ \eta $ of both generated muons forming the dimuon smaller than 2.0. The efficiencies obtained from simulation are corrected by the datatosimulation scale factors described in the paper. Efficiency in the TMSTMS dimuon category for dimuons with $ L_{\text{xy}}^\mathrm{true} > $ 70 cm is zero and is not shown. 
png pdf 
Additional Figure 18b:
Signal efficiencies in the TMSTMS (left) and STASTA (right) dimuon category as a function of the smaller of the two values of generated muon $ p_{\mathrm{T}} $ and $ d_{\text{0}} $ in dimuons with $ L_{\text{xy}}^\mathrm{true} $ smaller than 20 cm (upper), 2070 cm (middle), and 70500 cm (lower) in the HAHM signal model. The efficiency in each bin is computed as the ratio of the number of simulated signal dimuons in that bin that pass the trigger requirements and selection criteria to the total number of simulated signal dimuons in that bin and within the geometric acceptance. The geometric acceptance is defined as the generated longitudinal decay length $ L_{\text{z}}^\mathrm{true} $ smaller than 8 m and $ \eta $ of both generated muons forming the dimuon smaller than 2.0. The efficiencies obtained from simulation are corrected by the datatosimulation scale factors described in the paper. Efficiency in the TMSTMS dimuon category for dimuons with $ L_{\text{xy}}^\mathrm{true} > $ 70 cm is zero and is not shown. 
png pdf 
Additional Figure 18c:
Signal efficiencies in the TMSTMS (left) and STASTA (right) dimuon category as a function of the smaller of the two values of generated muon $ p_{\mathrm{T}} $ and $ d_{\text{0}} $ in dimuons with $ L_{\text{xy}}^\mathrm{true} $ smaller than 20 cm (upper), 2070 cm (middle), and 70500 cm (lower) in the HAHM signal model. The efficiency in each bin is computed as the ratio of the number of simulated signal dimuons in that bin that pass the trigger requirements and selection criteria to the total number of simulated signal dimuons in that bin and within the geometric acceptance. The geometric acceptance is defined as the generated longitudinal decay length $ L_{\text{z}}^\mathrm{true} $ smaller than 8 m and $ \eta $ of both generated muons forming the dimuon smaller than 2.0. The efficiencies obtained from simulation are corrected by the datatosimulation scale factors described in the paper. Efficiency in the TMSTMS dimuon category for dimuons with $ L_{\text{xy}}^\mathrm{true} > $ 70 cm is zero and is not shown. 
png pdf 
Additional Figure 18d:
Signal efficiencies in the TMSTMS (left) and STASTA (right) dimuon category as a function of the smaller of the two values of generated muon $ p_{\mathrm{T}} $ and $ d_{\text{0}} $ in dimuons with $ L_{\text{xy}}^\mathrm{true} $ smaller than 20 cm (upper), 2070 cm (middle), and 70500 cm (lower) in the HAHM signal model. The efficiency in each bin is computed as the ratio of the number of simulated signal dimuons in that bin that pass the trigger requirements and selection criteria to the total number of simulated signal dimuons in that bin and within the geometric acceptance. The geometric acceptance is defined as the generated longitudinal decay length $ L_{\text{z}}^\mathrm{true} $ smaller than 8 m and $ \eta $ of both generated muons forming the dimuon smaller than 2.0. The efficiencies obtained from simulation are corrected by the datatosimulation scale factors described in the paper. Efficiency in the TMSTMS dimuon category for dimuons with $ L_{\text{xy}}^\mathrm{true} > $ 70 cm is zero and is not shown. 
png pdf 
Additional Figure 18e:
Signal efficiencies in the TMSTMS (left) and STASTA (right) dimuon category as a function of the smaller of the two values of generated muon $ p_{\mathrm{T}} $ and $ d_{\text{0}} $ in dimuons with $ L_{\text{xy}}^\mathrm{true} $ smaller than 20 cm (upper), 2070 cm (middle), and 70500 cm (lower) in the HAHM signal model. The efficiency in each bin is computed as the ratio of the number of simulated signal dimuons in that bin that pass the trigger requirements and selection criteria to the total number of simulated signal dimuons in that bin and within the geometric acceptance. The geometric acceptance is defined as the generated longitudinal decay length $ L_{\text{z}}^\mathrm{true} $ smaller than 8 m and $ \eta $ of both generated muons forming the dimuon smaller than 2.0. The efficiencies obtained from simulation are corrected by the datatosimulation scale factors described in the paper. Efficiency in the TMSTMS dimuon category for dimuons with $ L_{\text{xy}}^\mathrm{true} > $ 70 cm is zero and is not shown. 
png pdf 
Additional Figure 19:
Signal efficiencies in the TMSTMS (left) and STASTA (right) dimuon category as a function of the smaller of the two values of generated muon $ p_{\mathrm{T}} $ and $ d_{\text{0}} $ in dimuons with $ L_{\text{xy}}^\mathrm{true} $ smaller than 20 cm (upper), 2070 cm (middle), and 70500 cm (lower) in the RPV SUSY signal model. The efficiency in each bin is computed as the ratio of the number of simulated signal dimuons in that bin that pass the trigger requirements and selection criteria to the total number of simulated signal dimuons in that bin and within the geometric acceptance. The geometric acceptance is defined as the generated longitudinal decay length $ L_{\text{z}}^\mathrm{true} $ smaller than 8 m and $ \eta $ of both generated muons forming the dimuon smaller than 2.0. The efficiencies obtained from simulation are corrected by the datatosimulation scale factors described in the paper. Efficiency in the TMSTMS dimuon category for dimuons with $ L_{\text{xy}}^\mathrm{true} > $ 70 cm is zero and is not shown. 
png pdf 
Additional Figure 19a:
Signal efficiencies in the TMSTMS (left) and STASTA (right) dimuon category as a function of the smaller of the two values of generated muon $ p_{\mathrm{T}} $ and $ d_{\text{0}} $ in dimuons with $ L_{\text{xy}}^\mathrm{true} $ smaller than 20 cm (upper), 2070 cm (middle), and 70500 cm (lower) in the RPV SUSY signal model. The efficiency in each bin is computed as the ratio of the number of simulated signal dimuons in that bin that pass the trigger requirements and selection criteria to the total number of simulated signal dimuons in that bin and within the geometric acceptance. The geometric acceptance is defined as the generated longitudinal decay length $ L_{\text{z}}^\mathrm{true} $ smaller than 8 m and $ \eta $ of both generated muons forming the dimuon smaller than 2.0. The efficiencies obtained from simulation are corrected by the datatosimulation scale factors described in the paper. Efficiency in the TMSTMS dimuon category for dimuons with $ L_{\text{xy}}^\mathrm{true} > $ 70 cm is zero and is not shown. 
png pdf 
Additional Figure 19b:
Signal efficiencies in the TMSTMS (left) and STASTA (right) dimuon category as a function of the smaller of the two values of generated muon $ p_{\mathrm{T}} $ and $ d_{\text{0}} $ in dimuons with $ L_{\text{xy}}^\mathrm{true} $ smaller than 20 cm (upper), 2070 cm (middle), and 70500 cm (lower) in the RPV SUSY signal model. The efficiency in each bin is computed as the ratio of the number of simulated signal dimuons in that bin that pass the trigger requirements and selection criteria to the total number of simulated signal dimuons in that bin and within the geometric acceptance. The geometric acceptance is defined as the generated longitudinal decay length $ L_{\text{z}}^\mathrm{true} $ smaller than 8 m and $ \eta $ of both generated muons forming the dimuon smaller than 2.0. The efficiencies obtained from simulation are corrected by the datatosimulation scale factors described in the paper. Efficiency in the TMSTMS dimuon category for dimuons with $ L_{\text{xy}}^\mathrm{true} > $ 70 cm is zero and is not shown. 
png pdf 
Additional Figure 19c:
Signal efficiencies in the TMSTMS (left) and STASTA (right) dimuon category as a function of the smaller of the two values of generated muon $ p_{\mathrm{T}} $ and $ d_{\text{0}} $ in dimuons with $ L_{\text{xy}}^\mathrm{true} $ smaller than 20 cm (upper), 2070 cm (middle), and 70500 cm (lower) in the RPV SUSY signal model. The efficiency in each bin is computed as the ratio of the number of simulated signal dimuons in that bin that pass the trigger requirements and selection criteria to the total number of simulated signal dimuons in that bin and within the geometric acceptance. The geometric acceptance is defined as the generated longitudinal decay length $ L_{\text{z}}^\mathrm{true} $ smaller than 8 m and $ \eta $ of both generated muons forming the dimuon smaller than 2.0. The efficiencies obtained from simulation are corrected by the datatosimulation scale factors described in the paper. Efficiency in the TMSTMS dimuon category for dimuons with $ L_{\text{xy}}^\mathrm{true} > $ 70 cm is zero and is not shown. 
png pdf 
Additional Figure 19d:
Signal efficiencies in the TMSTMS (left) and STASTA (right) dimuon category as a function of the smaller of the two values of generated muon $ p_{\mathrm{T}} $ and $ d_{\text{0}} $ in dimuons with $ L_{\text{xy}}^\mathrm{true} $ smaller than 20 cm (upper), 2070 cm (middle), and 70500 cm (lower) in the RPV SUSY signal model. The efficiency in each bin is computed as the ratio of the number of simulated signal dimuons in that bin that pass the trigger requirements and selection criteria to the total number of simulated signal dimuons in that bin and within the geometric acceptance. The geometric acceptance is defined as the generated longitudinal decay length $ L_{\text{z}}^\mathrm{true} $ smaller than 8 m and $ \eta $ of both generated muons forming the dimuon smaller than 2.0. The efficiencies obtained from simulation are corrected by the datatosimulation scale factors described in the paper. Efficiency in the TMSTMS dimuon category for dimuons with $ L_{\text{xy}}^\mathrm{true} > $ 70 cm is zero and is not shown. 
png pdf 
Additional Figure 19e:
Signal efficiencies in the TMSTMS (left) and STASTA (right) dimuon category as a function of the smaller of the two values of generated muon $ p_{\mathrm{T}} $ and $ d_{\text{0}} $ in dimuons with $ L_{\text{xy}}^\mathrm{true} $ smaller than 20 cm (upper), 2070 cm (middle), and 70500 cm (lower) in the RPV SUSY signal model. The efficiency in each bin is computed as the ratio of the number of simulated signal dimuons in that bin that pass the trigger requirements and selection criteria to the total number of simulated signal dimuons in that bin and within the geometric acceptance. The geometric acceptance is defined as the generated longitudinal decay length $ L_{\text{z}}^\mathrm{true} $ smaller than 8 m and $ \eta $ of both generated muons forming the dimuon smaller than 2.0. The efficiencies obtained from simulation are corrected by the datatosimulation scale factors described in the paper. Efficiency in the TMSTMS dimuon category for dimuons with $ L_{\text{xy}}^\mathrm{true} > $ 70 cm is zero and is not shown. 
HEPData Instructions for Reinterpretation 
where $ k_{n} $ is the number of dimuons in the $ n $th event, the sum is over the number of generated signal events $ N^\mathrm{acc} $ in the geometric acceptance defined above and with the true mass larger than 10 GeV, and $ N $ is the total number of generated signal events. In cases where more than one dimuon is present in the event, the one with the larger of the two $ \mathrm{min}( d_{0} ) $ values should be taken as a reference to apply the efficiency map. In the TMSTMS category, where the signal region is divided into three bins in the minimum of the two $ d_{\text{0}}/\sigma_{d_{\text{0}}} $ values, $ \epsilon_j $ should be subdivided into three efficiencies depending on $ \mathrm{min}( d_{0} ) $, namely 90150 $ \mu $m, 150300 $ \mu $m, and $ > $ 300 $ \mu $m approximately corresponding to the three chosen min($ d_{\text{0}}/\sigma_{d_{\text{0}}} $) bins. The combined signal efficiency, $ \epsilon_\mathrm{tot} $, can be computed as the sum of signal efficiencies in the two dimuon categories: where $ j $ runs over the TMSTMS and STASTA categories. We have checked that the generatorlevel efficiency $ \epsilon_\mathrm{tot} $ obtained from the provided 3D efficiency maps approximates the reconstructionlevel efficiencies for the HAHM and RPV SUSY signal, shown in Fig. A13 and Figs. A14A15, respectively, with an accuracy of 20\% or better when the ratio of the LLP mass m(LLP) to the mediator mass m(M) is between 0.05 and 0.35. The method tends to overestimate the efficiency of signal events with a large Lorentz boost (m(LLP)/m(M) $ < $ 0.05), and that of nonrelativistic LLPs (0.35 $ < $ m(LLP)/m(M) $ < $ 0.5) with $ c\tau > $ 250 cm. The method is valid for m(LLP) $ > $ 20 GeV.To obtain the exclusions limits, one should use the signal efficiencies $ \epsilon_j $ in each dimuon category together with the expected number of background events from the paper. (this text in pdf) In case of questions, contact Muhammad Ansar Iqbal and Alberto Escalante del Valle. 
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