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Compact Muon Solenoid
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CMS-MUO-21-001 ; CERN-EP-2024-040
Performance of CMS muon reconstruction from proton-proton to heavy ion collisions
JINST 19 (2024) P09012
Abstract: The performance of muon tracking, identification, triggering, momentum resolution, and momentum scale has been studied with the CMS detector at the LHC using data collected at $ \sqrt{\smash[b]{s_{_{\mathrm{NN}}}}}= $ 5.02 TeV in proton-proton (pp) and lead-lead (PbPb) collisions in 2017 and 2018, respectively, and at $ \sqrt{\smash[b]{s_{_{\mathrm{NN}}}}} = $ 8.16 TeV in proton-lead (pPb) collisions in 2016. Muon efficiencies, momentum resolutions, and momentum scales are compared by focusing on how the muon reconstruction performance varies from relatively small occupancy pp collisions to the larger occupancies of pPb collisions and, finally, to the highest track multiplicity PbPb collisions. We find the efficiencies of muon tracking, identification, and triggering to be above 90% throughout most of the track multiplicity range. The momentum resolution and scale are unaffected by the detector occupancy. The excellent muon reconstruction of the CMS detector enables precision studies across all available collision systems.
Figures & Tables Summary References CMS Publications
Figures

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Figure 1:
Longitudinal layout of one quadrant of the CMS detector. The drawing shows four DT stations in the muon barrel (MB1-MB4, yellow), four CSC stations in the muon endcap (ME1-ME4, green) and the RPC stations (RB1-RB4 and RE1-RE4, blue).

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Figure 2:
Left: Distribution of $ N_{\mathrm{tracks}} $ in pp collisions at $ \sqrt{s}= $ 5.02 TeV (black); pPb collisions at $ \sqrt{\smash[b]{s_{_{\mathrm{NN}}}}}= $ 5.02 TeV (magenta) and at 8.16 TeV (blue); and PbPb collisions at $ \sqrt{\smash[b]{s_{_{\mathrm{NN}}}}}= $ 5.02 TeV (red). The distribution of $ N_{\mathrm{tracks}} $ in the 0-20% most central PbPb collisions is shown in green. The values are not corrected for efficiency. Right: Translation of the centrality in PbPb collisions at $ \sqrt{\smash[b]{s_{_{\mathrm{NN}}}}}= $ 5.02 TeV into an equivalent pileup in pp collisions at $ \sqrt{s}= $ 14 TeV.

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Figure 2-a:
Left: Distribution of $ N_{\mathrm{tracks}} $ in pp collisions at $ \sqrt{s}= $ 5.02 TeV (black); pPb collisions at $ \sqrt{\smash[b]{s_{_{\mathrm{NN}}}}}= $ 5.02 TeV (magenta) and at 8.16 TeV (blue); and PbPb collisions at $ \sqrt{\smash[b]{s_{_{\mathrm{NN}}}}}= $ 5.02 TeV (red). The distribution of $ N_{\mathrm{tracks}} $ in the 0-20% most central PbPb collisions is shown in green. The values are not corrected for efficiency. Right: Translation of the centrality in PbPb collisions at $ \sqrt{\smash[b]{s_{_{\mathrm{NN}}}}}= $ 5.02 TeV into an equivalent pileup in pp collisions at $ \sqrt{s}= $ 14 TeV.

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Figure 2-b:
Left: Distribution of $ N_{\mathrm{tracks}} $ in pp collisions at $ \sqrt{s}= $ 5.02 TeV (black); pPb collisions at $ \sqrt{\smash[b]{s_{_{\mathrm{NN}}}}}= $ 5.02 TeV (magenta) and at 8.16 TeV (blue); and PbPb collisions at $ \sqrt{\smash[b]{s_{_{\mathrm{NN}}}}}= $ 5.02 TeV (red). The distribution of $ N_{\mathrm{tracks}} $ in the 0-20% most central PbPb collisions is shown in green. The values are not corrected for efficiency. Right: Translation of the centrality in PbPb collisions at $ \sqrt{\smash[b]{s_{_{\mathrm{NN}}}}}= $ 5.02 TeV into an equivalent pileup in pp collisions at $ \sqrt{s}= $ 14 TeV.

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Figure 3:
Dimuon event from a PbPb collision in the CMS detector. Particles reconstructed in the inner tracker are colored blue; two muons from a Z boson candidate are colored red. See text for details.

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Figure 4:
Example of a fit to the data in PbPb collisions. The three panels show invariant mass distributions of the tag-and-probe pairs in central 0-10% collisions fitted with the sum of signal and background components. Left panel: total spectrum. Middle panel: spectrum for pairs where the probe passed the muon identification selection. Right panel: spectrum for muon pairs where the probe failed the selection. The vertical scale of the failing probes is enhanced by a factor of 5 compared with the other panels for visibility. The efficiency is retrieved directly from the simultaneous fit and in this particular case is $ \epsilon = $ 0.968 $ \pm $ 0.002.

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Figure 5:
Muon reconstruction efficiency (defined as the probability that a given muon that produced a tracker track will be reconstructed as both a global and a PF muon) plotted as a function of the number of tracks in pp, pPb, and PbPb collisions. Open symbols are the MC results corresponding to each data set. Lower panel shows the ratio between data and MC simulation. Only statistical uncertainties are shown.

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Figure 6:
Tight ID efficiency for global and PF muons as a function of the number of tracks in pp, pPb, and PbPb collisions. Open symbols are the MC results corresponding to each data set. Lower panel shows the ratio between data and MC simulation. Only statistical uncertainties are shown.

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Figure 7:
Tight ID efficiency as a function of $ \eta $ (left) and $ p_{\mathrm{T}} $ (right) in pp, pPb, and PbPb collisions. The probe is both a global muon and a PF muon. Open symbols are the MC results corresponding to each data set. Lower panels show the ratio between data and MC simulation. Only statistical uncertainties are shown.

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Figure 7-a:
Tight ID efficiency as a function of $ \eta $ (left) and $ p_{\mathrm{T}} $ (right) in pp, pPb, and PbPb collisions. The probe is both a global muon and a PF muon. Open symbols are the MC results corresponding to each data set. Lower panels show the ratio between data and MC simulation. Only statistical uncertainties are shown.

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Figure 7-b:
Tight ID efficiency as a function of $ \eta $ (left) and $ p_{\mathrm{T}} $ (right) in pp, pPb, and PbPb collisions. The probe is both a global muon and a PF muon. Open symbols are the MC results corresponding to each data set. Lower panels show the ratio between data and MC simulation. Only statistical uncertainties are shown.

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Figure 8:
Trigger efficiency of tight muons as a function of the number of tracks. The trigger requires a single muon with $ p_{\mathrm{T}} $ above 12 GeV. The efficiency is calculated for muons with $ p_{\mathrm{T}} > $ 15 GeV to avoid threshold effects. Open symbols are the MC results corresponding to each data set. Lower panel shows the ratio between data and MC simulation. Only statistical uncertainties are shown.

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Figure 9:
Trigger efficiency of tight muons as a function of $ \eta $ (left) and $ p_{\mathrm{T}} $ (right) in pp, pPb, and PbPb collisions. Lower panels show the ratio between data and MC simulation (MC points are omitted in the upper panels for clarity). Only statistical uncertainties are shown.

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Figure 9-a:
Trigger efficiency of tight muons as a function of $ \eta $ (left) and $ p_{\mathrm{T}} $ (right) in pp, pPb, and PbPb collisions. Lower panels show the ratio between data and MC simulation (MC points are omitted in the upper panels for clarity). Only statistical uncertainties are shown.

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Figure 9-b:
Trigger efficiency of tight muons as a function of $ \eta $ (left) and $ p_{\mathrm{T}} $ (right) in pp, pPb, and PbPb collisions. Lower panels show the ratio between data and MC simulation (MC points are omitted in the upper panels for clarity). Only statistical uncertainties are shown.

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Figure 10:
Purity for the L1, L2, and L3 trigger steps, compared among pp, pPb, and PbPb collisions. The online muon must have $ p_{\mathrm{T}} > $ 15 GeV and the offline muon matched to it must pass the tight ID selection and have $ |\eta| < $ 2.4. Details of the purity definition are given in the text. Statistical uncertainties are smaller than the symbol sizes.

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Figure 11:
Regions of the CMS detector commonly used in the heavy ion muon analyses for pPb (left) and PbPb (right) collisions. For each panel, the combined reconstruction and identification efficiency for simulated muons is plotted as a function of generated muon $ |\eta| $ and $ p_{\mathrm{T}} $. The lower-threshold curves (red) are for muon identification, and are used only by those analyses that do not use a dedicated muon trigger. The higher-threshold curves (green) are used by most analyses (those using the muon trigger information).

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Figure 11-a:
Regions of the CMS detector commonly used in the heavy ion muon analyses for pPb (left) and PbPb (right) collisions. For each panel, the combined reconstruction and identification efficiency for simulated muons is plotted as a function of generated muon $ |\eta| $ and $ p_{\mathrm{T}} $. The lower-threshold curves (red) are for muon identification, and are used only by those analyses that do not use a dedicated muon trigger. The higher-threshold curves (green) are used by most analyses (those using the muon trigger information).

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Figure 11-b:
Regions of the CMS detector commonly used in the heavy ion muon analyses for pPb (left) and PbPb (right) collisions. For each panel, the combined reconstruction and identification efficiency for simulated muons is plotted as a function of generated muon $ |\eta| $ and $ p_{\mathrm{T}} $. The lower-threshold curves (red) are for muon identification, and are used only by those analyses that do not use a dedicated muon trigger. The higher-threshold curves (green) are used by most analyses (those using the muon trigger information).

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Figure 12:
Hybrid-soft ID efficiency for global muons as a function of $ \eta $ (left) and $ p_{\mathrm{T}} $ (right) in pp and PbPb collisions. The muons are restricted in acceptance as shown by the red line in the right panel of Fig. 11. Lower panels show the ratio between data and MC simulation. Only statistical uncertainties are shown.

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Figure 12-a:
Hybrid-soft ID efficiency for global muons as a function of $ \eta $ (left) and $ p_{\mathrm{T}} $ (right) in pp and PbPb collisions. The muons are restricted in acceptance as shown by the red line in the right panel of Fig. 11. Lower panels show the ratio between data and MC simulation. Only statistical uncertainties are shown.

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Figure 12-b:
Hybrid-soft ID efficiency for global muons as a function of $ \eta $ (left) and $ p_{\mathrm{T}} $ (right) in pp and PbPb collisions. The muons are restricted in acceptance as shown by the red line in the right panel of Fig. 11. Lower panels show the ratio between data and MC simulation. Only statistical uncertainties are shown.

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Figure 13:
Mass resolution at the Z boson peak (left) and the $ \mathrm{J}/\psi $ peak (right) as a function of the number of tracks from MC simulations (open points) and collision data (filled points) in pp, pPb, and PbPb collisions. The mass resolution is scaled by the world-average mass $ m_{\textrm{PDG}} $. Lower panels show the ratio between data and MC simulation. Only statistical uncertainties are shown.

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Figure 13-a:
Mass resolution at the Z boson peak (left) and the $ \mathrm{J}/\psi $ peak (right) as a function of the number of tracks from MC simulations (open points) and collision data (filled points) in pp, pPb, and PbPb collisions. The mass resolution is scaled by the world-average mass $ m_{\textrm{PDG}} $. Lower panels show the ratio between data and MC simulation. Only statistical uncertainties are shown.

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Figure 13-b:
Mass resolution at the Z boson peak (left) and the $ \mathrm{J}/\psi $ peak (right) as a function of the number of tracks from MC simulations (open points) and collision data (filled points) in pp, pPb, and PbPb collisions. The mass resolution is scaled by the world-average mass $ m_{\textrm{PDG}} $. Lower panels show the ratio between data and MC simulation. Only statistical uncertainties are shown.

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Figure 14:
Mass scale at the Z boson peak (left) and the $ \mathrm{J}/\psi $ peak (right) as a function of the number of tracks from MC simulations (open points) and collision data (filled points) in pp, pPb, and PbPb collisions, calculated as the measured mass $ m_{\textrm{fit}} $ divided by the world-average mass $ m_{\textrm{PDG}} $. Lower panels show the ratio between data and MC simulation. Only statistical uncertainties are shown.

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Figure 14-a:
Mass scale at the Z boson peak (left) and the $ \mathrm{J}/\psi $ peak (right) as a function of the number of tracks from MC simulations (open points) and collision data (filled points) in pp, pPb, and PbPb collisions, calculated as the measured mass $ m_{\textrm{fit}} $ divided by the world-average mass $ m_{\textrm{PDG}} $. Lower panels show the ratio between data and MC simulation. Only statistical uncertainties are shown.

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Figure 14-b:
Mass scale at the Z boson peak (left) and the $ \mathrm{J}/\psi $ peak (right) as a function of the number of tracks from MC simulations (open points) and collision data (filled points) in pp, pPb, and PbPb collisions, calculated as the measured mass $ m_{\textrm{fit}} $ divided by the world-average mass $ m_{\textrm{PDG}} $. Lower panels show the ratio between data and MC simulation. Only statistical uncertainties are shown.

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Figure 15:
Mass resolution at the Z boson peak (left) and $ \mathrm{J}/\psi $ peak (right) as a function of $ |y^{\mu\mu}| $ from MC simulations (open points) and collision data (filled points) in pp, pPb, and PbPb collisions. The mass resolution is scaled by the world-average mass $ m_{\textrm{PDG}} $. Lower panels show the ratio between data and MC simulation. Only statistical uncertainties are shown.

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Figure 15-a:
Mass resolution at the Z boson peak (left) and $ \mathrm{J}/\psi $ peak (right) as a function of $ |y^{\mu\mu}| $ from MC simulations (open points) and collision data (filled points) in pp, pPb, and PbPb collisions. The mass resolution is scaled by the world-average mass $ m_{\textrm{PDG}} $. Lower panels show the ratio between data and MC simulation. Only statistical uncertainties are shown.

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Figure 15-b:
Mass resolution at the Z boson peak (left) and $ \mathrm{J}/\psi $ peak (right) as a function of $ |y^{\mu\mu}| $ from MC simulations (open points) and collision data (filled points) in pp, pPb, and PbPb collisions. The mass resolution is scaled by the world-average mass $ m_{\textrm{PDG}} $. Lower panels show the ratio between data and MC simulation. Only statistical uncertainties are shown.

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Figure 16:
Mass scale at the Z boson peak (left) and the $ \mathrm{J}/\psi $ peak (right) as a function of $ |y^{\mu\mu}| $ from MC simulations (open points) and real data (filled points) in pp, pPb, and PbPb collisions, calculated as the measured mass $ m_{\textrm{fit}} $ divided by the PDG mass $ m_{\textrm{PDG}} $. Lower panels show the ratio between data and MC simulation. Only statistical uncertainties are shown.

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Figure 16-a:
Mass scale at the Z boson peak (left) and the $ \mathrm{J}/\psi $ peak (right) as a function of $ |y^{\mu\mu}| $ from MC simulations (open points) and real data (filled points) in pp, pPb, and PbPb collisions, calculated as the measured mass $ m_{\textrm{fit}} $ divided by the PDG mass $ m_{\textrm{PDG}} $. Lower panels show the ratio between data and MC simulation. Only statistical uncertainties are shown.

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Figure 16-b:
Mass scale at the Z boson peak (left) and the $ \mathrm{J}/\psi $ peak (right) as a function of $ |y^{\mu\mu}| $ from MC simulations (open points) and real data (filled points) in pp, pPb, and PbPb collisions, calculated as the measured mass $ m_{\textrm{fit}} $ divided by the PDG mass $ m_{\textrm{PDG}} $. Lower panels show the ratio between data and MC simulation. Only statistical uncertainties are shown.

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Figure 17:
Mass resolution (left) and mass scale (right) versus the muon pseudorapidity $ |\eta^\mu| $ at the $ \mathrm{J}/\psi $ peak in pp collisions. The values are scaled by the world-average mass $ m^{{\mathrm{J}/\psi} }_{\textrm{PDG}} $. The filled points are collision data and the open points are MC simulations. Our results (black diamonds) are compared with measurements from a previous pp analysis done at $ \sqrt{s}= $ 7 TeV (blue crosses) [40]. Only statistical uncertainties are shown. See details in text.

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Figure 17-a:
Mass resolution (left) and mass scale (right) versus the muon pseudorapidity $ |\eta^\mu| $ at the $ \mathrm{J}/\psi $ peak in pp collisions. The values are scaled by the world-average mass $ m^{{\mathrm{J}/\psi} }_{\textrm{PDG}} $. The filled points are collision data and the open points are MC simulations. Our results (black diamonds) are compared with measurements from a previous pp analysis done at $ \sqrt{s}= $ 7 TeV (blue crosses) [40]. Only statistical uncertainties are shown. See details in text.

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Figure 17-b:
Mass resolution (left) and mass scale (right) versus the muon pseudorapidity $ |\eta^\mu| $ at the $ \mathrm{J}/\psi $ peak in pp collisions. The values are scaled by the world-average mass $ m^{{\mathrm{J}/\psi} }_{\textrm{PDG}} $. The filled points are collision data and the open points are MC simulations. Our results (black diamonds) are compared with measurements from a previous pp analysis done at $ \sqrt{s}= $ 7 TeV (blue crosses) [40]. Only statistical uncertainties are shown. See details in text.

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Figure A1:
Distributions of $ N_{\mathrm{tracks}} $ in the PbPb collisions for various ranges of centrality in a minimum-bias (left) and a muon-triggered (right) data set.

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Figure A1-a:
Distributions of $ N_{\mathrm{tracks}} $ in the PbPb collisions for various ranges of centrality in a minimum-bias (left) and a muon-triggered (right) data set.

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Figure A1-b:
Distributions of $ N_{\mathrm{tracks}} $ in the PbPb collisions for various ranges of centrality in a minimum-bias (left) and a muon-triggered (right) data set.
Tables

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Table 1:
Average number of reconstructed tracks, $ \langle N_{\mathrm{tracks}} \rangle $, in our data sets. The values are not corrected for pileup nor efficiency. Two columns are shown for PbPb collisions. The left column shows the values that are obtained from a minimum-bias data set, and correspond to distributions shown in the left panel of Fig. 2. The right column shows the values in muon-triggered data, and correspond to the location of points shown in the performance plots of this paper. The values for pPb are for illustrative purposes only; pPb results are binned directly in $ N_{\mathrm{tracks}} $. Details of the centrality conversion to $ \langle N_{\mathrm{tracks}} \rangle $ are provided in Appendix A.

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Table 2:
Characteristics of selected collisions collected during LHC Run 2. More information on the corresponding luminosity measurements can be found in Refs. [23-26].

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Table 3:
Overview of muon identification and triggers used in the Z boson kinematic region (e.g., Z, W, and t analyses) and in the $ \mathrm{J}/\psi $ kinematic region (e.g., $ \mathrm{J}/\psi $ and $ \Upsilon $ analyses). A description of muon identification and triggers is given in the text.
Summary
We have presented efficiencies of muon reconstruction, identification, and triggering, as well as measurements of the dimuon mass scale and resolution of the CMS detector. The efficiencies were estimated using the data-driven tag-and-probe technique. Mass scale and resolution were derived through fits to the invariant mass spectra of $ \mathrm{J}/\psi $ and Z boson resonances. We have extended previous studies of the muon performance in pp collisions to the heavy ion environment using PbPb data at $ \sqrt{\smash[b]{s_{_{\mathrm{NN}}}}}= $ 5.02 TeV and pPb data at $ \sqrt{\smash[b]{s_{_{\mathrm{NN}}}}}= $ 8.16 TeV. All the results were also measured in pp data at $ \sqrt{s}= $ 5.02 TeV for comparison across all collision systems as a function of the charged particle multiplicity, $ N_{\mathrm{tracks}} $. The efficiencies are high (typically above 90%) in all cases, even at extremely high occupancy. In the low-$ p_{\mathrm{T}} $ region, the muon-identification efficiency is comparable between pp and PbPb collisions, except in the region of highest occupancy at very low $ p_{\mathrm{T}} $ ($ {<} $ 5 GeV) and forward pseudorapidity ($ |\eta| > $ 2). This drop in efficiency is expected because the high number of tracks in the inner parts of the detector complicates the matching of tracks between the muon chambers and the tracker. In the high-$ p_{\mathrm{T}} $ region, we observe a slight drop (1-2%) in the muon-identification efficiency in the most central PbPb events at multiplicities that are unattainable in pPb or pp events. A slight decrease ($ {\approx}3% $) in the reconstruction efficiency at high occupancies is also observed. Additionally, the trigger efficiency decreases in the most central PbPb events. A relative reduction of $ {\approx}8% $ in the trigger efficiency occurs between the lowest and highest $ N_{\mathrm{tracks}} $ bins in PbPb collisions. This reduction is more pronounced than the corresponding decrease in the muon identification and reconstruction efficiencies, suggesting that the CMS single-muon trigger is more sensitive to detector occupancy. In most cases, the efficiencies calculated using Monte Carlo simulations capture the trends seen in data, indicating that the main features are contained in the detector simulation. In a few instances, the MC efficiencies overestimate those obtained from collision data (by up to 4 percentage points), highlighting the need for independent techniques of efficiency estimation based directly on collision data. The excellent muon performance of the CMS detector has made possible a robust muon and dimuon program in the heavy ion environment, leading to many muon-based measurements, where some examples include heavy quarkonia, heavy-flavor mesons [41,3,42,43,44,45,46,47,48,49,50,51]; and electroweak bosons [33,52,31,53,32].
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1706.05984
49 CMS Collaboration Measurement of prompt and nonprompt charmonium suppression in PbPb collisions at 5.02 $ \,\text {Te}\text {V} $ EPJC 78 (2018) 509 CMS-HIN-16-025
1712.08959
50 CMS Collaboration Measurement of nuclear modification factors of $ \Upsilon $(1S), $ \Upsilon $(2S), and $ \Upsilon $(3S) mesons in PbPb collisions at $ \sqrt{\smash[b]{s_{_{\mathrm{NN}}}}} = $ 5.02 TeV PLB 790 (2019) 270 CMS-HIN-16-023
1805.09215
51 CMS Collaboration Measurement of the azimuthal anisotropy of $ \Upsilon(1S) $ and $ \Upsilon(2S) $ mesons in PbPb collisions at $ \sqrt{\smash[b]{s_{_{\mathrm{NN}}}}} = $ 5.02 TeV PLB 819 (2021) 136385 CMS-HIN-19-002
2006.07707
52 CMS Collaboration Observation of the $ B_c^+ $ meson in Pb-Pb and pp collisions at $ \sqrt{\smash[b]{s_{_{\mathrm{NN}}}}} =$ 5.02 TeV and measurement of its nuclear modification factor PRL 128 (2022) 252301 CMS-HIN-20-004
2201.02659
53 CMS Collaboration Study of jet quenching with $ Z+\text{jet} $ correlations in PbPb and pp collisions at $ {\sqrt{\smash[b]{s_{_{\mathrm{NN}}}}}=5.02}\,\mathrm{TeV} $ PRL 119 (2017) 082301 CMS-HIN-15-013
1702.01060
54 CMS Collaboration Study of Z boson production in PbPb collisions at $ \sqrt{\smash[b]{s_{_{\mathrm{NN}}}}} $ = 2.76 TeV PRL 106 (2011) 212301 CMS-HIN-10-003
1102.5435
Compact Muon Solenoid
LHC, CERN