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Compact Muon Solenoid
LHC, CERN

CMS-HIN-23-011 ; CERN-EP-2024-057
Overview of high-density QCD studies with the CMS experiment at the LHC
Accepted for publication in Physics Reports
Abstract: The heavy ion (HI) physics program has proven to be an essential part of the overall physics program at the Large Hadron Collider at CERN. Its main purpose has been to provide a detailed characterization of the quark-gluon plasma (QGP), a deconfined state of quarks and gluons created in high-energy nucleus-nucleus collisions. From the start of the LHC HI program with lead-lead collisions, the CMS Collaboration has performed measurements using additional data sets in different center-of-mass energies with xenon-xenon, proton-lead, and proton-proton collisions. A broad collection of observables related to high-density quantum chromodynamics (QCD), precision quantum electrodynamics (QED), and even novel searches of phenomena beyond the standard model (BSM) have been studied. Major advances toward understanding the macroscopic and microscopic QGP properties were achieved at the highest temperature reached in the laboratory and for vanishingly small values of the baryon chemical potential. This article summarizes key QCD, QED, as well as BSM physics, results of the CMS HI program for the LHC Runs 1 (2010-2013) and 2 (2015-2018). It reviews findings on the partonic content of nuclei and properties of the QGP and describes the surprising QGP-like effects in collision systems smaller than lead-lead or xenon-xenon. In addition, it outlines the scientific case of using ultrarelativistic HI collisions in the coming decades to characterize the QGP with unparalleled precision and to probe novel fundamental physics phenomena.
Figures & Tables Summary References CMS Publications
Figures

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Figure 1:
Integrated luminosity delivered to the CMS experiment with PbPb and pPb collisions at $ \sqrt{\smash[b]{s_{_{\mathrm{NN}}}}}= $ 5.02 [45] and 8.16 TeV [46], respectively, as a function of time during the LHC Run 2 period. The years of data collection shown correspond to 2015 (purple), 2016 (orange), and 2018 (navy blue). This plot shows the proton-equivalent luminosity, i.e.,, the values for the PbPb data have been scaled by $ A^2=208^2 $ and the values for the pPb data by $ A= $ 208.

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Figure 2:
A simplified sketch of the acceptance in $ \eta $ and $ \phi $ for the tracking, calorimetry (ECAL, HCAL, CASTOR, and ZDC) and muon identification (``Muons'') components of the CMS detector. In the lower section, the central elements (that is, excluding ZDC and CASTOR) are arranged based on their proximity to the beam, with the tracker being the closest element of the central detectors, and the muon detectors positioned farthest away. The size of a jet cone with $ R = $ 0.5 (to be discussed in Section 2.10) is also depicted for illustration. (Figure adapted from Ref. [4].)

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Figure 3:
An almost head-on collision event selected from the 2018 PbPb data set. The yellow lines show the huge number of charged-particle tracks and the two cones show nearly back-to-back candidate jets originating from bottom quarks. (Figure adapted from Ref. [76].)

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Figure 4:
Left: Efficiency for the 50 GeV single-jet trigger as a function of the corrected leading jet transverse momentum in PbPb collisions at 2.76 TeV. Right: Efficiency for the 15 GeV photon trigger as a function of the corrected photon transverse energy in PbPb collisions at 2.76 TeV. (Figures adapted from Refs. [103,104].)

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Figure 4-a:
Left: Efficiency for the 50 GeV single-jet trigger as a function of the corrected leading jet transverse momentum in PbPb collisions at 2.76 TeV. Right: Efficiency for the 15 GeV photon trigger as a function of the corrected photon transverse energy in PbPb collisions at 2.76 TeV. (Figures adapted from Refs. [103,104].)

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Figure 4-b:
Left: Efficiency for the 50 GeV single-jet trigger as a function of the corrected leading jet transverse momentum in PbPb collisions at 2.76 TeV. Right: Efficiency for the 15 GeV photon trigger as a function of the corrected photon transverse energy in PbPb collisions at 2.76 TeV. (Figures adapted from Refs. [103,104].)

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Figure 5:
The L1 and HLT trigger efficiencies for the high-multiplicity triggers as functions of $ N_\text{trk}^\text{offline} $ for 5.02 TeV pPb collision data taking in the year of 2013. (Figure adapted from Ref. [105].)

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Figure 5-a:
The L1 and HLT trigger efficiencies for the high-multiplicity triggers as functions of $ N_\text{trk}^\text{offline} $ for 5.02 TeV pPb collision data taking in the year of 2013. (Figure adapted from Ref. [105].)

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Figure 5-b:
The L1 and HLT trigger efficiencies for the high-multiplicity triggers as functions of $ N_\text{trk}^\text{offline} $ for 5.02 TeV pPb collision data taking in the year of 2013. (Figure adapted from Ref. [105].)

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Figure 6:
Charged hadron multiplicity density evaluated at $ \eta= $ 0 ($ \mathrm{d} N_{\text{ch}} / \mathrm{d} \eta |_{\eta=0} $) as a function of centrality class in PbPb collisions at $ \sqrt{\smash[b]{s_{_{\mathrm{NN}}}}}= $ 2.76 TeV from the CMS (solid circles) and ALICE [116] (open squares) experiments. The inner green band shows the measurement uncertainties affecting the scale of the measured distribution, while the outer grey band represents the full systematic uncertainty, i.e.,, affecting both the scale and the slope. (Figure adapted from Ref. [106].)

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Figure 7:
Muon reconstruction and identification efficiencies as functions of the simulated muon pseudorapidity and $ p_{\mathrm{T}} $ in pPb (left) and PbPb (right) collisions. The lines delimit the acceptance regions used for physics analyses: the red curves for measurements not relying on a dedicated muon trigger while the green ones are for analyses using the muon trigger information, i.e.,, for most of the quarkonia results presented in this paper. (Figure adapted from Ref. [125].)

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Figure 8:
Isolated photon detection efficiency in $ |\eta| < $ 1.44 as a function of $ E_{\mathrm{T}}^{\gamma} $ obtained from MC simulations. Left: PbPb collisions in the 0-10% centrality range. Right: pp collisions. Both the PbPb and pp collisions are at 5.02 TeV. The different colors represent efficiencies reached for successive application of the listed selection criteria: ratio of HCAL over ECAL energies $ H/E < $ 0.1, EM shower shape variable $ \sigma_{\eta\eta} < $ 0.01, isolation variable $ I < $ 1 GeV, and electron rejection criterion. (Figure adapted from Ref. [131].)

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Figure 9:
Left: Distribution of PF pseudotowers in $ \eta$-$\phi $ in a single central (top 3%) event in PbPb collisions before subtraction, with the $ z $ axis showing the corresponding tower energy per unit tower area. Right: The same event after full subtraction with flow modulation is applied. (Figure adapted from Ref. [134].)

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Figure 10:
Distribution of $ \rho $, the UE energy per unit area, as a function of centrality, found using the central-$ \eta $ strip of PF pseudotowers. (Figure adapted from Ref. [134].)

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Figure 11:
Performance of jet reconstruction in the HI environment for jet distance parameters of $ R= $ 0.2 (left) and $ R= $ 1.0 (right). The jet energy scale is shown in the upper panels, while the jet energy resolution is plotted in the lower panels. (Figure adapted from Ref. [139].)

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Figure 12:
Multiplicity distribution of the b-tagged jets in a top quark pair enriched final state using PbPb collisions. The distribution of the main background is taken from the data. Backgrounds and $ \mathrm{t} \overline{\mathrm{t}} $ signal are shown with the filled histograms and data are shown with the markers. The vertical bars on the markers represent the statistical uncertainties in data. The hatched regions show the uncertainties in the sum of $ \mathrm{t} \overline{\mathrm{t}} $ signal and backgrounds. The lower panel displays the ratio of the data to the predictions with bands representing the uncertainties in the predictions. (Figure adapted from Ref. [146].)

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Figure 13:
The differential cross sections (left) and forward-backward ratio for decay muon yields (right) for the process $ \mathrm{W^+}\to\mu^{+}\nu_{\!\mu} $ versus muon pseudorapidity in the center-of-mass frame ($ \eta_{\mathrm{CM}} $). Black horizontal lines above and below the data points represent the quadrature sum of statistical and systematic uncertainties, whereas the vertical bars show the statistical uncertainties only. The NLO calculations with CT14 PDF, and CT14+nCTEQ15 and CT14+EPPS16 nPDFs are displayed, including their 68% confidence interval uncertainty bands. The ratios of data, CT14+nCTEQ15 and CT14+EPPS16 with respect to CT14 are shown in the lower left panel. A global integrated luminosity uncertainty of 3.5% in the cross section is not shown. (Figure compiled from Ref. [150].)

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Figure 13-a:
The differential cross sections (left) and forward-backward ratio for decay muon yields (right) for the process $ \mathrm{W^+}\to\mu^{+}\nu_{\!\mu} $ versus muon pseudorapidity in the center-of-mass frame ($ \eta_{\mathrm{CM}} $). Black horizontal lines above and below the data points represent the quadrature sum of statistical and systematic uncertainties, whereas the vertical bars show the statistical uncertainties only. The NLO calculations with CT14 PDF, and CT14+nCTEQ15 and CT14+EPPS16 nPDFs are displayed, including their 68% confidence interval uncertainty bands. The ratios of data, CT14+nCTEQ15 and CT14+EPPS16 with respect to CT14 are shown in the lower left panel. A global integrated luminosity uncertainty of 3.5% in the cross section is not shown. (Figure compiled from Ref. [150].)

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Figure 13-b:
The differential cross sections (left) and forward-backward ratio for decay muon yields (right) for the process $ \mathrm{W^+}\to\mu^{+}\nu_{\!\mu} $ versus muon pseudorapidity in the center-of-mass frame ($ \eta_{\mathrm{CM}} $). Black horizontal lines above and below the data points represent the quadrature sum of statistical and systematic uncertainties, whereas the vertical bars show the statistical uncertainties only. The NLO calculations with CT14 PDF, and CT14+nCTEQ15 and CT14+EPPS16 nPDFs are displayed, including their 68% confidence interval uncertainty bands. The ratios of data, CT14+nCTEQ15 and CT14+EPPS16 with respect to CT14 are shown in the lower left panel. A global integrated luminosity uncertainty of 3.5% in the cross section is not shown. (Figure compiled from Ref. [150].)

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Figure 14:
Differential cross section for the Drell-Yan process measured in the muon channel as a function of the dimuon invariant mass (upper) and the forward-backward ratios for 15 $ < m_{\mu^{+}\mu^{-}} < $ 60 GeV (lower left) and 60 $ < m_{\mu^{+}\mu^{-}} < $ 120 GeV (lower right). Error bars represent the total measurement uncertainty. Theory predictions from the POWHEG NLO generator using the CT14 PDF (blue), or the CT14+EPPS16 (red) or CT14+nCTEQ15WZ (green) nPDF sets are shown. The standard deviation of the nPDF uncertainties are shown by the boxes. Ratios of theory predictions over data are shown in the lower panels. (Figures adapted from Ref. [161].)

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Figure 14-a:
Differential cross section for the Drell-Yan process measured in the muon channel as a function of the dimuon invariant mass (upper) and the forward-backward ratios for 15 $ < m_{\mu^{+}\mu^{-}} < $ 60 GeV (lower left) and 60 $ < m_{\mu^{+}\mu^{-}} < $ 120 GeV (lower right). Error bars represent the total measurement uncertainty. Theory predictions from the POWHEG NLO generator using the CT14 PDF (blue), or the CT14+EPPS16 (red) or CT14+nCTEQ15WZ (green) nPDF sets are shown. The standard deviation of the nPDF uncertainties are shown by the boxes. Ratios of theory predictions over data are shown in the lower panels. (Figures adapted from Ref. [161].)

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Figure 14-b:
Differential cross section for the Drell-Yan process measured in the muon channel as a function of the dimuon invariant mass (upper) and the forward-backward ratios for 15 $ < m_{\mu^{+}\mu^{-}} < $ 60 GeV (lower left) and 60 $ < m_{\mu^{+}\mu^{-}} < $ 120 GeV (lower right). Error bars represent the total measurement uncertainty. Theory predictions from the POWHEG NLO generator using the CT14 PDF (blue), or the CT14+EPPS16 (red) or CT14+nCTEQ15WZ (green) nPDF sets are shown. The standard deviation of the nPDF uncertainties are shown by the boxes. Ratios of theory predictions over data are shown in the lower panels. (Figures adapted from Ref. [161].)

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Figure 14-c:
Differential cross section for the Drell-Yan process measured in the muon channel as a function of the dimuon invariant mass (upper) and the forward-backward ratios for 15 $ < m_{\mu^{+}\mu^{-}} < $ 60 GeV (lower left) and 60 $ < m_{\mu^{+}\mu^{-}} < $ 120 GeV (lower right). Error bars represent the total measurement uncertainty. Theory predictions from the POWHEG NLO generator using the CT14 PDF (blue), or the CT14+EPPS16 (red) or CT14+nCTEQ15WZ (green) nPDF sets are shown. The standard deviation of the nPDF uncertainties are shown by the boxes. Ratios of theory predictions over data are shown in the lower panels. (Figures adapted from Ref. [161].)

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Figure 15:
Top quark pair production cross section in pp and pPb collisions as a function of the center-of-mass energy per nucleon pair; the CMS results at different center-of-mass energies in the dilepton and semileptonic channels. The measurements are compared to the NNLO+NNLL QCD theory predictions [167,168,169]. (Figure adapted from Ref. [166].)

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Figure 16:
The ratio of the dijet $ \eta $ spectra for pPb and pp data in a selection of $ p_\mathrm{T}^{\text{ave}} $ ranges. Theoretical predictions are from the NLO pQCD calculations of DSSZ [170] and EPS09 [171] are shown. Red boxes and bars indicate the systematic and statistical uncertainties in data, respectively. Green and blue boxes represent nPDF uncertainties. (Figure adapted from Ref. [172].)

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Figure 17:
The ratio of theoretical predictions to CMS data for the ratio of the pPb to pp dijet $ \eta $ spectra for 115 $ < p_\mathrm{T}^{\text{ave}} < $ 150 GeV. Theoretical predictions are from the NLO pQCD calculations of DSSZ [170], EPS09 [171], nCTEQ15 [154], and EPPS16 [153] nPDFs, using CT14 [152] as the baseline PDFs. Red boxes indicate the total uncertainties in data and the error bars on the points represent nPDF uncertainties. (Figure adapted from Ref. [172].)

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Figure 18:
The photon $ R_{\mathrm{AA}} $ versus photon $ E_{\mathrm{T}}^{\gamma} $ in four centrality ranges for 5.02 TeV PbPb collisions. The error bars indicate the statistical uncertainties and the systematic uncertainty, excluding $ T_{\mathrm{AA}} $ uncertainties, are shown by the colored boxes. The $ T_{\mathrm{AA}} $ uncertainties are common to all points in a given centrality range, and are indicated by a gray box on the left side of each panel. Similarly, a 2.3% pp collision integrated luminosity uncertainty is shown with a brown box. (Figure adapted from Ref. [131].)

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Figure 19:
Normalized yields (per $ \mathrm{NN} $ integrated luminosity and per unit rapidity) of $ \mathrm{W}\to\mu\nu $ production in 2.76 TeV PbPb collisions, shown for inclusive W (red), $ \mathrm{W^+} $ (violet), and $ \mathrm{W^-} $ (green). The open symbols at $ N_\text{part}= $ 120 represent values for MB collisions. At $ N_\text{part} = $ 2 the corresponding cross sections, divided by the muon pseudorapidity acceptance $ \Delta\eta $, for pp collisions at the same energy are displayed. For clarity the $ \mathrm{W^+} $ and $ \mathrm{W^-} $ points are slightly shifted horizontally. Error bars represent statistical uncertainties and horizontal lines show systematic uncertainties. (Figure adapted from Ref. [177].)

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Figure 20:
The $ T_{\mathrm{AA}} $-normalized yields of Z bosons versus centrality for 5.02 TeV PbPb collisions. The error bars, open boxes, and solid gray boxes represent the statistical, systematic, and $ T_{\mathrm{AA}} $ uncertainties, respectively. The value of the 0-90% data (pink) and the scaled HG-PYTHIA model (green) are displayed. The width of the bands represents the contribution from the total 0-90% data point uncertainty. (Figure adapted from Ref. [179].)

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Figure 21:
A comparison of results from the ALICE [182], ATLAS [181], and CMS [179] Collaborations for Z and W production in PbPb collisions. The data have been normalized so that the most central data point equals unity to enable comparison of the shape of the distribution. The left (right) panel shows data for $ \mathrm{W^-} $ ($ \mathrm{W^+} $) and Z bosons. For the ATLAS W data, the error bars represent the combined statistical and systematic uncertainty, while the boxes show $ T_{\mathrm{AA}} $-related uncertainties. For all other data sets, the error bars display statistical uncertainties and the boxes show combined systematic and $ T_{\mathrm{AA}} $ uncertainties.

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Figure 21-a:
A comparison of results from the ALICE [182], ATLAS [181], and CMS [179] Collaborations for Z and W production in PbPb collisions. The data have been normalized so that the most central data point equals unity to enable comparison of the shape of the distribution. The left (right) panel shows data for $ \mathrm{W^-} $ ($ \mathrm{W^+} $) and Z bosons. For the ATLAS W data, the error bars represent the combined statistical and systematic uncertainty, while the boxes show $ T_{\mathrm{AA}} $-related uncertainties. For all other data sets, the error bars display statistical uncertainties and the boxes show combined systematic and $ T_{\mathrm{AA}} $ uncertainties.

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Figure 21-b:
A comparison of results from the ALICE [182], ATLAS [181], and CMS [179] Collaborations for Z and W production in PbPb collisions. The data have been normalized so that the most central data point equals unity to enable comparison of the shape of the distribution. The left (right) panel shows data for $ \mathrm{W^-} $ ($ \mathrm{W^+} $) and Z bosons. For the ATLAS W data, the error bars represent the combined statistical and systematic uncertainty, while the boxes show $ T_{\mathrm{AA}} $-related uncertainties. For all other data sets, the error bars display statistical uncertainties and the boxes show combined systematic and $ T_{\mathrm{AA}} $ uncertainties.

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Figure 22:
Forward jet differential cross section, where forward jet is in the proton-going direction, as a function of jet energy in pPb collisions at 5.02 TeV. The kinematics of the collision allows to probe the small-$ x $ wave function in the Pb nucleus with a high-$ x $ parton from the proton. This measurement is compared with different Monte Carlo event generators, EPOS-LHC [118], HIJING [119], and QGSJETII-04 [189] (left) and predictions of the KATIE [190] and AAMQS [191] saturation models (right). (Figures adapted from Ref. [192].)

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Figure 22-a:
Forward jet differential cross section, where forward jet is in the proton-going direction, as a function of jet energy in pPb collisions at 5.02 TeV. The kinematics of the collision allows to probe the small-$ x $ wave function in the Pb nucleus with a high-$ x $ parton from the proton. This measurement is compared with different Monte Carlo event generators, EPOS-LHC [118], HIJING [119], and QGSJETII-04 [189] (left) and predictions of the KATIE [190] and AAMQS [191] saturation models (right). (Figures adapted from Ref. [192].)

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Figure 22-b:
Forward jet differential cross section, where forward jet is in the proton-going direction, as a function of jet energy in pPb collisions at 5.02 TeV. The kinematics of the collision allows to probe the small-$ x $ wave function in the Pb nucleus with a high-$ x $ parton from the proton. This measurement is compared with different Monte Carlo event generators, EPOS-LHC [118], HIJING [119], and QGSJETII-04 [189] (left) and predictions of the KATIE [190] and AAMQS [191] saturation models (right). (Figures adapted from Ref. [192].)

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Figure 23:
(Left) Forward jet differential cross section, where the forward jet is in the Pb-going direction, as a function of the jet energy in pPb collisions at 5.02 TeV. The kinematic properties of the collision probe the small-$ x $ wave function of the proton with a high-$ x $ parton from the Pb nucleus. The data are compared with different Monte Carlo event generators: EPOS-LHC [118], HIJING [119], and QGSJETII-04 [189]. (Right) The ratio of the inclusive jet cross sections; the numerator (denominator) of the ratio corresponds to the case where the jet is measured in the proton-going (Pb-going) direction. (Figure adapted from Ref. [192].)

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Figure 23-a:
(Left) Forward jet differential cross section, where the forward jet is in the Pb-going direction, as a function of the jet energy in pPb collisions at 5.02 TeV. The kinematic properties of the collision probe the small-$ x $ wave function of the proton with a high-$ x $ parton from the Pb nucleus. The data are compared with different Monte Carlo event generators: EPOS-LHC [118], HIJING [119], and QGSJETII-04 [189]. (Right) The ratio of the inclusive jet cross sections; the numerator (denominator) of the ratio corresponds to the case where the jet is measured in the proton-going (Pb-going) direction. (Figure adapted from Ref. [192].)

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Figure 23-b:
(Left) Forward jet differential cross section, where the forward jet is in the Pb-going direction, as a function of the jet energy in pPb collisions at 5.02 TeV. The kinematic properties of the collision probe the small-$ x $ wave function of the proton with a high-$ x $ parton from the Pb nucleus. The data are compared with different Monte Carlo event generators: EPOS-LHC [118], HIJING [119], and QGSJETII-04 [189]. (Right) The ratio of the inclusive jet cross sections; the numerator (denominator) of the ratio corresponds to the case where the jet is measured in the proton-going (Pb-going) direction. (Figure adapted from Ref. [192].)

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Figure 24:
Forward jet differential cross section, where the forward jet is in the $ \mathrm{p} $-going direction, as a function of the jet energy in pPb collisions at 5.02 TeV. The kinematics of the collision allows to probe the small-$ x $ wave function of the Pb nucleus with a high-$ x $ parton from the proton. The data points are from Ref. [193]. (Figure adapted from Ref. [192].)

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Figure 25:
The cross section in the $ {\gamma\mathrm{p}} $ center-of-mass frame $ \sigma(\gamma^{*}\mathrm{p} \to \rho(770)^0 \mathrm{p}) $ for exclusive $ \rho(770)^0 $ VM photoproduction as a function of $ W_{{\gamma\mathrm{p}}} $. CMS measurements during Run 2 extend up to $ W_{{\gamma\mathrm{p}}} = $ 1 TeV. The CMS data points are from Ref. [199]. The H1 and ZEUS data in electron-proton collisions are shown in the same panel. The data points are compared to predictions from PYTHIA8 [112] and STARLIGHT [110]. (Figure adapted from Ref. [199].)

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Figure 26:
Photoproduction cross section in the photon-proton center-of-mass frame $ \sigma(\gamma^* \mathrm{p} \to \Upsilon{\textrm{(1S)}} \mathrm{p}) $ for exclusive $ \Upsilon{\textrm{(1S)}} $ VM photoproduction as a function of $ W_{{\gamma\mathrm{p}}} $. The data are compared with different calculations with different implementations of nonlinear evolution in the parton distributions. (Figure adapted from Ref. [198].)

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Figure 27:
Differential $ \mathrm{J}/\psi $ meson photoproduction cross section as a function of rapidity in PbPb collisions at $ \sqrt{\smash[b]{s_{_{\mathrm{NN}}}}} = $ 2.76 TeV measured by ALICE [201,202] and CMS [203]. Data are compared with the leading twist [204] and the impulse approximation [204,205] predictions. The leading twist approximation is a perturbative QCD calculation that takes into account nuclear shadowing effects from multinucleon interference. (Figure adapted from Ref. [203].)

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Figure 28:
The left panel shows the correlation between energy distributions of the Minus and Plus ZDC detectors (one entry per event), while the right panel shows a multi-Gaussian function fit to the Minus ZDC energy distribution. The different ``peaks'' in the ZDC energy distribution can be assigned to different forward neutron multiplicities, the first peak is detector noise, which corresponds to no detected neutrons, the second peak can be associated with one neutron, and so on. (Figures adapted from Ref. [208].)

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Figure 29:
The differential coherent $ \mathrm{J}/\psi $ meson photoproduction cross section as a function of rapidity, in different neutron multiplicity classes (left): 0 $ \mathrm{n}0\mathrm{n} $, 0 $ \mathrm{n}\mathrm{X}\mathrm{n} $ and $ \mathrm{X}\mathrm{n}\mathrm{X}\mathrm{n} $ ($ \mathrm{X} \geq $ 1); (right): $ \mathrm{A}\mathrm{n}\mathrm{A}\mathrm{n} $ (inclusive in the number of neutrons detected in the ZDC). The small vertical bars and shaded boxes represent the statistical and systematic uncertainties, respectively. The horizontal bars represent the bin widths. Theoretical predictions from LTA weak/strong shadowing [206], color dipole models (CD_BGK, CD_BGW, and CD_IIM) [211], and STARLIGHT [110] are shown. (Figures adapted from Ref. [210].)

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Figure 29-a:
The differential coherent $ \mathrm{J}/\psi $ meson photoproduction cross section as a function of rapidity, in different neutron multiplicity classes (left): 0 $ \mathrm{n}0\mathrm{n} $, 0 $ \mathrm{n}\mathrm{X}\mathrm{n} $ and $ \mathrm{X}\mathrm{n}\mathrm{X}\mathrm{n} $ ($ \mathrm{X} \geq $ 1); (right): $ \mathrm{A}\mathrm{n}\mathrm{A}\mathrm{n} $ (inclusive in the number of neutrons detected in the ZDC). The small vertical bars and shaded boxes represent the statistical and systematic uncertainties, respectively. The horizontal bars represent the bin widths. Theoretical predictions from LTA weak/strong shadowing [206], color dipole models (CD_BGK, CD_BGW, and CD_IIM) [211], and STARLIGHT [110] are shown. (Figures adapted from Ref. [210].)

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Figure 29-b:
The differential coherent $ \mathrm{J}/\psi $ meson photoproduction cross section as a function of rapidity, in different neutron multiplicity classes (left): 0 $ \mathrm{n}0\mathrm{n} $, 0 $ \mathrm{n}\mathrm{X}\mathrm{n} $ and $ \mathrm{X}\mathrm{n}\mathrm{X}\mathrm{n} $ ($ \mathrm{X} \geq $ 1); (right): $ \mathrm{A}\mathrm{n}\mathrm{A}\mathrm{n} $ (inclusive in the number of neutrons detected in the ZDC). The small vertical bars and shaded boxes represent the statistical and systematic uncertainties, respectively. The horizontal bars represent the bin widths. Theoretical predictions from LTA weak/strong shadowing [206], color dipole models (CD_BGK, CD_BGW, and CD_IIM) [211], and STARLIGHT [110] are shown. (Figures adapted from Ref. [210].)

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Figure 30:
Total coherent $ \mathrm{J}/\psi $ meson photoproduction cross section as a function of $ W^{\mathrm{Pb}}_{\gamma\mathrm{N}} $ in PbPb UPCs at $ \sqrt{\smash[b]{s_{_{\mathrm{NN}}}}} = $ 5.02 TeV. The vertical bars and the shaded and open boxes represent the statistical, experimental, and theoretical (photon flux) uncertainties, respectively. The predictions from various theoretical calculations [204,213,214,206,215,211] are shown by the curves. (Figure adapted from Ref. [210].)

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Figure 31:
The $ (\mathrm{d}N_{\text{ch}}/\mathrm{d}\eta)/(N_\text{part}/2) $ in 2.76 TeV PbPb (Figure adapted from Ref. [106].) (left) and 5.44 TeV XeXe collisions (figure from Ref. [221]) (middle), and $ \mathrm{d}E_{\mathrm{T}}/\mathrm{d}\eta $ in 2.76 TeV PbPb collisions (figure from Ref. [222]) (right) distributions as functions of $ \eta $ in various centrality bins. The inner green band in the left panel shows the measurement uncertainties affecting the scale of the measured distribution, while the outer gray band shows the full systematic uncertainty, i.e., affecting both the scale and the slope.

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Figure 31-a:
The $ (\mathrm{d}N_{\text{ch}}/\mathrm{d}\eta)/(N_\text{part}/2) $ in 2.76 TeV PbPb (Figure adapted from Ref. [106].) (left) and 5.44 TeV XeXe collisions (figure from Ref. [221]) (middle), and $ \mathrm{d}E_{\mathrm{T}}/\mathrm{d}\eta $ in 2.76 TeV PbPb collisions (figure from Ref. [222]) (right) distributions as functions of $ \eta $ in various centrality bins. The inner green band in the left panel shows the measurement uncertainties affecting the scale of the measured distribution, while the outer gray band shows the full systematic uncertainty, i.e., affecting both the scale and the slope.

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Figure 31-b:
The $ (\mathrm{d}N_{\text{ch}}/\mathrm{d}\eta)/(N_\text{part}/2) $ in 2.76 TeV PbPb (Figure adapted from Ref. [106].) (left) and 5.44 TeV XeXe collisions (figure from Ref. [221]) (middle), and $ \mathrm{d}E_{\mathrm{T}}/\mathrm{d}\eta $ in 2.76 TeV PbPb collisions (figure from Ref. [222]) (right) distributions as functions of $ \eta $ in various centrality bins. The inner green band in the left panel shows the measurement uncertainties affecting the scale of the measured distribution, while the outer gray band shows the full systematic uncertainty, i.e., affecting both the scale and the slope.

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Figure 31-c:
The $ (\mathrm{d}N_{\text{ch}}/\mathrm{d}\eta)/(N_\text{part}/2) $ in 2.76 TeV PbPb (Figure adapted from Ref. [106].) (left) and 5.44 TeV XeXe collisions (figure from Ref. [221]) (middle), and $ \mathrm{d}E_{\mathrm{T}}/\mathrm{d}\eta $ in 2.76 TeV PbPb collisions (figure from Ref. [222]) (right) distributions as functions of $ \eta $ in various centrality bins. The inner green band in the left panel shows the measurement uncertainties affecting the scale of the measured distribution, while the outer gray band shows the full systematic uncertainty, i.e., affecting both the scale and the slope.

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Figure 32:
Average $ \mathrm{d}N_{\text{ch}}/\mathrm{d}\eta $\ at midrapidity normalised by $ \langle N_\text{part}\rangle $, shown as a function of $ \langle N_\text{part}\rangle $ (left) and $ \langle N_\text{part}\rangle/2A $ (right), where $ A $ is the mass number of the nuclei. (Figures adapted from Ref. [221].)

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Figure 32-a:
Average $ \mathrm{d}N_{\text{ch}}/\mathrm{d}\eta $\ at midrapidity normalised by $ \langle N_\text{part}\rangle $, shown as a function of $ \langle N_\text{part}\rangle $ (left) and $ \langle N_\text{part}\rangle/2A $ (right), where $ A $ is the mass number of the nuclei. (Figures adapted from Ref. [221].)

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Figure 32-b:
Average $ \mathrm{d}N_{\text{ch}}/\mathrm{d}\eta $\ at midrapidity normalised by $ \langle N_\text{part}\rangle $, shown as a function of $ \langle N_\text{part}\rangle $ (left) and $ \langle N_\text{part}\rangle/2A $ (right), where $ A $ is the mass number of the nuclei. (Figures adapted from Ref. [221].)

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Figure 33:
Normalized charged-particle pseudorapidity (left, figure adapted from Ref. [106]) and transverse energy density (right, figure adapted from Ref. [222]) at $ \eta= $ 0 as functions of center-of-mass energy, from various experiments. The fits to power-law functions are shown by lines.

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Figure 33-a:
Normalized charged-particle pseudorapidity (left, figure adapted from Ref. [106]) and transverse energy density (right, figure adapted from Ref. [222]) at $ \eta= $ 0 as functions of center-of-mass energy, from various experiments. The fits to power-law functions are shown by lines.

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Figure 33-b:
Normalized charged-particle pseudorapidity (left, figure adapted from Ref. [106]) and transverse energy density (right, figure adapted from Ref. [222]) at $ \eta= $ 0 as functions of center-of-mass energy, from various experiments. The fits to power-law functions are shown by lines.

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Figure 34:
The 2D (left) and 1D $ \Delta\phi $\ (right) two-particle correlation functions for 1 $ < p_{\mathrm{T}} < $ 3 GeV in 0-0.2% central PbPb collisions at $ \sqrt{\smash[b]{s_{_{\mathrm{NN}}}}} = $ 2.76 TeV. (Figures adapted from Ref. [233].)

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Figure 35:
Left: the $ v_2 $ to $ v_6 $ values as functions of $ p_{\mathrm{T}} $ in 0-0.2% central PbPb collisions at $ \sqrt{\smash[b]{s_{_{\mathrm{NN}}}}} = $ 2.76 TeV. Right: Comparison of $ p_{\mathrm{T}} $-integrated (0.3-3.0 GeV) $ v_{n} $ data with VISH2+1D hydrodynamic calculations for Glauber initial condition with $ \eta/s= $ 0.08 (blue) and MC-KLN initial condition with $ \eta/s= $ 0.2 (green), in 0-0.2% central PbPb collisions at $ \sqrt{\smash[b]{s_{_{\mathrm{NN}}}}} = $ 2.76 TeV. Error bars denote the statistical uncertainties, while the shaded color bands correspond to the systematic uncertainties. (Figures adapted from Ref. [233].)

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Figure 35-a:
Left: the $ v_2 $ to $ v_6 $ values as functions of $ p_{\mathrm{T}} $ in 0-0.2% central PbPb collisions at $ \sqrt{\smash[b]{s_{_{\mathrm{NN}}}}} = $ 2.76 TeV. Right: Comparison of $ p_{\mathrm{T}} $-integrated (0.3-3.0 GeV) $ v_{n} $ data with VISH2+1D hydrodynamic calculations for Glauber initial condition with $ \eta/s= $ 0.08 (blue) and MC-KLN initial condition with $ \eta/s= $ 0.2 (green), in 0-0.2% central PbPb collisions at $ \sqrt{\smash[b]{s_{_{\mathrm{NN}}}}} = $ 2.76 TeV. Error bars denote the statistical uncertainties, while the shaded color bands correspond to the systematic uncertainties. (Figures adapted from Ref. [233].)

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Figure 35-b:
Left: the $ v_2 $ to $ v_6 $ values as functions of $ p_{\mathrm{T}} $ in 0-0.2% central PbPb collisions at $ \sqrt{\smash[b]{s_{_{\mathrm{NN}}}}} = $ 2.76 TeV. Right: Comparison of $ p_{\mathrm{T}} $-integrated (0.3-3.0 GeV) $ v_{n} $ data with VISH2+1D hydrodynamic calculations for Glauber initial condition with $ \eta/s= $ 0.08 (blue) and MC-KLN initial condition with $ \eta/s= $ 0.2 (green), in 0-0.2% central PbPb collisions at $ \sqrt{\smash[b]{s_{_{\mathrm{NN}}}}} = $ 2.76 TeV. Error bars denote the statistical uncertainties, while the shaded color bands correspond to the systematic uncertainties. (Figures adapted from Ref. [233].)

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Figure 36:
Representative final unfolded $ p(v_2) $ distributions (closed black circles) in three centrality bins (15-20%, 30-35%, and 55-60%). Respective observed $ p(v_2^\text{obs}) $ distributions (open black squares) are shown to illustrate the statistical resolution present in each centrality bin prior to unfolding. Distributions are fitted with Bessel-Gaussian and elliptic power functions to infer information on the underlying $ p(\varepsilon_2) $ distributions. (Figure adapted from Ref. [235].)

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Figure 37:
Centrality dependence of the $ v_2 $, $ v_3 $, and $ v_4 $ harmonic coefficients from two-particle correlations method for 0.3 $ < p_{\mathrm{T}} < $ 3.0 GeV for $ \mathrm{Xe}\mathrm{Xe} $ collisions at $ \sqrt{\smash[b]{s_{_{\mathrm{NN}}}}}= $ 5.44 TeV and PbPb collisions at 5.02 TeV. The lower panels show the ratio of the results for the two systems. Theoretical predictions from Ref. [243] are compared to the data. The model calculation is done for the $ p_{\mathrm{T}} $ range 0.2 $ < p_{\mathrm{T}} < $ 5.0 GeV. (Figure adapted from Ref. [244].)

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Figure 38:
The $ p_{\mathrm{T}} $-dependent factorization ratios, $ r_2 $ and $ r_3 $, as functions of event multiplicity in pPb and PbPb collisions. The lines represent different hydrodynamics calculations. (Figure adapted from Ref. [234].)

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Figure 39:
The $ p_{\mathrm{T}} $-dependent factorization ratios, $ r_2(p_{\mathrm{T}}) $, in very central (0-0.2% centrality) PbPb collisions. The lines represent hydrodynamics calculations for different initial conditions and different values of $ \eta/s $. (Figure adapted from Ref. [234].)

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Figure 40:
Left: illustration of flow event plane decorrelations as functions of rapidity in the wounded nucleon picture (or ``torqued QGP fireball'') [249] and 3D color glass condensate model [250]. Right: measurement of elliptic flow decorrelations as functions of pseudorapidity in 0-5% central PbPb collisions at 2.76 TeV from CMS [234], with comparison to theoretical calculations [249,250].

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Figure 41:
The $ {F}^{{\eta}}_{\mathrm{n}} $ parameter as a function of event multiplicity in PbPb collisions at $ \sqrt{\smash[b]{s_{_{\mathrm{NN}}}}}= $ 2.76 TeV for $ n= $ 2-4 and pPb collisions at $ \sqrt{\smash[b]{s_{_{\mathrm{NN}}}}} = $ 5.02 TeV for $ n= $ 2. (Figure adapted from Ref. [234].)

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Figure 42:
Nonlinear-response coefficients, $ \chi_{422} $, $ \chi_{523} $, $ \chi_{6222} $, $ \chi_{633} $, and $ \chi_{7223} $ at 2.76 and 5.02 TeV, as functions of centrality. The results are compared with predictions from a hydrodynamics $ + $ hadronic cascade hybrid approach with the IP-Glasma initial conditions using $ \eta/s = $ 0.095 [257] at 5.02 TeV and from iEBE-VISHNU hydrodynamics with the KLN initial conditions using $ \eta/s = $ 0, 0.08, and 0.2 [252] at 2.76 TeV. (Figure adapted from Ref. [258].)

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Figure 43:
Left: Illustration of a typical BEC as functions of $ q_\text{inv} $, for pp collisions at 13 TeV, for opposite-sign pairs (no BEC), used to estimate the background contribution, and for same-sign pairs, together with the fits to both cases. (Figure adapted from Ref. [268].) Middle: Results for femtoscopic correlations of unidentified charged hadrons from pp collisions at various LHC energies and in different multiplicity ranges. (Figures adapted from Refs. [266,267,268].) Right: The plot shows results for identified pions (filled markers) and kaons (open markers) for different colliding systems and at several LHC energies. The error bars correspond to the statistical uncertainties, the colored boxes to the systematic uncertainties. The lines are cubic spline interpolations, added to guide the eye. (Figure adapted from Ref. [267].)

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Figure 43-a:
Left: Illustration of a typical BEC as functions of $ q_\text{inv} $, for pp collisions at 13 TeV, for opposite-sign pairs (no BEC), used to estimate the background contribution, and for same-sign pairs, together with the fits to both cases. (Figure adapted from Ref. [268].) Middle: Results for femtoscopic correlations of unidentified charged hadrons from pp collisions at various LHC energies and in different multiplicity ranges. (Figures adapted from Refs. [266,267,268].) Right: The plot shows results for identified pions (filled markers) and kaons (open markers) for different colliding systems and at several LHC energies. The error bars correspond to the statistical uncertainties, the colored boxes to the systematic uncertainties. The lines are cubic spline interpolations, added to guide the eye. (Figure adapted from Ref. [267].)

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Figure 43-b:
Left: Illustration of a typical BEC as functions of $ q_\text{inv} $, for pp collisions at 13 TeV, for opposite-sign pairs (no BEC), used to estimate the background contribution, and for same-sign pairs, together with the fits to both cases. (Figure adapted from Ref. [268].) Middle: Results for femtoscopic correlations of unidentified charged hadrons from pp collisions at various LHC energies and in different multiplicity ranges. (Figures adapted from Refs. [266,267,268].) Right: The plot shows results for identified pions (filled markers) and kaons (open markers) for different colliding systems and at several LHC energies. The error bars correspond to the statistical uncertainties, the colored boxes to the systematic uncertainties. The lines are cubic spline interpolations, added to guide the eye. (Figure adapted from Ref. [267].)

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Figure 43-c:
Left: Illustration of a typical BEC as functions of $ q_\text{inv} $, for pp collisions at 13 TeV, for opposite-sign pairs (no BEC), used to estimate the background contribution, and for same-sign pairs, together with the fits to both cases. (Figure adapted from Ref. [268].) Middle: Results for femtoscopic correlations of unidentified charged hadrons from pp collisions at various LHC energies and in different multiplicity ranges. (Figures adapted from Refs. [266,267,268].) Right: The plot shows results for identified pions (filled markers) and kaons (open markers) for different colliding systems and at several LHC energies. The error bars correspond to the statistical uncertainties, the colored boxes to the systematic uncertainties. The lines are cubic spline interpolations, added to guide the eye. (Figure adapted from Ref. [267].)

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Figure 44:
Left: Results for $ R_\text{inv} $ are shown as a function of $ k_{\mathrm{T}} $ for pp collisions at different energies and multiplicity ranges. (Figures adapted from Refs. [267,268].) Right: Similarly, $ R_\text{inv} $ values versus $ k_{\mathrm{T}} $ are shown for pPb collisions at 5.02 TeV. The error bars correspond to the statistical uncertainties, the colored boxes to the systematic uncertainties. The lines are cubic spline interpolations, added to guide the eye. (Figure adapted from Ref. [267].)

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Figure 44-a:
Left: Results for $ R_\text{inv} $ are shown as a function of $ k_{\mathrm{T}} $ for pp collisions at different energies and multiplicity ranges. (Figures adapted from Refs. [267,268].) Right: Similarly, $ R_\text{inv} $ values versus $ k_{\mathrm{T}} $ are shown for pPb collisions at 5.02 TeV. The error bars correspond to the statistical uncertainties, the colored boxes to the systematic uncertainties. The lines are cubic spline interpolations, added to guide the eye. (Figure adapted from Ref. [267].)

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Figure 44-b:
Left: Results for $ R_\text{inv} $ are shown as a function of $ k_{\mathrm{T}} $ for pp collisions at different energies and multiplicity ranges. (Figures adapted from Refs. [267,268].) Right: Similarly, $ R_\text{inv} $ values versus $ k_{\mathrm{T}} $ are shown for pPb collisions at 5.02 TeV. The error bars correspond to the statistical uncertainties, the colored boxes to the systematic uncertainties. The lines are cubic spline interpolations, added to guide the eye. (Figure adapted from Ref. [267].)

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Figure 45:
Left: The femtoscopic Bertsch-Pratt radius components in different directions, ($ R_\text{S} $, $ R_\text{L} $, $ R_\text{O} $), are shown as functions of multiplicity for charged hadrons from pp collisions at 7 TeV. Middle: The three variables are shown for pions from the pPb and PbPb systems at 2.76 TeV and 5.02 TeV, respectively. The lines are cubic spline interpolations, added to guide the eye. A similar tendency of increasing radius parameters with multiplicity is seen in each of the three directions, for all cases. Right: The variation of these components with $ k_{\mathrm{T}} $ is also shown for charged hadrons from pp collisions at 7 TeV. (All three figures were adapted from Ref. [267]).

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Figure 45-a:
Left: The femtoscopic Bertsch-Pratt radius components in different directions, ($ R_\text{S} $, $ R_\text{L} $, $ R_\text{O} $), are shown as functions of multiplicity for charged hadrons from pp collisions at 7 TeV. Middle: The three variables are shown for pions from the pPb and PbPb systems at 2.76 TeV and 5.02 TeV, respectively. The lines are cubic spline interpolations, added to guide the eye. A similar tendency of increasing radius parameters with multiplicity is seen in each of the three directions, for all cases. Right: The variation of these components with $ k_{\mathrm{T}} $ is also shown for charged hadrons from pp collisions at 7 TeV. (All three figures were adapted from Ref. [267]).

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Figure 45-b:
Left: The femtoscopic Bertsch-Pratt radius components in different directions, ($ R_\text{S} $, $ R_\text{L} $, $ R_\text{O} $), are shown as functions of multiplicity for charged hadrons from pp collisions at 7 TeV. Middle: The three variables are shown for pions from the pPb and PbPb systems at 2.76 TeV and 5.02 TeV, respectively. The lines are cubic spline interpolations, added to guide the eye. A similar tendency of increasing radius parameters with multiplicity is seen in each of the three directions, for all cases. Right: The variation of these components with $ k_{\mathrm{T}} $ is also shown for charged hadrons from pp collisions at 7 TeV. (All three figures were adapted from Ref. [267]).

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Figure 45-c:
Left: The femtoscopic Bertsch-Pratt radius components in different directions, ($ R_\text{S} $, $ R_\text{L} $, $ R_\text{O} $), are shown as functions of multiplicity for charged hadrons from pp collisions at 7 TeV. Middle: The three variables are shown for pions from the pPb and PbPb systems at 2.76 TeV and 5.02 TeV, respectively. The lines are cubic spline interpolations, added to guide the eye. A similar tendency of increasing radius parameters with multiplicity is seen in each of the three directions, for all cases. Right: The variation of these components with $ k_{\mathrm{T}} $ is also shown for charged hadrons from pp collisions at 7 TeV. (All three figures were adapted from Ref. [267]).

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Figure 46:
Left: Event geometry of one peripheral PbPb and one central pPb event using MC Glauber simulation at at $ \sqrt{\smash[b]{s_{_{\mathrm{NN}}}}}\ = $ 5.02 TeV. The red and black arrows point in the direction of the reaction and participant plane angle, respectively. Right: The cosine of the relative angle between the reaction plane and the participant plane. (Figures adapted from Ref. [299].)

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Figure 47:
Left: the difference of the opposite sign (OS) and same sign (SS) three-particle correlators as a function of $ N_\text{trk}^\text{offline} $ in pPb and PbPb collisions at $ \sqrt{\smash[b]{s_{_{\mathrm{NN}}}}} = $ 5.02 TeV. (Figure adapted from Ref. [299].) Right: ratio of $ \Delta\gamma_{112} $ and $ \Delta\gamma_{123} $ to the product of $ v_{n} $ and $ \delta $ in pPb collisions for the Pb-going direction at $ \sqrt{\smash[b]{s_{_{\mathrm{NN}}}}} = $ 8.16 TeV and PbPb collisions at 5.02 TeV. (Figure adapted from Ref. [301].)

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Figure 47-a:
Left: the difference of the opposite sign (OS) and same sign (SS) three-particle correlators as a function of $ N_\text{trk}^\text{offline} $ in pPb and PbPb collisions at $ \sqrt{\smash[b]{s_{_{\mathrm{NN}}}}} = $ 5.02 TeV. (Figure adapted from Ref. [299].) Right: ratio of $ \Delta\gamma_{112} $ and $ \Delta\gamma_{123} $ to the product of $ v_{n} $ and $ \delta $ in pPb collisions for the Pb-going direction at $ \sqrt{\smash[b]{s_{_{\mathrm{NN}}}}} = $ 8.16 TeV and PbPb collisions at 5.02 TeV. (Figure adapted from Ref. [301].)

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Figure 47-b:
Left: the difference of the opposite sign (OS) and same sign (SS) three-particle correlators as a function of $ N_\text{trk}^\text{offline} $ in pPb and PbPb collisions at $ \sqrt{\smash[b]{s_{_{\mathrm{NN}}}}} = $ 5.02 TeV. (Figure adapted from Ref. [299].) Right: ratio of $ \Delta\gamma_{112} $ and $ \Delta\gamma_{123} $ to the product of $ v_{n} $ and $ \delta $ in pPb collisions for the Pb-going direction at $ \sqrt{\smash[b]{s_{_{\mathrm{NN}}}}} = $ 8.16 TeV and PbPb collisions at 5.02 TeV. (Figure adapted from Ref. [301].)

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Figure 48:
Upper limits of the fraction of $ v_2 $-independent $ \gamma_{112} $ correlator component as a function of $ N_\text{trk}^\text{offline} $ in pPb collisions at $ \sqrt{\smash[b]{s_{_{\mathrm{NN}}}}} = $ 8.16 TeV and PbPb collisions at 5.02 TeV. (Figure adapted from Ref. [301].)

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Figure 49:
Left: The normalized difference in $ v_{n} $, $ (v^{-}_{n} - v^{+}_{n})/(v^{-}_{n} + v^{+}_{n}) $, for $ n= $ 2 and 3, as a function of true event charge asymmetry for the 30-40% centrality class in PbPb collisions at $ \sqrt{\smash[b]{s_{_{\mathrm{NN}}}}} = $ 5.02 TeV. Right: The linear slope parameters, $ {r}^{\text{norm}}_2 $ and $ {r}^{\text{norm}}_3 $, as functions of the centrality class in PbPb collisions. (Figures adapted from Ref. [308].)

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Figure 49-a:
Left: The normalized difference in $ v_{n} $, $ (v^{-}_{n} - v^{+}_{n})/(v^{-}_{n} + v^{+}_{n}) $, for $ n= $ 2 and 3, as a function of true event charge asymmetry for the 30-40% centrality class in PbPb collisions at $ \sqrt{\smash[b]{s_{_{\mathrm{NN}}}}} = $ 5.02 TeV. Right: The linear slope parameters, $ {r}^{\text{norm}}_2 $ and $ {r}^{\text{norm}}_3 $, as functions of the centrality class in PbPb collisions. (Figures adapted from Ref. [308].)

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Figure 49-b:
Left: The normalized difference in $ v_{n} $, $ (v^{-}_{n} - v^{+}_{n})/(v^{-}_{n} + v^{+}_{n}) $, for $ n= $ 2 and 3, as a function of true event charge asymmetry for the 30-40% centrality class in PbPb collisions at $ \sqrt{\smash[b]{s_{_{\mathrm{NN}}}}} = $ 5.02 TeV. Right: The linear slope parameters, $ {r}^{\text{norm}}_2 $ and $ {r}^{\text{norm}}_3 $, as functions of the centrality class in PbPb collisions. (Figures adapted from Ref. [308].)

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Figure 50:
Difference of $ v_2 $ between $ \mathrm{D^0} $ and $ \overline{\mathrm{D}}^{0} $ mesons as a function of rapidity. The average value ($ \Delta v_2^{\text{Avg}} $) is extracted by fitting the data considering the statistical uncertainties only. The systematic uncertainty of the $ \Delta v_2^{\text{Avg}} $ is estimated by shifting the each point up and down by its systematic uncertainty. (Figure adapted from Ref. [142].)

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Figure 51:
An ``unrolled'' calorimeter display of energy deposition in an event containing an unbalanced dijet pair in a $ \sqrt{\smash[b]{s_{_{\mathrm{NN}}}}}= $ 2.76 TeV PbPb collision, as recorded by the CMS detector in 2010. The tower-by-tower transverse energy sum combining the measurement in electromagnetic and hadronic calorimeters is plotted as a function of $ \eta $ and $ \phi $. The fully corrected transverse momenta of the unbalanced dijet pair are labeled and their position in $ \eta$-$\phi $ indicated with the red-highlighted constituent towers. (Figure adapted from Ref. [103].)

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Figure 52:
The $ A_{\mathrm{J}} $ distributions for jet pairs with a leading jet of $ p_{\mathrm{T,1}} > $ 120 GeV and subleading jet of $ p_{\mathrm{T,2}} > $ 30 GeV, presented for different event centrality classes. The dijet pair is required to fulfill a back-to-back requirement in azimuthal angle of $ \Delta\phi_{\mathrm{1,2}} > 2\pi/ $ 3. Black filled points represent the PbPb data, while the red hatched histogram shows the PYTHIAHYDJET simulation results. The open blue circles in the upper left panel are the results from $ \sqrt{\smash[b]{s}} = $ 2.76 TeV pp collisions, acting as an unquenched reference in conjunction with the simulations. Vertical bars represent statistical uncertainties only. (Figure adapted from Ref. [319].)

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Figure 53:
The $ \langle p_{\mathrm{T}}^{\shortparallel}\hspace{-1.02em}/\kern 0.5em\rangle $ values as a function of $ A_{\mathrm{J}} $ for tracks with $ p_{\mathrm{T}} > $ 0.5 GeV. Dijets are selected with $ p_{\mathrm{T,1}} > $ 120 GeV, $ p_{\mathrm{T,2}} > $ 50 GeV, and $ \Delta\phi_{\mathrm{1,2}} > 2\pi/ $ 3. The left panels are for peripheral, 30-100% centrality events, and the right panels are for central, 0-30% events. The upper row shows the results in PYTHIAHYDJET simulation (lacking quenching) while the lower row shows the result in PbPb data. Both data and simulation are for $ \sqrt{\smash[b]{s_{_{\mathrm{NN}}}}} = $ 2.76 TeV. Solid circles show the total average $ p_{\mathrm{T}}^{\shortparallel}\hspace{-1.02em}/\kern 0.5em $ while individual color-filled histograms show contributions from particles of $ p_{\mathrm{T}} $ ranging from 0.5-1.0 GeV to larger than 8.0 GeV. Vertical bars represent statistical uncertainties while the horizontal bars surrounding the solid black circles represent systematic uncertainties. (Figure adapted from Ref. [103].)

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Figure 54:
Inclusive jet $ R_{\mathrm{AA}} $ plotted as a function of the jet $ p_{\mathrm{T}} $ for $ |\eta| < $ 2.0. Each panel corresponds to a different centrality class (upper left) 70-90%, (upper middle) 50-70%, (upper right) 30-50%, (lower left) 10-30%, (lower middle) 5-10%, and (lower right) 0-5%. Results for three jet distance parameters, $ R = $ 0.2, 0.3, and 0.4, are overlaid as red stars, black diamonds, and blue crosses, respectively. Vertical bars (typically smaller than the markers) represent the statistical uncertainty, while horizontal bars around each point are the nonglobal systematic uncertainties. Finally, the combined global systematic uncertainty coming from $ T_{\mathrm{AA}} $ and the integrated luminosity measurement is plotted as a shaded green bar on the horizontal black-dashed unity line. (Figure adapted from Ref. [322].)

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Figure 55:
Jet $ R_{\mathrm{AA}} $ in the 0-10% centrality class as a function of jet $ p_{\mathrm{T}} $ for jets with $ |\eta| < $ 2.0. Each panel corresponds to a different distance parameter $ R $, as indicated. Filled red circle markers represent the data, with vertical red lines representing statistical uncertainties and horizontal red lines representing bin widths. The shaded red boxes around the points represent systematic uncertainties. Integrated luminosity (for pp collisions) and $ \langle T_{\mathrm{AA}} \rangle $ (for PbPb collisions) global uncertainties are shown as shaded boxes around the dashed horizontal line for $ R_{\mathrm{AA}} = $ 1. Predictions for the HYBRID [325,326], MARTINI [327], LBT [328], and CCNU [329,330,331] models are plotted for comparison. (Figure adapted from Ref. [139].)

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Figure 56:
Measurements of $ R_{\mathrm{AA}} $ in central heavy ion collisions at four different center-of-mass energies, for neutral pions (SPS, RHIC), charged hadrons ($ h^{\pm} $) (SPS, RHIC), and charged particles (LHC). Data are taken from Refs. [332,333,334,335,336,337,338,339,340]. Predictions of six models for $ \sqrt{\smash[b]{s_{_{\mathrm{NN}}}}}= $ 5.02 TeV PbPb collisions are shown [341,325,342,343,38,344]. The error bars represent the statistical uncertainties and the yellow boxes around the 5.02 TeV CMS data show systematic uncertainties. The $ T_{\mathrm{AA}} $ uncertainties, which are small, are not shown. (Figure adapted from Ref. [340].)

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Figure 57:
The charged-particle $ R_{\mathrm{AA}}^{*} $ for $ \mathrm{Xe}\mathrm{Xe} $ collisions at $ \sqrt{\smash[b]{s_{_{\mathrm{NN}}}}}= $ 5.44 TeV [122] and $ R_{\mathrm{AA}} $ for PbPb collisions at 5.02 TeV [340]. The asterisk in $ R_{\mathrm{AA}}^{*} $ indicates that the 5.44 TeV pp reference has been calculated by extrapolating a measured 5.02 TeV pp spectrum. The solid pink and open blue boxes represent the systematic uncertainties of the $ \mathrm{Xe}\mathrm{Xe} $ and PbPb data, respectively. The left panel shows the result as a function of particle $ p_{\mathrm{T}} $ for a 0-5% centrality selection. In the right panel, the results for the 6.4 $ < p_{\mathrm{T}} < $ 7.2 GeV range are plotted as functions of average $ N_\text{part} $. (Figures adapted from Refs. [340,122].)

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Figure 57-a:
The charged-particle $ R_{\mathrm{AA}}^{*} $ for $ \mathrm{Xe}\mathrm{Xe} $ collisions at $ \sqrt{\smash[b]{s_{_{\mathrm{NN}}}}}= $ 5.44 TeV [122] and $ R_{\mathrm{AA}} $ for PbPb collisions at 5.02 TeV [340]. The asterisk in $ R_{\mathrm{AA}}^{*} $ indicates that the 5.44 TeV pp reference has been calculated by extrapolating a measured 5.02 TeV pp spectrum. The solid pink and open blue boxes represent the systematic uncertainties of the $ \mathrm{Xe}\mathrm{Xe} $ and PbPb data, respectively. The left panel shows the result as a function of particle $ p_{\mathrm{T}} $ for a 0-5% centrality selection. In the right panel, the results for the 6.4 $ < p_{\mathrm{T}} < $ 7.2 GeV range are plotted as functions of average $ N_\text{part} $. (Figures adapted from Refs. [340,122].)

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Figure 57-b:
The charged-particle $ R_{\mathrm{AA}}^{*} $ for $ \mathrm{Xe}\mathrm{Xe} $ collisions at $ \sqrt{\smash[b]{s_{_{\mathrm{NN}}}}}= $ 5.44 TeV [122] and $ R_{\mathrm{AA}} $ for PbPb collisions at 5.02 TeV [340]. The asterisk in $ R_{\mathrm{AA}}^{*} $ indicates that the 5.44 TeV pp reference has been calculated by extrapolating a measured 5.02 TeV pp spectrum. The solid pink and open blue boxes represent the systematic uncertainties of the $ \mathrm{Xe}\mathrm{Xe} $ and PbPb data, respectively. The left panel shows the result as a function of particle $ p_{\mathrm{T}} $ for a 0-5% centrality selection. In the right panel, the results for the 6.4 $ < p_{\mathrm{T}} < $ 7.2 GeV range are plotted as functions of average $ N_\text{part} $. (Figures adapted from Refs. [340,122].)

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Figure 58:
Comparison between charged-hadron $ v_2 $ results from various methods as a function of $ p_{\mathrm{T}} $ in six centrality selections from 0-5% to 50-60%. The vertical bars represent the statistical uncertainties, while the shaded boxes represent systematic uncertainties. (Figure adapted from Ref. [349].)

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Figure 59:
The dijet $ v_2 $ (left), $ v_3 $ (middle), and $ v_4 $ (right) measured as functions of collision centrality in 5.02 TeV PbPb collisions. The dijet $ v_2 $ results are compared to CMS high-$ p_{\mathrm{T}} $ hadron $ v_2 $ results. The shaded boxes represent systematic uncertainties, while the vertical bars show statistical uncertainties. (Figure adapted from Ref. [351].)

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Figure 60:
Feynman diagrams depicting two leading-order processes producing a photon or a Z boson with a jet balancing the transverse momentum in the final state. The first diagram shows the outgoing jet to be initiated by a quark, while the other shows the outgoing jet to be initiated by a gluon. These rare hard scatterings have been used to study jet quenching in a number of CMS analyses [352].

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Figure 61:
The $ p_{\mathrm{T}} $ balancing observable $ x_{\mathrm{J}}\gamma $ for $ \gamma+\text{jet} $ pairs is plotted as a function of centrality class panel-by-panel, with the leftmost panel corresponding to the 50-100% peripheral selection, progressing to the 0-10% central selection in the rightmost panel. The distribution is normalized by the number of photons in a pp reference (open markers) and PbPb (full markers) data, per centrality class. Vertical lines display the statistical uncertainties while the shaded bars around the points (red for PbPb, green for pp) show the systematic uncertainties. The statistical uncertainties of the pp data are smaller than the markers for many data points. (Figure adapted from Ref. [352].)

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Figure 62:
Relative contributions of fragmentation (red), photon+quark jet (grey), and photon+gluon jet (blue) processes to the production of isolated photons in PYTHIA8 events. The requirement of an isolated photon in the event increases the fraction of quark-initiated jets relative to an inclusive jet sample. (Figure adapted from Ref. [352].)

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Figure 63:
Results for the gluon-like jet fractions in pp and PbPb data shown for different track $ p_{\mathrm{T}} $ threshold values and event centrality selections in PbPb collisions. The systematic and statistical uncertainties are represented by the shaded regions and vertical bars, respectively. The predictions for the gluon jet fractions from PYTHIA 6 are shown in dashed red lines. (Figure adapted from Ref. [354].)

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Figure 64:
Dijet imbalance for inclusive (left) dijets and b dijets (center) in pp collisions and for different centrality selections of 5.02 TeV PbPb collisions. The right panel shows the difference in the $ \langle x_{\mathrm{J}} \rangle $ values between PbPb and the smeared pp reference. Systematic uncertainties are shown as shaded boxes and statistical uncertainties are displayed as vertical lines. (Figure adapted from Ref. [320].)

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Figure 65:
Left: Observed and postfit predicted BDT discriminator distributions in the $ \mathrm{e}^\pm\mu^\mp $ final state separately in the 0b-, 1b-, and 2b-tagged jet multiplicity categories. The data are shown with markers, and the signal and background processes with filled histograms. The vertical bars on the markers represent the statistical uncertainties in data. The hatched regions show the uncertainties in the sum of $ \mathrm{t} \overline{\mathrm{t}} $ signal and backgrounds. The lower panel displays the ratio between the data and the predictions, including the $ \mathrm{t} \overline{\mathrm{t}} $ signal, with bands representing the uncertainties in the postfit predictions. Right: Inclusive $ \mathrm{t} \overline{\mathrm{t}} $ cross sections measured with two methods in the combined $ \mathrm{e}^\pm\mu^\mp $, $ \mu^{+}\mu^{-} $, and $ \mathrm{e}^+\mathrm{e}^- $ final states in PbPb collisions at $ \sqrt{\smash[b]{s_{_{\mathrm{NN}}}}}= $ 5.02 TeV, and pp results at $ \sqrt{\smash[b]{s}}= $ 5.02 TeV (scaled by $ A^2 $). The measurements are compared with theoretical predictions at NNLO+NNLL accuracy in QCD. The inner (outer) experimental uncertainty bars include statistical (statistical and systematic, added in quadrature) uncertainties. The inner (outer) theoretical uncertainty bands correspond to nPDF or PDF (PDF and scale, added in quadrature) uncertainties. (Figures adapted from Ref. [146].)

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Figure 65-a:
Left: Observed and postfit predicted BDT discriminator distributions in the $ \mathrm{e}^\pm\mu^\mp $ final state separately in the 0b-, 1b-, and 2b-tagged jet multiplicity categories. The data are shown with markers, and the signal and background processes with filled histograms. The vertical bars on the markers represent the statistical uncertainties in data. The hatched regions show the uncertainties in the sum of $ \mathrm{t} \overline{\mathrm{t}} $ signal and backgrounds. The lower panel displays the ratio between the data and the predictions, including the $ \mathrm{t} \overline{\mathrm{t}} $ signal, with bands representing the uncertainties in the postfit predictions. Right: Inclusive $ \mathrm{t} \overline{\mathrm{t}} $ cross sections measured with two methods in the combined $ \mathrm{e}^\pm\mu^\mp $, $ \mu^{+}\mu^{-} $, and $ \mathrm{e}^+\mathrm{e}^- $ final states in PbPb collisions at $ \sqrt{\smash[b]{s_{_{\mathrm{NN}}}}}= $ 5.02 TeV, and pp results at $ \sqrt{\smash[b]{s}}= $ 5.02 TeV (scaled by $ A^2 $). The measurements are compared with theoretical predictions at NNLO+NNLL accuracy in QCD. The inner (outer) experimental uncertainty bars include statistical (statistical and systematic, added in quadrature) uncertainties. The inner (outer) theoretical uncertainty bands correspond to nPDF or PDF (PDF and scale, added in quadrature) uncertainties. (Figures adapted from Ref. [146].)

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Figure 65-b:
Left: Observed and postfit predicted BDT discriminator distributions in the $ \mathrm{e}^\pm\mu^\mp $ final state separately in the 0b-, 1b-, and 2b-tagged jet multiplicity categories. The data are shown with markers, and the signal and background processes with filled histograms. The vertical bars on the markers represent the statistical uncertainties in data. The hatched regions show the uncertainties in the sum of $ \mathrm{t} \overline{\mathrm{t}} $ signal and backgrounds. The lower panel displays the ratio between the data and the predictions, including the $ \mathrm{t} \overline{\mathrm{t}} $ signal, with bands representing the uncertainties in the postfit predictions. Right: Inclusive $ \mathrm{t} \overline{\mathrm{t}} $ cross sections measured with two methods in the combined $ \mathrm{e}^\pm\mu^\mp $, $ \mu^{+}\mu^{-} $, and $ \mathrm{e}^+\mathrm{e}^- $ final states in PbPb collisions at $ \sqrt{\smash[b]{s_{_{\mathrm{NN}}}}}= $ 5.02 TeV, and pp results at $ \sqrt{\smash[b]{s}}= $ 5.02 TeV (scaled by $ A^2 $). The measurements are compared with theoretical predictions at NNLO+NNLL accuracy in QCD. The inner (outer) experimental uncertainty bars include statistical (statistical and systematic, added in quadrature) uncertainties. The inner (outer) theoretical uncertainty bands correspond to nPDF or PDF (PDF and scale, added in quadrature) uncertainties. (Figures adapted from Ref. [146].)

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Figure 66:
Upper: Fragmentation functions as a function of $ \xi $ in bins of PbPb centrality (left-to-right: 50-100%, 30-50%, 10-30%, and 0-10%) with the result from pp reference data overlaid. Lower: Ratios of the PbPb fragmentation functions over those for the pp reference. Jets are selected in the $ p_{\mathrm{T}} $ range 150 to 300 GeV and tracks with $ p_{\mathrm{T}} > $ 1 GeV. Vertical bars and shaded boxes represent the statistical and systematic uncertainties, respectively. (Figure adapted from Ref. [366].)

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Figure 67:
Comparison of $ \gamma $-tagged fragmentation functions in centrality bins 10-30% (left) and 0-10% (right) as a function of the observables $ \xi^{\text{jet}} $ (upper), defined in Eq. (21), and $ \xi^{\gamma}_{\mathrm{T}} $ (lower), defined in Eq. (22). For comparison, curves from the theoretical models SCETG [341], CoLBT-hydro [367,368,369], and HYBRID [370] are overlaid. The widths of the bands represent variations of the coupling strength in the SCETG case and of the dimensionless parameter $ \kappa $ in the HYBRID case. Vertical bars and shaded boxes represent the statistical and systematic uncertainties, respectively. (Figures adapted from Ref. [371].)

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Figure 67-a:
Comparison of $ \gamma $-tagged fragmentation functions in centrality bins 10-30% (left) and 0-10% (right) as a function of the observables $ \xi^{\text{jet}} $ (upper), defined in Eq. (21), and $ \xi^{\gamma}_{\mathrm{T}} $ (lower), defined in Eq. (22). For comparison, curves from the theoretical models SCETG [341], CoLBT-hydro [367,368,369], and HYBRID [370] are overlaid. The widths of the bands represent variations of the coupling strength in the SCETG case and of the dimensionless parameter $ \kappa $ in the HYBRID case. Vertical bars and shaded boxes represent the statistical and systematic uncertainties, respectively. (Figures adapted from Ref. [371].)

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Figure 67-b:
Comparison of $ \gamma $-tagged fragmentation functions in centrality bins 10-30% (left) and 0-10% (right) as a function of the observables $ \xi^{\text{jet}} $ (upper), defined in Eq. (21), and $ \xi^{\gamma}_{\mathrm{T}} $ (lower), defined in Eq. (22). For comparison, curves from the theoretical models SCETG [341], CoLBT-hydro [367,368,369], and HYBRID [370] are overlaid. The widths of the bands represent variations of the coupling strength in the SCETG case and of the dimensionless parameter $ \kappa $ in the HYBRID case. Vertical bars and shaded boxes represent the statistical and systematic uncertainties, respectively. (Figures adapted from Ref. [371].)

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Figure 68:
The angular jet momentum distribution $ P(\Delta r) $ of jets in pp (upper) and PbPb (middle) collisions. The PbPb results are shown for different centrality regions. The lower row shows the ratio between PbPb and pp data for the indicated intervals of $ p_{\mathrm{T}}^{\text{trk}} $. The shaded bands show the total systematic uncertainties. (Figure adapted from Ref. [380].)

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Figure 69:
Ratio of the differential jet shape for jets associated with an isolated photon for 5.02 TeV 0-10% PbPb collisions and pp reference data. The measurement is performed using jets having $ p_{\mathrm{T}}^\text{jet} > $ 30 GeV and tracks with $ p_{\mathrm{T}}^{\text{trk}} > $ 1 GeV. (Figure adapted from Ref. [385].)

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Figure 70:
Distribution of the ratio of the groomed jet splitting fraction in central PbPb data compared to a pp reference. Each panel corresponds to a different jet $ p_{\mathrm{T}} $ range and the different colored lines and bands are predictions from MC models. Statistical and systematic uncertainties in the data are shown by vertical bars and shaded boxes, respectively. (Figure adapted from Ref. [390].)

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Figure 71:
Distribution of the ratio of the groomed jet mass, $ M_{\mathrm{g}} $, in central PbPb data compared to the pp reference for two different grooming criteria in four ranges of jet $ p_{\mathrm{T}} $. The left panel shows more stringent grooming criteria, while the right panel shows the same measurement for the default grooming requirements. The different lines represent MC predictions; they show deviations from the data at larger masses. Statistical and systematic uncertainties in the data are shown by vertical bars and shaded boxes, respectively. (Figures adapted from Ref. [391].)

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Figure 71-a:
Distribution of the ratio of the groomed jet mass, $ M_{\mathrm{g}} $, in central PbPb data compared to the pp reference for two different grooming criteria in four ranges of jet $ p_{\mathrm{T}} $. The left panel shows more stringent grooming criteria, while the right panel shows the same measurement for the default grooming requirements. The different lines represent MC predictions; they show deviations from the data at larger masses. Statistical and systematic uncertainties in the data are shown by vertical bars and shaded boxes, respectively. (Figures adapted from Ref. [391].)

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Figure 71-b:
Distribution of the ratio of the groomed jet mass, $ M_{\mathrm{g}} $, in central PbPb data compared to the pp reference for two different grooming criteria in four ranges of jet $ p_{\mathrm{T}} $. The left panel shows more stringent grooming criteria, while the right panel shows the same measurement for the default grooming requirements. The different lines represent MC predictions; they show deviations from the data at larger masses. Statistical and systematic uncertainties in the data are shown by vertical bars and shaded boxes, respectively. (Figures adapted from Ref. [391].)

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Figure 72:
Nuclear modification factors of inclusive charged particles, prompt $ \mathrm{D^0} $ and $ {\mathrm{B}^{+}} $, and nonprompt $ \mathrm{D^0} $ and $ \mathrm{J}/\psi $ mesons, as a function of their $ p_{\mathrm{T}} $ in PbPb collisions. (Figures adapted from Refs. [340,392, 393,394,395].)

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Figure 73:
(Left) Azimuthal anisotropy coefficient $ v_2 $ of inclusive charged particles, prompt $ \mathrm{D^0} $, and nonprompt $ \mathrm{D^0} $ and $ \mathrm{J}/\psi $ mesons as a function of $ p_{\mathrm{T}} $ in PbPb collisions. (Figures adapted from Refs. [349,142,144,397].) (Right) Prompt $ \mathrm{D^0} $ meson $v_2\{2\}$, $v_2\{4\}$ and their ratio as functions of centrality. (Figure adapted from Ref. [143].)

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Figure 73-a:
(Left) Azimuthal anisotropy coefficient $ v_2 $ of inclusive charged particles, prompt $ \mathrm{D^0} $, and nonprompt $ \mathrm{D^0} $ and $ \mathrm{J}/\psi $ mesons as a function of $ p_{\mathrm{T}} $ in PbPb collisions. (Figures adapted from Refs. [349,142,144,397].) (Right) Prompt $ \mathrm{D^0} $ meson $v_2\{2\}$, $v_2\{4\}$ and their ratio as functions of centrality. (Figure adapted from Ref. [143].)

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Figure 73-b:
(Left) Azimuthal anisotropy coefficient $ v_2 $ of inclusive charged particles, prompt $ \mathrm{D^0} $, and nonprompt $ \mathrm{D^0} $ and $ \mathrm{J}/\psi $ mesons as a function of $ p_{\mathrm{T}} $ in PbPb collisions. (Figures adapted from Refs. [349,142,144,397].) (Right) Prompt $ \mathrm{D^0} $ meson $v_2\{2\}$, $v_2\{4\}$ and their ratio as functions of centrality. (Figure adapted from Ref. [143].)

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Figure 74:
Distributions of $ \mathrm{D^0} $ mesons in jets, as a function of the distance from the jet axis. The ratios of the $ \mathrm{D^0} $ meson radial distributions in PbPb and pp data are shown in the middle panel, whereas in the lower panel the ratios of the $ \mathrm{D^0} $ meson radial distributions of pp over the two MC event generators are presented. (Figure adapted from Ref. [404].)

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Figure 75:
The ratio of the production cross sections of prompt $ \Lambda_{c}^{+} $ to prompt $ \mathrm{D^0} $ versus $ p_{\mathrm{T}} $ from pp collisions. The data are compared to various models (left) and to similar measurements in PbPb collisions (right). (Figure adapted from Ref. [409].)

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Figure 75-a:
The ratio of the production cross sections of prompt $ \Lambda_{c}^{+} $ to prompt $ \mathrm{D^0} $ versus $ p_{\mathrm{T}} $ from pp collisions. The data are compared to various models (left) and to similar measurements in PbPb collisions (right). (Figure adapted from Ref. [409].)

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Figure 75-b:
The ratio of the production cross sections of prompt $ \Lambda_{c}^{+} $ to prompt $ \mathrm{D^0} $ versus $ p_{\mathrm{T}} $ from pp collisions. The data are compared to various models (left) and to similar measurements in PbPb collisions (right). (Figure adapted from Ref. [409].)

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Figure 76:
The $ p_{\mathrm{T}} $-differential cross sections for prompt $ \Lambda_{c}^{+} $ baryon production in pp collisions, together with model calculations. (Figure adapted from Ref. [409].)

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Figure 77:
Left: The ratio of $ \mathrm{B}_{s}^{0} $ and $ {\mathrm{B}^{+}} $ production yields as a function of $ p_{\mathrm{T}} $ in pp and PbPb collisions, together with model calculations. Right: The nuclear modification factor of $ \mathrm{B}_{c}^{+} $ and other hadrons in PbPb collisions. (Figures adapted from Refs. [410,411].)

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Figure 77-a:
Left: The ratio of $ \mathrm{B}_{s}^{0} $ and $ {\mathrm{B}^{+}} $ production yields as a function of $ p_{\mathrm{T}} $ in pp and PbPb collisions, together with model calculations. Right: The nuclear modification factor of $ \mathrm{B}_{c}^{+} $ and other hadrons in PbPb collisions. (Figures adapted from Refs. [410,411].)

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Figure 77-b:
Left: The ratio of $ \mathrm{B}_{s}^{0} $ and $ {\mathrm{B}^{+}} $ production yields as a function of $ p_{\mathrm{T}} $ in pp and PbPb collisions, together with model calculations. Right: The nuclear modification factor of $ \mathrm{B}_{c}^{+} $ and other hadrons in PbPb collisions. (Figures adapted from Refs. [410,411].)

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Figure 79:
Upper: Nuclear modification factors, as a function of the mean number of participants, for the promptly-produced $ \mathrm{J}/\psi $ and $\psi(2\mathrm{S})$ mesons (left), as well as for the $ \Upsilon{\textrm{(1S)}} $, $ \Upsilon{\textrm{(2S)}} $, and $ \Upsilon{\textrm{(3S)}} $ (right), as measured from pp and PbPb data at 5.02 TeV. Lower: Corresponding $\psi(2\mathrm{S})$/ $ \mathrm{J}/\psi $ (left) and $ \Upsilon{\textrm{(3S)}} $/$ \Upsilon{\textrm{(2S)}} $ (right) double-ratios. (Figures adapted from Refs. [395,452,453].)

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Figure 80:
The dimuon invariant mass distribution measured in PbPb collisions when integrating over the full kinematic range of $ p_{\mathrm{T}} < $ 30 GeV and $ |y| < $ 2.4. The solid curves show the fit results, and the orange dashed and blue dash-dotted curves display the three $ \Upsilon $ states and the background, respectively. The inset shows the region around the $ \Upsilon{\textrm{(3S)}} $ meson mass. (Figures adapted from Refs. [452].)

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Figure 81:
Normalized $ z $ distribution of $ \mathrm{J}/\psi $ mesons in jets measured in pp collisions at 5.02 TeV, compared to prompt and nonprompt $ \mathrm{J}/\psi $ in PYTHIA8. (Figure adapted from Ref. [455].)

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Figure 82:
Nuclear modification factors $ R_{\mathrm{AA}} $ for the promptly-produced $ \mathrm{J}/\psi $, as a function of $ p_{\mathrm{T}} $, compared with $ \mathrm{D^0} $ mesons (left) and as a function of $ z $ (right), as measured from pp and PbPb data at 5.02 TeV. (Figures adapted from Refs. [392,395,455].)

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Figure 82-a:
Nuclear modification factors $ R_{\mathrm{AA}} $ for the promptly-produced $ \mathrm{J}/\psi $, as a function of $ p_{\mathrm{T}} $, compared with $ \mathrm{D^0} $ mesons (left) and as a function of $ z $ (right), as measured from pp and PbPb data at 5.02 TeV. (Figures adapted from Refs. [392,395,455].)

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Figure 82-b:
Nuclear modification factors $ R_{\mathrm{AA}} $ for the promptly-produced $ \mathrm{J}/\psi $, as a function of $ p_{\mathrm{T}} $, compared with $ \mathrm{D^0} $ mesons (left) and as a function of $ z $ (right), as measured from pp and PbPb data at 5.02 TeV. (Figures adapted from Refs. [392,395,455].)

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Figure 83:
The prompt $ \mathrm{J}/\psi $ $ v_2 $ as a function of $ p_{\mathrm{T}} $ (left) and $ N_\text{part} $ (right), in PbPb collisions at 5.02 TeV. (Figure adapted from Ref. [397].)

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Figure 84:
Left: Pseudorapidity density of charged hadrons in the range $ |\eta_{\mathrm{lab}}| < $ 2.4 in pPb collisions at 8.16 TeV. The results are compared to predictions from the MC event generators EPOS LHC [461,118] (v3400), HIJING [119] (versions 1.3 [462] and 2.1 [463]), and DPMJET-III [464], as well as from the KLN model [465]. The shaded boxes around the data points indicate their systematic uncertainties. The proton beam goes in the positive $ \eta_{\mathrm{lab}} $ direction. Right: Comparison of the measured density at midrapidity, scaled by $ N_\text{part} $ in pPb [466,467], $ \mathrm{p}\mathrm{Au} $ [468], $ \text{dAu} $ [469,470,471] and central heavy ion collisions [224,472,473,474,475,476,477,478,479,480,481,106,470,482,483], as well as NSD [229,484,228,483,485,226,225] and inelastic [486,228,227,224,487] pp collisions. The dashed curves, included to guide the eye, are from Refs. [227,480].

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Figure 84-a:
Left: Pseudorapidity density of charged hadrons in the range $ |\eta_{\mathrm{lab}}| < $ 2.4 in pPb collisions at 8.16 TeV. The results are compared to predictions from the MC event generators EPOS LHC [461,118] (v3400), HIJING [119] (versions 1.3 [462] and 2.1 [463]), and DPMJET-III [464], as well as from the KLN model [465]. The shaded boxes around the data points indicate their systematic uncertainties. The proton beam goes in the positive $ \eta_{\mathrm{lab}} $ direction. Right: Comparison of the measured density at midrapidity, scaled by $ N_\text{part} $ in pPb [466,467], $ \mathrm{p}\mathrm{Au} $ [468], $ \text{dAu} $ [469,470,471] and central heavy ion collisions [224,472,473,474,475,476,477,478,479,480,481,106,470,482,483], as well as NSD [229,484,228,483,485,226,225] and inelastic [486,228,227,224,487] pp collisions. The dashed curves, included to guide the eye, are from Refs. [227,480].

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Figure 84-b:
Left: Pseudorapidity density of charged hadrons in the range $ |\eta_{\mathrm{lab}}| < $ 2.4 in pPb collisions at 8.16 TeV. The results are compared to predictions from the MC event generators EPOS LHC [461,118] (v3400), HIJING [119] (versions 1.3 [462] and 2.1 [463]), and DPMJET-III [464], as well as from the KLN model [465]. The shaded boxes around the data points indicate their systematic uncertainties. The proton beam goes in the positive $ \eta_{\mathrm{lab}} $ direction. Right: Comparison of the measured density at midrapidity, scaled by $ N_\text{part} $ in pPb [466,467], $ \mathrm{p}\mathrm{Au} $ [468], $ \text{dAu} $ [469,470,471] and central heavy ion collisions [224,472,473,474,475,476,477,478,479,480,481,106,470,482,483], as well as NSD [229,484,228,483,485,226,225] and inelastic [486,228,227,224,487] pp collisions. The dashed curves, included to guide the eye, are from Refs. [227,480].

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Figure 85:
Average transverse momentum of identified charged hadrons in the range $ |y| < $ 1 as a function of the corrected track multiplicity for $ |\eta| < $ 2.4, for pp collisions (open symbols) at several energies [488] and for pPb collisions (filled symbols) at $ \sqrt{\smash[b]{s_{_{\mathrm{NN}}}}} = $ 5.02 TeV. Left: Results compared to predictions from event generators. Right: Comparison of pp, pPb, and PbPb data. The ranges of $ \langle p_{\mathrm{T}}\rangle $ values measured by ALICE in various centrality PbPb collisions at $ \sqrt{\smash[b]{s_{_{\mathrm{NN}}}}}= $ 2.76 TeV [489] are indicated with horizontal bands.

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Figure 85-a:
Average transverse momentum of identified charged hadrons in the range $ |y| < $ 1 as a function of the corrected track multiplicity for $ |\eta| < $ 2.4, for pp collisions (open symbols) at several energies [488] and for pPb collisions (filled symbols) at $ \sqrt{\smash[b]{s_{_{\mathrm{NN}}}}} = $ 5.02 TeV. Left: Results compared to predictions from event generators. Right: Comparison of pp, pPb, and PbPb data. The ranges of $ \langle p_{\mathrm{T}}\rangle $ values measured by ALICE in various centrality PbPb collisions at $ \sqrt{\smash[b]{s_{_{\mathrm{NN}}}}}= $ 2.76 TeV [489] are indicated with horizontal bands.

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Figure 85-b:
Average transverse momentum of identified charged hadrons in the range $ |y| < $ 1 as a function of the corrected track multiplicity for $ |\eta| < $ 2.4, for pp collisions (open symbols) at several energies [488] and for pPb collisions (filled symbols) at $ \sqrt{\smash[b]{s_{_{\mathrm{NN}}}}} = $ 5.02 TeV. Left: Results compared to predictions from event generators. Right: Comparison of pp, pPb, and PbPb data. The ranges of $ \langle p_{\mathrm{T}}\rangle $ values measured by ALICE in various centrality PbPb collisions at $ \sqrt{\smash[b]{s_{_{\mathrm{NN}}}}}= $ 2.76 TeV [489] are indicated with horizontal bands.

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Figure 86:
Ratios of $ p_{\mathrm{T}} $ spectra for $ \Lambda/2\mathrm{K^0_S} $ in the center-of-mass rapidity range $ |y_\mathrm{cm}| < $ 1.0 for pp collisions at $ \sqrt{\smash[b]{s}} = $ 7 TeV (left), pPb collisions at $ \sqrt{\smash[b]{s}} = $ 5.02 TeV (middle), and PbPb collisions at $ \sqrt{\smash[b]{s_{_{\mathrm{NN}}}}} = $ 2.76 TeV (right). Two (for pp) or three (for pPb and PbPb) representative multiplicity intervals are presented. (Figure adapted from Ref. [491].)

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Figure 87:
Panels (a), (b), and (c) show the 2D two-particle correlation functions for pairs of charged particles with 1 $ < p_{\mathrm{T}} < $ 3 GeV for high multiplicity events in pp at 7 TeV and pPb at 5.02 TeV, as well as peripheral PbPb collisions at 2.76 TeV. Panel (d) displays the ridge yield as a function of multiplicity in pp, pPb, and PbPb collisions. The vertical bars and shaded boxes denote the statistical and systematic uncertainties, respectively. (Figures adapted from Refs. [293,296,105,294].)

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Figure 88:
Left: The $ v_2\{2, |\Delta\eta| > 2\} $, $ v_2^\text{sub}\{2, |\Delta\eta| > 2\} $, $ v_2\{4\} $, and $ v_2\{6\} $ values as functions of $ N_\text{trk}^\text{offline} $ for charged particles, averaged over 0.3 $ < p_{\mathrm{T}} < $ 3.0 GeV and $ |\eta| < $ 2.4, in pp collisions at 13 TeV. Middle: The $ v_2{2, |\Delta\eta| > 2} $, $ v_2^\text{sub}\{2, |\Delta\eta| > 2\} $, $ v_2\{4\} $, $ v_2\{6\} $, $ v_2\{8\} $, and $ v_2{\mathrm{LYZ}} $ values in pPb collisions at 5 TeV. Right: The $ v_2{2, |\Delta\eta| > 2} $, $ v_2^\text{sub}\{2, |\Delta\eta| > 2\} $, $ v_2\{4\} $, $ v_2\{6\} $, $ v_2\{8\} $, and $ v_2{\mathrm{LYZ}} $ values in PbPb collisions at 2.76 TeV. The vertical bars and shaded boxes for $ v_2^\text{sub}\{2, |\Delta\eta| > 2\} $ and $ v_2\{4\} $ denote the statistical and systematic uncertainties, respectively, with the former generally being smaller than the symbols. For $ v_2\{6\} $, $ v_2\{8\} $, and $ v_2\{\mathrm{LYZ}\} $, vertical bars show statistical uncertainties and systematic uncertainties are shown by green, red, and gray shaded bands, respectively. (Figure adapted from Ref. [295].)

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Figure 89:
Cumulant ratios $v_2\{6\}/v_2\{4\}$ (upper) and $v_2\{8\}/v_2\{6\}$ (lower) as functions of $ v_2\{4\}/v^{\text{sub}}_2\{2\} $ in pPb collisions at 5.02 and 8.16 TeV. The solid curves show the expected behavior based on a hydrodynamics-motivated study of the role of initial-state fluctuations [494]. (Figure adapted from Ref. [495].)

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Figure 90:
The \SCnm23 (left panel) and \SCnm24 (right panel) distributions as functions of $ N_\text{trk}^\text{offline} $ from methods using no (open black circles), 2 (full blue circles), 3 (red squares), and 4 (green crosses) subevents for pPb at 8.16 TeV. Statistical and systematic uncertainties are shown by vertical bars and shaded boxes, respectively. (Figure adapted from Ref. [496].)

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Figure 91:
Upper: The $ v_2^{\text{sub}} $ values for prompt $ \mathrm{J}/\psi $\ mesons at forward rapidities ($ -2.86 < y_{\text{cm}} < - $ 1.86 or 0.94 $ < y_{\text{cm}} < $ 1.94), as well as for $ \mathrm{K^0_S} $\ and $ \Lambda $ hadrons, and prompt $ \mathrm{D^0} $\ mesons at midrapidity ($ -1.46 < y_{\text{cm}} < $ 0.54), as a function of $ p_{\mathrm{T}} $\ for pPb\ collisions at $ \sqrt{\smash[b]{s_{_{\mathrm{NN}}}}} = $ 8.16 TeV with 185 $ \leq N_\text{trk}^\text{offline} < $ 250. Lower: The $ n_\mathrm{q} $-normalized $ v_2^{\text{sub}} $ results. The vertical bars correspond to statistical uncertainties, while the shaded boxes denote the systematic uncertainties. (Figure adapted from Ref. [510].)

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Figure 92:
Results of $ v_2^{\text{sub}} $ for prompt $ \mathrm{D^0} $ mesons, as a function of $ p_{\mathrm{T}} $ for $ |y_{\text{lab}}| < $ 1, with $ N_\text{trk}^\text{offline} \geq $ 100 in pp collisions at $ \sqrt{\smash[b]{s}} = $ 13 TeV. The results for charged particles, $ \mathrm{K^0_S} $ mesons, and $ \Lambda $ baryons are shown for comparison. Vertical bars correspond to the statistical uncertainties, while the shaded boxes denote the systematic uncertainties. The horizontal bars represent the width of the $ p_{\mathrm{T}} $ bins for prompt $ \mathrm{D^0} $ mesons. (Figure adapted from Ref. [511].)

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Figure 93:
Results of $ v_2^{\text{sub}} $ for prompt $ \mathrm{D^0} $ mesons, as a function of event multiplicity for three different $ p_{\mathrm{T}} $ ranges, with $ |y_{\text{lab}}| < $ 1 in pp collisions at $ \sqrt{\smash[b]{s}} = $ 13 TeV, and pPb collisions at $ \sqrt{\smash[b]{s_{_{\mathrm{NN}}}}} = $ 8.16 TeV. The vertical bars correspond to statistical uncertainties, while the shaded boxes denote the systematic uncertainties. Vertical bars extending beyond the y-axis are symmetric with respect to the central values. The horizontal bars represent the width of the $ N_\text{trk}^\text{offline} $ bins. The right-most points with right-hand arrows correspond to $ N_\text{trk}^\text{offline}\geq $ 100 for pp collisions and $ N_\text{trk}^\text{offline}\geq $ 250 for pPb collisions. (Figure adapted from Ref. [511].)

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Figure 94:
Results of $ v_2^{\text{sub}} $ for prompt and nonprompt $ \mathrm{D^0} $ mesons, as well as $ \mathrm{K^0_S} $ mesons, $ \Lambda $ baryons for $ |y_{\text{lab}}| < $ 1, and prompt $ \mathrm{J}/\psi $\ mesons for 1.2 $ < |y_{\text{lab}}| < $ 2.4, as a function of $ p_{\mathrm{T}} $ with 185 $ \leq N_\text{trk}^\text{offline} < $ 250 in pPb collisions at $ \sqrt{\smash[b]{s_{_{\mathrm{NN}}}}} = $ 8.16 TeV. The vertical bars correspond to statistical uncertainties, while the shaded boxes denote the systematic uncertainties. The horizontal bars represent the width of the nonprompt $ \mathrm{D^0} p_{\mathrm{T}} $ bins. The red dashed, blue dash-dotted, and green solid lines show the theoretical calculations for prompt $ \mathrm{D^0} $, $ \mathrm{J}/\psi $, and nonprompt $ \mathrm{D^0} $ mesons, respectively, within the CGC framework [518,519]. (Figure adapted from Ref. [511].)

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Figure 95:
The $ N_\text{trk}^\text{offline} $ spectra for $ {\gamma\mathrm{p}} $ and minimum bias pPb samples. The simulated $ N_\text{trk}^\text{offline} $ distribution for $ {\gamma\mathrm{p}} $ events has been normalized to the same event yield as the $ {\gamma\mathrm{p}} $-enhanced data sample.

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Figure 96:
Single-particle azimuthal anisotropy $ v_2 $ versus $ N_\text{trk}^\text{offline} $ for $ {\gamma\mathrm{p}} $-enhanced and pPb samples in two $ p_{\mathrm{T}} $ regions. The systematic uncertainties are shown by the shaded bars in the two panels. Predictions from the PYTHIA8 and HIJING generators are shown for the $ {\gamma\mathrm{p}} $ and MB pPb samples respectively. For the $ {\gamma\mathrm{p}} $ events, the same $ N_\text{trk}^\text{offline} $ bin arrangement as in Fig. 95 is kept, while for pPb the bins $ [2, 5) $, $ [5, 10) $, $ [10, 15) $, and $ [15, 20) $ are used.

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Figure 97:
Left: Rapidity dependence of $ R_{\mathrm{p}\mathrm{b}} $ for prompt $\psi(2\mathrm{S})$ meson in the $ p_{\mathrm{T}} $ range 6.5 $ < p_{\mathrm{T}} < $ 10 GeV. For comparison, the prompt $ \mathrm{J}/\psi $ meson nuclear modification factor is also shown. (Figures adapted from Refs. [527,528].) Right: Nuclear modification factor of $ \Upsilon{\textrm{(1S)}} $ (red dots), $ \Upsilon{\textrm{(2S)}} $ (blue squares), and $ \Upsilon{\textrm{(3S)}} $ (green diamonds) at forward and backward rapidity [528]. For both panels, statistical and systematic uncertainties are represented with vertical bars and boxes, respectively. The fully correlated global uncertainty of 4.2%, affecting both charmonia equally, is displayed as the gray box around $ R_{\mathrm{p}\mathrm{b}}= $ 1.

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Figure 97-a:
Left: Rapidity dependence of $ R_{\mathrm{p}\mathrm{b}} $ for prompt $\psi(2\mathrm{S})$ meson in the $ p_{\mathrm{T}} $ range 6.5 $ < p_{\mathrm{T}} < $ 10 GeV. For comparison, the prompt $ \mathrm{J}/\psi $ meson nuclear modification factor is also shown. (Figures adapted from Refs. [527,528].) Right: Nuclear modification factor of $ \Upsilon{\textrm{(1S)}} $ (red dots), $ \Upsilon{\textrm{(2S)}} $ (blue squares), and $ \Upsilon{\textrm{(3S)}} $ (green diamonds) at forward and backward rapidity [528]. For both panels, statistical and systematic uncertainties are represented with vertical bars and boxes, respectively. The fully correlated global uncertainty of 4.2%, affecting both charmonia equally, is displayed as the gray box around $ R_{\mathrm{p}\mathrm{b}}= $ 1.

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Figure 97-b:
Left: Rapidity dependence of $ R_{\mathrm{p}\mathrm{b}} $ for prompt $\psi(2\mathrm{S})$ meson in the $ p_{\mathrm{T}} $ range 6.5 $ < p_{\mathrm{T}} < $ 10 GeV. For comparison, the prompt $ \mathrm{J}/\psi $ meson nuclear modification factor is also shown. (Figures adapted from Refs. [527,528].) Right: Nuclear modification factor of $ \Upsilon{\textrm{(1S)}} $ (red dots), $ \Upsilon{\textrm{(2S)}} $ (blue squares), and $ \Upsilon{\textrm{(3S)}} $ (green diamonds) at forward and backward rapidity [528]. For both panels, statistical and systematic uncertainties are represented with vertical bars and boxes, respectively. The fully correlated global uncertainty of 4.2%, affecting both charmonia equally, is displayed as the gray box around $ R_{\mathrm{p}\mathrm{b}}= $ 1.

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Figure 98:
Nuclear modification factors versus $ p_{\mathrm{T}} $ for an inclusive centrality selection for both PbPb and pPb collisions. The green and orange boxes show the systematic uncertainties for $ R_{\mathrm{p}\mathrm{A}} $ and $ R_{\mathrm{AA}} $, respectively, while the $ T_{\mathrm{p}\mathrm{A}} $, $ T_{\mathrm{AA}} $, and pp integrated luminosity uncertainties are shown as grey boxes around unity at low $ p_{\mathrm{T}} $. Statistical uncertainties are shown as vertical bars. (Figure adapted from Ref. [340].)

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Figure 99:
Average ratios of jet transverse momenta as a function of $ E_{\mathrm{T}}^{4 < |\eta| < 5.2} $. The inclusive HF activity results for pPb and PYTHIA+HIJING are shown as blue solid and black empty squares, respectively. The systematic (statistical) uncertainties are indicated by the yellow, grey, and blue boxes (vertical bars). Various theoretical calculations are shown by the open square and circles and the grey band at about 0.7. (Figure adapted from Ref. [120].)

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Figure 100:
Event display of a candidate $ \gamma\gamma\to\tau^{+}\tau^{-} $ event measured in a PbPb UPC at CMS. The event is reconstructed as corresponding to a leptonic $ \tau $ decay (red), $ \tau\to\mu\overline{\nu}_{\!\mu}\nu_{\!\tau} $, and a hadronic $ \tau $ decay (yellow), $ \tau\to\pi^{\pm}\pi^{\mp}\pi^{\pm}\nu_{\!\tau} $. (Figure adapted from Ref. [536].)

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Figure 101:
Neutron multiplicity dependence of acoplanarity distributions from $ \gamma\gamma\to\mu^{+}\mu^{-} $ in ultraperipheral PbPb collisions at $ \sqrt{\smash[b]{s_{_{\mathrm{NN}}}}} = $ 5.02 TeV. The $ \alpha $ distributions are normalized to unit integral over their measured range. The dot-dot-dashed and dotted lines indicate the core and tail contributions, respectively. The vertical lines on data points depict the statistical uncertainties, while the systematic uncertainties and horizontal bin widths are shown as gray boxes. (Figure adapted from Ref. [208].)

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Figure 102:
Neutron multiplicity dependence of the (upper) average acoplanarity $ \langle \alpha^\text{core} \rangle $ and (lower) average invariant mass $ \langle m_{\mu\mu} \rangle $ of $ \mu^{+}\mu^{-} $ pairs in ultraperipheral PbPb collisions at $ \sqrt{\smash[b]{s_{_{\mathrm{NN}}}}} = $ 5.02 TeV. The vertical lines on data points depict the statistical uncertainties while the systematic uncertainties of the data are shown as shaded areas. The dot-dashed line shows the STARLIGHT MC prediction and the dashed line corresponds to the LO QED calculation of Ref. [558]. The calculation incorporating Sudakov radiative corrections is also compared to data in Ref. [208], leading to an overall better agreement. (Figure adapted from Ref. [208].)

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Figure 103:
Schematic diagrams of light-by-light scattering ($ \gamma\gamma \to \gamma\gamma $, left), QED dielectron ($ \gamma\gamma \to \mathrm{e}^+\mathrm{e}^- $, center), and central exclusive diphoton ($ \mathrm{g}\mathrm{g} \to \gamma\gamma $, right) production in ultraperipheral PbPb collisions. The ``($ \ast $)'' superscript indicates a potential electromagnetic excitation of the outgoing ions. (Figure adapted from Ref. [535].)

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Figure 104:
Acoplanarity distribution of exclusive $ \mathrm{e}^+\mathrm{e}^- $ events measured in data (circles), compared to the expected QED $ \mathrm{e}^+\mathrm{e}^- $ spectrum in a LO MC simulation (histogram). The curve shows a $ \chi^2 $ fit to the sum of two exponential distributions, corresponding to exclusive $ \mathrm{e}^+\mathrm{e}^- $ plus any residual (nonacoplanar) background pairs. The error bars represent statistical uncertainties while the hashed bands around the histogram represent the systematic and MC statistical uncertainties added in quadrature. The horizontal bars indicate the bin size. (Figure adapted from Ref. [535].)

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Figure 105:
Comparison of data (circles) and MC expectation (histogram) for the exclusive $ \mathrm{e}^+\mathrm{e}^- $ events passing the selection criteria, as a function of dielectron acoplanarity (upper left), mass (upper right), $ p_{\mathrm{T}} $ (lower left), and rapidity $ y $ (lower right). The error bars around the data points represent statistical uncertainties, while the hashed bands around the histograms represent the systematic and MC statistical uncertainties added in quadrature. The horizontal bars indicate the bin size. The ratio of the data to the MC expectation is shown in the lower panels. (Figures adapted from Ref. [535].)

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Figure 105-a:
Comparison of data (circles) and MC expectation (histogram) for the exclusive $ \mathrm{e}^+\mathrm{e}^- $ events passing the selection criteria, as a function of dielectron acoplanarity (upper left), mass (upper right), $ p_{\mathrm{T}} $ (lower left), and rapidity $ y $ (lower right). The error bars around the data points represent statistical uncertainties, while the hashed bands around the histograms represent the systematic and MC statistical uncertainties added in quadrature. The horizontal bars indicate the bin size. The ratio of the data to the MC expectation is shown in the lower panels. (Figures adapted from Ref. [535].)

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Figure 105-b:
Comparison of data (circles) and MC expectation (histogram) for the exclusive $ \mathrm{e}^+\mathrm{e}^- $ events passing the selection criteria, as a function of dielectron acoplanarity (upper left), mass (upper right), $ p_{\mathrm{T}} $ (lower left), and rapidity $ y $ (lower right). The error bars around the data points represent statistical uncertainties, while the hashed bands around the histograms represent the systematic and MC statistical uncertainties added in quadrature. The horizontal bars indicate the bin size. The ratio of the data to the MC expectation is shown in the lower panels. (Figures adapted from Ref. [535].)

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Figure 105-c:
Comparison of data (circles) and MC expectation (histogram) for the exclusive $ \mathrm{e}^+\mathrm{e}^- $ events passing the selection criteria, as a function of dielectron acoplanarity (upper left), mass (upper right), $ p_{\mathrm{T}} $ (lower left), and rapidity $ y $ (lower right). The error bars around the data points represent statistical uncertainties, while the hashed bands around the histograms represent the systematic and MC statistical uncertainties added in quadrature. The horizontal bars indicate the bin size. The ratio of the data to the MC expectation is shown in the lower panels. (Figures adapted from Ref. [535].)

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Figure 105-d:
Comparison of data (circles) and MC expectation (histogram) for the exclusive $ \mathrm{e}^+\mathrm{e}^- $ events passing the selection criteria, as a function of dielectron acoplanarity (upper left), mass (upper right), $ p_{\mathrm{T}} $ (lower left), and rapidity $ y $ (lower right). The error bars around the data points represent statistical uncertainties, while the hashed bands around the histograms represent the systematic and MC statistical uncertainties added in quadrature. The horizontal bars indicate the bin size. The ratio of the data to the MC expectation is shown in the lower panels. (Figures adapted from Ref. [535].)

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Figure 106:
Distributions of the single photon $ E_{\mathrm{T}} $ (upper left) and $ \eta $ (upper right), as well as diphoton invariant mass (lower left) and $ p_{\mathrm{T}} $ (lower right), measured for the exclusive events passing the selection criteria (squares), compared to the expectations of LbL scattering signal (orange), QED $ \mathrm{e}^+ \mathrm{e}^- $ MC generator predictions (yellow), and the CEP background (light blue). The error bars indicate statistical uncertainties. (Figures adapted from Ref. [535].)

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Figure 106-a:
Distributions of the single photon $ E_{\mathrm{T}} $ (upper left) and $ \eta $ (upper right), as well as diphoton invariant mass (lower left) and $ p_{\mathrm{T}} $ (lower right), measured for the exclusive events passing the selection criteria (squares), compared to the expectations of LbL scattering signal (orange), QED $ \mathrm{e}^+ \mathrm{e}^- $ MC generator predictions (yellow), and the CEP background (light blue). The error bars indicate statistical uncertainties. (Figures adapted from Ref. [535].)

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Figure 106-b:
Distributions of the single photon $ E_{\mathrm{T}} $ (upper left) and $ \eta $ (upper right), as well as diphoton invariant mass (lower left) and $ p_{\mathrm{T}} $ (lower right), measured for the exclusive events passing the selection criteria (squares), compared to the expectations of LbL scattering signal (orange), QED $ \mathrm{e}^+ \mathrm{e}^- $ MC generator predictions (yellow), and the CEP background (light blue). The error bars indicate statistical uncertainties. (Figures adapted from Ref. [535].)

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Figure 106-c:
Distributions of the single photon $ E_{\mathrm{T}} $ (upper left) and $ \eta $ (upper right), as well as diphoton invariant mass (lower left) and $ p_{\mathrm{T}} $ (lower right), measured for the exclusive events passing the selection criteria (squares), compared to the expectations of LbL scattering signal (orange), QED $ \mathrm{e}^+ \mathrm{e}^- $ MC generator predictions (yellow), and the CEP background (light blue). The error bars indicate statistical uncertainties. (Figures adapted from Ref. [535].)

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Figure 106-d:
Distributions of the single photon $ E_{\mathrm{T}} $ (upper left) and $ \eta $ (upper right), as well as diphoton invariant mass (lower left) and $ p_{\mathrm{T}} $ (lower right), measured for the exclusive events passing the selection criteria (squares), compared to the expectations of LbL scattering signal (orange), QED $ \mathrm{e}^+ \mathrm{e}^- $ MC generator predictions (yellow), and the CEP background (light blue). The error bars indicate statistical uncertainties. (Figures adapted from Ref. [535].)

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Figure 107:
Transverse momentum of the muon originating from the $ \tau_{\mu} $ candidate (upper left). Invariant mass of the three pions forming the $ \tau_{\text{3prong}} $ candidate (upper right). Invariant mass of the $ \tau^{+}\tau^{-} $ system (lower left). The $ \Delta\phi(\tau_{\mu},\tau_{\text{3prong}}) $ azimuthal difference (lower right). In all plots, the signal component (magenta histogram) is stacked on top of the background component (green histogram). The sum of signal and background is displayed by a blue line and the shaded area shows the statistical uncertainty. The data are represented with black points and the uncertainty is statistical only. The lower panels show the ratios of data to the signal-plus-background prediction and the shaded bands represent the statistical uncertainty in the prefit expectation. (Figures adapted from Ref. [536].)

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Figure 107-a:
Transverse momentum of the muon originating from the $ \tau_{\mu} $ candidate (upper left). Invariant mass of the three pions forming the $ \tau_{\text{3prong}} $ candidate (upper right). Invariant mass of the $ \tau^{+}\tau^{-} $ system (lower left). The $ \Delta\phi(\tau_{\mu},\tau_{\text{3prong}}) $ azimuthal difference (lower right). In all plots, the signal component (magenta histogram) is stacked on top of the background component (green histogram). The sum of signal and background is displayed by a blue line and the shaded area shows the statistical uncertainty. The data are represented with black points and the uncertainty is statistical only. The lower panels show the ratios of data to the signal-plus-background prediction and the shaded bands represent the statistical uncertainty in the prefit expectation. (Figures adapted from Ref. [536].)

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Figure 107-b:
Transverse momentum of the muon originating from the $ \tau_{\mu} $ candidate (upper left). Invariant mass of the three pions forming the $ \tau_{\text{3prong}} $ candidate (upper right). Invariant mass of the $ \tau^{+}\tau^{-} $ system (lower left). The $ \Delta\phi(\tau_{\mu},\tau_{\text{3prong}}) $ azimuthal difference (lower right). In all plots, the signal component (magenta histogram) is stacked on top of the background component (green histogram). The sum of signal and background is displayed by a blue line and the shaded area shows the statistical uncertainty. The data are represented with black points and the uncertainty is statistical only. The lower panels show the ratios of data to the signal-plus-background prediction and the shaded bands represent the statistical uncertainty in the prefit expectation. (Figures adapted from Ref. [536].)

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Figure 107-c:
Transverse momentum of the muon originating from the $ \tau_{\mu} $ candidate (upper left). Invariant mass of the three pions forming the $ \tau_{\text{3prong}} $ candidate (upper right). Invariant mass of the $ \tau^{+}\tau^{-} $ system (lower left). The $ \Delta\phi(\tau_{\mu},\tau_{\text{3prong}}) $ azimuthal difference (lower right). In all plots, the signal component (magenta histogram) is stacked on top of the background component (green histogram). The sum of signal and background is displayed by a blue line and the shaded area shows the statistical uncertainty. The data are represented with black points and the uncertainty is statistical only. The lower panels show the ratios of data to the signal-plus-background prediction and the shaded bands represent the statistical uncertainty in the prefit expectation. (Figures adapted from Ref. [536].)

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Figure 107-d:
Transverse momentum of the muon originating from the $ \tau_{\mu} $ candidate (upper left). Invariant mass of the three pions forming the $ \tau_{\text{3prong}} $ candidate (upper right). Invariant mass of the $ \tau^{+}\tau^{-} $ system (lower left). The $ \Delta\phi(\tau_{\mu},\tau_{\text{3prong}}) $ azimuthal difference (lower right). In all plots, the signal component (magenta histogram) is stacked on top of the background component (green histogram). The sum of signal and background is displayed by a blue line and the shaded area shows the statistical uncertainty. The data are represented with black points and the uncertainty is statistical only. The lower panels show the ratios of data to the signal-plus-background prediction and the shaded bands represent the statistical uncertainty in the prefit expectation. (Figures adapted from Ref. [536].)

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Figure 108:
The $ \sigma(\gamma\gamma\to\tau^{+}\tau^{-}) $ cross section, measured in a fiducial phase space region at $ \sqrt{\smash[b]{s_{_{\mathrm{NN}}}}} = $ 5.02 TeV. The theoretical predictions [568,569] are computed with leading order accuracy in QED and are represented by the vertical solid lines, which can be compared with the vertical dotted line representing this measurement. The outer blue (inner red) error bars represent the total (statistical) uncertainties, whereas the green hatched bands correspond to the uncertainty in the theoretical predictions, as described in the text. The potential electromagnetic excitation of the outgoing Pb ions is denoted by $ (^{\ast}) $. (Figure adapted from Ref. [536].)

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Figure 109:
Comparison of the constraints on $ a_{\tau} $ at 68% CL from the analysis in Ref. [536] and the DELPHI experiment at LEP [572]. The projection to the integrated PbPb luminosity expected from the high-luminosity LHC program is included. (Figure adapted from Ref. [536].)

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Figure 110:
Exclusion limits at 95% CL in the ALP-photon coupling $ g_{\mathrm{a}\gamma} $ vs. ALP mass $ m_\mathrm{a} $ plane, for the operators $ \mathrm{a} F\widetilde{F}/4\Lambda $ assuming ALP coupling to photons only, derived in Refs. [574,580] from measurements at beam dumps [581], in $ \mathrm{e}^+\mathrm{e}^- $ collisions at LEP 1 [580] and LEP 2 [582], and in pp collisions at the LHC [561,583,584], and compared to the limits obtained from Ref. [535]. (Figure adapted from Ref. [535].)
Tables

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Table 1:
Summary of HI data-taking periods during Runs 1 and 2.

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Table 2:
Summary of reference pp data-taking periods during Runs 1 and 2. To compare with the nucleon-nucleon-equivalent luminosities from Table 1, it is important to note that the listed integrated luminosities should be divided by factors of either $ \mathrm{A}^2 $ (for the PbPb case) or A (for the pPb case), where $ \mathrm{A}= $ 208 is the Pb mass number.

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Table 3:
Summary of low-PU pp data-taking periods during Runs 1 and 2.

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Table 5:
Geometric quantities and their systematic uncertainties averaged over centrality ranges in PbPb collisions at 5.02 TeV.

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Table 6:
Fraction of MB triggered events after event selections in each multiplicity bin, and the average multiplicity of reconstructed tracks per bin with $ |\eta| < $ 2.4 and $ p_{\mathrm{T}} > $ 0.4 GeV, before ($ N_\text{trk}^\text{offline} $) and after ($ N_\text{trk}^\text{corrected} $) acceptance and efficiency corrections, for pPb and PbPb collisions at 5.02 TeV and 2.76 TeV, respectively [105].
Summary
Discoveries and insights from high-density QCD studies
This review presents the first comprehensive summary of studies conducted by the Compact Muon Solenoid (CMS) Collaboration at the Large Hadron Collider (LHC) in the realm of heavy ion (HI) collisions during the years spanned by Runs 1 (2010-2013) and 2 (2015-2018). The measured processes have shed light on multiple aspects of the physics of high-density quantum chromodynamics (QCD), precision quantum electrodynamics (QED), and even novel searches of phenomena beyond the standard model (BSM). Relative to what was initially envisioned as a compelling HI physics program in CMS, a series of observations and extensions have been achieved, on top of benchmark measurements, that have helped resolve puzzles raised by preceding experimental programs. After successfully addressing experimental challenges (Section 2), measurements in ultrarelativistic HI collisions at the LHC have entered a high-precision era, with major progress in the areas of online event selection and offline physics object reconstruction. The initial state of the nucleons and nuclei before a HI collision strongly influences the subsequent evolution of the created medium. The density of quarks and gluons within a nucleon, as a function of the fraction of the nucleon momentum ($ x $) carried by each parton and the squared transverse momentum transfer ($ Q^2 $), is parameterized in terms of parton distribution functions (PDFs). When the nucleon is embedded in a nucleus, this density is expressed as nuclear PDFs (nPDFs). Proton-lead (pPb) collision data have been used to constrain the quark and gluon nPDFs through measurements of the cross section of electroweak gauge bosons, dijets, and top quark pairs (Section 3). Some of these results have been used as input to the latest nPDF fits, leading to a significant improvement in the precision across an extended phase space region. For studying the small-$ x $ region, which is primarily driven by the evolution of the gluon density, the measurements of forward inclusive jet cross sections in pPb collisions and the cross sections for exclusive vector meson production in pPb and lead-lead (PbPb) collisions have been used. As part of these studies, a technique has been developed to use forward neutron multiplicities in order to unfold the cross sections for exclusive vector meson production in the photon-nucleus frame, giving unprecedented access to the small-$ x $ regime. As expected, the LHC collaborations find a significant increase in the charged particle density and average transverse energy per charged particle compared to those found at RHIC energies, indicating a denser and hotter medium formed at the LHC. The CMS Collaboration has an extensive program for studying such bulk properties of the quark-gluon plasma (QGP) in ultrarelativistic nuclear collisions and searching for novel phenomena (Section 4). Taking advantage of the wide pseudorapidity ($ \eta $) coverage of the CMS apparatus, long-range collective particle correlations (``flow'') are observed with unprecedented high precision. At the same time, factorization breaking in flow harmonics ($ v_n $) has been observed and studied for the first time by the CMS Collaboration and has been shown to have a strong sensitivity to the granularity of initial-state fluctuations. The observation of an $ \eta $-dependent factorization breaking has provided sensitivity to the longitudinal dynamics of the QGP. In addition, the shape and size of the systems produced in different colliding systems and at various LHC energies were also investigated via femtoscopic correlation measurements. In relativistic HI collisions leading to QGP formation, the resulting medium may experience intense magnetic fields produced by the colliding ions. If net chiral (left- or right-handed) quarks are present, a localized current can be generated, leading to a charge separation known as the chiral magnetic effect (CME) and, as a separate process, a long-wavelength collective excitation known as a chiral magnetic wave (CMW). In searching for CME and CMW effects, CMS has unambiguously demonstrated that the signals are too small at LHC energies for either of these two phenomena to be observed. The experimental use of hard probes as a way to study the short-wavelength structure of the QGP has greatly advanced during the LHC Runs 1 and 2 (Section 5). With the initial studies, the depletion of particles with high transverse momentum ($ p_{\mathrm{T}} $) observed in two-particle correlations, at BNL RHIC was confirmed to be the result of jet quenching with LHC measurements of dijet asymmetries using fully reconstructed jets. Further evidence comes from the suppression of jet and hadron yields in HI collisions compared to those expected by scaling up the results from pp collisions. The yield suppression is generally expressed in terms of the nuclear modification factor ($ R_{\mathrm{AA}} $) and can be associated with parton energy loss. Subsequent detailed studies of hadrons and jets have provided information regarding the path-length dependence of parton energy loss. The associated production of jets with electroweak bosons has made possible the determination of the absolute magnitude of the jet energy loss and these studies are now applied to test the survivor bias in inclusive jet samples. A multitude of measurements, including those of jet fragmentation functions and jet shapes, have established a qualitative picture in which quenching redistributes jet energy from the high-$ p_{\mathrm{T}} $ jet constituents to softer particles, and from small to large angles relative to the jet axis. Novel background subtraction algorithms and jet grooming techniques (which remove wide-angle soft radiation from a jet) allow the investigation of the early stages (early vacuum) of a parton shower in the QGP, well before its later medium-modified stage. These studies suggest that jet modifications can be sensitive to the earliest splittings in the evolution of the parton shower. However, further investigations are needed to properly account for a bias when selecting broader early-vacuum structures, and hence more heavily quenched jet momenta. The CMS Collaboration has also performed systematic studies (Section 5) of the mass dependence of quark energy loss by comparing the $ R_{\mathrm{AA}} $ and $ v_2 $ results for fully reconstructed light- and heavy-flavor (charm and beauty) hadrons over an unprecedentedly large $ p_{\mathrm{T}} $ range. These studies led to unique measurements of $ {\mathrm{B}} $ mesons in heavy ion collisions. The hadronization of heavy-flavor particles has also been examined in detail using various ratios of their yields, including, for the first time, details of the internal structure of exotic hadrons in the presence of the QGP. With five quarkonium states at hand ($ \mathrm{J}/\psi $, $\psi(2\mathrm{S})$, and $ \Upsilon{{(n\mathrm{S})}} $, $ n= $ 1-3 ), measurements of the modification of their production in pPb and PbPb collisions provide detailed data to improve models aiming to describe the interaction of heavy-quark bound states in strongly interacting matter. The study of the collectivity of charged hadrons in high-multiplicity pp and pPb collisions (Section 6) has provided the first observations of long-range correlations similar to those seen in HI collisions. The CMS Collaboration has offered further evidence of collectivity through multiparticle correlation and heavy-flavor meson analyses. The study of multiparticle correlations has been extended to smaller collision systems using ultraperipheral collisions (UPCs), where the separation of the ions in the transverse plane strongly reduces the role of interactions mediated by quarks and gluons. One of the motivations for the small collision system studies was to search for evidence of jet quenching in these systems, to compare to the results obtained in collisions involving two heavy ions. Jet quenching effects have not been observed in pPb collisions at high $ p_{\mathrm{T}} $. In addition to nuclear hadronic interactions, electromagnetic interactions can also be studied in UPCs (Section 7) since heavy ions with energies of several TeV per nucleon can interact through very intense electromagnetic fields. The Lorentz factor of the Pb beam at the LHC determines the maximum quasireal photon energy of approximately 80 GeV, leading to photon-photon collisions of center-of-mass energies up to 160 GeV, i.e.,, similar to those reached at LEP 2 but with $ Z^4 $ enhanced production cross sections. A broad range of precision SM and BSM processes has been studied in these photon-induced interactions, including exclusive high-mass dilepton ($ m_{\ell^{+}\ell^{-}}\gtrsim $ 5 GeV) production as well as the rare processes of light-by-light (LbL ) scattering and $ \tau $ lepton production.

Future physics opportunities at CMS for high-density QCD measurements
The QCD theory, a cornerstone of the standard model (SM), remains a crucial aspect in our understanding of the strong interaction, albeit with lingering questions. The large values of strong coupling ($ \alpha_\mathrm{S} $) at low $ Q^2 $ render the traditional small-$ \alpha_\mathrm{S} $ perturbation theory inapplicable, such that collective phenomena in nuclei are nonperturbative. However, a coordinated application of the QCD parton model for conventional hadrons, an effort to grasp the exotic hadron spectroscopy, and advances from lattice QCD calculations hold promise of a fundamentally improved understanding of the characteristics of nuclei and their interactions and how deconfinement arises. Many unresolved questions remain regarding the precise nature of the initial state from which thermal QCD matter potentially emerges. How the parton density varies across the broad nuclear $ (x, Q^2) $ phase space is still only partially known and, in particular, no unambiguous evidence has yet been found to mark the onset of parton saturation. Additionally, it is not yet quantitatively understood how the collective properties of the quark-gluon plasma emerge at a microscopic level from the interactions among the individual quarks and gluons that make up this medium. Therefore, a crucial aspect of nuclear studies is the exploitation of future opportunities for high-density QCD studies with ion and proton beams. This will allow for the study of cold nuclear matter effects, the onset of nuclear saturation, and the emergence of long-range correlations. Examination of high-$ p_{\mathrm{T}} $ hadrons, fully reconstructed jets, heavy quarkonia, open heavy-flavor particles, as well as novel tools [585] to investigate more detailed aspects [586] of jet quenching, will provide additional information about the strongly coupled QGP, complementing the bulk and collective observables of the soft sector. Long-term initiatives, such as the use of top quarks to unravel the intricacies of jet quenching at different time scales of the QGP evolution, are in their early stages and are projected to rapidly progress with the increased luminosity anticipated in the LHC Run 3 (2022-2025) and beyond. A pilot run of oxygen-oxygen and proton-oxygen collisions will help answer the key prerequisite conditions for the onset of hot-medium effects [587]. It is also important to understand the level at which these effects could be phenomenologically limited by knowledge of nPDFs. At present, there is a lack of experimental oxygen data for comprehensive global nPDF fitting, underscoring the importance of proton-oxygen collisions in ensuring the accuracy of nPDFs for lighter ions. This also has far-reaching implications for modeling ultrahigh-energy (cosmic ray) phenomena, and is crucial for addressing significant unresolved questions in this field [588]. In addition to the larger luminosity, the detector upgrades planned for the CMS experiment in the LHC Run 4 (starting in year 2029) will significantly benefit the HI program. In particular, the increased $ \eta $ acceptance for charged particles resulting from tracker upgrades [589] will be very beneficial for bulk particle measurements. The upgraded Zero Degree Calorimeters [590] will further improve the existing triggering and identification of UPCs. The addition of time-of-flight particle identification capability, enabled by the Minimum Ionizing Particle Timing Detector [591], will allow identification between low-momentum charged hadrons, such as pions, kaons, and protons, which will improve the measurements of heavy-flavored particles and neutral strange hadrons, while improving the prospects for identified jet substructure measurements [592]. Proton-nucleus collisions have been an integral part of the LHC program since the 2011 and 2012 pilot runs. Within collinear factorization, constraints on our knowledge of the nuclear wave functions were extended at high $ Q^2 $ using dijet, heavy gauge boson, and top quark production processes available for the first time in nuclear collisions. Further insights have been gained at lower $ Q^2 $ with heavy-flavor production based on the assumption that the nuclear modification of their yields can be accurately incorporated in global analyses of nPDFs. In Run 2, the increased luminosity and detector improvements allowed for increased statistical precision, expanding the kinematic reach to encompass a broader range of accessible processes. Following the discoveries of collective-like effects in small collision systems, an order of magnitude higher integrated luminosity target for pPb collisions is set for Runs 3 and 4, including a large sample of pp collisions at the highest LHC energy, but with moderate pileup to reach the largest possible multiplicities over a full range of hadronic colliding systems. The large PbPb integrated luminosity in Runs 3 and 4, coupled with high-accuracy theoretical QED calculations and several detector upgrades, will maximize the potential of UPC measurements. Collectively, these factors will broaden the phase space region and overall scope of physics exploration in the studies of low-mass resonances, the continuum, and heavy-flavor mesons in UPC events. The primary goal will be to cover a much wider range of masses: the expected spectrum obtainable by CMS for a 13 nb$^{-1}$ integrated luminosity run can extend to masses up to about 200 GeV, bridging the gap for BSM searches between PbPb and pp collisions (in the latter case, by employing the forward proton tagging technique) and overall extending the physics reach not only for (pseudo)scalar but also for tensor resonances [575]. Interestingly, these high-mass pairs correspond to two-photon interactions in, or in close proximity to the two nuclei, enhancing the effects owing to interactions with the medium and magnetic fields associated with the QGP. Lower masses should be accessible with looser requirements for track and electron $ p_{\mathrm{T}} $ and their overall identification quality [593]. Exclusive dimuon production can offer a precision measurement of photon fluxes associated with ion beams, and as such can be used to constrain predictions for all other UPC processes. Additional LbL scattering data will also be crucial in determining the nature of newly discovered resonant structures, such as the X(6900) state [594]. Continuing the LHC HI physics program into the HL-LHC era [595,596] offers the opportunity to collide intermediate-mass nuclei (e.g., oxygen and argon), facilitating the study of the initial stage of ion collisions, small-$ x $ physics, and the determination of nPDFs. Furthermore, higher luminosities will allow vastly improved access to rare probes of the QGP. At the same time, it complements other key research efforts in the nuclear physics QCD community (e.g., ongoing efforts at RHIC [597] and the upcoming Electron-Ion Collider [598]), as well as technical developments in the high-energy and cosmic-ray [546] physics communities. Collectively, these initiatives will be pivotal in deepening our understanding of both QCD and QED, illuminating the intricate nature of matter in the early microseconds of the universe.
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