Quarkonia and Deconfined Quark-Gluon Matter in Heavy-Ion Collisions

1. INTRODUCTION

• Color screening in the hot, dense QGP was proposed to weaken quark-antiquark binding, suppressing quarkonium production, with more loosely bound states expected to be suppressed first as temperature rises.The screening length is inversely proportional to QGP temperature.Source: §1 · p. 2
• At the SPS, J/ψ and ψ(2S) were anomalously suppressed beyond cold nuclear matter effects, and ψ(2S) yields were more reduced, consistent with sequential suppression.These observations, together with other SPS results, preceded CERN's 2000 announcement of evidence for QGP formation in Pb-Pb collisions.Source: §1 · p. 2
• At higher collision energies, (re)generation from nearby charm quarks partially balances quarkonium suppression, with central-collision charm-pair production rising from about 0.2 at top SPS energy to ∼120 at top LHC energy.Quarks and antiquarks can combine during the deconfined phase or at hadronization.Source: §1 · p. 3
• LHC energies enabled measurements of bottomonia, complementing SPS studies of J/ψ and ψ(2S), while the different binding energies across quarkonium states provide varied probes of the medium.Bottomonia are bound states of b and ¯b quarks.Source: §1 · p. 3
• Measurements spanning broad rapidity and transverse-momentum ranges are available at RHIC and the LHC, providing detailed quarkonium studies and severe constraints on theory models.Across collision energies and a full family of particles, these measurements support quarkonium's role as a signature of QGP formation.Source: §1 · p. 3

2.1. The vacuum properties of quarkonia

• Table 1 collects vacuum properties, lepton-pair branching ratios, and feed-down fractions; Δm serves as a proxy for binding energy.Feed-down fractions are approximate averages, depend on pT, and differ in nucleus-nucleus collisions from proton-proton collisions; for J/ψ, the cited pp averages include about 8% from ψ(2S) and 22% from χc1,2.Source: §2.1 · pp. 3–4, Table 1 · p. 3

2.2. General considerations

• Heavy-quark pairs are produced in the initial stage on sub-1 fm/c timescales, while quarkonium formation takes about 1 fm/c or longer.Charm and bottom quarks are expected to thermalize more slowly than the bulk medium; lattice calculations find little temperature dependence in the real potential but strong dependence in its imaginary part, making a screening-only quarkonium thermometer too simplistic.Source: §2.2 · p. 4

2.3. Theoretical models.

• The review distinguishes statistical hadronization from dynamical transport approaches to quarkonium in the QGP.The statistical hadronization model assumes full dissociation in the QGP and regeneration at the QCD phase boundary; its applicability requires complete heavy-quark thermalization down to crossover.Source: §2.3 · p. 5, §2.3.1 · p. 5

2.3.1. The Statistical Hadronization Model.

• SHMc uses initial charm production and thermal hadron densities to determine heavy-hadron yields, with the charm fugacity entering linearly for single-charm hadrons and quadratically for charmonia.The approach also uses a canonical correction for exact charm conservation; the bottom-sector application must account for incomplete bottom-quark thermalization.Source: §2.3.1 · pp. 5–6

2.3.2. Transport Models.

• Transport rate equations combine quarkonium loss through dissociation with gain through regeneration from heavy-quark pairs in the medium.The fireball temperature history is constrained using hydrodynamic comparisons to flow data, while reaction rates are phenomenologically modeled; implementations differ in rate and in-medium binding-energy inputs, and excited-state rates and their model spread are larger.Source: §2.3.2 · pp. 6–7
• Open-quantum-system approaches use quantum master equations and, under specified conditions, can reduce to a Lindblad equation in the quantum Brownian-motion regime.Current quantum-transport approaches mostly focus on bottomonia, include regeneration within a single b-bbar pair, and find quantum effects most significant in early evolution.Source: §2.3.2 · p. 7
• SHMc describes the measured J/ψ-to-D0 relative yield, while TAMU predicts centrality-dependent regeneration reaching about 80% in central collisions.In central collisions, initially produced J/ψ contributes about 5% of the total yield; at ⟨Npart⟩ ≃ 100, TAMU predicts regeneration equal to the primordial yield, whereas SHMc generates all yield at the QCD crossover boundary.Source: §2.3.2 · pp. 7–8, Figure 2 · p. 8
• The SHMc and TAMU predictions use different charm-production cross sections, 0.68 ± 0.10 mb and 0.93 ± 0.12 mb, respectively.The review identifies this mismatch as needing resolution; a precise measurement requires all ground-state open-charm mesons and baryons down to zero pT in nuclear collisions.Source: §2.3.2 · p. 8

• The report outlines the status of quarkonium measurements in nucleus-nucleus collisions.Source: §3 · p. 9
• Its emphasis is on RHIC and LHC data.Source: §3 · p. 9
• A separate review covers SPS and early RHIC data and their theoretical interpretation (19, 29).Source: §3 · p. 9

3.1. Quarkonium observables

• The nuclear modification factor RAA compares quarkonium yield in AA collisions with its yield in proton-proton interactions.Source: §3.1 · p. 9
• Elliptic flow v2 and polarization provide additional information about quarkonium behavior and the interplay between suppression and (re)generation.Source: §3.1 · p. 9
• In non-central collisions, v2 measures the second Fourier coefficient of particle azimuthal distribution relative to the reaction plane; thermalized charm quarks would yield nonzero quarkonium v2.Source: §3.1 · p. 9
• Quarkonium polarization may be influenced by the early strong magnetic field or QGP vorticity, and regenerated J/ψ might differ from primordial J/ψ.Source: §3.1 · p. 9

3.2. pp and pA collision systems for quarkonium studies

• pp measurements provide a reference for AA results and must match the AA data in collision energy and kinematic range.Source: §3.2 · p. 10
• CNM effects include nuclear shadowing or CGC formation, parton and pair energy loss, and dissociation by nucleons; dissociation is negligible at LHC energies.Source: §3.2 · p. 10
• pA or dA collisions help isolate cold nuclear matter effects, whose size must be assessed to establish the impact of QGP effects in AA collisions.Source: §3.2 · p. 10
• At LHC and RHIC energies, final-state breakup effects are negligible because quarkonium formation takes longer than the c¯c pair spends in the medium.Source: §3.2 · p. 10
• The ψ(2S) shows greater RpA suppression than J/ψ, particularly at backward rapidity, suggesting additional final-state effects in high-multiplicity p(d)-A collisions.Source: §3.2 · p. 10

3.3.1. J/ψ in AA collisions.

• At LHC energies, J/ψ RAA rises toward unity in central collisions and low pT, unlike the stronger suppression and weak pT dependence at RHIC.The contrast across collision energies suggests that mechanisms beyond color screening contribute; the low-pT observations are interpreted as consistent with (re)generation.Source: §3.3.1 · pp. 11–12
• Both SHMc and TAMU describe J/ψ RAA centrality dependence and low-pT data, but SHMc shows high-pT discrepancies.TAMU estimates (re)generation accounts for about 80% of J/ψ production in central midrapidity collisions and about 50% at forward rapidity; the fractions are higher at very low pT.Source: §3.3.1 · pp. 13–14

3.3.2. J/ψ elliptic flow.

• J/ψ v2 reaches 0.1 near pT ∼4 GeV/c in semi-central LHC collisions; TAMU describes the measured range, while SHMc overestimates the data.The observed flow is interpreted as consistent with a large fraction of J/ψ originating from (re)generation of charm quarks participating in collective expansion.Source: §3.3.2 · pp. 14–15

3.3.3. J/ψ polarization.

• ALICE polarization parameters are compatible with zero, while event-plane analysis finds small transverse polarization with significance up to 3.9σ at intermediate pT and centrality.Quantitative interpretation requires more detailed theory connecting J/ψ production to QGP properties and larger experimental luminosities.Source: §3.3.3 · pp. 15–16

3.3.4. ψ(2S) in AA collisions.

• Measurements of χc in AA are unavailable, while ψ(2S) measurement is challenging because its dimuon branching ratio is about 7.5 times lower than J/ψ and its pp cross section about six times smaller.Reconstructing χc also faces difficulties in its radiative decay to J/ψ γ.Source: §3.3.4 · p. 16
• At LHC forward rapidity, the ψ(2S)-to-J/ψ production ratio shows no significant centrality dependence in ALICE's four bins, unlike the decreasing SPS trend.TAMU describes the ALICE trend within uncertainties; SHMc slightly underestimates the most-central data.Source: §3.3.4 · pp. 16–17
• Across the explored pT range, ψ(2S) RAA follows a trend similar to J/ψ but is suppressed by almost a factor of two more.The low-pT rise is interpreted as evidence that (re)generation also contributes for ψ(2S); TAMU describes its RAA, with most ψ(2S) regenerated at low pT in central and semi-central collisions.Source: §3.3.4 · p. 17

3.4. Bottomonium experimental results

• Υ(1S) suppression follows a similar multiplicity trend at RHIC and LHC, falling by almost a factor of four from peripheral to most central LHC events.Unlike charmonia, the Υ(1S) results show no significant energy dependence and have similar suppression at forward and midrapidity, with mild pT dependence.Source: §3.4 · p. 18
• In central collisions, Υ(1S), Υ(2S), and Υ(3S) are suppressed by factors of about 3, 10, and nearly complete disappearance, respectively.The pattern is termed sequential suppression; feed-down from excited states and cold nuclear matter effects complicate interpretation of Υ(1S) suppression.Source: §3.4 · p. 18
• TAMU and OQS+pNRQCD describe the bottomonium measurements, with regeneration improving OQS+pNRQCD agreement and contributing about 20% for Υ(1S) and 40% for Υ(2S) in TAMU.The TAMU regeneration fractions depend on centrality and pT; statistical hadronization describes the data assuming 30–50% of bottom-quark pairs thermalize.Source: §3.4 · pp. 18–19
• Υ(1S) shows only a small increase in RAA with pT, while its elliptic flow and that of Υ(2S) are compatible with zero within large uncertainties.The pT data are for midrapidity in 0–90% Pb–Pb collisions; sequential suppression is also seen across centrality.Source: §3.4 · p. 19

4. WRAP UP ON CURRENT UNDERSTANDING OF QUARKONIA IN QGP

• Quarkonium states span binding energies from about 50 MeV for ψ(2S) to about 1.1 GeV for Υ(1S), with measurements covering √sNN from 17 GeV to 5.36 TeV.The variety of binding energies and broad measurement coverage provide handles for studying QGP properties.Source: §4 · p. 20
• At LHC, J/ψ RAA rises slightly above unity at low pT and midrapidity before decreasing strongly at high pT, and its nonzero v2 suggests charm thermalization and collective flow.At lower energies, the pT dependence is milder.Source: §4 · p. 20
• At LHC midrapidity and low pT, J/ψ production is dominated by (re)generation, with about 16 c¯c pairs in a central Pb–Pb QGP volume of about 5000 fm^3.Models describe RAA and v2 through an interplay of suppression and (re)generation, with charmonium produced predominantly at or near the QCD crossover boundary.Source: §4 · p. 20
• In central Pb–Pb collisions, Υ(1S) RAA reaches 0.4, Υ(2S) reaches 0.1, and Υ(3S) is almost vanished; suppression dominates, though some (re)generation may occur.Several models describe the measurements while differing in how they represent destruction and (re)generation.Source: §4 · p. 20
• At high pT, p–A RpA approaches unity while Pb–Pb RAA remains reduced for J/ψ and Υ(1S), indicating different mechanisms in the two collision systems.For charmonium, the shadowing-corrected SJ/ψ reaches about 0.3 at high pT and exceeds unity at low pT.Source: §4 · pp. 20–21
• The Υ(1S) shadowing-corrected SΥ(1S) approaches unity at low pT and matches SJ/ψ suppression at high pT, but direct Υ(1S) suppression remains uncertain.Quantification requires feed-down values and their pT dependence, suppression of excited states, and χb measurements, which are unavailable.Source: §4 · p. 21

5. WHAT’S NEXT?

• The χc has not been measured in LHC nucleus-nucleus collisions because reconstructing its radiative decay is extremely difficult.Its 15–30% contribution to J/ψ production, depending on pT, makes χc measurements useful for studying the medium and direct J/ψ modification.Source: §5 · pp. 21–22
• Precise measurements of excited bottomonium states and their feed-down fractions could test whether observed Υ(1S) suppression matches suppression of direct Υ(1S).Source: §5 · p. 22
• Measurements of χc1(3872), whose nature remains unknown, could inform its nature and the roles of (re)generation and suppression, but current uncertainties prevent an answer.The state has been measured in pA and AA collisions; its quantum numbers are JP C = 1++ (142, 143), with proposed interpretations including charmonium, tetraquark, and D∗0 ¯D0 molecule (144, 145, 146).Source: §5 · p. 22
• sPHENIX aims to collect high-luminosity Au-Au data at top RHIC energies in 2025, with measurements expected to resolve three Υ states over a kinematic range comparable to the LHC.The experiment began commissioning and data taking in 2023.Source: §5 · p. 22
• Proposed ALICE 3 would use vertexing and particle identification to study P-wave quarkonia and the as-yet-unmeasured ηc and ηb after LHC LS4, currently foreseen for 2034–2035.The proposal is for a new CERN LHC experiment after LS4 (149).Source: §5 · p. 22
• Proposed NA60+ would scan Pb-beam energies at 6 < √sNN < 17.3 GeV to study charmonium in the high-µB region and correlate J/ψ modification with system temperature.Thermal dimuons would measure temperature; the proposed high-µB coverage is approximately 220–550 MeV (150).Source: §5 · p. 22
• CBM at FAIR would study subthreshold quarkonium production in Au-Au collisions below √sNN = 5 GeV, where collider-energy concepts of QGP melting and charm thermalization do not apply.Transport model calculations are available for these low energies (151, 152).Source: §5 · p. 22

SUMMARY POINTS

• LHC J/ψ production is suppressed at high pT but rises at low pT, while ψ(2S) suppression is roughly twice as strong and bottomonium suppression increases from Υ(1S) to Υ(3S).J/ψ enhancement can exceed unity at midrapidity; J/ψ v2 is significant, whereas Υ(1S) v2 is consistent with zero within large uncertainties.Source: SUMMARY POINTS · p. 23

• The authors report no known affiliations or memberships that might be perceived as affecting the review’s objectivity.Source: DISCLOSURE STATEMENT · p. 23
• The authors report no known funding that might be perceived as affecting the review’s objectivity.Source: DISCLOSURE STATEMENT · p. 23
• The authors report no known financial holdings that might be perceived as affecting the review’s objectivity.Source: DISCLOSURE STATEMENT · p. 23