Pith. sign in

REVIEW 4 major objections 5 minor 63 references

Charm and charmonium transport can be described by one nonperturbative interaction, the thermodynamic T-matrix, coupled through Langevin and Boltzmann equations, with in-medium spectral functions providing a consistent link between charm qu

Reviewed by Pith at T0; open to challenge. T0 means a machine referee read the full paper against a public rubric. the ladder, T0–T4 →

Challenge this review Re-run · record.json Download PDF Read on arXiv ↗

T0 review · deepseek-v4-flash

2026-08-02 18:45 UTC pith:HY3SIDOO

load-bearing objection Same-T-matrix coupling of open and hidden charm is a real step; the off-shell off-equilibrium regeneration factor in Eq. (21) is imposed, not derived, and carries the peripheral R_AA conclusions. the 4 major comments →

arxiv 2603.04674 v2 pith:HY3SIDOO submitted 2026-03-04 nucl-th

Coupled charm and charmonium transport in a strongly coupled quark-gluon plasma

Kaiyu Fu , Biaogang Wu , Ralf Rapp This is my paper
classification nucl-th
keywords charmonium transportquark-gluon plasmacharm quark diffusionT-matrixLangevin dynamicsBoltzmann equationregenerationWilson-line correlators
verification ladder T0 review T1 audit T2 compute T3 formal T4 reserved

The pith

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

Charm quarks and charmonia (bound charm–anticharm states) have usually been treated with separate models in heavy-ion collisions: one for how charm quarks diffuse, another for how J/psi and its excited states dissociate and reform. This paper argues that a single nonperturbative interaction—the thermodynamic T-matrix with in-medium spectral functions constrained by lattice QCD—can govern both. It feeds the same interaction into a Langevin simulation of charm diffusion coupled to a Boltzmann equation for charmonium kinetics, and shows that the charmonium equilibrium limit is recovered when charm quarks thermalize. The framework then reproduces the measured centrality and transverse-momentum dependence of charmonium production in Pb-Pb collisions at the LHC without tuned rates. A sympathetic reader would care because this is a step toward one consistent description of all heavy-flavor probes in the strongly coupled quark-gluon plasma.

Core claim

The paper constructs a closed transport description in which charm-quark and charmonium transport coefficients are computed from the same underlying heavy-light interaction: the nonperturbative T-matrix with broad in-medium spectral functions and a potential constrained by Wilson-line correlators from lattice QCD. It derives the charmonium regeneration rate using off-shell spectral functions, imposes detailed balance with the dissociation rate, and extends the rate to off-equilibrium charm-quark distributions from Langevin dynamics by inserting a thermal off-shell weighting factor. In the thermalized limit this factor reduces to the equilibrium detailed-balance relation and reproduces the st

What carries the argument

The central object is the thermodynamic T-matrix: a nonperturbative scattering amplitude that encodes how a heavy charm quark interacts with light quarks, antiquarks, and gluons, computed self-consistently with in-medium spectral functions and a heavy-quark potential constrained by lattice-QCD Wilson-line correlators. From this single input the paper computes the charm-quark relaxation rate, which feeds the Langevin equation, and the charmonium dissociation and regeneration rates, which feed the Boltzmann equation. The regeneration rate is the mechanism that connects the two sectors: it takes the time-dependent off-equilibrium charm distribution from the Langevin simulation and converts corr

Load-bearing premise

The load-bearing premise is that the off-shell regeneration rate can be modeled by taking the Langevin charm distribution and multiplying by an extra thermal factor exp[-[omega'-epsilon_c]/T] chosen to enforce detailed balance; this factor is not derived from the dynamics, and the predicted suppression of regeneration in peripheral collisions depends on it.

What would settle it

Compute the same off-shell 3-to-2 regeneration rate from a fully quantum nonequilibrium Green's function treatment and compare its thermalized limit to the statistical-model equilibrium limit: if the detailed-balance form is not recovered with the imposed weighting factor, the central phenomenological result fails. Alternatively, a high-precision measurement of peripheral J/psi R_AA at low pT, where off-equilibrium suppression is largest, would test the prediction.

Watch this falsifier — get emailed when new claim-graph text bears on it.

If this is right

  • The same T-matrix interaction now links open-charm, e.g. D-meson, phenomenology to charmonium suppression, so both become tests of one in-medium QCD force without K-factors.
  • When charm quarks thermalize, the ratio of regeneration to dissociation rates reproduces the statistical-model charmonium equilibrium limit, validating the rate construction.
  • Incomplete charm thermalization lowers the effective equilibrium limit relative to the statistical model, most strongly in peripheral collisions, and flattens the regenerated pT spectra.
  • Charmonium states are predicted to survive as broad resonances up to higher temperatures (about 500, 350, and 250 MeV for J/psi, chi_c, and psi(2S)), extending the window in which regeneration can occur.
  • Primordial charmonia are essentially eliminated in central collisions up to pT around 5 GeV, with the final yield dominated by regeneration.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • A consequence the paper leaves implicit: if one interaction governs all heavy-flavor transport, then simultaneous measurements of D mesons, J/psi, chi_c, psi(2S), and bottomonia could be fit globally to pin down the in-medium potential, turning qualitative agreement into a quantitative constraint.
  • The off-shell weighting factor in the regeneration rate is an assumption, not a derivation; a fully quantum nonequilibrium Green's function calculation of the same process would either confirm it or replace it, and the same prescription would then carry over to bottomonium.
  • The centrality-dependent suppression of regeneration implies that the effective charmonium fugacity is not a constant; comparing psi(2S)/J/psi and chi_c/J/psi ratios across centrality could expose this off-equilibrium effect directly.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit.

Referee Report

4 major / 5 minor

Summary. This paper presents a coupled transport framework for open and hidden charm in the quark–gluon plasma formed in Pb–Pb collisions at the LHC. Charm-quark diffusion is simulated with relativistic Langevin dynamics, with the input relaxation rate A(p) computed from a thermodynamic T-matrix constrained by lattice-QCD Wilson-line correlators and including off-shell charm and light-parton spectral functions. Charmonium dissociation rates α for J/ψ, χ_c, and ψ(2S) are computed from the same T-matrix in a quasifree approximation, and the regeneration rate β is constructed from α through a detailed-balance relation (Eq. 17), which fixes the charmonium equilibrium limit to f_eq = γ_c² d_Ψ exp(−E_Ψ/T) (Eq. 26). The new element is the off-equilibrium extension of the regeneration rate (Eq. 21), in which the thermal charm occupation n_c(ω′) is replaced by the Langevin-evolved distribution f_c(p′) multiplied by an additional thermal off-shell weight exp[−(ω′−ε_c(p′))/T]; this is the paper's mechanism for controlling regeneration from non-thermalized charm. The framework is applied to Pb–Pb at √s_NN = 5.02 TeV using a schematic blast-wave fireball, producing R_AA as a function of centrality and p_T for J/ψ, χ_c, and ψ(2S), with fair agreement with ALICE data.

Significance. If the construction holds, this is a significant step: for the first time the same nonperturbative heavy-light interaction and the same in-medium spectral functions determine both open-charm diffusion and charmonium kinetics in a coupled Langevin–Boltzmann simulation, without K-factors. Strengths include the transparent derivation of the thermal regeneration rate (Eq. 20) from Eq. (16) via the identity n(E)=e^{−E/T}(1±n(E)); the internally consistent equilibrium limit, which is non-trivial to realize with broad spectral functions; the absence of tuned transport parameters; and falsifiable predictions for χ_c and ψ(2S) R_AA(p_T) and centrality dependence that can be confronted with LHC data. The improved peripheral low-p_T description relative to earlier blast-wave treatments is a concrete, credit-worthy result. However, the central novelty—the off-equilibrium regeneration rate in Eq. (21)—rests on an underexplained ansatz, the equilibrium-limit 'recovery' is enforced by construction, and the theoretical uncertainties on the rates are unquantified. These issues are addressable but currently limit the strength of the phenomenological claims.

major comments (4)
  1. [Sec. 3.2, Eq. (21)] The central new ingredient is introduced by replacing n_c(ω′) with f_c(p′_c) exp[−(ω′−ε_c(p′_c))/T], justified only by 'It turns out that…' and the requirement of the correct equilibrium limit. Since ρ_c(ω′,p′) already weights off-shell energies, the exponential is a further dynamical assumption: off-shell fluctuations are thermally populated at temperature T even when the momentum distribution f_c is far from equilibrium. The peripheral suppression of the equilibrium limit (dashed curves in Fig. 11) and the low-p_T regenerated R_AA in Figs. 13–15 inherit this prescription; no derivation (e.g., from a Kadanoff–Baym G^< ansatz) and no sensitivity estimate are given. Please derive the weight or test alternatives (no extra weight; on-shell projection; n(ω′)/n(ε(p′)) ratio) and report the effect on Fig. 11 and the peripheral R_AA. Note also that Eq. (23) yields exp(−ω′/T), whereas Eq. (20) c
  2. [Sec. 3.3, Eqs. (17),(26); Fig. 10] The equilibrium limit f^eq = β/α = γ_c² d_Ψ exp(−E_Ψ/T) is enforced by construction: β is defined in Eq. (17) as γ_c² d_Ψ exp(−E_Ψ/T) α, and Eq. (26) then follows from the stationary limit of Eq. (8). The comparison with the statistical-model curve in Fig. 10 therefore validates the internal consistency of the off-shell phase-space integrals, not the statistical-model equilibrium limit independently. Moreover, the two curves share the same charm fugacity from Eq. (27), the same masses, and the same binding energies, so the agreement is not an independent check. The abstract's wording ('the equilibrium limit of the statistical model is recovered') should be softened; the non-trivial content—consistency of the off-shell integral structure with the identity n=e^{−E/T}(1±n)—should be stated as such.
  3. [Sec. 4.2 (hadronic-phase matching); Fig. 11] The hadronic-phase regeneration is bridged by rescaling the QGP off-equilibrium suppression factor and holding it fixed throughout the hadronic evolution: 'we utilize the reduction of the equilibrium limit from the QGP phase at T_H ... and use the same rescaling factor throughout the hadronic medium evolution.' This is an ad hoc assumption; charm-quark distributions continue to evolve (or freeze) through hadronization, and the final R_AA values—especially for peripheral and semi-central collisions, where the hadronic phase occupies a sizeable fraction of the fireball lifetime—inherit this choice directly. A sensitivity estimate (e.g., varying the rescale factor between its central value and unity, or matching to a hadronic Langevin evolution) is needed to establish that the reported centrality trends do not depend on this bridge.
  4. [Secs. 2.2, 3.2, 4.3] The central transport inputs (A(p), α_Ψ, β, m*_c(T)) are presented as single curves with no propagated uncertainties from the WLC lattice constraints or the T-matrix fits. The shadowing bands in Figs. 12–15 are included, but the dominant theoretical uncertainty likely lies in the rates themselves. Since the paper's phenomenological statements are comparative ('capture the measured centrality and momentum dependence fairly well', 'slight underestimation', 'overshoot'), an estimate of the rate uncertainty, or a scan over, e.g., the WLC scenarios or the correlation-volume parameters (as done for κ in Sec. 3.3), would materially strengthen those conclusions.
minor comments (5)
  1. [Sec. 3.2, Eq. (21)] The notation f_c(p′_c, T(t)) is misleading: the Langevin distribution has time, not temperature, as its second argument. Write f_c(p′_c, t), and state the normalization convention (per state vs total number) so that the γ_c² prefactor does not double-count charm number.
  2. [Eq. (27)] Please clarify the volume factors: the canonical open-charm term carries a V_FB prefactor while the Bessel argument uses V_co. If this is the intended Zhao–Rapp convention, a parenthetical justification would prevent confusion.
  3. [Eq. (16); Fig. 2] The interference factor '1−e ik·r' should be typeset as 1−e^{ik·r}, and its sign/real-part convention relative to Ref. [19] should be stated explicitly.
  4. [Fig. 1 caption] The temperature list ('700 500 352 293 251 195 174') is printed below the legend boxes; a color bar or direct labeling of the curves would be clearer.
  5. [Sec. 5] The phrase 'up to about p_T ≃ 5(2) GeV' is unclear; specify which states correspond to which values.

Circularity Check

2 steps flagged

Equilibrium limit is enforced by the detailed-balance ansatz (Eq. 17) and the off-shell regeneration weight in Eq. (21) is an imposed, underived factor; nevertheless the central transport framework is anchored to external lattice-QCD inputs and independent Langevin dynamics.

specific steps
  1. self definitional [Sec. 3.2, Eq. (17); Sec. 3.3, Eqs. (25)-(26)]
    "We start from the detailed-balance relation in thermal equilibrium [27], β(PΨ, T)=γ_c^2 d_Ψ e^{-E_Ψ(P_Ψ)/T} α(P_Ψ,T), ... and thus f^eq_Ψ(x,p,t)=γ_c^2 d_Ψ e^{-E_Ψ/T(t)}."

    Since β is defined in Eq. (17) as γ^2 d e^{-E/T} times α, inserting this into Eq. (25), f_eq=β/α, yields f_eq=γ^2 d e^{-E/T} identically. The dissociation rate α, including all broad spectral functions and T-matrix details, cancels exactly. Thus the 'equilibrium limit' is not independently derived from the in-medium spectral functions; it is imposed by the detailed-balance ansatz. The comparison with the statistical model in Fig. 10 uses the same charm fugacity, densities, and masses, so it is a consistency check rather than an external validation.

  2. other [Sec. 3.2, Eq. (21)]
    "It turns out that an additional factor e^{-[ω'−ε_c(p'_c)]/T(t)} , which essentially represents a thermal off-shell weighting, results in the correct equilibrium limit."

    This exponential weight is not derived from the Kadanoff-Baym or Boltzmann dynamics used for the dissociation rate and the charm relaxation rate. It is inserted precisely so that in the thermal limit f_c→exp(-ε_c/T) the combination f_c exp[-[ω'-ε_c]/T] reduces to exp(-ω'/T), recovering Eq. (20). Consequently, the claimed suppression of the equilibrium limit in peripheral collisions, and hence the off-equilibrium regeneration rate, is partly a consequence of this chosen ansatz rather than a first-principles prediction. Since the spectral function ρ_c already encodes off-shell fluctuations, adding a second thermal off-shell weight is an extra dynamical assumption, not a derived result.

full rationale

The paper's core transport framework is not globally circular: the T-matrix interaction is constrained by lattice-QCD Wilson-line correlators, the effective charm mass used for the fugacity is fitted to lattice charm-number susceptibility, and the Langevin-evolved f_c(p,t) is an independent dynamical input. These are external or independent anchors, and the final R_AA comparison to ALICE data is a genuine phenomenological test. The self-citations to prior T-matrix work (Refs. [15,19,21,27,31]) are not used as uniqueness theorems or as substitutes for derivation; they carry lattice/empirical constraints. However, two load-bearing elements reduce to construction rather than independent derivation. First, the equilibrium limit f_eq=β/α is fixed by the detailed-balance definition of β in Eq. (17), so the 'recovery' of the statistical-model limit is a tautology once that ansatz is adopted. Second, the off-shell regeneration rate in Eq. (21) contains an inserted thermal weight that is justified only as 'It turns out that...' and is chosen to reproduce Eq. (20). The peripheral suppression of regeneration is therefore partly an artifact of this imposed weighting. These points warrant a moderate circularity score: the equilibrium claim is definitional, but the broader coupled-transport derivation retains independent content.

Axiom & Free-Parameter Ledger

6 free parameters · 7 axioms · 0 invented entities

No new particles or fields are invented. Effective masses, spectral functions, and the off-shell weighting factor are model constructs within the T-matrix framework, not independent entities. The free parameters are dominated by fitted spectra, shadowing coefficients, and the effective charm-quark mass, which are inputs needed to connect the framework to data.

free parameters (6)
  • Effective charm-quark mass m*_c(T) = ≈1.46 GeV at T=500 MeV; ≈1.76 GeV at T_H=170 MeV
    Fitted to lattice-QCD charm susceptibility χ_c2 via Eq. (28); used only for open-charm density and charm fugacity, not for transport.
  • Correlation-volume parameters r0, <v_c>, κ = r0=1.2 fm, <v_c>=0.6, κ=1
    Hand-set parameters for canonical-to-grand-canonical switching in the charm fugacity; κ sensitivity is checked (10-20% yield variation).
  • Schematic fireball/blast-wave parameters = not listed in text
    Chosen to mimic hydrodynamic temperature evolution, based on Ref. [10]; affects the medium evolution and all R_AA predictions.
  • CNM shadowing parameterization coefficients (Eq. 31) = a1=-0.27, b1=0.17, d1=1.00, a2=-65.39, b2=0.52, d2=-11.14, c1=1.02
    Adopted from Ref. [52] and fitted to p-Pb J/psi data; determines cold-nuclear-matter suppression.
  • pp and charm pT power-law fit parameters (N,A,c,n) = e.g., J/psi forward N=0.0599, A=3.81, c=2, n=3.73; c-quark N=0.045, A=3.3, c=2.2, n=2.7
    Fitted to measured pp spectra and FONLL charm production; set initial charmonium and charm-quark spectra and thus regeneration phase space.
  • Regeneration onset temperatures from pole analysis = J/psi≈500 MeV, chi_c≈350 MeV, psi(2S)≈250 MeV
    Taken from Ref. [21] and used to switch on regeneration; these temperatures are not re-derived in this paper.
axioms (7)
  • standard math Kadanoff-Baym/Fokker-Planck reduction gives the relaxation rate A(p) in Eq. (5).
    The relaxation rate expression is borrowed from Ref. [31]; it underpins the Langevin simulation.
  • domain assumption Thermodynamic T-matrix constrained by static Wilson-line correlators describes off-shell dynamical heavy-light scattering.
    Extrapolates static lattice-QCD potential information to finite-momentum transport coefficients; central input from Ref. [15].
  • ad hoc to paper Quasifree approximation: the 2→3 dissociation process is reduced to 2→2 with effective charm mass m̃_c = m_c - E_B (Eq. 11).
    Replaces explicit three-body kinematics; necessary to use T-matrix amplitudes in the transport rates.
  • ad hoc to paper Off-shell off-equilibrium regeneration factor exp[-[ω'-ε_c]/T] in Eq. (21).
    Inserted to force the correct equilibrium limit; not derived microscopically. It is the weakest structural assumption in the paper.
  • domain assumption Charm-number conservation via fugacity γ_c in Eq. (27), with open-charm density from the fitted effective charm-quark mass.
    Standard statistical-hadronization assumption; the density input is fitted to lattice susceptibility.
  • domain assumption Semiclassical Boltzmann equation for charmonia (Eq. 8), neglecting elastic scattering and quantum coherence.
    This is the fundamental transport framework; quantum effects are deferred to future work.
  • ad hoc to paper No open-charm diffusion in the hadronic phase; the QGP equilibrium-limit reduction factor is rescaled through the hadronic phase.
    Stated in Sec. 4.2; needed for hadronic regeneration but not derived from a hadronic transport calculation.

pith-pipeline@v1.3.0-alltime-deepseek · 21493 in / 10529 out tokens · 95450 ms · 2026-08-02T18:45:42.854423+00:00 · methodology

0 comments
read the original abstract

The quark-gluon plasma (QGP) is a strongly coupled medium in which both open and hidden charm particles experience substantial nonperturbative interactions. This poses a major challenge for a quantitative description of charmonium transport in ultra-relativistic heavy-ion collisions, as it requires a mutually consistent treatment of pertinent transport coefficients. In this work, we present a coupled charm-charmonium transport framework for a strongly coupled QGP based on thermodynamic $T$-matrix interactions with recent constraints from Wilson-line correlators (WLCs) computed in lattice QCD. For the first time, the same underlying heavy-light interactions and in-medium spectral functions are used to self-consistently evaluate charm-quark diffusion and charmonium kinetics. In particular, the charmonium equilibrium limit, a critical transport parameter for regeneration, is evaluated in the presence of broad spectral functions. Charm-quark diffusion is simulated via Langevin dynamics and coupled to a Boltzmann equation for charmonium dissociation and regeneration. The equilibrium limit of the statistical model is recovered once charm quarks thermalize, and its extension to describe off-equilibrium is constructed. Preliminary applications to charmonium observables in Pb--Pb collisions at the LHC capture the measured centrality and momentum dependence fairly well.

discussion (0)

Sign in with ORCID, Apple, or X to comment. Anyone can read and Pith papers without signing in.

Reference graph

Works this paper leans on

63 extracted references · 1 canonical work pages

  1. [1]

    Matsui, T., Satz, H.:J/ψSuppression by Quark-Gluon Plasma Formation. Phys. Lett. B178, 416–422 (1986)

    1986

  2. [2]

    Rapp, R., Blaschke, D., Crochet, P.: Char- monium and bottomonium production in heavy-ion collisions. Prog. Part. Nucl. Phys. 65, 209–266 (2010) https://doi.org/10.1016/ j.ppnp.2010.07.002 arXiv:0807.2470 [hep-ph]

    Pith/arXiv arXiv 2010

  3. [3]

    Landolt- Bornstein23, 424 (2010) https://doi.org/10

    Braun-Munzinger, P., Stachel, J.: Char- monium from Statistical Hadronization of Heavy Quarks – a Probe for Deconfine- ment in the Quark-Gluon Plasma. Landolt- Bornstein23, 424 (2010) https://doi.org/10. 1007/978-3-642-01539-7 14 arXiv:0901.2500 [nucl-th]

    Pith/arXiv arXiv 2010

  4. [4]

    Mocsy, A., Petreczky, P., Strickland, M.: Quarkonia in the Quark Gluon Plasma. Int. J. Mod. Phys. A28, 1340012 (2013) https: //doi.org/10.1142/S0217751X13400125 arXiv:1302.2180 [hep-ph]

    Pith/arXiv arXiv 2013

  5. [5]

    Andronic, A.,et al.: Comparative study of quarkonium transport in hot QCD matter. Eur. Phys. J. A60(4), 88 (2024) https: //doi.org/10.1140/epja/s10050-024-01306-6 arXiv:2402.04366 [nucl-th]

    Pith/arXiv arXiv 2024

  6. [6]

    Braun-Munzinger, P., Stachel, J.: 18 (Non)thermal aspects of charmonium pro- duction and a new look at J / psi suppression. Phys. Lett. B490, 196–202 (2000) https: //doi.org/10.1016/S0370-2693(00)00991-6 arXiv:nucl-th/0007059

    Pith/arXiv arXiv 2000

  7. [7]

    Thews, R.L., Schroedter, M., Rafelski, J.: EnhancedJ/ψproduction in deconfined quark matter. Phys. Rev. C63, 054905 (2001) https://doi.org/10.1103/PhysRevC. 63.054905 arXiv:hep-ph/0007323

    Pith/arXiv arXiv 2001

  8. [8]

    Grandchamp, L., Rapp, R.: Thermal versus direct J / Psi production in ultrarelativistic heavy ion collisions. Phys. Lett. B523, 60–66 (2001) https: //doi.org/10.1016/S0370-2693(01)01311-9 arXiv:hep-ph/0103124

    Pith/arXiv arXiv 2001

  9. [9]

    Du, X., Rapp, R.: Sequential Regeneration of Charmonia in Heavy-Ion Collisions. Nucl. Phys. A943, 147–158 (2015) https://doi. org/10.1016/j.nuclphysa.2015.09.006

    work page doi:10.1016/j.nuclphysa.2015.09.006 2015

  10. [10]

    Universe 10(6), 244 (2024) https://doi.org/10.3390/ universe10060244 arXiv:2404.09881 [nucl-th]

    Wu, B., Rapp, R.: Charmonium Transport in Heavy-Ion Collisions at the LHC. Universe 10(6), 244 (2024) https://doi.org/10.3390/ universe10060244 arXiv:2404.09881 [nucl-th]

    arXiv 2024

  11. [11]

    Shuryak, E.V.: What RHIC experiments and theory tell us about properties of quark- gluon plasma? Nucl. Phys. A750, 64–83 (2005) https://doi.org/10.1016/j.nuclphysa. 2004.10.022 arXiv:hep-ph/0405066

    Pith/arXiv arXiv 2005

  12. [12]

    Hees, H., Greco, V., Rapp, R.: Heavy-quark probes of the quark-gluon plasma at RHIC. Phys. Rev. C73, 034913 (2006) https: //doi.org/10.1103/PhysRevC.73.034913 arXiv:nucl-th/0508055 [nucl-th]

    Pith/arXiv arXiv 2006

  13. [13]

    Beraudo, A.,et al.: Extraction of Heavy- Flavor Transport Coefficients in QCD Matter. Nucl. Phys. A979, 21–86 (2018) https://doi.org/10.1016/j.nuclphysa.2018.09. 002 arXiv:1803.03824 [nucl-th]

    Pith/arXiv arXiv 2018

  14. [14]

    Altenkort, L., Cruz, D., Kaczmarek, O., Larsen, R., Moore, G.D., Mukherjee, S., Petreczky, P., Shu, H.-T., Stendebach, S.: Quark Mass Dependence of Heavy Quark Diffusion Coefficient from Lattice QCD. Phys. Rev. Lett.132(5), 051902 (2024) https: //doi.org/10.1103/PhysRevLett.132.051902 arXiv:2311.01525 [hep-lat]

    Pith/arXiv arXiv 2024

  15. [15]

    Tang, Z., Mukherjee, S., Petreczky, P., Rapp, R.: T-matrix analysis of static Wil- son line correlators from lattice QCD at finite temperature. Eur. Phys. J. A 60(4), 92 (2024) https://doi.org/10.1140/ epja/s10050-024-01310-w arXiv:2310.18864 [hep-lat]

    Pith/arXiv arXiv 2024

  16. [16]

    Wu, B., Rapp, R.: Bottomonium transport in a strongly coupled quark-gluon plasma. Phys. Lett. B873, 140223 (2026) https: //doi.org/10.1016/j.physletb.2026.140223 arXiv:2508.20995 [nucl-th]

    arXiv 2026

  17. [17]

    Bala, D., Kaczmarek, O., Larsen, R., Mukherjee, S., Parkar, G., Petreczky, P., Rothkopf, A., Weber, J.H.: Static quark-antiquark interactions at nonzero temperature from lattice QCD. Phys. Rev. D105(5), 054513 (2022) https: //doi.org/10.1103/PhysRevD.105.054513 arXiv:2110.11659 [hep-lat]

    Pith/arXiv arXiv 2022

  18. [18]

    Krishna, T., Rapp, R., Fu, Y., Bass, S.A., Ke, W.: Nonperturbative heavy-flavor transport approach for hot QCD matter. Phys. Lett. B871, 139999 (2025) https: //doi.org/10.1016/j.physletb.2025.139999 arXiv:2509.13881 [nucl-th]

    arXiv 2025

  19. [19]

    JHEP07, 162 (2025) https://doi.org/10.1007/JHEP07(2025)162 arXiv:2503.10089 [nucl-th]

    Wu, B., Tang, Z., Rapp, R.: Non- perturbative quarkonium dissociation rates in strongly coupled quark- gluon plasma. JHEP07, 162 (2025) https://doi.org/10.1007/JHEP07(2025)162 arXiv:2503.10089 [nucl-th]

    arXiv 2025

  20. [20]

    Thapa, S., Wu, B., Vogt, R., Rapp, R.: Semiclassical treatment of bottomonium sup- pression and regeneration inp+ Pb collisions (2025) arXiv:2510.03456 [nucl-th]

    arXiv 2025

  21. [21]

    Tang, Z., Wu, B., Hanlon, A., Mukherjee, S., Petreczky, P., Rapp, R.: Quarkonium Spec- troscopy in the Quark-Gluon Plasma. Phys. Rev. Lett.135(14), 142302 (2025) https:// doi.org/10.1103/7zby-gy46 arXiv:2502.09044 [nucl-th] 19

    arXiv 2025

  22. [22]

    Grandchamp, L., Rapp, R.: Charmonium suppression and regeneration from SPS to RHIC. Nucl. Phys. A709, 415–439 (2002) https://doi.org/10.1016/S0375-9474(02) 01027-8 arXiv:hep-ph/0205305

    Pith/arXiv arXiv 2002

  23. [23]

    Song, T., Han, K.C., Ko, C.M.: Charmonium production from nonequilibrium charm and anticharm quarks in quark-gluon plasma. Phys. Rev. C85, 054905 (2012) https: //doi.org/10.1103/PhysRevC.85.054905 arXiv:1203.2964 [nucl-th]

    Pith/arXiv arXiv 2012

  24. [24]

    Moore, G.D., Teaney, D.: How much do heavy quarks thermalize in a heavy ion colli- sion? Phys. Rev. C71, 064904 (2005) https: //doi.org/10.1103/PhysRevC.71.064904 arXiv:hep-ph/0412346

    Pith/arXiv arXiv 2005

  25. [25]

    Hees, H., Rapp, R.: Thermalization of heavy quarks in the quark-gluon plasma. Phys. Rev. C71, 034907 (2005) https: //doi.org/10.1103/PhysRevC.71.034907 arXiv:nucl-th/0412015

    Pith/arXiv arXiv 2005

  26. [26]

    Mustafa, M.G.: Energy loss of charm quarks in the quark-gluon plasma: Col- lisional versus radiative. Phys. Rev. C 72, 014905 (2005) https://doi.org/10.1103/ PhysRevC.72.014905 arXiv:hep-ph/0412402

    Pith/arXiv arXiv 2005

  27. [27]

    Du, X., Rapp, R.: Non-equilibrium charmonium regeneration in strongly coupled quark-gluon plasma. Phys. Lett. B834, 137414 (2022) https: //doi.org/10.1016/j.physletb.2022.137414 arXiv:2207.00065 [nucl-th]

    arXiv 2022

  28. [28]

    Svetitsky, B.: Diffusion of charmed quarks in the quark-gluon plasma. Phys. Rev. D37, 2484–2491 (1988)

    1988

  29. [29]

    (eds.) Quark-Gluon Plasma 4, p

    Rapp, R., Hees, H.: In: Hwa, R., Wang, X.N. (eds.) Quark-Gluon Plasma 4, p. 111. World Scientific, Singapore (2010)

    2010

  30. [30]

    He, M., Hees, H., Gossiaux, P.B., Fries, R.J., Rapp, R.: Relativistic Langevin Dynam- ics in Expanding Media. Phys. Rev. E 88, 032138 (2013) https://doi.org/10.1103/ PhysRevE.88.032138 arXiv:1305.1425 [nucl- th]

    Pith/arXiv arXiv 2013

  31. [31]

    Liu, S.Y.F., He, M., Rapp, R.: Prob- ing the in-Medium QCD Force by Open Heavy-Flavor Observables. Phys. Rev. C 99(5), 055201 (2019) https://doi.org/10. 1103/PhysRevC.99.055201 arXiv:1806.05669 [nucl-th]

    Pith/arXiv arXiv 2019

  32. [32]

    Yan, L., Zhuang, P., Xu, N.:j/ψproduc- tion in quark-gluon plasma. Phys. Rev. Lett. 97, 232301 (2006) https://doi.org/10.1103/ PhysRevLett.97.232301

    2006

  33. [33]

    Grandchamp, L., Rapp, R., Brown, G.E.: In medium effects on charmonium produc- tion in heavy ion collisions. Phys. Rev. Lett.92, 212301 (2004) https://doi.org/ 10.1103/PhysRevLett.92.212301 arXiv:hep- ph/0306077

    arXiv 2004

  34. [34]

    JHEP0703, 054 (2007)

    Laine, M., Philipsen, O., Romatschke, P., Tassler, M.: Real-time static potential in hot QCD. JHEP0703, 054 (2007)

    2007

  35. [35]

    Zhao, X., Rapp, R.: Charmonium in Medium: From Correlators to Experiment. Phys. Rev. C82, 064905 (2010) https://doi.org/10. 1103/PhysRevC.82.064905 arXiv:1008.5328 [hep-ph]

    Pith/arXiv arXiv 2010

  36. [36]

    Du, X., He, M., Rapp, R.: Color Screening and Regeneration of Bottomonia in High- Energy Heavy-Ion Collisions. Phys. Rev. C96(5), 054901 (2017) https://doi.org/10. 1103/PhysRevC.96.054901 arXiv:1706.08670 [hep-ph]

    Pith/arXiv arXiv 2017

  37. [37]

    Hamieh, S., Redlich, K., Tounsi, A.: Canonical description of strangeness enhancement from p-A to Pb Pb collisions. Phys. Lett. B486, 61–66 (2000) https: //doi.org/10.1016/S0370-2693(00)00762-0 arXiv:hep-ph/0006024

    Pith/arXiv arXiv 2000

  38. [38]

    Bellwied, R., Borsanyi, S., Fodor, Z., Katz, S.D., Pasztor, A., Ratti, C., Szabo, K.K.: Fluctuations and correlations in high temperature QCD. Phys. Rev. D 92(11), 114505 (2015) https://doi.org/10. 1103/PhysRevD.92.114505 arXiv:1507.04627 [hep-lat]

    Pith/arXiv arXiv 2015

  39. [39]

    Kaczmarek, O., Karsch, F., Petreczky, 20 P., Schmidt, C., Sharma, S.: General- ized susceptibilities and the properties of charm degrees of freedom across the QCD crossover temperature. Phys. Rev. D 112(3), 034509 (2025) https://doi.org/10. 1103/tz74-d3kh arXiv:2505.01734 [hep-lat]

    Pith/arXiv arXiv 2025

  40. [40]

    Acharya, S.,et al.: Inclusive quarkonium pro- duction in pp collisions at √s= 5.02 TeV. Eur. Phys. J. C83(1), 61 (2023) https: //doi.org/10.1140/epjc/s10052-022-10896-8 arXiv:2109.15240 [nucl-ex]

    Pith/arXiv arXiv 2023

  41. [41]

    Aaij, R.,et al.: Measurement ofψ(2S) production cross-sections in proton-proton collisions at √s= 7 and 13 TeV. Eur. Phys. J. C80(3), 185 (2020) https: //doi.org/10.1140/epjc/s10052-020-7638-y arXiv:1908.03099 [hep-ex]

    arXiv 2020

  42. [42]

    JHEP10, 084 (2019) https://doi.org/ 10.1007/JHEP10(2019)084 arXiv:1905.07211 [nucl-ex]

    Acharya, S.,et al.: Inclusive J/ψproduction at mid-rapidity in pp collisions at √s= 5.02 TeV. JHEP10, 084 (2019) https://doi.org/ 10.1007/JHEP10(2019)084 arXiv:1905.07211 [nucl-ex]

    Pith/arXiv arXiv 2019

  43. [43]

    Navas, S.,et al.: Review of particle physics. Phys. Rev. D110(3), 030001 (2024) https: //doi.org/10.1103/PhysRevD.110.030001

    doi:10.1103/physrevd.110.030001 2024

  44. [44]

    Miller, M.L., Reygers, K., Sanders, S.J., Steinberg, P.: Glauber modeling in high energy nuclear collisions. Ann. Rev. Nucl. Part. Sci.57, 205–243 (2007) https://doi. org/10.1146/annurev.nucl.57.090506.123020 arXiv:nucl-ex/0701025

    arXiv 2007

  45. [45]

    JHEP11, 181 (2021) https://doi.org/ 10.1007/JHEP11(2021)181 arXiv:2109.00220 [hep-ex]

    Aaij, R.,et al.: Measurement ofJ/ψproduc- tion cross-sections inppcollisions at √s= 5 TeV. JHEP11, 181 (2021) https://doi.org/ 10.1007/JHEP11(2021)181 arXiv:2109.00220 [hep-ex]

    arXiv 2021

  46. [46]

    Aaij, R.,et al.: Measurement of the ratio of promptχ c toJ/ψproduction inpp collisions at √s= 7 TeV. Phys. Lett. B718, 431–440 (2012) https://doi.org/10. 1016/j.physletb.2012.10.068 arXiv:1204.1462 [hep-ex]

    Pith/arXiv arXiv 2012

  47. [47]

    Aaij, R.,et al.: Measurement ofψ(2S) meson production inppcollisions at √s=7 TeV. Eur. Phys. J. C72, 2100 (2012) https: //doi.org/10.1140/epjc/s10052-012-2100-4 arXiv:1204.1258 [hep-ex]. [Erratum: Eur.Phys.J.C 80, 49 (2020)]

    Pith/arXiv arXiv 2012

  48. [48]

    JHEP 06, 055 (2015) https://doi.org/10.1007/ JHEP06(2015)055 arXiv:1503.07179 [nucl- ex]

    Adam, J.,et al.: Rapidity and transverse- momentum dependence of the inclusive J/ψ nuclear modification factor in p-Pb col- lisions at √sN N = 5.02 TeV. JHEP 06, 055 (2015) https://doi.org/10.1007/ JHEP06(2015)055 arXiv:1503.07179 [nucl- ex]

    Pith/arXiv arXiv 2015

  49. [49]

    Acharya, S.,et al.: Charm-quark fragmenta- tion fractions and production cross section at midrapidity in pp collisions at the LHC. Phys. Rev. D105(1), 011103 (2022) https: //doi.org/10.1103/PhysRevD.105.L011103 arXiv:2105.06335 [nucl-ex]

    Pith/arXiv arXiv 2022

  50. [50]

    Bierlich, C., Wilkinson, J., Sun, J., Manca, G., Cassagnac, R., Otwinowski, J.: Open charm production cross section from com- bined LHC experiments in pp collisions at√s= 5.02 TeV. Eur. Phys. J. Plus139(7), 593 (2024) https://doi.org/10.1140/epjp/ s13360-024-05355-0 arXiv:2311.11426 [hep- ph]

    Pith/arXiv arXiv 2024

  51. [51]

    JHEP10, 137 (2012) https://doi.org/10.1007/JHEP10(2012)137 arXiv:1205.6344 [hep-ph]

    Cacciari, M., Frixione, S., Houdeau, N., Mangano, M.L., Nason, P., Ridolfi, G.: The- oretical predictions for charm and bottom production at the LHC. JHEP10, 137 (2012) https://doi.org/10.1007/JHEP10(2012)137 arXiv:1205.6344 [hep-ph]

    Pith/arXiv arXiv 2012

  52. [52]

    Emel’yanov, V., Khodinov, A., Klein, S.R., Vogt, R.: Charm quark production in non- central heavy ion collisions. Phys. Rev. C56, 2726–2735 (1997) https://doi.org/10.1103/ PhysRevC.56.2726 arXiv:nucl-th/9706085

    Pith/arXiv arXiv 1997

  53. [53]

    Zhao, X., Rapp, R.: Forward and midra- pidity charmonium production at RHIC. Eur. Phys. J. C62, 109–117 (2009) https: //doi.org/10.1140/epjc/s10052-009-0905-6 arXiv:0810.4566 [nucl-th]

    Pith/arXiv arXiv 2009

  54. [54]

    Zhao, S., He, M.: Simulation of heavy quarkonium equilibration in the quark- gluon plasma. Phys. Rev. D112(9), 094018 (2025) https://doi.org/10.1103/4rdc-9dkx 21 arXiv:2508.11897 [hep-ph]

    Pith/arXiv arXiv 2025

  55. [55]

    Adam, J.,et al.: J/ψsuppression at forward rapidity in Pb-Pb collisions at√sNN =5.02TeV. Phys. Lett. B766, 212–224 (2017) https://doi.org/10.1016/j. physletb.2016.12.064 arXiv:1606.08197 [nucl- ex]

    Pith/arXiv arXiv 2017

  56. [56]

    Acharya, S.,et al.:ψ(2S) Suppression in Pb-Pb Collisions at the LHC. Phys. Rev. Lett.132(4), 042301 (2024) https: //doi.org/10.1103/PhysRevLett.132.042301 arXiv:2210.08893 [nucl-ex]

    Pith/arXiv arXiv 2024

  57. [57]

    Acharya, S.,et al.: Measurements of inclusive J/ψproduction at midrapidity and forward rapidity in Pb–Pb collisions at sNN = 5.02 TeV. Phys. Lett. B849, 138451 (2024) https: //doi.org/10.1016/j.physletb.2024.138451 arXiv:2303.13361 [nucl-ex]

    arXiv 2024

  58. [58]

    JHEP 02, 041 (2020) https://doi.org/10.1007/ JHEP02(2020)041 arXiv:1909.03158 [nucl- ex]

    Acharya, S.,et al.: Studies of J/ψpro- duction at forward rapidity in Pb-Pb collisions at √sNN = 5.02 TeV. JHEP 02, 041 (2020) https://doi.org/10.1007/ JHEP02(2020)041 arXiv:1909.03158 [nucl- ex]

    Pith/arXiv arXiv 2020

  59. [59]

    Zhao, X., Rapp, R.: Transverse Momentum Spectra ofJ/ψin Heavy-Ion Collisions. Phys. Lett. B664, 253–257 (2008) https: //doi.org/10.1016/j.physletb.2008.03.068 arXiv:0712.2407 [hep-ph]

    Pith/arXiv arXiv 2008

  60. [60]

    He, M., Wu, B., Rapp, R.: Collectivity of J/ψMesons in Heavy-Ion Collisions. Phys. Rev. Lett.128(16), 162301 (2022) https: //doi.org/10.1103/PhysRevLett.128.162301 arXiv:2111.13528 [nucl-th]

    Pith/arXiv arXiv 2022

  61. [61]

    Young, C., Shuryak, E.: Charmonium in strongly coupled quark-gluon plasma. Phys. Rev. C79, 034907 (2009) https://doi.org/10. 1103/PhysRevC.79.034907 arXiv:0803.2866 [nucl-th]

    Pith/arXiv arXiv 2009

  62. [62]

    Oei, N., Krenz, N., Hees, H., Greiner, C., Torres-Rincon, J.M.: Formation, dis- sociation, and regeneration of charmonia within microscopic Langevin simulations. Phys. Rev. D111(7), 074012 (2025) https: //doi.org/10.1103/PhysRevD.111.074012 arXiv:2410.19619 [hep-ph]

    Pith/arXiv arXiv 2025

  63. [63]

    Daddi-Hammou, A., Delorme, S., Blaizot, J.-P., Gossiaux, P.B., Gousset, T.: Quan- tum vs semiclassical description of in-QGP quarkonia in the quantum Brownian regime. Phys. Rev. D113(1), 014017 (2026) https:// doi.org/10.1103/kyc5-mrj3 arXiv:2506.19194 [hep-ph] 22

    arXiv 2026