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arxiv: 2605.29479 · v1 · pith:HDAOTM23new · submitted 2026-05-28 · ✦ hep-ph

Charmonium production at SPS and FAIR energies

Pith reviewed 2026-06-29 06:53 UTC · model grok-4.3

classification ✦ hep-ph
keywords charmonium productionRemler formalismheavy-ion collisionsSPS energiesFAIR energiesin-medium potentialJ/ψ dissociationPHSD transport model
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The pith

The Remler formalism with an in-medium heavy quark potential describes charmonium production at SPS energies.

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

The paper applies the Remler formalism inside the PHSD transport model to track charmonium production and dissociation across p+p, p+A, and A+A collisions. Nuclear absorption cross sections are first fixed from proton-nucleus data and then carried over to heavy-ion systems. When an in-medium heavy-quark potential is included that causes the J/ψ to dissociate near the critical temperature Tc, the calculated yields match SPS measurements. The same setup is then used to estimate charmonium production at the lower beam energies planned for GSI/FAIR, where baryon densities are higher.

Core claim

The Remler formalism, implemented within PHSD and supplied with an in-medium heavy-quark potential in which the J/ψ dissociates near Tc, reproduces the measured charmonium yields in heavy-ion collisions at SPS energies once the nuclear absorption cross section extracted from p+A collisions is inserted; the same framework is then applied to predict charmonium production at GSI/FAIR energies.

What carries the argument

Remler formalism for charmonium production and dissociation, combined with an in-medium heavy-quark potential inside the PHSD transport model.

If this is right

  • Charmonium suppression at SPS is accounted for by the in-medium potential without extra medium-dependent adjustments.
  • The same nuclear absorption cross section and potential can be used to forecast charmonium yields at GSI/FAIR beam energies.
  • Baryon-rich matter effects on charmonium are captured through the temperature-dependent dissociation near Tc.
  • The approach supplies a consistent baseline for comparing SPS data with future FAIR measurements.

Where Pith is reading between the lines

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

  • If the FAIR predictions hold, the same potential may govern quarkonium behavior in other dense baryonic environments such as neutron-star mergers.
  • The framework could be tested by extending it to bottomonium states under identical SPS and FAIR conditions.
  • Discrepancies between the model and new FAIR data would point to additional baryon-density-dependent dissociation channels not included here.

Load-bearing premise

The nuclear absorption cross section fitted to p+A data can be used unchanged in heavy-ion collisions once the chosen in-medium potential is active.

What would settle it

A measurement of J/ψ or ψ' yields in central Pb+Pb collisions at SPS energies that lies significantly outside the band predicted by the Remler formalism with the in-medium potential.

Figures

Figures reproduced from arXiv: 2605.29479 by Elena Bratkovskaya, Jiaxing Zhao, Joerg AICHELIN, Taesoo Song.

Figure 1
Figure 1. Figure 1: FIG. 1: The parameterized cross section for charm produc [PITH_FULL_IMAGE:figures/full_fig_p002_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: FIG. 2: Charm quark scattering cross sections with (upper) [PITH_FULL_IMAGE:figures/full_fig_p003_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: FIG. 3: Cross sections for [PITH_FULL_IMAGE:figures/full_fig_p006_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: FIG. 4: Differential cross sections for charmonium production, multiplied by the branching ratio to dimuon decay, as a function [PITH_FULL_IMAGE:figures/full_fig_p007_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: FIG. 5: A schematic illustration of the simulation setup for [PITH_FULL_IMAGE:figures/full_fig_p008_5.png] view at source ↗
Figure 4
Figure 4. Figure 4: Furthermore, nuclear absorption cross sections of [PITH_FULL_IMAGE:figures/full_fig_p009_4.png] view at source ↗
Figure 7
Figure 7. Figure 7: presents the PHSD simulation results for the production cross sections of J/ψ and ψ ′ , multiplied by the branching ratio to dimuons and divided by the target mass number, in p+Be and p+Pb collisions at Ekin=400 A GeV. The results are compared with experimental data from the NA50 Collaboration [79]. The dimuon branch￾ing ratios Bµµ are taken to be 6 % for J/ψ and 0.8 % for ψ ′ according to the Particle Dat… view at source ↗
Figure 9
Figure 9. Figure 9: shows the ratio of the J/ψ production cross sec￾tion per nucleon in p+A collisions at Ekin= 400 and 158 GeV to that in p+Be collisions, plotted as a function of the average path length of nuclear matter traversed by the produced J/ψ in p+A collisions. In our calculations, the ratio is evaluated only for p+Pb collisions (L ≈ 4.3), and straight lines are drawn to qualitatively compare the results with experi… view at source ↗
Figure 10
Figure 10. Figure 10: FIG. 10: Fraction of QGP (parton) energy relative to the total [PITH_FULL_IMAGE:figures/full_fig_p011_10.png] view at source ↗
Figure 11
Figure 11. Figure 11: shows the ratio of dimuons from J/ψ decay to dimuons from the Drell-Yan process with an invari￾ant mass between 2.9 and 4.5 GeV as a function of the number of participant nucleons in Pb+Pb and In+In col￾lisions at E/A= 158 GeV. In p+p collisions (Npart =2), this ratio is measured to be 35.7±3.0 [93]. V0 in [PITH_FULL_IMAGE:figures/full_fig_p011_11.png] view at source ↗
Figure 12
Figure 12. Figure 12: We therefore slightly modify the radius so that [PITH_FULL_IMAGE:figures/full_fig_p012_12.png] view at source ↗
Figure 10
Figure 10. Figure 10: As shown in Fig. 13, the inclusion of these inter [PITH_FULL_IMAGE:figures/full_fig_p012_10.png] view at source ↗
Figure 14
Figure 14. Figure 14: FIG. 14: Rapidity distributions of (upper) [PITH_FULL_IMAGE:figures/full_fig_p013_14.png] view at source ↗
Figure 16
Figure 16. Figure 16: FIG. 16: Same as the upper panel of Fig. 11 but with in [PITH_FULL_IMAGE:figures/full_fig_p014_16.png] view at source ↗
Figure 15
Figure 15. Figure 15: FIG. 15: Time evolution of (blue solid) nuclear absorption, [PITH_FULL_IMAGE:figures/full_fig_p014_15.png] view at source ↗
Figure 17
Figure 17. Figure 17: FIG. 17: Dependence of dilepton production from [PITH_FULL_IMAGE:figures/full_fig_p015_17.png] view at source ↗
Figure 18
Figure 18. Figure 18: FIG. 18 [PITH_FULL_IMAGE:figures/full_fig_p015_18.png] view at source ↗
Figure 19
Figure 19. Figure 19: FIG. 19: Differential cross sections for the production of (up [PITH_FULL_IMAGE:figures/full_fig_p016_19.png] view at source ↗
Figure 21
Figure 21. Figure 21: FIG. 21: Distribution of nucleon-nucleon scattering energies [PITH_FULL_IMAGE:figures/full_fig_p017_21.png] view at source ↗
read the original abstract

In this study we apply the Remler formalism to charmonium production at SPS and GSI/FAIR energies in order to investigate the effects of baryon-rich matter on charmonium production and dissociation in heavy-ion collisions within the Parton-Hadron-String Dynamics (PHSD). As a first step the Remler formalism is tested in p+p collisions and then applied to p+A collisions in order to extract the nuclear absorption cross section of charmonium, which is then utilized in heavy-ion collisions. We find that the Remler formalism successfully describes charmonium production in heavy-ion collisions at SPS energies when an in-medium heavy quark potential is implemented, in which $J/\psi$ dissociates near $T_c$. Finally the same formalism is applied to the GSI/FAIR energies, where we estimate charmonium production.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

2 major / 1 minor

Summary. The manuscript applies the Remler formalism inside the PHSD transport model to charmonium production and dissociation. It first validates the approach in p+p collisions, extracts a nuclear absorption cross section from p+A data, inserts that cross section into A+A calculations at SPS energies together with an in-medium heavy-quark potential that dissociates J/ψ near Tc, and finally estimates charmonium yields at GSI/FAIR energies.

Significance. If the transfer of the absorption cross section proves valid, the work would supply evidence that the Remler formalism plus a temperature-dependent potential can account for SPS charmonium data in baryon-rich matter and would furnish concrete predictions for the lower beam energies accessible at FAIR.

major comments (2)
  1. [Abstract; p+A to A+A application] Abstract and the section describing the transition from p+A to A+A collisions: the nuclear absorption cross section is fitted to p+A data and then used unchanged in the heavy-ion calculation; this data-driven parameter directly controls the SPS description, yet the manuscript provides no sensitivity study or additional justification for the assumption that cold-nuclear-matter absorption remains unmodified by the finite-temperature, baryon-rich environment beyond the chosen in-medium potential.
  2. [Heavy-ion collisions at SPS energies] Heavy-ion results section: the claim of successful description at SPS energies is stated without quantitative metrics (χ², error bands, or comparison to alternative potentials), rendering the central assertion only partially verifiable from the presented material.
minor comments (1)
  1. [Abstract] The abstract would benefit from a brief statement of the numerical values obtained for the nuclear absorption cross section and the in-medium potential parameters.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the constructive comments on our manuscript. We address each major point below and indicate the planned revisions.

read point-by-point responses
  1. Referee: [Abstract; p+A to A+A application] Abstract and the section describing the transition from p+A to A+A collisions: the nuclear absorption cross section is fitted to p+A data and then used unchanged in the heavy-ion calculation; this data-driven parameter directly controls the SPS description, yet the manuscript provides no sensitivity study or additional justification for the assumption that cold-nuclear-matter absorption remains unmodified by the finite-temperature, baryon-rich environment beyond the chosen in-medium potential.

    Authors: We agree that the transfer of the absorption cross section merits explicit justification and a sensitivity analysis. In the revised manuscript we will add a dedicated paragraph explaining why cold-nuclear-matter absorption is expected to remain largely unmodified (with the temperature-dependent potential handling hot-medium dissociation) and will include a sensitivity study in which the cross section is varied within its p+A uncertainty range, showing the resulting variation in SPS yields. revision: yes

  2. Referee: [Heavy-ion collisions at SPS energies] Heavy-ion results section: the claim of successful description at SPS energies is stated without quantitative metrics (χ², error bands, or comparison to alternative potentials), rendering the central assertion only partially verifiable from the presented material.

    Authors: We accept that quantitative metrics are needed for verifiability. The revised version will report χ² values (or χ²/dof) for the comparison to SPS charmonium data, include error bands on the theoretical curves where statistics permit, and add a brief comparison to results obtained with an alternative (constant) heavy-quark potential to illustrate the role of the in-medium dissociation. revision: yes

Circularity Check

0 steps flagged

No significant circularity in derivation chain

full rationale

The paper extracts a nuclear absorption cross section from p+A data for use in A+A calculations at SPS energies, alongside the Remler formalism, PHSD transport, and an in-medium heavy-quark potential with J/ψ dissociation near Tc. This is a standard parameter transfer between collision systems rather than any reduction of the A+A result to the p+A input by construction; the A+A description incorporates additional independent dynamics and is tested against separate data, remaining falsifiable. No self-definitional steps, fitted inputs renamed as predictions, self-citation load-bearing arguments, uniqueness theorems, or ansatz smuggling are present in the provided text. The central claim retains independent content from the model components.

Axiom & Free-Parameter Ledger

1 free parameters · 0 axioms · 0 invented entities

Abstract-only review supplies insufficient detail to enumerate free parameters, axioms, or invented entities beyond the in-medium potential and the transferred absorption cross section; both are model inputs whose independent justification is not visible here.

free parameters (1)
  • nuclear absorption cross section
    Extracted from p+A collisions and applied to heavy-ion systems; its value is not stated in the abstract.

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