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arxiv: 2602.19072 · v2 · pith:EN7L7HKFnew · submitted 2026-02-22 · ⚛️ nucl-th · hep-ph

Charmonium suppression in fixed target proton-nucleus collisions

Sourav Kanti Giri , Partha Pratim Bhaduri , Biswarup Paul , Santosh K. Das This is my paper

Pith reviewed 2026-05-25 07:13 UTC · model grok-4.3

classification ⚛️ nucl-th hep-ph
keywords charmoniumJ/ψcold nuclear matterproton-nucleus collisionssuppressionabsorptionNA60+CBM
0
0 comments X

The pith

Charmonium suppression in proton-nucleus collisions arises from the combined effects of parton energy loss, nuclear shadowing, and final-state absorption.

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

The paper examines how cold nuclear matter affects the production of charmonium states like J/ψ and ψ(2S) in fixed-target proton-nucleus collisions. It models the suppression using three mechanisms: initial-state parton energy loss, nuclear shadowing, and absorption of the resonant states. Data from past experiments at SPS, Fermilab, and HERA-B are analyzed to understand the beam energy dependence. This analysis helps predict the expected normal absorption levels in future experiments at NA60+ and CBM. A sympathetic reader would care because these predictions provide a baseline for distinguishing cold nuclear matter effects from hot quark-gluon plasma signals in heavy-ion collisions.

Core claim

The beam energy dependence of the observed J/ψ production patterns in fixed target p+A collisions are utilized to anticipate the level of normal absorption in the upcoming proton induced collisions by the NA60+ experiment at CERN SPS and the CBM experiment at FAIR SIS100 accelerator facilities, after accounting for the interplay of initial-state parton energy loss, nuclear shadowing, and final-state absorption.

What carries the argument

The interplay of initial-state parton energy loss, nuclear shadowing, and final-state absorption of the resonant states in charmonium production cross sections.

If this is right

  • Predictions for the level of normal absorption in NA60+ at CERN SPS.
  • Predictions for the level of normal absorption in CBM at FAIR SIS100.
  • The model describes data from SPS, Fermilab, and HERA-B experiments.
  • Charmonium production cross sections are modified by the three CNM effects.
  • Beam energy dependence is key to separating the effects.

Where Pith is reading between the lines

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

  • If the three effects suffice, then deviations in future data would indicate additional mechanisms.
  • These baselines could help isolate quark-gluon plasma effects in nucleus-nucleus collisions.
  • Similar modeling might apply to other heavy quarkonia or different collision systems.

Load-bearing premise

The three cold nuclear matter effects are the dominant mechanisms and their standard phenomenological implementations are sufficient to describe the full set of p+A data without additional unaccounted processes.

What would settle it

Measurements of J/ψ production in the upcoming NA60+ or CBM proton-nucleus runs that show absorption levels significantly different from the energy-dependent predictions based on existing data.

Figures

Figures reproduced from arXiv: 2602.19072 by Biswarup Paul, Partha Pratim Bhaduri, Santosh K. Das, Sourav Kanti Giri.

Figure 1
Figure 1. Figure 1: FIG. 1 [PITH_FULL_IMAGE:figures/full_fig_p003_1.png] view at source ↗
Figure 3
Figure 3. Figure 3: FIG. 3: Variation of the shadowing ratio for p+W collisions as a function of centre-of-mass rapidity ( [PITH_FULL_IMAGE:figures/full_fig_p005_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: FIG. 4: Variation of the shadowing ratio for p+W collisions as a function of centre-of-mass rapidity ( [PITH_FULL_IMAGE:figures/full_fig_p007_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: FIG. 5: Variation of the mid-rapidity shadowing ratio as a function of target mass (A) in fixed target p+A collisions [PITH_FULL_IMAGE:figures/full_fig_p008_5.png] view at source ↗
Figure 6
Figure 6. Figure 6: FIG. 6: Variation of the [PITH_FULL_IMAGE:figures/full_fig_p010_6.png] view at source ↗
Figure 7
Figure 7. Figure 7: FIG. 7: Target mass ( [PITH_FULL_IMAGE:figures/full_fig_p011_7.png] view at source ↗
Figure 8
Figure 8. Figure 8: FIG. 8: Ratio of the per nucleon [PITH_FULL_IMAGE:figures/full_fig_p012_8.png] view at source ↗
Figure 9
Figure 9. Figure 9: FIG. 9: Ratio of the per nucleon [PITH_FULL_IMAGE:figures/full_fig_p014_9.png] view at source ↗
Figure 10
Figure 10. Figure 10: FIG. 10: Parametrization of the beam energy dependence of the extracted values of [PITH_FULL_IMAGE:figures/full_fig_p014_10.png] view at source ↗
Figure 11
Figure 11. Figure 11: FIG. 11: The predicted level of [PITH_FULL_IMAGE:figures/full_fig_p016_11.png] view at source ↗
read the original abstract

In this article, we perform a systematic investigation of the cold nuclear matter (CNM) effects, operative on charmonium ($J/\psi$, $\psi(2S)$) production, in fixed target proton-nucleus (p+A) collisions. Influence on charmonium production cross section due to the interplay of three different plausible CNM effects namely the initial-state parton energy loss, nuclear shadowing, and final-state absorption of the resonant states, are evaluated in detail. The available data on charmonium production in fixed target p+A collision experiments from SPS, Fermilab and HERA-B are examined for this purpose. The beam energy dependence of the observed $J/\psi$ production patterns are utilized to anticipate level of "normal" absorption in the upcoming proton induced collisions by the NA60+ experiment at CERN SPS and the CBM experiment at FAIR SIS100 accelerator facilities.

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 / 2 minor

Summary. The paper performs a systematic investigation of cold nuclear matter (CNM) effects on charmonium (J/ψ, ψ(2S)) production in fixed-target p+A collisions. It models the interplay of initial-state parton energy loss, nuclear shadowing, and final-state absorption using data from SPS, Fermilab, and HERA-B experiments, then uses the observed beam-energy dependence of J/ψ production patterns to predict the level of 'normal' absorption expected in upcoming proton-induced collisions at the NA60+ experiment (CERN SPS) and the CBM experiment (FAIR SIS100).

Significance. If the decomposition into the three CNM mechanisms is robust and the energy extrapolation is reliable, the work would provide useful baseline predictions for charmonium suppression at lower beam energies. This could help future experiments distinguish cold nuclear matter effects from potential hot nuclear matter signals in heavy-ion collisions. The systematic use of energy dependence across multiple facilities is a positive aspect, though its value hinges on demonstrating that the standard phenomenological implementations suffice without additional mechanisms.

major comments (2)
  1. [section describing predictions for NA60+ and CBM] The central extrapolation to NA60+ and CBM energies is derived from beam-energy trends fitted to the same class of p+A data used to constrain the three CNM parameters (parton energy loss parameter, nuclear shadowing factors, absorption cross section). The section on predictions for future experiments should explicitly demonstrate that the energy dependence is not over-determined by the input data and that the decomposition between initial-state and final-state effects is unique; otherwise the output absorption values are largely determined by the input fit rather than providing an independent prediction.
  2. [data analysis and model description sections] The assumption that the three standard CNM effects with their conventional parametrizations fully describe the energy-dependent J/ψ patterns (without additional unaccounted energy-dependent processes) is load-bearing for the claim. The data-analysis section should report quantitative measures (e.g., goodness-of-fit across the full energy range or sensitivity tests to shadowing at low x) showing that no residual energy dependence remains after the fit; any unaccounted process would propagate directly into the extrapolated absorption cross section at the new facilities' energies.
minor comments (2)
  1. Notation for the three CNM parameters should be defined consistently when first introduced and used in the fitting procedure.
  2. The abstract states the goal clearly but the manuscript would benefit from an explicit statement of the fitted parameter values and their uncertainties in a dedicated table or equation.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the thorough review and valuable comments on our manuscript. We address each major comment below and indicate the revisions we will make to strengthen the paper.

read point-by-point responses

  1. Referee: [section describing predictions for NA60+ and CBM] The central extrapolation to NA60+ and CBM energies is derived from beam-energy trends fitted to the same class of p+A data used to constrain the three CNM parameters (parton energy loss parameter, nuclear shadowing factors, absorption cross section). The section on predictions for future experiments should explicitly demonstrate that the energy dependence is not over-determined by the input data and that the decomposition between initial-state and final-state effects is unique; otherwise the output absorption values are largely determined by the input fit rather than providing an independent prediction.

    Authors: We agree with the referee that demonstrating the robustness of the extrapolation is crucial. The model uses the distinct energy dependencies of the CNM effects to separate their contributions: initial-state energy loss and shadowing vary with beam energy due to the parton kinematics, while final-state absorption is expected to have a weaker or different dependence. In the revised version, we will add a dedicated subsection in the predictions section that includes parameter variation studies and comparisons using subsets of the data to show that the decomposition is not over-determined and that the predictions for NA60+ and CBM are not solely determined by the input fit but informed by the energy trends. revision: yes

  2. Referee: [data analysis and model description sections] The assumption that the three standard CNM effects with their conventional parametrizations fully describe the energy-dependent J/ψ patterns (without additional unaccounted energy-dependent processes) is load-bearing for the claim. The data-analysis section should report quantitative measures (e.g., goodness-of-fit across the full energy range or sensitivity tests to shadowing at low x) showing that no residual energy dependence remains after the fit; any unaccounted process would propagate directly into the extrapolated absorption cross section at the new facilities' energies.

    Authors: The analysis in the manuscript is phenomenological, comparing the model to data trends rather than performing a global statistical fit, owing to the different experimental conditions and systematic uncertainties across SPS, Fermilab, and HERA-B datasets. We will revise the data analysis section to include sensitivity tests to the nuclear shadowing parametrization, particularly at low x, and provide a more quantitative assessment of the agreement across the energy range. While a formal chi-squared per degree of freedom may not be straightforward due to the nature of the data, we will report the level of description and any remaining discrepancies to address the concern about unaccounted processes. revision: partial

Circularity Check

0 steps flagged

No significant circularity; standard phenomenological fit and extrapolation

full rationale

The paper fits parameters of three standard CNM mechanisms (parton energy loss, shadowing, absorption) to existing fixed-target p+A data sets from SPS/Fermilab/HERA-B, then applies the resulting model to anticipate absorption levels at the different beam energies of NA60+ and CBM. This constitutes ordinary data-driven extrapolation rather than any reduction of the output to the input by construction, self-definition, or self-citation chain. No load-bearing uniqueness theorem, ansatz smuggling, or renaming of known results is present. The central claim remains falsifiable against new data and rests on the explicit (testable) assumption that the three mechanisms suffice, which is independent of the fitting procedure itself.

Axiom & Free-Parameter Ledger

3 free parameters · 2 axioms · 0 invented entities

The central claim rests on three standard phenomenological CNM models whose parameters are adjusted to existing data; the extrapolation therefore inherits all assumptions and parameter choices of those models.

free parameters (3)
  • parton energy loss parameter
    Controls initial-state energy loss and is adjusted to data
  • nuclear shadowing factors
    Nuclear modification of parton distributions, fitted or taken from global fits
  • absorption cross section
    Final-state break-up cross section for charmonium states, fitted to p+A data
axioms (2)
  • domain assumption Standard nuclear parton distribution functions and energy-loss models remain valid for charmonium kinematics
    Invoked when modeling initial-state effects
  • domain assumption Data sets from SPS, Fermilab and HERA-B can be described by a common set of CNM parameters
    Required to extract a single energy-dependent absorption trend

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Forward citations

Cited by 1 Pith paper

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score.

  1. Charmonium production in low energy nuclear collisions at SPS and FAIR: achievements $\&$ prospects

    nucl-ex 2026-05 unverdicted novelty 2.0

    A review summarizing existing charmonium data in low-energy nuclear collisions, medium effects, and future measurement prospects at FAIR and SPS.

Reference graph

Works this paper leans on

71 extracted references · 71 canonical work pages · cited by 1 Pith paper · 27 internal anchors

  1. [1]

    In the literature, different parametrizations have been in- dependently proposed for modeling the fractional en- ergy loss of projectile quarks inside the nuclear mat- ter of the target. Within the Brodsky-Hoyer (BH) for- malism [50], utilizing an analogy to the photon Brem sstrahlung process in quantum electrodynamics (QED), a formula for gluon radiation...

    work page 1996

  2. [2]

    Matsui and H

    T. Matsui and H. Satz, Phys. Lett. B178, 416-422 (1986) doi:10.1016/0370-2693(86)91404-8

    work page doi:10.1016/0370-2693(86)91404-8 1986

  3. [3]

    Vogt, Phys

    R. Vogt, Phys. Rept.310(1999), 197-260 doi:10.1016/S0370-1573(98)00074-X

    work page doi:10.1016/s0370-1573(98)00074-x 1999

  4. [4]

    Kluberg and H

    L. Kluberg and H. Satz, doi:10.1007/978-3-642-01539- 7 13 [arXiv:0901.3831 [hep-ph]]

    work page doi:10.1007/978-3-642-01539-

  5. [5]

    Charmonium physics with heavy ions: experimental results

    E. Scomparin, PoSCHARM2016(2016), 008 doi:10.22323/1.289.0008 [arXiv:1611.02557 [nucl-ex]]

    work page internal anchor Pith review Pith/arXiv arXiv doi:10.22323/1.289.0008 2016

  6. [6]

    P. P. Bhaduri, AAPPS Bull.30(2020) no.5, 14-18 doi:10.22661/AAPPSBL.2020.30.5.14

    work page doi:10.22661/aappsbl.2020.30.5.14 2020

  7. [7]

    Badieret al.[NA3], Z

    J. Badieret al.[NA3], Z. Phys. C20, 101 (1983) doi:10.1007/BF01573213

    work page doi:10.1007/bf01573213 1983

  8. [8]

    M. C. Abreuet al.[NA38], Phys. Lett. B444(1998), 516-522 doi:10.1016/S0370-2693(98)01398-7

    work page doi:10.1016/s0370-2693(98)01398-7 1998

  9. [9]

    M. C. Abreuet al.[NA38], Phys. Lett. B449(1999), 128-136 doi:10.1016/S0370-2693(99)00057-X

    work page doi:10.1016/s0370-2693(99)00057-x 1999

  10. [10]

    M. C. Abreuet al.[NA51], Phys. Lett. B438(1998), 35-40 doi:10.1016/S0370-2693(98)01014-4

    work page doi:10.1016/s0370-2693(98)01014-4 1998

  11. [11]

    Alessandroet al.[NA50], Phys

    B. Alessandroet al.[NA50], Phys. Lett. B553, 167-178 (2003) doi:10.1016/S0370-2693(02)03265-3

    work page doi:10.1016/s0370-2693(02)03265-3 2003

  12. [12]

    Alessandroet al.[NA50], Eur

    B. Alessandroet al.[NA50], Eur. Phys. J. C48, 329 (2006) doi:10.1140/epjc/s10052-006-0079-4 [arXiv:nucl- ex/0612012 [nucl-ex]]

    work page doi:10.1140/epjc/s10052-006-0079-4 2006

  13. [13]

    Alessandroet al.[NA50], Eur

    B. Alessandroet al.[NA50], Eur. Phys. J. C39, 335- 345 (2005) doi:10.1140/epjc/s2004-02107-9 [arXiv:hep- ex/0412036 [hep-ex]]

    work page doi:10.1140/epjc/s2004-02107-9 2005

  14. [14]

    J/psi production in proton-nucleus collisions at 158 and 400 GeV

    R. Arnaldiet al.[NA60], Phys. Lett. B706, 263-267 (2012) doi:10.1016/j.physletb.2011.11.042 [arXiv:1004.5523 [nucl-ex]]

    work page internal anchor Pith review Pith/arXiv arXiv doi:10.1016/j.physletb.2011.11.042 2012

  15. [15]

    D. M. Alde, H. W. Baer, T. A. Carey, G. T. Garvey, A. Klein, C. Lee, M. J. Leitch, J. Lillberg, P. L. Mc- Gaughey and C. S. Mishra,et al.Phys. Rev. Lett.66, 133-136 (1991) doi:10.1103/PhysRevLett.66.133

    work page doi:10.1103/physrevlett.66.133 1991

  16. [16]

    M. J. Leitchet al.[NuSea], Phys. Rev. Lett. 84, 3256-3260 (2000) doi:10.1103/PhysRevLett.84.3256 [arXiv:nucl-ex/9909007 [nucl-ex]]

    work page internal anchor Pith review Pith/arXiv arXiv doi:10.1103/physrevlett.84.3256 2000

  17. [17]

    Shahoian, PhD Thesis, Instituto Su- perior T´ ecnico, Lisbon, 2001, available at http://cern.ch/NA50/theses.html

    R. Shahoian, PhD Thesis, Instituto Su- perior T´ ecnico, Lisbon, 2001, available at http://cern.ch/NA50/theses.html

    work page 2001

  18. [18]

    Kinematic distributions and nuclear effects of $J/\psi$ production in 920 GeV fixed-target proton-nucleus collisions

    I. Abtet al.[HERA-B], Eur. Phys. J. C60, 525-542 (2009) doi:10.1140/epjc/s10052-009-0965-7 [arXiv:0812.0734 [hep-ex]]

    work page internal anchor Pith review Pith/arXiv arXiv doi:10.1140/epjc/s10052-009-0965-7 2009

  19. [19]

    M. L. Miller, K. Reygers, S. J. Sanders and P. Stein- berg, Ann. Rev. Nucl. Part. Sci.57, 205-243 (2007) doi:10.1146/annurev.nucl.57.090506.123020 [arXiv:nucl- ex/0701025 [nucl-ex]]

    work page doi:10.1146/annurev.nucl.57.090506.123020 2007

  20. [20]

    A Quantitative Analysis of Charmonium Suppression in Nuclear Collisions

    D. Kharzeev, C. Lourenco, M. Nardi and H. Satz, Z. Phys. C74(1997), 307-318 doi:10.1007/s002880050392 [arXiv:hep-ph/9612217 [hep-ph]]

    work page internal anchor Pith review Pith/arXiv arXiv doi:10.1007/s002880050392 1997

  21. [21]

    J. w. Qiu, J. P. Vary and X. f. Zhang, Phys. Rev. Lett. 88, 232301 (2002) doi:10.1103/PhysRevLett.88.232301 [arXiv:hep-ph/9809442 [hep-ph]]

    work page internal anchor Pith review Pith/arXiv arXiv doi:10.1103/physrevlett.88.232301 2002

  22. [22]

    P. P. Bhaduri, A. K. Chaudhuri and S. Chat- topadhyay, Phys. Rev. C84, 054914 (2011) doi:10.1103/PhysRevC.84.054914 [arXiv:1110.4268 [hep-ph]]

    work page internal anchor Pith review Pith/arXiv arXiv doi:10.1103/physrevc.84.054914 2011

  23. [23]

    J/psi suppression in p-A collisions from parton energy loss in cold QCD matter

    F. Arleo and S. Peigne, Phys. Rev. Lett.109, 122301 (2012) doi:10.1103/PhysRevLett.109.122301 [arXiv:1204.4609 [hep-ph]]

    work page internal anchor Pith review Pith/arXiv arXiv doi:10.1103/physrevlett.109.122301 2012

  24. [24]

    Arleo and V

    F. Arleo and V. N. Tram, Eur. Phys. J. C55(2008), 449-461 doi:10.1140/epjc/s10052-008-0604-8 [arXiv:hep- ph/0612043 [hep-ph]]

    work page doi:10.1140/epjc/s10052-008-0604-8 2008

  25. [25]

    V. N. Tram and F. Arleo, Eur. Phys. J. C 61(2009), 847-852 doi:10.1140/epjc/s10052-009-0864-y [arXiv:0907.0043 [hep-ph]]

    work page internal anchor Pith review Pith/arXiv arXiv doi:10.1140/epjc/s10052-009-0864-y 2009

  26. [26]

    Energy dependence of J/psi absorption in proton-nucleus collisions

    C. Lourenco, R. Vogt and H. K. Woehri, JHEP 02(2009), 014 doi:10.1088/1126-6708/2009/02/014 [arXiv:0901.3054 [hep-ph]]

    work page internal anchor Pith review Pith/arXiv arXiv doi:10.1088/1126-6708/2009/02/014 2009

  27. [27]

    Role of parton shadowing in the comparison of p-A and A-A results on jpsi suppression at energies available at the CERN Super Proton Synchrotron

    R. Arnaldi, P. Cortese and E. Scomparin, Phys. Rev. C81(2010), 014903 doi:10.1103/PhysRevC.81.014903 [arXiv:0909.2199 [hep-ph]]

    work page internal anchor Pith review Pith/arXiv arXiv doi:10.1103/physrevc.81.014903 2010

  28. [28]

    P. P. Bhaduri, A. K. Chaudhuri and S. Chat- topadhyay, Phys. Rev. C89(2014) no.4, 044912 doi:10.1103/PhysRevC.89.044912

    work page doi:10.1103/physrevc.89.044912 2014

  29. [29]

    G. A. Schuler, [arXiv:hep-ph/9403387 [hep-ph]]

    work page internal anchor Pith review Pith/arXiv arXiv

  30. [30]

    G. A. Schuler and R. Vogt, Phys. Lett. B387(1996), 181-186 doi:10.1016/0370-2693(96)00999-9 [arXiv:hep- ph/9606410 [hep-ph]]

    work page doi:10.1016/0370-2693(96)00999-9 1996

  31. [31]

    J. P. Lansberg, [arXiv:hep-ph/0201111 [hep-ph]]

    work page internal anchor Pith review Pith/arXiv arXiv

  32. [32]

    G. T. Bodwin, [arXiv:1208.5506 [hep-ph]]

    work page internal anchor Pith review Pith/arXiv arXiv

  33. [33]

    A. P. Chen, Y. Q. Ma and H. Zhang, Adv. High Energy Phys.2022(2022), 7475923 doi:10.1155/2022/7475923 [arXiv:2109.04028 [hep-ph]]

    work page doi:10.1155/2022/7475923 2022

  34. [34]

    R. V. Gavai, S. Gupta, P. L. McGaughey, E. Quack, P. V. Ruuskanen, R. Vogt and X. N. Wang, Int. J. Mod. Phys. A10, 2999-3042 (1995) doi:10.1142/S0217751X95001431 [arXiv:hep-ph/9411438 [hep-ph]]

    work page internal anchor Pith review Pith/arXiv arXiv doi:10.1142/s0217751x95001431 1995

  35. [35]

    Quarkonium production in hadronic collisions

    R. Gavai, D. Kharzeev, H. Satz, G. A. Schuler, K. Sridhar and R. Vogt, Int. J. Mod. Phys. A10, 3043-3070 (1995) doi:10.1142/S0217751X95001443 [arXiv:hep-ph/9502270 [hep-ph]]

    work page internal anchor Pith review Pith/arXiv arXiv doi:10.1142/s0217751x95001443 1995

  36. [36]

    Global Analysis of Nuclear Parton Distributions

    D. de Florian, R. Sassot, P. Zurita and M. Stratmann, Phys. Rev. D85, 074028 (2012) doi:10.1103/PhysRevD.85.074028 [arXiv:1112.6324 [hep-ph]]

    work page internal anchor Pith review Pith/arXiv arXiv doi:10.1103/physrevd.85.074028 2012

  37. [37]

    nCTEQ15 - Global analysis of nuclear parton distributions with uncertainties in the CTEQ framework

    K. Kovarik, A. Kusina, T. Jezo, D. B. Clark, C. Keppel, F. Lyonnet, J. G. Morfin, F. I. Olness, J. F. Owens and I. Schienbein,et al.Phys. Rev. D93, no.8, 085037 (2016) doi:10.1103/PhysRevD.93.085037 [arXiv:1509.00792 [hep-ph]]

    work page internal anchor Pith review Pith/arXiv arXiv doi:10.1103/physrevd.93.085037 2016

  38. [38]

    K. J. Eskola, P. Paakkinen, H. Paukkunen and C. A. Salgado, Eur. Phys. J. C77, no.3, 163 (2017) doi:10.1140/epjc/s10052-017-4725-9 [arXiv:1612.05741 [hep-ph]]

    work page internal anchor Pith review Pith/arXiv arXiv doi:10.1140/epjc/s10052-017-4725-9 2017

  39. [39]

    K. J. Eskola, P. Paakkinen, H. Paukkunen and C. A. Salgado, Eur. Phys. J. C82, no.5, 413 (2022) doi:10.1140/epjc/s10052-022-10359-0 [arXiv:2112.12462 [hep-ph]]

    work page doi:10.1140/epjc/s10052-022-10359-0 2022

  40. [40]

    A. D. Martin, W. J. Stirling, R. S. Thorne and G. Watt, Eur. Phys. J. C63, 189-285 (2009) doi:10.1140/epjc/s10052-009-1072-5 [arXiv:0901.0002 [hep-ph]]

    work page internal anchor Pith review Pith/arXiv arXiv doi:10.1140/epjc/s10052-009-1072-5 2009

  41. [41]

    Stump, J

    D. Stump, J. Huston, J. Pumplin, W. K. Tung, H. L. Lai, S. Kuhlmann and J. F. Owens, JHEP10, 046 (2003) doi:10.1088/1126-6708/2003/10/046 [arXiv:hep- ph/0303013 [hep-ph]]

    work page doi:10.1088/1126-6708/2003/10/046 2003

  42. [42]

    Charm Quark Production in Non-central Heavy Ion Collisions

    V. Emel’yanov, A. Khodinov, S. R. Klein and R. Vogt, Phys. Rev. C56, 2726-2735 (1997) doi:10.1103/PhysRevC.56.2726 [arXiv:nucl-th/9706085 [nucl-th]]

    work page internal anchor Pith review Pith/arXiv arXiv doi:10.1103/physrevc.56.2726 1997

  43. [43]

    Emel’yanov, A

    V. Emel’yanov, A. Khodinov, S. R. Klein and 19 R. Vogt, Phys. Rev. Lett.81, 1801-1804 (1998) doi:10.1103/PhysRevLett.81.1801 [arXiv:nucl- th/9805027 [nucl-th]]

    work page doi:10.1103/physrevlett.81.1801 1998

  44. [44]

    Emel’yanov, A

    V. Emel’yanov, A. Khodinov, S. R. Klein and R. Vogt, Phys. Rev. C61, 044904 (2000) doi:10.1103/PhysRevC.61.044904 [arXiv:hep- ph/9909427 [hep-ph]]

    work page doi:10.1103/physrevc.61.044904 2000

  45. [45]

    S. R. Klein and R. Vogt, Phys. Rev. Lett.91, 142301 (2003) doi:10.1103/PhysRevLett.91.142301 [arXiv:nucl- th/0305046 [nucl-th]]

    work page doi:10.1103/physrevlett.91.142301 2003

  46. [46]

    Impact-parameter dependent nuclear parton distribution functions: EPS09s and EKS98s and their applications in nuclear hard processes

    I. Helenius, K. J. Eskola, H. Honkanen and C. A. Salgado, JHEP07, 073 (2012) doi:10.1007/JHEP07(2012)073 [arXiv:1205.5359 [hep-ph]]

    work page internal anchor Pith review Pith/arXiv arXiv doi:10.1007/jhep07(2012)073 2012

  47. [47]

    D. C. McGlinchey, A. D. Frawley and R. Vogt, Phys. Rev. C87, no.5, 054910 (2013) doi:10.1103/PhysRevC.87.054910 [arXiv:1208.2667 [nucl-th]]

    work page internal anchor Pith review Pith/arXiv arXiv doi:10.1103/physrevc.87.054910 2013

  48. [48]

    T. J. Hou, K. Xie, J. Gao, S. Dulat, M. Guzzi, T. J. Hobbs, J. Huston, P. Nadolsky, J. Pumplin and C. Schmidt,et al.[arXiv:1908.11394 [hep-ph]]

    work page arXiv 1908

  49. [49]

    Cunqueiro and A

    L. Cunqueiro and A. M. Sickles, Prog. Part. Nucl. Phys. 124, 103940 (2022) doi:10.1016/j.ppnp.2022.103940 [arXiv:2110.14490 [nucl-ex]]

    work page doi:10.1016/j.ppnp.2022.103940 2022

  50. [50]

    J. D. Bjorken, FERMILAB-PUB-82-059-THY

    work page

  51. [51]

    S. J. Brodsky and P. Hoyer, Phys. Lett. B298, 165-170 (1993) doi:10.1016/0370-2693(93)91724-2 [arXiv:hep- ph/9210262 [hep-ph]]

    work page doi:10.1016/0370-2693(93)91724-2 1993

  52. [52]

    R. Baieret. al., Nucl. Phys. B484, 265 (1997)

    work page 1997

  53. [53]

    S. K. Giri, P. P. Bhaduri, B. Paul and S. K. Das, Eur. Phys. J. C85, no.3, 264 (2025) doi:10.1140/epjc/s10052- 025-13973-w [arXiv:2502.16259 [nucl-th]]

    work page doi:10.1140/epjc/s10052- 2025

  54. [54]

    Gavin and J

    S. Gavin and J. Milana, Phys. Rev. Lett.68, 1834-1837 (1992) doi:10.1103/PhysRevLett.68.1834

    work page doi:10.1103/physrevlett.68.1834 1992

  55. [55]

    L. H. Song, C. G. Duan and N. Liu, Phys. Lett. B708, 68-74 (2012) doi:10.1016/j.physletb.2012.01.019 [arXiv:1206.3815 [hep-ph]]

    work page internal anchor Pith review Pith/arXiv arXiv doi:10.1016/j.physletb.2012.01.019 2012

  56. [56]

    R. B. Neufeld, I. Vitev and B. W. Zhang, Phys. Lett. B 704, 590-595 (2011) doi:10.1016/j.physletb.2011.09.045 [arXiv:1010.3708 [hep-ph]]

    work page internal anchor Pith review Pith/arXiv arXiv doi:10.1016/j.physletb.2011.09.045 2011

  57. [57]

    C. W. De Jager, H. De Vries and C. De Vries, Atom. Data Nucl. Data Tabl.14, 479-508 (1974) [erratum: Atom. Data Nucl. Data Tabl.16, 580-580 (1975)] doi:10.1016/S0092-640X(74)80002-1

    work page doi:10.1016/s0092-640x(74)80002-1 1974

  58. [58]

    De Vries, C

    H. De Vries, C. W. De Jager and C. De Vries, Atom. Data Nucl. Data Tabl.36, 495-536 (1987) doi:10.1016/0092- 640X(87)90013-1

    work page doi:10.1016/0092- 1987

  59. [59]

    Kharzeev and H

    D. Kharzeev and H. Satz, Phys. Lett. B366, 316-322 (1996) doi:10.1016/0370-2693(95)01328-8 [arXiv:hep- ph/9508276 [hep-ph]]

    work page doi:10.1016/0370-2693(95)01328-8 1996

  60. [60]

    E. G. Ferreiro, F. Fleuret and E. Maurice, Eur. Phys. J. C82, no.3, 201 (2022) doi:10.1140/epjc/s10052-022- 10152-z [arXiv:2107.01150 [hep-ph]]

    work page doi:10.1140/epjc/s10052-022- 2022

  61. [61]

    C. G. Duan, J. C. Xu and L. H. Song, Eur. Phys. J. C 67, 173-179 (2010) doi:10.1140/epjc/s10052-010-1270-1 [arXiv:1109.5337 [hep-ph]]

    work page internal anchor Pith review Pith/arXiv arXiv doi:10.1140/epjc/s10052-010-1270-1 2010

  62. [62]

    Vogt, Phys

    R. Vogt, Phys. Rev. C61(2000), 035203 doi:10.1103/PhysRevC.61.035203 [arXiv:hep- ph/9907317 [hep-ph]]

    work page doi:10.1103/physrevc.61.035203 2000

  63. [63]

    James and M

    F. James and M. Roos, Comput. Phys. Commun.10, 343 (1975)

    work page 1975

  64. [64]

    V.5.34/32, CERN ROOT, 2015, http://root.cern.ch

    work page 2015

  65. [65]

    Chatterjee, P

    S. Chatterjee, P. P. Bhaduri and S. Chat- topadhyay, Nucl. Phys. A1029, 122554 (2023) doi:10.1016/j.nuclphysa.2022.122554 [arXiv:2210.10844 [hep-ph]]

    work page doi:10.1016/j.nuclphysa.2022.122554 2023

  66. [66]

    Y. Q. Ma and R. Vogt, Phys. Rev. D94, no.11, 114029 (2016) doi:10.1103/PhysRevD.94.114029 [arXiv:1609.06042 [hep-ph]]

    work page internal anchor Pith review Pith/arXiv arXiv doi:10.1103/physrevd.94.114029 2016

  67. [67]

    G. T. Bodwin, E. Braaten and G. P. Lepage, Phys. Rev. D51, 1125-1171 (1995) [erratum: Phys. Rev. D55, 5853 (1997)] doi:10.1103/PhysRevD.55.5853 [arXiv:hep- ph/9407339 [hep-ph]]

    work page doi:10.1103/physrevd.55.5853 1995

  68. [68]

    G. R. Farrar, L. L. Frankfurt, M. I. Strikman and H. Liu, Phys. Rev. Lett.64(1990), 2996-2998 doi:10.1103/PhysRevLett.64.2996

    work page doi:10.1103/physrevlett.64.2996 1990

  69. [69]

    J. P. Blaizot and J. Y. Ollitrault, Phys. Lett. B217 (1989), 386-391 doi:10.1016/0370-2693(89)90065-8

    work page doi:10.1016/0370-2693(89)90065-8 1989

  70. [70]

    Gavin and R

    S. Gavin and R. Vogt, Nucl. Phys. B345(1990), 104-124 doi:10.1016/0550-3213(90)90610-P

    work page doi:10.1016/0550-3213(90)90610-p 1990

  71. [71]

    Arleo, P

    F. Arleo, P. B. Gossiaux, T. Gousset and J. Aichelin, Phys. Rev. C61(2000), 054906 doi:10.1103/PhysRevC.61.054906 [arXiv:hep- ph/9907286 [hep-ph]]

    work page doi:10.1103/physrevc.61.054906 2000