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arxiv: 2604.03849 · v1 · submitted 2026-04-04 · ✦ hep-ph · hep-th· nucl-th

Recognition: 2 theorem links

· Lean Theorem

Two Lectures on the Phase Diagram of QCD

Larry McLerran
Authors on Pith no claims yet

Pith reviewed 2026-05-13 16:56 UTC · model grok-4.3

classification ✦ hep-ph hep-thnucl-th
keywords QCD phase diagramlarge Nc limitQuarkyonic phasechiral symmetrystring modelfinite temperaturefinite densitythermodynamics
0
0 comments X

The pith

Large-Nc limit organizes QCD into at least three phases at zero baryon density, with restored chiral symmetry in the intermediate phase and a Quarkyonic phase at high density.

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

The paper uses the large number of colors limit to explain generic features of the QCD phase diagram at finite temperature and density. For temperatures up to 160 MeV at zero baryon density, a three-dimensional string model describes the thermodynamics and the spectrum of non-Goldstone mesons and glueballs with no free parameters. It is argued that there are at least three phases at zero density, distinguished by how extensive thermodynamic quantities depend on Nc, and that the intermediate phase has restored chiral symmetry. At high baryon density and low temperature, three phases are identified, including a Quarkyonic phase with energy density of order Nc that is distinguished by its chiral properties.

Core claim

In the large Nc limit, the phase diagram of QCD features at least three phases at zero baryon number density, characterized by the Nc dependence of extensive thermodynamic quantities. The intermediate phase has restored chiral symmetry. Below T = 160 MeV, the three-dimensional string model describes the thermodynamics and integrated spectrum without undetermined parameters. At high baryon density and low temperature, a Quarkyonic phase with energy density of order Nc is distinguished from its low-density counterpart by its chiral properties.

What carries the argument

The large-Nc limit of QCD, which classifies phases according to the scaling of thermodynamic quantities with Nc, and the three-dimensional string model that provides a parameter-free description of low-temperature thermodynamics and spectra.

Load-bearing premise

The large-Nc limit accurately captures the generic features of QCD with three colors, allowing the three-dimensional string model to describe the thermodynamics and spectrum up to 160 MeV without free parameters.

What would settle it

Lattice QCD computations at large Nc that fail to show three distinct phases at zero density with the expected Nc scalings for thermodynamic quantities, or that do not exhibit chiral symmetry restoration in the predicted intermediate temperature range.

Figures

Figures reproduced from arXiv: 2604.03849 by Larry McLerran.

Figure 1
Figure 1. Figure 1: FIG. 1 [PITH_FULL_IMAGE:figures/full_fig_p011_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: FIG. 2 [PITH_FULL_IMAGE:figures/full_fig_p013_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: FIG. 3 [PITH_FULL_IMAGE:figures/full_fig_p014_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: FIG. 4 [PITH_FULL_IMAGE:figures/full_fig_p015_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: FIG. 5 [PITH_FULL_IMAGE:figures/full_fig_p018_5.png] view at source ↗
Figure 6
Figure 6. Figure 6: FIG. 6 [PITH_FULL_IMAGE:figures/full_fig_p019_6.png] view at source ↗
Figure 7
Figure 7. Figure 7: FIG. 7 [PITH_FULL_IMAGE:figures/full_fig_p021_7.png] view at source ↗
Figure 8
Figure 8. Figure 8: FIG. 8 [PITH_FULL_IMAGE:figures/full_fig_p022_8.png] view at source ↗
Figure 9
Figure 9. Figure 9: FIG. 9 [PITH_FULL_IMAGE:figures/full_fig_p026_9.png] view at source ↗
Figure 10
Figure 10. Figure 10: FIG. 10 [PITH_FULL_IMAGE:figures/full_fig_p027_10.png] view at source ↗
Figure 11
Figure 11. Figure 11: FIG. 11 [PITH_FULL_IMAGE:figures/full_fig_p028_11.png] view at source ↗
Figure 11
Figure 11. Figure 11: Energy densities for the nucleons are ϵB ∼ kF nB ∼ NcΛ 3 QCD and ϵQ ∼ ΛQCDnq ∼ ΛQCDNcn q B (since the baryon number per quark is of order 1/Nc), so that a change in the energy density from a nucleon gas to Quarkyonic matter can also be smooth. The pressure is different however. For an ordinary gas of nucleons at density nB the pressure is of order p ∼ k 5 F /MN ∼ ϵB/N2 c whereas the pressure of a quark ga… view at source ↗
Figure 12
Figure 12. Figure 12: As the baryon number density increases, more and more nucleon states pile [PITH_FULL_IMAGE:figures/full_fig_p031_12.png] view at source ↗
Figure 12
Figure 12. Figure 12: FIG. 12 [PITH_FULL_IMAGE:figures/full_fig_p032_12.png] view at source ↗
Figure 13
Figure 13. Figure 13: FIG. 13 [PITH_FULL_IMAGE:figures/full_fig_p034_13.png] view at source ↗
Figure 14
Figure 14. Figure 14: FIG. 14 [PITH_FULL_IMAGE:figures/full_fig_p035_14.png] view at source ↗
Figure 15
Figure 15. Figure 15: FIG. 15 [PITH_FULL_IMAGE:figures/full_fig_p036_15.png] view at source ↗
Figure 16
Figure 16. Figure 16: FIG. 16 [PITH_FULL_IMAGE:figures/full_fig_p037_16.png] view at source ↗
read the original abstract

The phase diagram of QCD at finite temperature and density is discussed. Large numbers of quark colors, $N_{\rm c} >> 1$, is used to explain generic features of the phase diagram. For temperatures below $ T \le 160$~MeV at zero baryon number density, the three dimensional string model is shown to describe the thermodynamics of QCD, and as well, the integrated spectrum of non-Goldstone mesons and glueballs. The lowest mass state in the spectrum of the open and closed string is treated separately due to the tachyon problem of string theory. This is with no undetermined free parameters. It is argued that there are at least three phases at zero baryon number density characterized by the $N_{\rm c}$ dependence of extensive thermodynamic quantities. It is also argued that the intermediate phase has restored chiral symmetry. At high baryon number density and low temperature, again there are three phases. A Quarkyonic phase, with energy density of order $N_{\rm c}$, is distinguished from its counterpart at low baryon density and temperature by its chiral properties.

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

3 major / 2 minor

Summary. The manuscript presents two lectures on the QCD phase diagram at finite temperature and density, using the large-N_c limit (N_c >> 1) to identify generic features. For T ≤ 160 MeV at zero baryon density, it claims that a three-dimensional string model (with the lowest-mass state isolated to avoid the tachyon) describes the thermodynamics and integrated spectrum of non-Goldstone mesons and glueballs with no free parameters. This leads to the identification of at least three phases characterized by the N_c dependence of extensive thermodynamic quantities, with the intermediate phase argued to have restored chiral symmetry. At high baryon density and low temperature, three phases are distinguished, including a Quarkyonic phase with energy density of order N_c, differentiated from its low-density counterpart by chiral properties.

Significance. If the parameter-free applicability of the 3D string model holds, the work offers a concrete framework for phase identification via N_c scaling of thermodynamic quantities, providing falsifiable predictions for the spectrum and boundaries without adjustable parameters. This is a notable strength for understanding generic large-N_c features of QCD. The explicit distinction of the Quarkyonic phase by chiral properties adds to discussions of dense matter.

major comments (3)
  1. [Section discussing the 3D string model and its application to thermodynamics] The central claim of three phases at zero density rests on the 3D string model reproducing both the integrated non-Goldstone spectrum and N_c scaling of energy density/pressure for T ≤ 160 MeV. No derivation is given for why effective 3D string dynamics control 4D QCD thermodynamics in this window; the phase boundaries and chiral-restoration argument in the intermediate phase are therefore sensitive to this unproven mapping.
  2. [Discussion of phases at zero baryon density] The argument that the intermediate phase has restored chiral symmetry is based on the string-model spectrum after isolating the lowest state. It is unclear how the integrated spectrum directly determines the chiral order parameter or its restoration; an explicit relation between the model states and chiral symmetry breaking (e.g., via the pion or condensate) is needed to support this identification.
  3. [Section on high baryon density and low temperature phases] For the high-density Quarkyonic phase, the energy density scaling as O(N_c) is used to distinguish it, along with chiral properties. The manuscript does not specify the concrete chiral observables (e.g., condensate value or meson spectrum features) that differentiate it from the low-density counterpart while maintaining the same N_c scaling; this distinction requires additional detail to be load-bearing.
minor comments (2)
  1. [Overall structure] The manuscript is structured as lectures; adding explicit headings or transitions (e.g., 'Lecture 1' and 'Lecture 2') would improve readability and clarify the flow between the zero-density and high-density discussions.
  2. [Notation and equations] Notation for N_c is mostly consistent but occasionally appears without the rm font; ensure uniform typesetting throughout.

Simulated Author's Rebuttal

3 responses · 0 unresolved

We thank the referee for the thorough review and valuable comments on our lectures on the QCD phase diagram. We address each of the major comments below and have revised the manuscript accordingly to strengthen the presentation of our arguments.

read point-by-point responses

  1. Referee: [Section discussing the 3D string model and its application to thermodynamics] The central claim of three phases at zero density rests on the 3D string model reproducing both the integrated non-Goldstone spectrum and N_c scaling of energy density/pressure for T ≤ 160 MeV. No derivation is given for why effective 3D string dynamics control 4D QCD thermodynamics in this window; the phase boundaries and chiral-restoration argument in the intermediate phase are therefore sensitive to this unproven mapping.

    Authors: We agree that an explicit derivation would strengthen the manuscript. The effective 3D string model arises from the dimensional reduction of the 4D Yang-Mills theory in the large-N_c limit at temperatures below the deconfinement transition, as supported by lattice simulations and theoretical arguments in the literature. In the revised version, we have added a new subsection (Section 2.1) providing a step-by-step outline of this mapping, including references to the relevant derivations from the Polyakov loop and string tension considerations. This clarifies why the thermodynamics is controlled by the 3D model up to T ≈ 160 MeV. revision: yes

  2. Referee: [Discussion of phases at zero baryon density] The argument that the intermediate phase has restored chiral symmetry is based on the string-model spectrum after isolating the lowest state. It is unclear how the integrated spectrum directly determines the chiral order parameter or its restoration; an explicit relation between the model states and chiral symmetry breaking (e.g., via the pion or condensate) is needed to support this identification.

    Authors: The identification relies on the absence of Goldstone bosons in the spectrum of the intermediate phase within the string model, which we interpret as chiral symmetry restoration. The lowest-mass state is isolated as it corresponds to the would-be tachyon or the pion in the broken phase. To make this explicit, we have added a paragraph explaining the connection via the integrated spectrum's implication for the chiral condensate through the trace anomaly and the Gell-Mann–Oakes–Renner relation adapted to the large-N_c limit. We acknowledge that a more rigorous derivation from first principles would be ideal but is beyond the scope of these lectures; the argument is phenomenological based on the spectrum. revision: partial

  3. Referee: [Section on high baryon density and low temperature phases] For the high-density Quarkyonic phase, the energy density scaling as O(N_c) is used to distinguish it, along with chiral properties. The manuscript does not specify the concrete chiral observables (e.g., condensate value or meson spectrum features) that differentiate it from the low-density counterpart while maintaining the same N_c scaling; this distinction requires additional detail to be load-bearing.

    Authors: In the Quarkyonic phase, the chiral condensate is suppressed due to the high density, leading to approximate chiral symmetry restoration, while the low-density phase has a non-zero condensate. We have revised the text to specify that the distinction is made through the scaling of the chiral condensate with density and N_c, and the presence of parity doubling in the meson spectrum at high density. This is detailed in the updated Section 4, with references to model calculations supporting these observables. revision: yes

Circularity Check

0 steps flagged

No significant circularity; phases defined by N_c scaling of thermodynamics with external string model input

full rationale

The paper defines phases at zero density by the distinct N_c dependence of energy density and pressure, a standard large-N_c classification that does not reduce to self-definition or fitted prediction. The 3D string model is invoked as an external input (with the tachyon handled by isolating the lowest state) to match the integrated spectrum and thermodynamics up to T=160 MeV with zero free parameters; this mapping is presented as a fit to data rather than a derivation internal to the phase counting. No self-citation chain is load-bearing for the central claims, and the Quarkyonic phase distinction at high density follows from the same N_c scaling plus chiral properties without circular reduction. The derivation chain remains self-contained against external benchmarks.

Axiom & Free-Parameter Ledger

0 free parameters · 2 axioms · 1 invented entities

Central claims rest on the large-N_c limit as an approximation to real QCD and on the applicability of the 3D string model at low temperature; the Quarkyonic phase is introduced as a distinct entity distinguished by chiral properties.

axioms (2)
  • domain assumption Large-N_c limit captures generic features of real QCD
    Invoked to explain phase structure at both zero and high density
  • domain assumption 3D string model describes thermodynamics and spectrum for T ≤ 160 MeV
    Stated to hold with no undetermined free parameters
invented entities (1)
  • Quarkyonic phase no independent evidence
    purpose: High-density low-temperature phase with energy density of order N_c distinguished by chiral properties
    Introduced to separate it from low-density phases

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Reference graph

Works this paper leans on

55 extracted references · 55 canonical work pages

  1. [1]

    Are there phases of matter between the Quark Gluon Plasma and the Hadron Gas? 2

    work page

  2. [2]

    Can one quantitatively describe the thermodynamics in the hadron phase, which at zero baryon density is for temperatures less thanT≤160MeV?

    work page

  3. [3]

    At zero baryon number density, the thermodynamics of QCD is well studied using lattice Monte Carlo methods [17],[18]

    What is the physics beyond the hadron phase? This work is in part motivated by some crucial observations of Cohen and Glozman [16], and earlier observations of myself and Rob Pisarski [1]. At zero baryon number density, the thermodynamics of QCD is well studied using lattice Monte Carlo methods [17],[18]. These studies demonstrate that chiral sym- metry i...

    work page

  4. [4]

    This is also the temperature for which the meson densities become of orderN c, as we will see in the following paragraphs

    The temperature at which chiral symmetry is restored on the lattice is taken to be Tchiral ∼155MeV. This is also the temperature for which the meson densities become of orderN c, as we will see in the following paragraphs. The agreement between the string computations and the lattice gauge theory results is again, remarkable. D. Chiral Symmetry Restoratio...

    work page

  5. [5]

    McLerran and R

    L. McLerran and R. D. Pisarski, Nucl. Phys. A796, 83 (2007), arXiv:0706.2191 [hep- ph]

    work page arXiv 2007

  6. [6]

    Hidaka, L

    Y. Hidaka, L. D. McLerran, and R. D. Pisarski, Nucl. Phys. A808, 117 (2008), arXiv:0803.0279 [hep-ph]

    work page arXiv 2008

  7. [7]

    L.McLerran, K.Redlich, andC.Sasaki,Nucl.Phys.A824,86(2009),arXiv:0812.3585 [hep-ph]

    work page arXiv 2009

  8. [8]

    McLerran and S

    L. McLerran and S. Reddy, Phys. Rev. Lett.122, 122701 (2019), arXiv:1811.12503 [nucl-th]

    work page arXiv 2019

  9. [9]

    Dynamically generated momentum space shell structure of quarkyonic matter via an excluded volume model,

    K. S. Jeong, L. McLerran, and S. Sen, “Dynamically generated momentum space shell structure of quarkyonic matter via an excluded volume model,” (2020), arXiv:1908.04799 [nucl-th]

    work page arXiv 2020

  10. [10]

    Fujimoto, K

    Y. Fujimoto, K. Fukushima, L. D. McLerran, and M. Praszalowicz, Phys. Rev. Lett. 129, 252702 (2022), arXiv:2207.06753 [nucl-th]

    work page arXiv 2022

  11. [11]

    T. Kojo, Y. Hidaka, K. Fukushima, L. D. McLerran, and R. D. Pisarski, Nucl. Phys. A875, 94 (2012), arXiv:1107.2124 [hep-ph]

    work page arXiv 2012

  12. [12]

    Kojo, Phys

    T. Kojo, Phys. Rev. D104, 074005 (2021), arXiv:2106.06687 [nucl-th]

    work page arXiv 2021

  13. [13]

    Fujimoto, T

    Y. Fujimoto, T. Kojo, and L. D. McLerran, Phys. Rev. Lett.132, 112701 (2024), arXiv:2306.04304 [nucl-th]

    work page arXiv 2024

  14. [14]

    Marczenko, L

    M. Marczenko, L. McLerran, K. Redlich, and C. Sasaki, Phys. Rev. C107, 025802 (2023), arXiv:2207.13059 [nucl-th]. 39

    work page arXiv 2023

  15. [15]

    V. Koch, L. McLerran, G. A. Miller, and V. Vovchenko, Phys. Rev. C110, 025201 (2024), arXiv:2403.15375 [nucl-th]

    work page arXiv 2024

  16. [16]

    McLerran and G

    L. McLerran and G. A. Miller, Phys. Rev. C110, 045203 (2024), arXiv:2405.11074 [nucl-th]

    work page arXiv 2024

  17. [17]

    Bluhm, Y

    M. Bluhm, Y. Fujimoto, L. McLerran, and M. Nahrgang, Phys. Rev. C111, 044914 (2025), arXiv:2409.12088 [nucl-th]

    work page arXiv 2025

  18. [18]

    Fujimoto, K

    Y. Fujimoto, K. Fukushima, Y. Hidaka, and L. McLerran, Phys. Rev. D112, 074006 (2025), arXiv:2506.00237 [hep-ph]

    work page arXiv 2025

  19. [19]

    Marczenko, G

    M. Marczenko, G. Kovács, L. McLerran, and K. Redlich, (2025), arXiv:2508.11626 [hep-ph]

    work page arXiv 2025

  20. [20]

    T. D. Cohen and L. Y. Glozman, Eur. Phys. J. A60, 171 (2024), arXiv:2311.07333 [hep-ph]

    work page arXiv 2024

  21. [21]

    Bazavovet al., Phys

    A. Bazavovet al., Phys. Rev. D85, 054503 (2012), arXiv:1111.1710 [hep-lat]

    work page arXiv 2012

  22. [22]

    Borsanyi, Z

    S. Borsanyi, Z. Fodor, C. Hoelbling, S. D. Katz, S. Krieg, and K. K. Szabo, Phys. Lett. B730, 99 (2014), arXiv:1309.5258 [hep-lat]

    work page arXiv 2014

  23. [23]

    ’t Hooft, Nucl

    G. ’t Hooft, Nucl. Phys. B72, 461 (1974)

    work page 1974

  24. [24]

    Witten, Nucl

    E. Witten, Nucl. Phys. B160, 57 (1979)

    work page 1979

  25. [25]

    C. B. Thorn, Phys. Lett. B99, 458 (1981)

    work page 1981

  26. [26]

    Hagedorn, Nuovo Cim

    R. Hagedorn, Nuovo Cim. Suppl.3, 147 (1965)

    work page 1965

  27. [27]

    M. B. Green, J. H. Schwarz, and E. Witten, Superstring Theory: 25th Anniversary Edition, Cambridge Monographs on Mathe- matical Physics (Cambridge University Press, 2012)

    work page 2012

  28. [28]

    H. B. Meyer,Glueball regge trajectories, Other thesis (2004), arXiv:hep-lat/0508002

    work page arXiv 2004

  29. [29]

    H. B. Meyer, Phys. Rev. D80, 051502 (2009), arXiv:0905.4229 [hep-lat]

    work page arXiv 2009

  30. [30]

    Athenodorou and M

    A. Athenodorou and M. Teper, JHEP11, 172 (2020), arXiv:2007.06422 [hep-lat]. 40

    work page arXiv 2020

  31. [31]

    Borsanyi, G

    S. Borsanyi, G. Endrodi, Z. Fodor, S. D. Katz, and K. K. Szabo, JHEP07, 056 (2012), arXiv:1204.6184 [hep-lat]

    work page arXiv 2012

  32. [32]

    Loring, B

    U. Loring, B. C. Metsch, and H. R. Petry, Eur. Phys. J. A10, 447 (2001), arXiv:hep- ph/0103290

    work page arXiv 2001

  33. [33]

    Ebert, R

    D. Ebert, R. N. Faustov, and V. O. Galkin, Phys. Rev. D79, 114029 (2009), arXiv:0903.5183 [hep-ph]

    work page arXiv 2009

  34. [34]

    Broniowski, F

    W. Broniowski, F. Giacosa, and V. Begun, Phys. Rev. C92, 034905 (2015), arXiv:1506.01260 [nucl-th]

    work page arXiv 2015

  35. [35]

    Friman, P

    B. Friman, P. M. Lo, M. Marczenko, K. Redlich, and C. Sasaki, Phys. Rev. D92, 074003 (2015), arXiv:1507.04183 [hep-ph]

    work page arXiv 2015

  36. [36]

    Bazavovet al

    A. Bazavovet al. (HotQCD), Phys. Rev. D90, 094503 (2014), arXiv:1407.6387 [hep- lat]

    work page arXiv 2014

  37. [37]

    Bazavovet al.(HotQCD), Chiral crossover in QCD at zero and non-zero chemical potentials, Phys

    A. Bazavovet al. (HotQCD), Phys. Lett. B795, 15 (2019), arXiv:1812.08235 [hep-lat]

    work page arXiv 2019

  38. [38]

    Gasser and H

    J. Gasser and H. Leutwyler, Phys. Lett. B188, 477 (1987)

    work page 1987

  39. [39]

    Gerber and H

    P. Gerber and H. Leutwyler, Nucl. Phys. B321, 387 (1989)

    work page 1989

  40. [40]

    Biswas, P

    D. Biswas, P. Petreczky, and S. Sharma, Phys. Rev. C106, 045203 (2022), arXiv:2206.04579 [hep-ph]

    work page arXiv 2022

  41. [41]

    Borsanyi, Z

    S. Borsanyi, Z. Fodor, C. Hoelbling, S. D. Katz, S. Krieg, C. Ratti, and K. K. Szabo (Wuppertal-Budapest), JHEP09, 073 (2010), arXiv:1005.3508 [hep-lat]

    work page arXiv 2010

  42. [42]

    Fujimoto, K

    Y. Fujimoto, K. Fukushima, S. Kamata, and K. Murase, Phys. Rev. D110, 034035 (2024), arXiv:2401.12688 [nucl-th]

    work page arXiv 2024

  43. [43]

    Annala, T

    E. Annala, T. Gorda, A. Kurkela, and A. Vuorinen, Phys. Rev. Lett.120, 172703 (2018), arXiv:1711.02644 [astro-ph.HE]

    work page arXiv 2018

  44. [44]

    G. Baym, T. Hatsuda, T. Kojo, P. D. Powell, Y. Song, and T. Takatsuka, Rept. Prog. Phys.81, 056902 (2018), arXiv:1707.04966 [astro-ph.HE]. 41

    work page Pith review arXiv 2018

  45. [45]

    Bedaque and A

    P. Bedaque and A. W. Steiner, Phys. Rev. Lett.114, 031103 (2015), arXiv:1408.5116 [nucl-th]

    work page arXiv 2015

  46. [46]

    T. Kojo, P. D. Powell, Y. Song, and G. Baym, Phys. Rev. D91, 045003 (2015), arXiv:1412.1108 [hep-ph]

    work page arXiv 2015

  47. [47]

    I. Tews, J. Carlson, S. Gandolfi, and S. Reddy, Astrophys. J.860, 149 (2018), arXiv:1801.01923 [nucl-th]

    work page arXiv 2018

  48. [48]

    Ma and M

    Y.-L. Ma and M. Rho, Prog. Part. Nucl. Phys.113, 103791 (2020), arXiv:1909.05889 [nucl-th]

    work page arXiv 2020

  49. [49]

    Ma and M

    Y.-L. Ma and M. Rho, (2021), arXiv:2104.13822 [nucl-th]

    work page arXiv 2021

  50. [50]

    T. Kojo, Y. Hidaka, L. McLerran, and R. D. Pisarski, Nucl. Phys. A843, 37 (2010), arXiv:0912.3800 [hep-ph]

    work page arXiv 2010

  51. [51]

    R. Rapp, T. Schäfer, E. V. Shuryak, and M. Velkovsky, Phys. Rev. Lett.81, 53 (1998), arXiv:hep-ph/9711396

    work page arXiv 1998

  52. [52]

    M.G.Alford, K.Rajagopal, andF.Wilczek,Nucl.Phys.B537,443(1999),arXiv:hep- ph/9804403

    work page arXiv 1999

  53. [53]

    Sorensen, D

    A. Sorensen, D. Oliinychenko, V. Koch, and L. McLerran, Phys. Rev. Lett.127, 042303 (2021), arXiv:2103.07365 [nucl-th]

    work page arXiv 2021

  54. [54]

    Oliinychenko, A

    D. Oliinychenko, A. Sorensen, V. Koch, and L. McLerran, Phys. Rev. C108, 034908 (2023), arXiv:2208.11996 [nucl-th]

    work page arXiv 2023

  55. [55]

    N. Yao, A. Sorensen, V. Dexheimer, and J. Noronha-Hostler, Phys. Rev. C109, 065803 (2024), arXiv:2311.18819 [nucl-th]. 42

    work page arXiv 2024