Thank you for visiting nature.com. You are using a browser version with limited support for CSS. To obtain the best experience, we recommend you use a more up to date browser (or turn off compatibility mode in Internet Explorer). In the meantime, to ensure continued support, we are displaying the site without styles and JavaScript.

# Decoding the phase structure of QCD via particle production at high energy

## Abstract

Recent studies based on lattice Monte Carlo simulations of quantum chromodynamics (QCD)—the theory of strong interactions—have demonstrated that at high temperature there is a phase change from confined hadronic matter to a deconfined quark–gluon plasma in which quarks and gluons can travel distances that greatly exceed the size of hadrons. Here we show that the phase structure of such strongly interacting matter can be decoded by analysing particle production in high-energy nuclear collisions within the framework of statistical hadronization, which accounts for the thermal distribution of particle species. Our results represent a phenomenological determination of the location of the phase boundary of strongly interacting matter, and imply quark–hadron duality at this boundary.

This is a preview of subscription content, access via your institution

## Relevant articles

• ### Spectral functions of heavy quarkonia in a bulk-viscous quark gluon plasma

Journal of High Energy Physics Open Access 28 February 2022

• ### Study of nuclear modification factors of deuteron and anti-deuteron in Pb–Pb collisions at $$\sqrt{s_{\mathrm{NN}}} =2.76\,\hbox {TeV}$$

Scientific Reports Open Access 02 February 2022

• ### Prompt D0, D+, and D*+ production in Pb–Pb collisions at $$\sqrt{s_{\mathrm{NN}}}$$ = 5.02 TeV

Journal of High Energy Physics Open Access 28 January 2022

## Access options

\$32.00

All prices are NET prices.

## References

1. Gyulassy, M. & McLerran, L. New forms of QCD matter discovered at RHIC. Nucl. Phys. A 750, 30–63 (2005).

2. Braun-Munzinger, P. & Stachel, J. The quest for the quark–gluon plasma. Nature 448, 302–309 (2007). Concise review of pre-LHC situation and summary of expectations.

3. Jacak, B. V. & Müller, B. The exploration of hot nuclear matter. Science 337, 310–314 (2012).

4. Itoh, N. Hydrostatic equilibrium of hypothetical quark stars. Prog. Theor. Phys. 44, 291–292 (1970).

5. Collins, J. C. & Perry, M. Superdense matter: neutrons or asymptotically free quarks? Phys. Rev. Lett. 34, 1353–1356 (1975).

6. Cabibbo, N. & Parisi, G. Exponential hadronic spectrum and quark liberation. Phys. Lett. B 59, 67–69 (1975).

7. Chapline, G. & Nauenberg, M. Asymptotic freedom and the baryon-quark phase transition. Phys. Rev. D 16, 450–456 (1977).

8. Shuryak, E. V. Quark-gluon plasma and hadronic production of leptons, photons and psions. Phys. Lett. B 78, 150–153 (1978).

9. Boyanovsky, D., de Vega, H. & Schwarz, D. Phase transitions in the early and the present universe. Annu. Rev. Nucl. Part. Sci. 56, 441–500 (2006).

10. Rajagopal, K. & Wilczek, F. in At The Frontier Of Particle Physics. Handbook of QCD Vol. 3 (ed. Shifman, M.) 2061–2151 (World Scientific, New Jersey, 2001).

11. Heinz, U. W. & Jacob, M. Evidence for a new state of matter: an assessment of the results from the CERN lead beam program. Preprint at https://arxiv.org/abs/nucl-th/0002042 (2000).

12. E877 Collaboration. Observation of anisotropic event shapes and transverse flow in Au + Au collisions at AGS energy. Phys. Rev. Lett. 73, 2532–2535 (1994).

13. STAR Collaboration. Experimental and theoretical challenges in the search for the quark gluon plasma: the STAR Collaboration’s critical assessment of the evidence from RHIC collisions. Nucl. Phys. A 757, 102–183 (2005).

14. BRAHMS Collaboration. Quark gluon plasma and color glass condensate at RHIC? The perspective from the BRAHMS experiment. Nucl. Phys. A 757, 1–27 (2005).

15. PHENIX Collaboration. Formation of dense partonic matter in relativistic nucleus-nucleus collisions at RHIC: experimental evaluation by the PHENIX Collaboration. Nucl. Phys. A 757, 184–283 (2005).

16. PHOBOS Collaboration. The PHOBOS perspective on discoveries at RHIC. Nucl. Phys. A 757, 28–101 (2005).

17. Müller, B., Schukraft, J. & Wyslouch, B. First results from Pb+Pb collisions at the LHC. Annu. Rev. Nucl. Part. Sci. 62, 361–386 (2012). Impact of the first LHC data on QGP research.

18. Schukraft, J. Heavy ion physics at the Large Hadron Collider: what is new? What is next? Phys. Scr. T 158, 014003 (2013).

19. Braun-Munzinger, P., Koch, V., Schäfer, T. & Stachel, J. Properties of hot and dense matter from relativistic heavy ion collisions. Phys. Rep. 621, 76–126 (2016).

20. Braun-Munzinger, P. & Wambach, J. The phase diagram of strongly-interacting matter. Rev. Mod. Phys. 81, 1031–1050 (2009).

21. Müller, B. Investigation of hot QCD matter: theoretical aspects. Phys. Scr. T 158, 014004 (2013).

22. Satz, H. Probing the states of matter in QCD. Int. J. Mod. Phys. A 28, 1330043 (2013).

23. Particle Data Group Collaboration. Review of particle physics. Chin. Phys. C 40, 100001 (2016).

24. Gross, D. J. & Wilczek, F. Ultraviolet behavior of nonabelian gauge theories. Phys. Rev. Lett. 30, 1343–1346 (1973).

25. Politzer, H. D. Reliable perturbative results for strong interactions? Phys. Rev. Lett. 30, 1346–1349 (1973).

26. Karsch, F. Lattice QCD at high temperature and density. Lect. Notes Phys. 583, 209–249 (2002).

27. Wilczek, F. QCD made simple. Phys. Today 53, 22–28 (2000).

28. Bazavov, A. et al. The chiral and deconfinement aspects of the QCD transition. Phys. Rev. D 85, 054503 (2012).

29. Aoki, Y., Endrodi, G., Fodor, Z., Katz, S. & Szabo, K. The order of the quantum chromodynamics transition predicted by the standard model of particle physics. Nature 443, 675–678 (2006).

30. HotQCD Collaboration. The equation of state in (2+1)-flavor QCD. Phys. Rev. D 90, 094503 (2014). Determination of the equation of state of hot QGP from LQCD.

31. Borsányi, S. et al. Is there still any T c mystery in lattice QCD? Results with physical masses in the continuum limit III. J. High Energy Phys. 9, 73 (2010).

32. Borsányi, S. et al. Full result for the QCD equation of state with 2+1 flavors. Phys. Lett. B 730, 99–104 (2014).

33. Luo, X. & Xu, N. Search for the QCD critical point with fluctuations of conserved quantities in relativistic heavy-ion collisions at RHIC: an overview. Nucl. Sci. Tech. 28, 112 (2017).

34. Karsch, F. The last word(s) on CPOD 2013. Proc. Sci. 185, 46 (2013).

35. Dürr, S. et al. Ab-initio determination of light hadron masses. Science 322, 1224–1227 (2008).

36. Bazavov, A. et al. The QCD equation of state to $${\mathscr{O}}({\mu }_{B}^{6})$$ from lattice QCD. Phys. Rev. D 95, 054504 (2017).

37. Andronic, A., Braun-Munzinger, P., Stachel, J. & Winn, M. Interacting hadron resonance gas meets lattice QCD. Phys. Lett. B 718, 80–85 (2012).

38. Karsch, F. Thermodynamics of strong interaction matter from lattice QCD and the hadron resonance gas model. Acta Phys. Polon. B 7, 117–126 (2014).

39. Dashen, R., Ma, S.-K. & Bernstein, H. J. S Matrix formulation of statistical mechanics. Phys. Rev. 187, 345–370 (1969).

40. Cleymans, J. & Satz, H. Thermal hadron production in high-energy heavy ion collisions. Z. Phys. C 57, 135–147 (1993).

41. Braun-Munzinger, P., Stachel, J., Wessels, J. & Xu, N. Thermal equilibration and expansion in nucleus-nucleus collisions at the AGS. Phys. Lett. B 344, 43–48 (1995). Comprehensive application of the statistical hadronization model to data.

42. Braun-Munzinger, P., Redlich, K. & Stachel, J. in Quark Gluon Plasma Vol. 3 (eds Hwa, R. C. & Wang, X.-N.) 491–599 (World Scientific, Singapore, 2004).

43. Braun-Munzinger, P., Magestro, D., Redlich, K. & Stachel, J. Hadron production in Au–Au collisions at RHIC. Phys. Lett. B 518, 41–46 (2001). Establishing the statistical hadronization model in the RHIC era.

44. Letessier, J. & Rafelski, J. Hadron production and phase changes in relativistic heavy ion collisions. Eur. Phys. J. A 35, 221–242 (2008).

45. Stachel, J., Andronic, A., Braun-Munzinger, P. & Redlich, K. Confronting LHC data with the statistical hadronization model. J. Phys. Conf. Ser. 509, 012019 (2014).

46. Hagedorn, R. How we got to QCD matter from the hadron side by trial and error. Lect. Notes Phys. 221, 53–76 (1985).

47. Cleymans, J. & Redlich, K. Unified description of freezeout parameters in relativistic heavy ion collisions. Phys. Rev. Lett. 81, 5284–5286 (1998). First interpretation of the chemical freeze-out line.

48. Stock, R. The parton to hadron phase transition observed in Pb+Pb collisions at 158-GeV per nucleon. Phys. Lett. B 456, 277–282 (1999).

49. Braun-Munzinger, P. & Stachel, J. Particle ratios, equilibration, and the QCD phase boundary. J. Phys. G 28, 1971–1976 (2002).

50. Braun-Munzinger, P., Stachel, J. & Wetterich, C. Chemical freezeout and the QCD phase transition temperature. Phys. Lett. B 596, 61–69 (2004).

51. Andronic, A., Braun-Munzinger, P. & Stachel, J. Thermal hadron production in relativistic nuclear collisions: the hadron mass spectrum, the horn, and the QCD phase transition. Phys. Lett. B 673, 142–145 (2009).

52. Floerchinger, S. & Wetterich, C. Chemical freeze-out in heavy ion collisions at large baryon densities. Nucl. Phys. A 890–891, 11–24 (2012).

53. Bazavov, A. et al. Freeze-out conditions in heavy ion collisions from QCD thermodynamics. Phys. Rev. Lett. 109, 192302 (2012).

54. ALICE Collaboration. Centrality dependence of π, K, p production in Pb-Pb collisions at $$\sqrt{{s}_{{\rm{NN}}}}$$ = 2.76 TeV. Phys. Rev. C 88, 044910 (2013).

55. ALICE Collaboration. $${K}_{S}^{0}$$ and Λ production in Pb-Pb collisions at $$\sqrt{{s}_{{\rm{NN}}}}$$  = 2.76 TeV. Phys. Rev. Lett. 111, 222301 (2013).

56. ALICE Collaboration. Multi-strange baryon production at mid-rapidity in Pb-Pb collisions at $$\sqrt{{s}_{{\rm{NN}}}}$$ = 2.76 TeV. Phys. Lett. B 728, 216–227 (2014).

57. ALICE Collaboration. K *(892)0 and ϕ(1020) production in Pb-Pb collisions at $$\sqrt{{s}_{{\rm{NN}}}}$$ = 2.76 TeV. Phys. Rev. C 91, 024609 (2015).

58. ALICE Collaboration. $${}_{\Lambda }^{3}{\rm{H}}$$ and $${}_{\bar{\Lambda }}^{3}\bar{{\rm{H}}}$$ production in Pb-Pb collisions at $$\sqrt{{s}_{{\rm{NN}}}}$$ = 2.76 TeV. Phys. Lett. B 754, 360–372 (2016).

59. ALICE Collaboration. Production of light nuclei and anti-nuclei in pp and Pb-Pb collisions at energies available at the CERN Large Hadron Collider. Phys. Rev. C 93, 024917 (2016).

60. ALICE Collaboration. Production of 4He and $$\bar{{}^{4}{\rm{H}}{\rm{e}}}$$ in Pb–Pb collisions at $$\sqrt{{s}_{{\rm{NN}}}}$$ = 2.76 TeV at the LHC. Nucl. Phys. A 971, 1–20 (2018).

61. ALICE Collaboration. Pion, kaon, and proton production in central Pb–Pb collisions at $$\sqrt{{s}_{{\rm{NN}}}}$$ = 2.76 TeV. Phys. Rev. Lett. 109, 252301 (2012).

62. Becattini, F., Grossi, E., Bleicher, M., Steinheimer, J. & Stock, R. Centrality dependence of hadronization and chemical freeze-out conditions in heavy ion collisions at $$\sqrt{{s}_{{\rm{NN}}}}$$ = 2.76 TeV. Phys. Rev. C 90, 054907 (2014).

63. ALICE Collaboration. Enhanced production of multi-strange hadrons in high-multiplicity proton-proton collisions. Nat. Phys. 13, 535–539 (2017).

64. Andronic, A., Braun-Munzinger, P., Stachel, J. & Stöcker, H. Production of light nuclei, hypernuclei and their antiparticles in relativistic nuclear collisions. Phys. Lett. B 697, 203–207 (2011).

65. Chapline, G. & Kerman, A. On the Possibility of Making Quark Matter in Nuclear Collisions. Report No. MIT-CTP-695, https://inspirehep.net/record/134446/files/CTP-695.pdf (MIT Center of Theoretical Physics, 1978).

66. Csernai, L. P. & Kapusta, J. I. Entropy and cluster production in nuclear collisions. Phys. Rep. 131, 223–318 (1986).

67. Hirenzaki, S., Suzuki, T. & Tanihata, I. A general formula of the coalescence model. Phys. Rev. C 48, 2403–2408 (1993).

68. ExHIC Collaboration. Exotic hadrons from heavy ion collisions. Prog. Part. Nucl. Phys. 95, 279–322 (2017).

69. NPLQCD Collaboration. Light nuclei and hypernuclei from quantum chromodynamics in the limit of SU(3) flavor symmetry. Phys. Rev. D 87, 034506 (2013).

70. Hagedorn, R. & Redlich, K. Statistical thermodynamics in relativistic particle and ion physics: canonical or grand canonical? Z. Phys. C 27, 541–551 (1985). Theoretical foundations of the statistical thermodynamics of particle production.

71. Hamieh, S., Redlich, K. & Tounsi, A. Canonical description of strangeness enhancement from p–A to Pb–Pb collisions. Phys. Lett. B 486, 61–66 (2000).

72. Braun-Munzinger, P. & Stachel, J. (Non)thermal aspects of charmonium production and a new look at J/ψ suppression. Phys. Lett. B 490, 196–202 (2000). Statistical hadronization model for heavy quarks.

73. NA57 Collaboration. Energy dependence of hyperon production in nucleus nucleus collisions at SPS. Phys. Lett. B 595, 68–74 (2004).

74. Becattini, F. A thermodynamical approach to hadron production in e+e collisions. Z. Phys. C 69, 485–492 (1996).

75. Becattini, F., Castorina, P., Manninen, J. & Satz, H. The thermal production of strange and non-strange hadrons in e+e collisions. Eur. Phys. J. C 56, 493–510 (2008).

76. Andronic, A., Beutler, F., Braun-Munzinger, P., Redlich, K. & Stachel, J. Thermal description of hadron production in e+e collisions revisited. Phys. Lett. B 675, 312–318 (2009).

77. STAR Collaboration. Bulk properties of the medium produced in relativistic heavy-ion collisions from the beam energy scan program. Phys. Rev. C 96, 044904 (2017).

78. Cleymans, J., Oeschler, H. & Redlich, K. Influence of impact parameter on thermal description of relativistic heavy ion collisions at (1–2)A GeV. Phys. Rev. C 59, 1663–1673 (1999).

79. Braun-Munzinger, P., Heppe, I. & Stachel, J. Chemical equilibration in Pb + Pb collisions at the SPS. Phys. Lett. B 465, 15–20 (1999).

80. Manninen, J. & Becattini, F. Chemical freeze-out in ultra-relativistic heavy ion collisions at $$\sqrt{{s}_{{\rm{NN}}}}$$ = 130 and 200 GeV. Phys. Rev. C 78, 054901 (2008).

81. STAR Collaboration. Identified particle production, azimuthal anisotropy, and interferometry measurements in Au+Au collisions at $$\sqrt{{s}_{{\rm{NN}}}}$$ = 9.2 GeV. Phys. Rev. C 81, 024911 (2010).

82. Braun-Munzinger, P. & Stachel, J. Dynamics of ultrarelativistic nuclear collisions with heavy beams: an experimental overview. Nucl. Phys. A 638, 3c–18c (1998). Establishing the boundary line for chemical freeze-out.

83. Hagedorn, R. Statistical thermodynamics of strong interactions at high-energies. Nuovo Cim. 3 (Suppl.), 147–186 (1965).

84. Hagedorn, R. Miscellaneous Elementary Remarks about the Phase Transition from a Hadron Gas to a Quark-Gluon Plasma. Report No. CERN-TH-4100, http://cds.cern.ch/record/158166/files/198504017.pdf (CERN, 1985).

85. Stephanov, M. A., Rajagopal, K. & Shuryak, E. V. Signatures of the tricritical point in QCD. Phys. Rev. Lett. 81, 4816–4819 (1998).

86. Braun-Munzinger, P., Cleymans, J., Oeschler, H. & Redlich, K. Maximum relative strangeness content in heavy ion collisions around 30 GeV/A. Nucl. Phys. A 697, 902–912 (2002).

87. ALICE Collaboration. Centrality dependence of the charged-particle multiplicity density at midrapidity in Pb-Pb collisions at $$\sqrt{{s}_{{\rm{NN}}}}$$ = 5.02 TeV. Phys. Rev. Lett. 116, 222302 (2016).

88. Dainese, A. et al. Heavy ions at the Future Circular Collider. CERN Yellow Rep. 3, 635–691 (2017); https://e-publishing.cern.ch/index.php/CYRM/article/view/515/371.

89. Pierre Auger Collaboration. Ultra-high energy cosmic rays: recent results and future plans of Auger. AIP Conf. Proc. 1852, 040001 (2017).

90. Borsanyi, S. et al. QCD equation of state at nonzero chemical potential: continuum results with physical quark masses at order μ 2. J. High Energy Phys. 8, 53 (2012).

91. PHENIX Collaboration. Enhanced production of direct photons in Au+Au collisions at $$\sqrt{{s}_{{\rm{NN}}}}$$ = 200 GeV and implications for the initial temperature. Phys. Rev. Lett. 104, 132301 (2010).

92. ALICE Collaboration. Direct photon production in Pb-Pb collisions at $$\sqrt{{s}_{{\rm{NN}}}}$$ = 2.76 TeV. Phys. Lett. B 754, 235–248 (2016).

93. Braun-Munzinger, P., Kalweit, A., Redlich, K. & Stachel, J. Confronting fluctuations of conserved charges in central nuclear collisions at the LHC with predictions from lattice QCD. Phys. Lett. B 747, 292–298 (2015).

94. Karsch, F. Determination of freeze-out conditions from lattice QCD calculations. Cent. Eur. J. Phys. 10, 1234–1237 (2012).

95. Borsanyi, S. et al. Freeze-out parameters from electric charge and baryon number fluctuations: is there consistency? Phys. Rev. Lett. 113, 052301 (2014).

96. PHENIX Collaboration. Measurement of higher cumulants of net-charge multiplicity distributions in Au+Au collisions at $$\sqrt{{s}_{{\rm{NN}}}}$$ = 7.7–200 GeV. Phys. Rev. C 93, 011901 (2016).

97. Braun-Munzinger, P. & Redlich, K. Charmonium production from the secondary collisions at LHC energy. Eur. Phys. J. C 16, 519–525 (2000).

98. Zhang, B.-W., Ko, C.-M. & Liu, W. Thermal charm production in a quark-gluon plasma in Pb-Pb collisions at $$\sqrt{{s}_{{\rm{NN}}}}$$ = 25.5 TeV. Phys. Rev. C 77, 024901 (2008).

99. Zhou, K., Chen, Z., Greiner, C. & Zhuang, P. Thermal charm and charmonium production in quark gluon plasma. Phys. Lett. B 758, 434–439 (2016).

100. Cacciari, M. et al. Theoretical predictions for charm and bottom production at the LHC. J. High Energy Phys. 10, 137 (2012).

101. Andronic, A., Braun-Munzinger, P., Redlich, K. & Stachel, J. Statistical hadronization of heavy quarks in ultra-relativistic nucleus-nucleus collisions. Nucl. Phys. A 789, 334–356 (2007). Working out predictions for charmonium and bottomonium production at collider energies.

102. ALICE Collaboration. Suppression of high transverse momentum D mesons in central Pb-Pb collisions at $$\sqrt{{s}_{{\rm{NN}}}}$$ = 2.76 TeV. J. High Energy Phys. 9, 112 (2012).

103. ALICE Collaboration. D meson elliptic flow in noncentral Pb-Pb collisions at $$\sqrt{{s}_{{\rm{NN}}}}$$ = 2.76 TeV. Phys. Rev. Lett. 111, 102301 (2013).

104. STAR Collaboration. Observation of D 0 meson nuclear modifications in Au+Au collisions at $$\sqrt{{s}_{{\rm{NN}}}}$$ = 200 GeV. Phys. Rev. Lett. 113, 142301 (2014).

105. Matsui, T. & Satz, H. J/ψ suppression by quark-gluon plasma formation. Phys. Lett. B 178, 416–422 (1986). Debye screening of J / ψ mesons in a QGP.

106. Vogt, R. J/ψ production and suppression. Phys. Rep. 310, 197–260 (1999).

107. Braun-Munzinger, P. & Stachel, J. in Relativistic Heavy Ion Physics (ed. Stock, R.) 424–444 (Landolt-Börnstein – Group I: Elementary Particles, Nuclei and Atoms Vol. 23, Springer, Berlin, 2010).

108. Andronic, A., Braun-Munzinger, P., Redlich, K. & Stachel, J. The thermal model on the verge of the ultimate test: particle production in Pb-Pb collisions at the LHC. J. Phys. G 38, 124081 (2011).

109. Thews, R. L., Schroedter, M. & Rafelski, J. Enhanced J/ψ production in deconfined quark matter. Phys. Rev. C 63, 054905 (2001). Continuous formation and destruction of charmonia in the QGP.

110. Liu, Y.-P., Qu, Z., Xu, N. & Zhuang, P.-F. J/ψ transverse momentum distribution in high energy nuclear collisions at RHIC. Phys. Lett. B 678, 72–76 (2009).

111. Grandchamp, L., Rapp, R. & Brown, G. E. In medium effects on charmonium production in heavy ion collisions. Phys. Rev. Lett. 92, 212301 (2004).

112. Emerick, A., Zhao, X. & Rapp, R. Bottomonia in the quark-gluon plasma and their production at RHIC and LHC. Eur. Phys. J. A 48, 72 (2012).

113. Zhou, K., Xu, N., Xu, Z. & Zhuang, P. Medium effects on charmonium production at ultrarelativistic energies available at the CERN Large Hadron Collider. Phys. Rev. C 89, 054911 (2014).

114. NA50 Collaboration. ψ′ production in Pb-Pb collisions at 158 GeV/nucleon. Eur. Phys. J. C 49, 559–567 (2007).

115. ALICE Collaboration. J/ψ elliptic flow in Pb–Pb collisions at $$\sqrt{{s}_{{\rm{NN}}}}$$ =2.76 TeV. Phys. Rev. Lett. 111, 162301 (2013).

116. ALICE Collaboration. J/ψ elliptic flow in Pb-Pb collisions at $$\sqrt{{s}_{{\rm{NN}}}}$$ = 5.02 TeV. Phys. Rev. Lett. 119, 242301 (2017).

117. ALICE Collaboration. D-meson azimuthal anisotropy in mid-central Pb-Pb collisions at $$\sqrt{{s}_{{\rm{NN}}}}$$ = 5.02 TeV. Phys. Rev. Lett. 120, 102301 (2018).

118. STAR Collaboration. Measurement of J/ψ azimuthal anisotropy in Au+Au collisions at $$\sqrt{{s}_{{\rm{NN}}}}$$ = 200 GeV. Phys. Rev. Lett. 111, 052301 (2013).

119. NA50 Collaboration. J/ψ azimuthal anisotropy relative to the reaction plane in Pb-Pb collisions at 158 GeV per nucleon. Eur. Phys. J. C 61, 853–858 (2009).

120. Kluberg, L. & Satz, H. in Relativistic Heavy Ion Physics (ed. Stock, R.) 373–423 (Landolt-Börnstein – Group I: Elementary Particles, Nuclei and Atoms Vol. 23, Springer, Berlin, 2010).

121. Andronic, A., Braun-Munzinger, P., Redlich, K. & Stachel, J. Evidence for charmonium generation at the phase boundary in ultra-relativistic nuclear collisions. Phys. Lett. B 652, 259–261 (2007).

122. ALICE Collaboration. Centrality, rapidity and transverse momentum dependence of J/ψ suppression in Pb-Pb collisions at $$\sqrt{{s}_{{\rm{NN}}}}$$ = 2.76 TeV. Phys. Lett. B 743, 314–327 (2014). First experimental evidence of reduced J / ψ suppression at LHC energy.

123. ALICE Collaboration. J/ψ suppression at forward rapidity in Pb-Pb collisions at $$\sqrt{{s}_{{\rm{NN}}}}$$ = 5.02 TeV. Phys. Lett. B 766, 212–224 (2017).

124. Zhao, X. & Rapp, R. Medium modifications and production of charmonia at LHC. Nucl. Phys. A 859, 114–125 (2011).

125. CMS Collaboration. Event activity dependence of ϒ(nS) production in $$\sqrt{{s}_{{\rm{NN}}}}$$=5.02 TeV pPb and $$\sqrt{{s}_{{\rm{NN}}}}$$=2.76 TeV pp collisions. J. High Energy Phys. 4, 103 (2014).

126. CMS Collaboration. Observation of sequential ϒ suppression in PbPb collisions. Phys. Rev. Lett. 109, 222301 (2012).

127. ALICE Collaboration. Suppression of ϒ(1S) at forward rapidity in Pb–Pb collisions at $$\sqrt{{s}_{{\rm{NN}}}}$$ = 2.76 TeV. Phys. Lett. B 738, 361–372 (2014).

128. PHENIX Collaboration. Measurement of ϒ(1S + 2S + 3S) production in p+p and Au+Au collisions at $$\sqrt{{s}_{{\rm{NN}}}}$$ = 200 GeV. Phys. Rev. C 91, 024913 (2015).

129. Rigol, M., Dunjko, V. & Olshanii, M. Thermalization and its mechanism for generic isolated quantum systems. Nature 452, 854–858 (2008).

130. Gring, M. et al. Relaxation and prethermalization in an isolated quantum system. Science 337, 1318–1322 (2012).

131. Andronic, A. An overview of the experimental study of quark-gluon matter in high-energy nucleus-nucleus collisions. Int. J. Mod. Phys. A 29, 1430047 (2014).

132. Vovchenko, V., Begun, V. V. & Gorenstein, M. I. Hadron multiplicities and chemical freeze-out conditions in proton-proton and nucleus-nucleus collisions. Phys. Rev. C 93, 064906 (2016).

133. Becattini, F., Steinheimer, J., Stock, R. & Bleicher, M. Hadronization conditions in relativistic nuclear collisions and the QCD pseudo-critical line. Phys. Lett. B 764, 241–246 (2017).

134. NA51 Collaboration. J/ψ, ψ′ and Drell-Yan production in pp and pd interactions at 450 GeV/c. Phys. Lett. B 438, 35–40 (1998).

135. HERA-B Collaboration. A measurement of the ψ′ to J/ψ production ratio in 920-GeV proton-nucleus interactions. Eur. Phys. J. C 49, 545–558 (2007).

136. PHENIX Collaboration. Measurement of the relative yields of ψ(2S) to ψ(1S) mesons produced at forward and backward rapidity in p+p, p+Al, p+Au and 3He+Au collisions at $$\sqrt{{s}_{{\rm{NN}}}}$$ = 200 GeV. Phys. Rev. C 95, 034904 (2017).

137. LHCb Collaboration. Measurement of J/ψ production in pp collisions at $$\sqrt{s}$$ = 7 TeV. Eur. Phys. J. C 71, 1645 (2011).

138. LHCb Collaboration. Measurement of ψ(2S) meson production in pp collisions at $$\sqrt{s}$$ =7 TeV. Eur. Phys. J. C 72, 2100 (2012).

139. ALICE Collaboration. Energy dependence of forward-rapidity J/ψ and ψ(2S) production in pp collisions at the LHC. Eur. Phys. J. C 77, 392 (2017).

140. PHENIX Collaboration. J/ψ production vs centrality, transverse momentum, and rapidity in Au+Au collisions at $$\sqrt{{s}_{{\rm{NN}}}}$$ = 200 GeV. Phys. Rev. Lett. 98, 232301 (2007).

141. PHENIX Collaboration. J/ψ suppression at forward rapidity in Au+Au collisions at $$\sqrt{{s}_{{\rm{NN}}}}$$ = 200 GeV. Phys. Rev. C 84, 054912 (2011).

142. STAR Collaboration. J/ψ production at low p T in Au+Au and Cu+Cu collisions at $$\sqrt{{s}_{{\rm{NN}}}}$$ = 200 GeV at STAR. Phys. Rev. C 90, 024906 (2014).

143. Andronic, A. et al. The thermal proton yield anomaly in Pb-Pb collisions at the LHC and its resolution. Preprint at https://arxiv.org/abs/1808.03102 (2018).

144. Steinbrecher, P. The QCD crossover at zero and non-zero baryon densities from lattice QCD. Preprint at https://arxiv.org/abs/1807.05607 (2018).

## Acknowledgements

K.R. acknowledges support by the Polish National Science Centre under Maestro grant DEC-2013/10/A/ST2/00106. This work is part of and supported by the DFG Collaborative Research Centre ‘SFB1225/ISOQUANT’.

### Author contributions

All authors contributed equally to the physics analysis and to writing the manuscript.

## Author information

Authors

### Corresponding author

Correspondence to Peter Braun-Munzinger.

## Ethics declarations

### Competing interests

The authors declare no competing interests.

Publisher’s note: Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

## Rights and permissions

Reprints and Permissions

Andronic, A., Braun-Munzinger, P., Redlich, K. et al. Decoding the phase structure of QCD via particle production at high energy. Nature 561, 321–330 (2018). https://doi.org/10.1038/s41586-018-0491-6

• Accepted:

• Published:

• Issue Date:

• DOI: https://doi.org/10.1038/s41586-018-0491-6

### Keywords

• Ultra-relativistic Nuclear Collisions
• Relativistic Heavy Ion Collider (RHIC)
• Heavy Quark

• ### Study of nuclear modification factors of deuteron and anti-deuteron in Pb–Pb collisions at $$\sqrt{s_{\mathrm{NN}}} =2.76\,\hbox {TeV}$$

• Feng-Xian Liu
• Zhi-Lei She
• Ben-Hao Sa

Scientific Reports (2022)

• ### Spectral functions of heavy quarkonia in a bulk-viscous quark gluon plasma

• Lata Thakur
• Yuji Hirono

Journal of High Energy Physics (2022)

• ### Energy and centrality dependence of light nuclei production in relativistic heavy-ion collisions

• Li-Lin Zhu
• Bo Wang
• Hua Zheng

Nuclear Science and Techniques (2022)

• ### Dissociation of Pseudotensor Mesons π2(1670), η2(1645) and η2(1870) through Critical Temperature

• A. Türkan
• J.Y. Süngü
• E. Veli Veliev

International Journal of Theoretical Physics (2022)

• ### Production of light (anti)nuclei in pp collisions at $$\sqrt{s}$$ = 13 TeV

• S. Acharya
• N. Zurlo

Journal of High Energy Physics (2022)