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  • Letter
  • Open Access

Ripples of the QCD critical point

Wei-jie Fu1, Xiaofeng Luo2, Jan M. Pawlowski3,4, Fabian Rennecke5,6, and Shi Yin1,*

  • 1School of Physics, Dalian University of Technology, Dalian 116024, People’s Republic of China
  • 2Key Laboratory of Quark & Lepton Physics (MOE) and Institute of Particle Physics, Central China Normal University, Wuhan 430079, People’s Republic of China
  • 3Institut für Theoretische Physik, Universität Heidelberg, Philosophenweg 16, 69120 Heidelberg, Germany
  • 4ExtreMe Matter Institute EMMI, GSI, Planckstraße 1, D-64291 Darmstadt, Germany
  • 5Institut für Theoretische Physik, Justus-Liebig-Universität Gießen, 35392 Gießen, Germany
  • 6Helmholtz Research Academy Hesse for FAIR, Campus Gießen, 35392 Gießen, Germany

  • *Contact author: yinshi2014@mail.dlut.edu.cn
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Phys. Rev. D 111, L031502 – Published 10 February, 2025

DOI: https://doi.org/10.1103/PhysRevD.111.L031502

Abstract

We investigate the impact of a critical end point (CEP) on the experimentally accessible baryon-number fluctuations of different orders. By now, its potential location has been constrained fairly accurately within first principles functional QCD, together with the location of the chiral crossover line and further thermodynamic observables. This information is incorporated in an advanced QCD-assisted low-energy effective theory which is used for the computation of baryon-number fluctuations at the chemical freeze-out. This computation also takes care of global baryon-number conservation at larger density, where the system changes from grand-canonical to canonical statistics. We observe a prominent peak structure, whose amplitude depends on the location of the CEP, while its position is more sensitive to the location of the freeze-out curve. Our results provide guidance for future low-energy heavy-ion experiments.

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References (69)

  1. K. Fukushima and T. Hatsuda, The phase diagram of dense QCD, Rep. Prog. Phys. 74, 014001 (2011).
  2. W.-j. Fu, J. M. Pawlowski, and F. Rennecke, QCD phase structure at finite temperature and density, Phys. Rev. D 101, 054032 (2020).
  3. R. D. Pisarski and F. Rennecke, Signatures of moat regimes in heavy-ion collisions, Phys. Rev. Lett. 127, 152302 (2021).
  4. F. Rennecke, R. D. Pisarski, and D. H. Rischke, Particle interferometry in a moat regime, Phys. Rev. D 107, 116011 (2023).
  5. M. Arslandok et al., Hot QCD White Paper, arXiv:2303.17254.
  6. Properties of QCD Matter at High Baryon Density, edited by X. Luo, Q. Wang, N. Xu, and P. Zhuang (Springer, New York, 2022).
  7. M. A. Stephanov, K. Rajagopal, and E. V. Shuryak, Event-by-event fluctuations in heavy ion collisions and the QCD critical point, Phys. Rev. D 60, 114028 (1999).
  8. M. Stephanov, Non-Gaussian fluctuations near the QCD critical point, Phys. Rev. Lett. 102, 032301 (2009).
  9. X. Luo and N. Xu, 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).
  10. J. Adam et al. (STAR Collaboration), Nonmonotonic energy dependence of net-proton number fluctuations, Phys. Rev. Lett. 126, 092301 (2021).
  11. M. Abdallah et al. (STAR Collaboration), Cumulants and correlation functions of net-proton, proton, and antiproton multiplicity distributions in Au+Au collisions at energies available at the BNL Relativistic Heavy Ion Collider, Phys. Rev. C 104, 024902 (2021).
  12. D. Mroczek, A. R. Nava Acuna, J. Noronha-Hostler, P. Parotto, C. Ratti, and M. A. Stephanov, Quartic cumulant of baryon number in the presence of a QCD critical point, Phys. Rev. C 103, 034901 (2021).
  13. T. Dore, J. M. Karthein, I. Long, D. Mroczek, J. Noronha-Hostler, P. Parotto, C. Ratti, and Y. Yamauchi, Critical lensing and kurtosis near a critical point in the QCD phase diagram in and out of equilibrium, Phys. Rev. D 106, 094024 (2022).
  14. W.-j. Fu, X. Luo, J. M. Pawlowski, F. Rennecke, R. Wen, and S. Yin, Hyper-order baryon number fluctuations at finite temperature and density, Phys. Rev. D 104, 094047 (2021).
  15. J. Braun et al., Soft modes in hot QCD matter, arXiv:2310.19853.
  16. M. S. Abdallah et al. (STAR Collaboration), Measurements of proton high order cumulants in sNN=3  GeV Au+Au collisions and implications for the QCD critical point, Phys. Rev. Lett. 128, 202303 (2022).
  17. M. Abdallah et al. (STAR Collaboration), Higher-order cumulants and correlation functions of proton multiplicity distributions in sNN=3  GeV Au+Au collisions at the RHIC STAR experiment, Phys. Rev. C 107, 024908 (2023).
  18. F. Gao and J. M. Pawlowski, QCD phase structure from functional methods, Phys. Rev. D 102, 034027 (2020).
  19. F. Gao and J. M. Pawlowski, Chiral phase structure and critical end point in QCD, Phys. Lett. B 820, 136584 (2021).
  20. P. J. Gunkel and C. S. Fischer, Locating the critical endpoint of QCD: Mesonic backcoupling effects, Phys. Rev. D 104, 054022 (2021).
  21. C. S. Fischer, QCD at finite temperature and chemical potential from Dyson–Schwinger equations, Prog. Part. Nucl. Phys. 105, 1 (2019).
  22. N. Dupuis, L. Canet, A. Eichhorn, W. Metzner, J. M. Pawlowski, M. Tissier, and N. Wschebor, The nonperturbative functional renormalization group and its applications, Phys. Rep. 910, 1 (2021).
  23. W.-j. Fu, QCD at finite temperature and density within the fRG approach: An overview, Commun. Theor. Phys. 74, 097304 (2022).
  24. R. Bellwied, S. Borsanyi, Z. Fodor, J. Guenther, S. D. Katz, C. Ratti, and K. K. Szabo, The QCD phase diagram from analytic continuation, Phys. Lett. B 751, 559 (2015).
  25. A. Bazavov et al., The QCD equation of state to O(μB6) from lattice QCD, Phys. Rev. D 95, 054504 (2017).
  26. A. Bazavov et al. (HotQCD Collaboration), Skewness and kurtosis of net baryon-number distributions at small values of the baryon chemical potential, Phys. Rev. D 96, 074510 (2017).
  27. A. Bazavov et al. (HotQCD Collaboration), Chiral crossover in QCD at zero and non-zero chemical potentials, Phys. Lett. B 795, 15 (2019).
  28. S. Borsanyi, Z. Fodor, J. N. Guenther, S. K. Katz, K. K. Szabo, A. Pasztor, I. Portillo, and C. Ratti, Higher order fluctuations and correlations of conserved charges from lattice QCD, J. High Energy Phys. 10 (2018) 205.
  29. A. Bazavov et al., Skewness, kurtosis, and the fifth and sixth order cumulants of net baryon-number distributions from lattice QCD confront high-statistics STAR data, Phys. Rev. D 101, 074502 (2020).
  30. D. Bollweg, D. A. Clarke, J. Goswami, O. Kaczmarek, F. Karsch, S. Mukherjee, P. Petreczky, C. Schmidt, and S. Sharma (HotQCD Collaboration), Equation of state and speed of sound of (2+1)-flavor QCD in strangeness-neutral matter at nonvanishing net baryon-number density, Phys. Rev. D 108, 014510 (2023).
  31. G. Aarts et al., Phase transitions in particle physics—results and perspectives from lattice quantum chromo-dynamics, Prog. Part. Nucl. Phys. 133, 104070 (2023).
  32. S. Mukherjee and V. Skokov, Universality driven analytic structure of the QCD crossover: Radius of convergence in the baryon chemical potential, Phys. Rev. D 103, L071501 (2021).
  33. D. Bollweg, J. Goswami, O. Kaczmarek, F. Karsch, S. Mukherjee, P. Petreczky, C. Schmidt, and P. Scior (HotQCD Collaboration), Taylor expansions and Padé approximants for cumulants of conserved charge fluctuations at nonvanishing chemical potentials, Phys. Rev. D 105, 074511 (2022).
  34. S. Borsanyi, Z. Fodor, M. Giordano, J. N. Guenther, S. D. Katz, A. Pasztor, and C. H. Wong, Equation of state of a hot-and-dense quark gluon plasma: Lattice simulations at real μB vs extrapolations, Phys. Rev. D 107, L091503 (2023).
  35. J. Braun, H. Gies, and J. M. Pawlowski, Quark confinement from color confinement, Phys. Lett. B 684, 262 (2010).
  36. J. Braun, L. M. Haas, F. Marhauser, and J. M. Pawlowski, Phase structure of two-flavor QCD at finite chemical potential, Phys. Rev. Lett. 106, 022002 (2011).
  37. M. Mitter, J. M. Pawlowski, and N. Strodthoff, Chiral symmetry breaking in continuum QCD, Phys. Rev. D 91, 054035 (2015).
  38. J. Braun, L. Fister, J. M. Pawlowski, and F. Rennecke, From quarks and gluons to hadrons: Chiral symmetry breaking in dynamical QCD, Phys. Rev. D 94, 034016 (2016).
  39. F. Rennecke, Vacuum structure of vector mesons in QCD, Phys. Rev. D 92, 076012 (2015).
  40. A. K. Cyrol, L. Fister, M. Mitter, J. M. Pawlowski, and N. Strodthoff, Landau gauge Yang-Mills correlation functions, Phys. Rev. D 94, 054005 (2016).
  41. A. K. Cyrol, M. Mitter, J. M. Pawlowski, and N. Strodthoff, Nonperturbative quark, gluon, and meson correlators of unquenched QCD, Phys. Rev. D 97, 054006 (2018).
  42. A. K. Cyrol, M. Mitter, J. M. Pawlowski, and N. Strodthoff, Nonperturbative finite-temperature Yang-Mills theory, Phys. Rev. D 97, 054015 (2018).
  43. W.-j. Fu, J. M. Pawlowski, and F. Rennecke, Strangeness neutrality and QCD thermodynamics, SciPost Phys. Core 2, 002 (2020).
  44. W.-j. Fu, J. M. Pawlowski, and F. Rennecke, Strangeness neutrality and baryon-strangeness correlations, Phys. Rev. D 100, 111501 (2019).
  45. R. Wen and W.-j. Fu, Correlations of conserved charges and QCD phase structure, Chin. Phys. C 45, 044112 (2021).
  46. Y. Hatta and M. A. Stephanov, Proton number fluctuation as a signal of the QCD critical endpoint, Phys. Rev. Lett. 91, 102003 (2003); 91, 129901(E) (2003).
  47. A. Bazavov et al., Freeze-out conditions in heavy ion collisions from QCD thermodynamics, Phys. Rev. Lett. 109, 192302 (2012).
  48. S. Borsanyi, Z. Fodor, S. D. Katz, S. Krieg, C. Ratti, and K. K. Szabo, Freeze-out parameters: Lattice meets experiment, Phys. Rev. Lett. 111, 062005 (2013).
  49. S. Borsanyi, Z. Fodor, S. D. Katz, S. Krieg, C. Ratti, and K. K. Szabo, Freeze-out parameters from electric charge and baryon number fluctuations: Is there consistency?, Phys. Rev. Lett. 113, 052301 (2014).
  50. W.-j. Fu and J. M. Pawlowski, Relevance of matter and glue dynamics for baryon number fluctuations, Phys. Rev. D 92, 116006 (2015).
  51. W.-j. Fu and J. M. Pawlowski, Correlating the skewness and kurtosis of baryon number distributions, Phys. Rev. D 93, 091501 (2016).
  52. W.-j. Fu, J. M. Pawlowski, F. Rennecke, and B.-J. Schaefer, Baryon number fluctuations at finite temperature and density, Phys. Rev. D 94, 116020 (2016).
  53. G. A. Almasi, B. Friman, and K. Redlich, Baryon number fluctuations in chiral effective models and their phenomenological implications, Phys. Rev. D 96, 014027 (2017).
  54. P. Isserstedt, M. Buballa, C. S. Fischer, and P. J. Gunkel, Baryon number fluctuations in the QCD phase diagram from Dyson-Schwinger equations, Phys. Rev. D 100, 074011 (2019).
  55. A. Bzdak, V. Koch, and V. Skokov, Baryon number conservation and the cumulants of the net proton distribution, Phys. Rev. C 87, 014901 (2013).
  56. V. Vovchenko, O. Savchuk, R. V. Poberezhnyuk, M. I. Gorenstein, and V. Koch, Connecting fluctuation measurements in heavy-ion collisions with the grand-canonical susceptibilities, Phys. Lett. B 811, 135868 (2020).
  57. P. Braun-Munzinger, B. Friman, K. Redlich, A. Rustamov, and J. Stachel, Relativistic nuclear collisions: Establishing a non-critical baseline for fluctuation measurements, Nucl. Phys. A1008, 122141 (2021).
  58. P. Braun-Munzinger, A. Rustamov, and J. Stachel, Bridging the gap between event-by-event fluctuation measurements and theory predictions in relativistic nuclear collisions, Nucl. Phys. A960, 114 (2017).
  59. See Supplemental Material at http://link.aps.org/supplemental/10.1103/PhysRevD.111.L031502 for details of computation and truncation.
  60. A. Andronic, P. Braun-Munzinger, K. Redlich, and J. Stachel, Decoding the phase structure of QCD via particle production at high energy, Nature (London) 561, 321 (2018).
  61. L. Adamczyk et al. (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).
  62. B. E. Aboona et al. (STAR Collaboration), Beam energy dependence of fifth- and sixth-order net-proton number fluctuations in Au+Au collisions at RHIC, Phys. Rev. Lett. 130, 082301 (2023).
  63. M. Abdallah et al. (STAR Collaboration), Measurement of the sixth-order cumulant of net-proton multiplicity distributions in Au+Au collisions at sNN=27, 54.4, and 200 GeV at RHIC, Phys. Rev. Lett. 127, 262301 (2021).
  64. A. Bzdak, S. Esumi, V. Koch, J. Liao, M. Stephanov, and N. Xu, Mapping the phases of quantum chromodynamics with beam energy scan, Phys. Rep. 853, 1 (2020).
  65. V. Vovchenko, V. Koch, and C. Shen, Proton number cumulants and correlation functions in Au-Au collisions at sNN=7.7–200  GeV from hydrodynamics, Phys. Rev. C 105, 014904 (2022).
  66. B. Berdnikov and K. Rajagopal, Slowing out-of-equilibrium near the QCD critical point, Phys. Rev. D 61, 105017 (2000).
  67. S. Mukherjee, R. Venugopalan, and Y. Yin, Universal off-equilibrium scaling of critical cumulants in the QCD phase diagram, Phys. Rev. Lett. 117, 222301 (2016).
  68. M. Buballa and S. Carignano, Inhomogeneous chiral condensates, Prog. Part. Nucl. Phys. 81, 39 (2015).
  69. J. Braun, Y.-r. Chen, W.-j. Fu, F. Gao, F. Ihssen, A. Geissel, J. Horak, C. Huang, J. M. Pawlowski, F. Rennecke, F. Sattler, B. Schallmo, J. Stoll, Y.-y. Tan, S. Töpfel, J. Turnwald, R. Wen, J. Wessely, N. Wink, S. Yin, and N. Zorbach, fQCD Collaboration, (2023).

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Phys. Rev. D 111, L031502– Published 10 February, 2025
  • Received 30 September 2023
  • Accepted 21 January 2025
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