Heavy quarks in turbulent QCD plasmas

  • Stanisław Mrówczyński
Open Access
Regular Article - Theoretical Physics


The quark-gluon plasma, which is produced at an early stage of ultrarelativistic heavy-ion collisions, is expected to be initially strongly populated with chromodynamic fields. We address the question of how heavy quarks interact with such a turbulent plasma in comparison with an equilibrated one of the same energy density. For this purpose we derive a Fokker-Planck transport equation of heavy quarks embedded in a plasma of light quarks and gluons. We first discuss the equilibrium plasma and then the turbulent one applying the same approach, where the heavy quarks interact not with the plasma constituents but rather with the long wavelength classical fields. We first consider the three schematic models of isotropic trubulent plasma and then the simplified model of glasma with the chromodynamic fields only along the beam direction. The momentum broadening and collisional energy loss of a test heavy quark are computed and compared to those of the equilibrium plasma of the same energy density.


  1. 1.
    F. Gelis, Int. J. Mod. Phys. A 28, 1330001 (2013)ADSCrossRefGoogle Scholar
  2. 2.
    St. Mrówczyński, B. Schenke, M. Strickland, Phys. Rep. 682, 1 (2017)ADSMathSciNetCrossRefGoogle Scholar
  3. 3.
    F. Prino, R. Rapp, J. Phys. G 43, 093002 (2016)ADSCrossRefGoogle Scholar
  4. 4.
    S.K. Das, M. Ruggieri, F. Scardina, S. Plumari, V. Greco, J. Phys. G 44, 095102 (2017)ADSCrossRefGoogle Scholar
  5. 5.
    G.D. Moore, D. Teaney, Phys. Rev. C 71, 064904 (2005)ADSCrossRefGoogle Scholar
  6. 6.
    B. Svetitsky, Phys. Rev. D 37, 2484 (1988)ADSMathSciNetCrossRefGoogle Scholar
  7. 7.
    H. van Hees, R. Rapp, Phys. Rev. C 71, 034907 (2005)ADSCrossRefGoogle Scholar
  8. 8.
    M.G. Mustafa, Phys. Rev. C 72, 014905 (2005)ADSCrossRefGoogle Scholar
  9. 9.
    E.M. Lifshitz, L.P. Pitaevskii, Physical Kinetics (Pergamon Press, Oxford, 1981)Google Scholar
  10. 10.
    A.A. Vedenov, E.P. Velikhov, R.Z. Sagdeev, Usp. Fiz. Nauk 73, 701 (1961)CrossRefGoogle Scholar
  11. 11.
    St. Mrówczyński, B. Müller, Phys. Rev. D 81, 065021 (2010)ADSCrossRefGoogle Scholar
  12. 12.
    St. Mrówczyński, Phys. Rev. D 77, 105022 (2008)ADSCrossRefGoogle Scholar
  13. 13.
    T.H. Dupree, Phys. Fluids 9, 1773 (1966)ADSMathSciNetCrossRefGoogle Scholar
  14. 14.
    M. Asakawa, S.A. Bass, B. Müller, Prog. Theor. Phys. 116, 725 (2006)ADSCrossRefGoogle Scholar
  15. 15.
    A. Majumder, B. Muller, X.N. Wang, Phys. Rev. Lett. 99, 192301 (2007)ADSCrossRefGoogle Scholar
  16. 16.
    V. Chandra, S.K. Das, Phys. Rev. D 93, 094036 (2016)ADSCrossRefGoogle Scholar
  17. 17.
    T. Song, T. Epelbaum, arXiv:1512.05625 [nucl-th]Google Scholar
  18. 18.
    R. Baier, Y.L. Dokshitzer, A.H. Mueller, S. Peigne, D. Schiff, Nucl. Phys. B 484, 265 (1997)ADSCrossRefGoogle Scholar
  19. 19.
    N.G. van Kampen, Stochastic Processes in Physics and Chemistry (North-Holland, Amsterdam, 1987)Google Scholar
  20. 20.
    P.B. Arnold, G.D. Moore, Phys. Rev. D 73, 025006 (2006)ADSCrossRefGoogle Scholar
  21. 21.
    N.K. Nielsen, P. Olesen, Nucl. Phys. B 144, 376 (1978)ADSCrossRefGoogle Scholar
  22. 22.
    J. Berges, S. Scheffler, S. Schlichting, D. Sexty, Phys. Rev. D 85, 034507 (2012)ADSCrossRefGoogle Scholar
  23. 23.
    A. Kurkela, G.D. Moore, Phys. Rev. D 86, 056008 (2012)ADSCrossRefGoogle Scholar
  24. 24.
    G. Chen, R.J. Fries, J.I. Kapusta, Y. Li, Phys. Rev. C 92, 064912 (2015)ADSCrossRefGoogle Scholar
  25. 25.
    T. Lappi, L. McLerran, Nucl. Phys. A 772, 200 (2006)ADSCrossRefGoogle Scholar
  26. 26.
    F.S. Navarra, O.V. Utyuzh, G. Wilk, Z. Włodarczyk, Phys. Rev. D 67, 114002 (2003)ADSCrossRefGoogle Scholar
  27. 27.
    M. Le Bellac, Thermal Field Theory (Cambridge University Press, Cambridge, 2000)Google Scholar

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© The Author(s) 2018

Open Access This article is distributed under the terms of the Creative Commons Attribution 4.0 License (, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Authors and Affiliations

  1. 1.Institute of PhysicsJan Kochanowski UniversityKielcePoland
  2. 2.National Centre for Nuclear ResearchWarsawPoland

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