Journal of High Energy Physics

, 2017:123 | Cite as

Bulk viscous corrections to screening and damping in QCD at high temperatures

  • Qianqian Du
  • Adrian Dumitru
  • Yun Guo
  • Michael Strickland
Open Access
Regular Article - Theoretical Physics


Non-equilibrium corrections to the distribution functions of quarks and gluons in a hot and dense QCD medium modify the “hard thermal loops” (HTL). The HTLs determine the retarded, advanced, and symmetric (time-ordered) propagators for gluons with soft momenta as well as the Debye screening and Landau damping mass scales. We compute such corrections to a thermal as well as to a non-thermal fixed point. The screening and damping mass scales are sensitive to the bulk pressure and hence to (pseudo-) critical dynamical scaling of the bulk viscosity in the vicinity of a second-order critical point. This could be reflected in the properties of quarkonium bound states in the deconfined phase and in the dynamics of soft gluon fields.


Perturbative QCD Quark-Gluon Plasma 


Open Access

This article is distributed under the terms of the Creative Commons Attribution License (CC-BY 4.0), which permits any use, distribution and reproduction in any medium, provided the original author(s) and source are credited.


  1. [1]
    H.A. Weldon, Covariant Calculations at Finite Temperature: The Relativistic Plasma, Phys. Rev. D 26 (1982) 1394 [INSPIRE].ADSGoogle Scholar
  2. [2]
    E. Braaten and R.D. Pisarski, Soft Amplitudes in Hot Gauge Theories: A General Analysis, Nucl. Phys. B 337 (1990) 569 [INSPIRE].ADSCrossRefGoogle Scholar
  3. [3]
    J. Frenkel and J.C. Taylor, High Temperature Limit of Thermal QCD, Nucl. Phys. B 334 (1990) 199 [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  4. [4]
    E. Braaten and R.D. Pisarski, Simple effective Lagrangian for hard thermal loops, Phys. Rev. D 45 (1992) R1827 [INSPIRE].ADSGoogle Scholar
  5. [5]
    N. Haque, A. Bandyopadhyay, J.O. Andersen, M.G. Mustafa, M. Strickland and N. Su, Three-loop HTLpt thermodynamics at finite temperature and chemical potential, JHEP 05 (2014) 027 [arXiv:1402.6907] [INSPIRE].ADSCrossRefGoogle Scholar
  6. [6]
    J.O. Andersen, L.E. Leganger, M. Strickland and N. Su, Three-loop HTL QCD thermodynamics, JHEP 08 (2011) 053 [arXiv:1103.2528] [INSPIRE].ADSCrossRefMATHGoogle Scholar
  7. [7]
    J.O. Andersen, E. Braaten and M. Strickland, Hard thermal loop resummation of the free energy of a hot gluon plasma, Phys. Rev. Lett. 83 (1999) 2139 [hep-ph/9902327] [INSPIRE].
  8. [8]
    M. Laine, O. Philipsen, P. Romatschke and M. Tassler, Real-time static potential in hot QCD, JHEP 03 (2007) 054 [hep-ph/0611300] [INSPIRE].
  9. [9]
    N. Brambilla, J. Ghiglieri, A. Vairo and P. Petreczky, Static quark-antiquark pairs at finite temperature, Phys. Rev. D 78 (2008) 014017 [arXiv:0804.0993] [INSPIRE].ADSGoogle Scholar
  10. [10]
    M.A. Escobedo and J. Soto, Non-relativistic bound states at finite temperature (I): The Hydrogen atom, Phys. Rev. A 78 (2008) 032520 [arXiv:0804.0691] [INSPIRE].ADSCrossRefGoogle Scholar
  11. [11]
    M. Strickland, Thermalization and isotropization in heavy-ion collisions, Pramana 84 (2015) 671 [arXiv:1312.2285] [INSPIRE].ADSCrossRefGoogle Scholar
  12. [12]
    M. Strickland, Anisotropic Hydrodynamics: Three lectures, Acta Phys. Polon. B 45 (2014) 2355 [arXiv:1410.5786] [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  13. [13]
    A. Dumitru, Y. Guo and M. Strickland, The heavy-quark potential in an anisotropic (viscous) plasma, Phys. Lett. B 662 (2008) 37 [arXiv:0711.4722] [INSPIRE].ADSCrossRefGoogle Scholar
  14. [14]
    A. Dumitru, Y. Guo and M. Strickland, The imaginary part of the static gluon propagator in an anisotropic (viscous) QCD plasma, Phys. Rev. D 79 (2009) 114003 [arXiv:0903.4703] [INSPIRE].ADSGoogle Scholar
  15. [15]
    Y. Burnier, M. Laine and M. Vepsäläinen, Quarkonium dissociation in the presence of a small momentum space anisotropy, Phys. Lett. B 678 (2009) 86 [arXiv:0903.3467] [INSPIRE].ADSCrossRefGoogle Scholar
  16. [16]
    M. Strickland, Thermal υ 1s and χ b1 suppression in \( \sqrt{s_{\;N\;N}}=2.76 \) TeV Pb-Pb collisions at the LHC, Phys. Rev. Lett. 107 (2011) 132301 [arXiv:1106.2571] [INSPIRE].ADSCrossRefGoogle Scholar
  17. [17]
    M. Strickland and D. Bazow, Thermal Bottomonium Suppression at RHIC and LHC, Nucl. Phys. A 879 (2012) 25 [arXiv:1112.2761] [INSPIRE].ADSCrossRefGoogle Scholar
  18. [18]
    B. Krouppa, R. Ryblewski and M. Strickland, Bottomonia suppression in 2.76 TeV Pb-Pb collisions, Phys. Rev. C 92 (2015) 061901 [arXiv:1507.03951] [INSPIRE].
  19. [19]
    B. Krouppa and M. Strickland, Predictions for bottomonia suppression in 5.023 TeV Pb-Pb collisions, Universe 2 (2016) 16 [arXiv:1605.03561] [INSPIRE].
  20. [20]
    S. Ryu et al., Importance of the Bulk Viscosity of QCD in Ultrarelativistic Heavy-Ion Collisions, Phys. Rev. Lett. 115 (2015) 132301 [arXiv:1502.01675] [INSPIRE].ADSCrossRefGoogle Scholar
  21. [21]
    P.B. Arnold, C. Dogan and G.D. Moore, The Bulk Viscosity of High-Temperature QCD, Phys. Rev. D 74 (2006) 085021 [hep-ph/0608012] [INSPIRE].
  22. [22]
    HotQCD collaboration, A. Bazavov et al., Equation of state in (2 + 1)-flavor QCD, Phys. Rev. D 90 (2014) 094503 [arXiv:1407.6387] [INSPIRE].
  23. [23]
    D. Kharzeev and K. Tuchin, Bulk viscosity of QCD matter near the critical temperature, JHEP 09 (2008) 093 [arXiv:0705.4280] [INSPIRE].ADSCrossRefGoogle Scholar
  24. [24]
    F. Karsch, D. Kharzeev and K. Tuchin, Universal properties of bulk viscosity near the QCD phase transition, Phys. Lett. B 663 (2008) 217 [arXiv:0711.0914] [INSPIRE].ADSCrossRefGoogle Scholar
  25. [25]
    F.R. Brown et al., On the existence of a phase transition for QCD with three light quarks, Phys. Rev. Lett. 65 (1990) 2491 [INSPIRE].ADSCrossRefGoogle Scholar
  26. [26]
    S. Gavin, A. Gocksch and R.D. Pisarski, QCD and the chiral critical point, Phys. Rev. D 49 (1994) R3079 [hep-ph/9311350] [INSPIRE].
  27. [27]
    J. Berges and K. Rajagopal, Color superconductivity and chiral symmetry restoration at nonzero baryon density and temperature, Nucl. Phys. B 538 (1999) 215 [hep-ph/9804233] [INSPIRE].
  28. [28]
    A.M. Halasz, A.D. Jackson, R.E. Shrock, M.A. Stephanov and J.J.M. Verbaarschot, On the phase diagram of QCD, Phys. Rev. D 58 (1998) 096007 [hep-ph/9804290] [INSPIRE].
  29. [29]
    M.A. Stephanov, K. Rajagopal and E.V. Shuryak, Signatures of the tricritical point in QCD, Phys. Rev. Lett. 81 (1998) 4816 [hep-ph/9806219] [INSPIRE].
  30. [30]
    G.D. Moore and O. Saremi, Bulk viscosity and spectral functions in QCD, JHEP 09 (2008) 015 [arXiv:0805.4201] [INSPIRE].ADSCrossRefGoogle Scholar
  31. [31]
    A. Monnai, S. Mukherjee and Y. Yin, Phenomenological Consequences of Enhanced Bulk Viscosity Near the QCD Critical Point, arXiv:1606.00771 [INSPIRE].
  32. [32]
    G.S. Denicol, S. Jeon and C. Gale, Transport Coefficients of Bulk Viscous Pressure in the 14-moment approximation, Phys. Rev. C 90 (2014) 024912 [arXiv:1403.0962] [INSPIRE].ADSGoogle Scholar
  33. [33]
    G.S. Denicol, W. Florkowski, R. Ryblewski and M. Strickland, Shear-bulk coupling in nonconformal hydrodynamics, Phys. Rev. C 90 (2014) 044905 [arXiv:1407.4767] [INSPIRE].ADSGoogle Scholar
  34. [34]
    A. Jaiswal, R. Ryblewski and M. Strickland, Transport coefficients for bulk viscous evolution in the relaxation time approximation, Phys. Rev. C 90 (2014) 044908 [arXiv:1407.7231] [INSPIRE].ADSGoogle Scholar
  35. [35]
    D. Bazow, U.W. Heinz and M. Martinez, Nonconformal viscous anisotropic hydrodynamics, Phys. Rev. C 91 (2015) 064903 [arXiv:1503.07443] [INSPIRE].ADSGoogle Scholar
  36. [36]
    S. Mrowczynski and M.H. Thoma, Hard loop approach to anisotropic systems, Phys. Rev. D 62 (2000) 036011 [hep-ph/0001164] [INSPIRE].
  37. [37]
    M.E. Carrington, D.-f. Hou and M.H. Thoma, Ward identities in nonequilibrium QED, Phys. Rev. D 58 (1998) 085025 [hep-th/9801103] [INSPIRE].ADSGoogle Scholar
  38. [38]
    M.E. Carrington, D.-f. Hou and M.H. Thoma, Equilibrium and nonequilibrium hard thermal loop resummation in the real time formalism, Eur. Phys. J. C 7 (1999) 347 [hep-ph/9708363] [INSPIRE].
  39. [39]
    M. Nopoush, R. Ryblewski and M. Strickland, Bulk viscous evolution within anisotropic hydrodynamics, Phys. Rev. C 90 (2014) 014908 [arXiv:1405.1355] [INSPIRE].ADSGoogle Scholar
  40. [40]
    Y. Burnier, O. Kaczmarek and A. Rothkopf, Static quark-antiquark potential in the quark-gluon plasma from lattice QCD, Phys. Rev. Lett. 114 (2015) 082001 [arXiv:1410.2546] [INSPIRE].ADSCrossRefGoogle Scholar
  41. [41]
    A. Mócsy, P. Petreczky and M. Strickland, Quarkonia in the Quark Gluon Plasma, Int. J. Mod. Phys. A 28 (2013) 1340012 [arXiv:1302.2180] [INSPIRE].CrossRefGoogle Scholar
  42. [42]
    A. Andronic et al., Heavy-flavour and quarkonium production in the LHC era: from proton-proton to heavy-ion collisions, Eur. Phys. J. C 76 (2016) 107 [arXiv:1506.03981] [INSPIRE].ADSCrossRefGoogle Scholar
  43. [43]
    J.P. Blaizot and E. Iancu, Kinetic equations for long wavelength excitations of the quark-gluon plasma, Phys. Rev. Lett. 70 (1993) 3376 [hep-ph/9301236] [INSPIRE].
  44. [44]
    J.P. Blaizot and E. Iancu, Soft collective excitations in hot gauge theories, Nucl. Phys. B 417 (1994) 608 [hep-ph/9306294] [INSPIRE].
  45. [45]
    V.P. Nair, Hamiltonian analysis of the effective action for hard thermal loops in QCD, Phys. Rev. D 50 (1994) 4201 [hep-th/9403146] [INSPIRE].ADSGoogle Scholar

Copyright information

© The Author(s) 2017

Authors and Affiliations

  • Qianqian Du
    • 1
  • Adrian Dumitru
    • 2
    • 3
  • Yun Guo
    • 1
  • Michael Strickland
    • 4
  1. 1.Department of PhysicsGuangxi Normal UniversityGuilinChina
  2. 2.Department of Natural SciencesBaruch College, CUNYNew YorkU.S.A.
  3. 3.The Graduate School and University Center, The City University of New YorkNew YorkU.S.A.
  4. 4.Department of PhysicsKent State UniversityKentU.S.A.

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