Initial conditions for hydrodynamics from weakly coupled pre-equilibrium evolution


We use effective kinetic theory, accurate at weak coupling, to simulate the preequilibrium evolution of transverse energy and flow perturbations in heavy-ion collisions. We provide a Green function which propagates the initial perturbations to the energymomentum tensor at a time when hydrodynamics becomes applicable. With this map, the complete pre-thermal evolution from saturated nuclei to hydrodynamics can be modelled in a perturbatively controlled way.

A preprint version of the article is available at ArXiv.


  1. [1]

    U. Heinz and R. Snellings, Collective flow and viscosity in relativistic heavy-ion collisions, Ann. Rev. Nucl. Part. Sci. 63 (2013) 123 [arXiv:1301.2826] [INSPIRE].

    ADS  Article  Google Scholar 

  2. [2]

    M. Luzum and H. Petersen, Initial state fluctuations and final state correlations in relativistic heavy-ion collisions, J. Phys. G 41 (2014) 063102 [arXiv:1312.5503] [INSPIRE].

    ADS  Article  Google Scholar 

  3. [3]

    D.A. Teaney, Viscous hydrodynamics and the quark gluon plasma, arXiv:0905.2433 [INSPIRE].

  4. [4]

    R. Baier, P. Romatschke, D.T. Son, A.O. Starinets and M.A. Stephanov, Relativistic viscous hydrodynamics, conformal invariance and holography, JHEP 04 (2008) 100 [arXiv:0712.2451] [INSPIRE].

    ADS  MathSciNet  Article  MATH  Google Scholar 

  5. [5]

    J.E. Bernhard, P.W. Marcy, C.E. Coleman-Smith, S. Huzurbazar, R.L. Wolpert and S.A. Bass, Quantifying properties of hot and dense QCD matter through systematic model-to-data comparison, Phys. Rev. C 91 (2015) 054910 [arXiv:1502.00339] [INSPIRE].

    ADS  Google Scholar 

  6. [6]

    J. Liu, C. Shen and U. Heinz, Pre-equilibrium evolution effects on heavy-ion collision observables, Phys. Rev. C 91 (2015) 064906 [Erratum ibid. C 92 (2015) 049904] [arXiv:1504.02160] [INSPIRE].

  7. [7]

    W. van der Schee, P. Romatschke and S. Pratt, Fully dynamical simulation of central nuclear collisions, Phys. Rev. Lett. 111 (2013) 222302 [arXiv:1307.2539] [INSPIRE].

    ADS  Article  Google Scholar 

  8. [8]

    P. Romatschke, Light-heavy ion collisions: a window into pre-equilibrium QCD dynamics?, Eur. Phys. J. C 75 (2015) 305 [arXiv:1502.04745] [INSPIRE].

    ADS  Article  Google Scholar 

  9. [9]

    A. Kurkela, Initial state of heavy-ion collisions: isotropization and thermalization, in 25th International Conference on Ultra-Relativistic Nucleus-Nucleus Collisions (Quark Matter 2015), Kobe Japan September 27-October 3 2015 [arXiv:1601.03283] [INSPIRE].

  10. [10]

    H. Niemi, K.J. Eskola and R. Paatelainen, Event-by-event fluctuations in a perturbative QCD + saturation + hydrodynamics model: determining QCD matter shear viscosity in ultrarelativistic heavy-ion collisions, Phys. Rev. C 93 (2016) 024907 [arXiv:1505.02677] [INSPIRE].

    ADS  Google Scholar 

  11. [11]

    W. Broniowski, W. Florkowski, M. Chojnacki and A. Kisiel, Free-streaming approximation in early dynamics of relativistic heavy-ion collisions, Phys. Rev. C 80 (2009) 034902 [arXiv:0812.3393] [INSPIRE].

    ADS  Google Scholar 

  12. [12]

    B. Schenke, P. Tribedy and R. Venugopalan, Fluctuating glasma initial conditions and flow in heavy ion collisions, Phys. Rev. Lett. 108 (2012) 252301 [arXiv:1202.6646] [INSPIRE].

    ADS  Article  Google Scholar 

  13. [13]

    H. Niemi and G.S. Denicol, How large is the Knudsen number reached in fluid dynamical simulations of ultrarelativistic heavy ion collisions?, arXiv:1404.7327 [INSPIRE].

  14. [14]

    J. Noronha-Hostler, J. Noronha and M. Gyulassy, Sensitivity of flow harmonics to subnucleon scale fluctuations in heavy ion collisions, Phys. Rev. C 93 (2016) 024909 [arXiv:1508.02455] [INSPIRE].

    ADS  Google Scholar 

  15. [15]

    P.B. Arnold, G.D. Moore and L.G. Yaffe, Effective kinetic theory for high temperature gauge theories, JHEP 01 (2003) 030 [hep-ph/0209353] [INSPIRE].

  16. [16]

    A. Kurkela and Y. Zhu, Isotropization and hydrodynamization in weakly coupled heavy-ion collisions, Phys. Rev. Lett. 115 (2015) 182301 [arXiv:1506.06647] [INSPIRE].

    ADS  Article  Google Scholar 

  17. [17]

    E. Iancu, A. Leonidov and L. McLerran, The color glass condensate: an introduction, in QCD perspectives on hot and dense matter. Proceedings, NATO Advanced Study Institute, Summer School, Cargese France August 6-18 2001, pg. 73 [hep-ph/0202270] [INSPIRE].

  18. [18]

    E. Iancu and R. Venugopalan, The color glass condensate and high-energy scattering in QCD, in Quark gluon plasma, R.C. Hwa et al. eds., (2003), pg. 249 [hep-ph/0303204] [INSPIRE].

  19. [19]

    F. Gelis, E. Iancu, J. Jalilian-Marian and R. Venugopalan, The color glass condensate, Ann. Rev. Nucl. Part. Sci. 60 (2010) 463 [arXiv:1002.0333] [INSPIRE].

    ADS  Article  Google Scholar 

  20. [20]

    F. Gelis, T. Lappi and R. Venugopalan, High energy scattering in quantum chromodynamics, Int. J. Mod. Phys. E 16 (2007) 2595 [arXiv:0708.0047] [INSPIRE].

    ADS  Article  Google Scholar 

  21. [21]

    T. Lappi, Gluon spectrum in the glasma from JIMWLK evolution, Phys. Lett. B 703 (2011) 325 [arXiv:1105.5511] [INSPIRE].

    ADS  Article  Google Scholar 

  22. [22]

    A. Mazeliauskas and D. Teaney, Subleading harmonic flows in hydrodynamic simulations of heavy ion collisions, Phys. Rev. C 91 (2015) 044902 [arXiv:1501.03138] [INSPIRE].

    ADS  Google Scholar 

  23. [23]

    J. Vredevoogd and S. Pratt, Universal flow in the first stage of relativistic heavy ion collisions, Phys. Rev. C 79 (2009) 044915 [arXiv:0810.4325] [INSPIRE].

    ADS  Google Scholar 

  24. [24]

    L. Keegan, A. Kurkela, P. Romatschke, W. van der Schee and Y. Zhu, Weak and strong coupling equilibration in non-Abelian gauge theories, JHEP 04 (2016) 031 [arXiv:1512.05347] [INSPIRE].

    ADS  Article  Google Scholar 

  25. [25]

    P.B. Arnold, G.D. Moore and L.G. Yaffe, Transport coefficients in high temperature gauge theories. 2. Beyond leading log, JHEP 05 (2003) 051 [hep-ph/0302165] [INSPIRE].

  26. [26]

    M.A. York and G.D. Moore, Second order hydrodynamic coefficients from kinetic theory, Phys. Rev. D 79 (2009) 054011 [arXiv:0811.0729] [INSPIRE].

    ADS  Google Scholar 

  27. [27]

    A. Kovner, L.D. McLerran and H. Weigert, Gluon production from non-Abelian Weizsacker-Williams fields in nucleus-nucleus collisions, Phys. Rev. D 52 (1995) 6231 [hep-ph/9502289] [INSPIRE].

  28. [28]

    T. Lappi and L. McLerran, Some features of the glasma, Nucl. Phys. A 772 (2006) 200 [hep-ph/0602189] [INSPIRE].

  29. [29]

    T. Epelbaum and F. Gelis, Pressure isotropization in high energy heavy ion collisions, Phys. Rev. Lett. 111 (2013) 232301 [arXiv:1307.2214] [INSPIRE].

    ADS  Article  Google Scholar 

  30. [30]

    G. Chen, R.J. Fries, J.I. Kapusta and Y. Li, Early time dynamics of gluon fields in high energy nuclear collisions, Phys. Rev. C 92 (2015) 064912 [arXiv:1507.03524] [INSPIRE].

    ADS  Google Scholar 

  31. [31]

    M. Li and J.I. Kapusta, Pressure anisotropy in heavy ion collisions from color glass condensate, arXiv:1602.09060 [INSPIRE].

  32. [32]

    A. Kurkela and G.D. Moore, Thermalization in weakly coupled non-Abelian plasmas, JHEP 12 (2011) 044 [arXiv:1107.5050] [INSPIRE].

  33. [33]

    A. Kurkela and G.D. Moore, Bjorken flow, plasma instabilities and thermalization, JHEP 11 (2011) 120 [arXiv:1108.4684] [INSPIRE].

  34. [34]

    J. Berges, K. Boguslavski, S. Schlichting and R. Venugopalan, Universal attractor in a highly occupied non-Abelian plasma, Phys. Rev. D 89 (2014) 114007 [arXiv:1311.3005] [INSPIRE].

    ADS  Google Scholar 

  35. [35]

    R. Baier, A.H. Mueller, D. Schiff and D.T. Son, ‘Bottom up’ thermalization in heavy ion collisions, Phys. Lett. B 502 (2001) 51 [hep-ph/0009237] [INSPIRE].

  36. [36]

    A.H. Mueller and D.T. Son, On the equivalence between the Boltzmann equation and classical field theory at large occupation numbers, Phys. Lett. B 582 (2004) 279 [hep-ph/0212198] [INSPIRE].

  37. [37]

    S. Jeon, The Boltzmann equation in classical and quantum field theory, Phys. Rev. C 72 (2005) 014907 [hep-ph/0412121] [INSPIRE].

  38. [38]

    M.C. Abraao York, A. Kurkela, E. Lu and G.D. Moore, UV cascade in classical Yang-Mills theory via kinetic theory, Phys. Rev. D 89 (2014) 074036 [arXiv:1401.3751] [INSPIRE].

    ADS  Google Scholar 

  39. [39]

    M. Luzum and P. Romatschke, Conformal relativistic viscous hydrodynamics: applications to RHIC results at \( \sqrt{s_{NN}}=200 \) GeV, Phys. Rev. C 78 (2008) 034915 [Erratum ibid. C 79 (2009) 039903] [arXiv:0804.4015] [INSPIRE].

  40. [40]

    P. Romatschke, Retarded correlators in kinetic theory: branch cuts, poles and hydrodynamic onset transitions, Eur. Phys. J. C 76 (2016) 352 [arXiv:1512.02641] [INSPIRE].

    ADS  Article  Google Scholar 

  41. [41]

    G. Policastro, D.T. Son and A.O. Starinets, The shear viscosity of strongly coupled N = 4 supersymmetric Yang-Mills plasma, Phys. Rev. Lett. 87 (2001) 081601 [hep-th/0104066] [INSPIRE].

    ADS  Article  Google Scholar 

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Correspondence to Aleksas Mazeliauskas.

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ArXiv ePrint: 1605.04287

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Keegan, L., Kurkela, A., Mazeliauskas, A. et al. Initial conditions for hydrodynamics from weakly coupled pre-equilibrium evolution. J. High Energ. Phys. 2016, 171 (2016).

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  • Quark-Gluon Plasma
  • Thermal Field Theory