Collective flow and hydrodynamics in large and small systems at the LHC

  • Huichao Song
  • You Zhou
  • Katarína Gajdošová


In this article, we briefly review the recent progress on collective flow and hydrodynamics in large and small systems at the Large Hadron Collider (LHC), which includes the following topics: extracting the QGP viscosity from the flow data, initial-state fluctuations and final-state correlations at 2.76 A TeV Pb–Pb collisions, correlations, and collective flow in high-energy p–Pb and p–p collisions.


Collective flow Hydrodynamics QGP 


  1. 1.
    T.D. Lee, G.C. Wick, Vacuum stability and vacuum excitation in a spin 0 field theory. Phys. Rev. D 9, 2291–2316 (1974). doi: 10.1103/PhysRevD.9.2291 CrossRefGoogle Scholar
  2. 2.
    J.C. Collins, M.J. Perry, Superdense matter: neutrons or asymptotically free quarks? Phys. Rev. Lett. 34, 1353 (1975). doi: 10.1103/PhysRevLett.34.1353 CrossRefGoogle Scholar
  3. 3.
    H.G. Baumgardt, J.U. Schott, Y. Sakamoto et al., Shock waves and MACH cones in fast nucleus–nucleus collisions. Z. Phys. A 273, 359–371 (1975). doi: 10.1007/BF01435578 CrossRefGoogle Scholar
  4. 4.
    I. Arsene, I.G. Bearden, D. Beavis et al., Quark gluon plasma and color glass condensate at RHIC? The perspective from the BRAHMS experiment. Nucl. Phys. A 757, 1–27 (2005). doi: 10.1016/j.nuclphysa.2005.02.130 CrossRefGoogle Scholar
  5. 5.
    B.B. Back, M.D. Baker, M. Ballintijin et al., The PHOBOS perspective on discoveries at RHIC. Nucl. Phys. A 757, 28–101 (2005). doi: 10.1016/j.nuclphysa.2005.03.084 CrossRefGoogle Scholar
  6. 6.
    J. Adams, M.M. Aggarwal, Z. Ahammed et al., Experimental and theoretical challenges in the search for the quark gluon plasma: the STAR Collaboration’s critical assessment of the evidence from RHIC collisions. Nucl. Phys. A 757, 102–183 (2005). doi: 10.1016/j.nuclphysa.2005.03.085 CrossRefGoogle Scholar
  7. 7.
    K. Adcox, S.S. Adler, S. Afamasiev et al., Formation of dense partonic matter in relativistic nucleus–nucleus collisions at RHIC: experimental evaluation by the PHENIX collaboration. Nucl. Phys. A 757, 184–283 (2005). doi: 10.1016/j.nuclphysa.2005.03.086 CrossRefGoogle Scholar
  8. 8.
    M. Gyulassy, The QGP discovered at RHIC (2004), arXiv: nucl-th/0403032
  9. 9.
    B. Muller, J.L. Nagle, Results from the relativistic heavy ion collider. Annu. Rev. Nucl. Part. Sci. 56, 93–135 (2006). doi: 10.1146/annurev.nucl.56.080805.140556 CrossRefGoogle Scholar
  10. 10.
    P.F. Kolb, U.W. Heinz, Hydrodynamic description of ultrarelativistic heavy ion collisions (2003), arXiv: nucl-th/0305084
  11. 11.
    B. Alver, B.B. Back, M.D. Baker et al., System size, energy, pseudorapidity, and centrality dependence of elliptic flow. Phys. Rev. Lett. 98, 242302 (2007). doi: 10.1103/PhysRevLett.98.242302 CrossRefGoogle Scholar
  12. 12.
    M. Miller, R. Snellings, Eccentricity fluctuations and its possible effect on elliptic flow measurements (2003), arXiv: nucl-ex/0312008
  13. 13.
    B. Alver, B.B. Back, M.D. Baker et al., Importance of correlations and fluctuations on the initial source eccentricity in high-energy nucleus–nucleus collisions. Phys. Rev. C 77, 014906 (2008). doi: 10.1103/PhysRevC.77.014906 CrossRefGoogle Scholar
  14. 14.
    J.Y. Ollitrault, Anisotropy as a signature of transverse collective flow. Phys. Rev. D 46, 229–245 (1992). doi: 10.1103/PhysRevD.46.229 CrossRefGoogle Scholar
  15. 15.
    S. Voloshin, Y. Zhang, Flow study in relativistic nuclear collisions by Fourier expansion of azimuthal particle distributions. Z. Phys. C 70, 665–672 (1996). doi: 10.1007/s002880050141 CrossRefGoogle Scholar
  16. 16.
    S.A. Voloshin, A.M. Poskanzer, R. Snellings, Collective phenomena in non-central nuclear collisions (2008), arXiv: 0809.2949
  17. 17.
    R. Snellings, Elliptic flow: a brief review. New J. Phys. 13, 055008 (2011). doi: 10.1088/1367-2630/13/5/055008 CrossRefGoogle Scholar
  18. 18.
    U. Heinz, R. Snellings, Collective flow and viscosity in relativistic heavy-ion collisions. Annu. Rev. Nucl. Part. Sci. 63, 123–151 (2013). doi: 10.1146/annurev-nucl-102212-170540 CrossRefGoogle Scholar
  19. 19.
    C. Gale, S. Jeon, B. Schenke, Hydrodynamic modeling of heavy-ion collisions. Int. J. Mod. Phys. A 28, 1340011 (2013). doi: 10.1142/S0217751X13400113 CrossRefGoogle Scholar
  20. 20.
    H.C. Song, Hydrodynamic modelling for relativistic heavy-ion collisions at RHIC and LHC. Pramana 84, 703–715 (2015). doi: 10.1007/s12043-015-0971-2 CrossRefGoogle Scholar
  21. 21.
    M. Luzum, H. Petersen, Initial state fluctuations and final state correlations in relativistic heavy-ion collisions. J. Phys. G 41, 063102 (2014). doi: 10.1088/0954-3899/41/6/063102 CrossRefGoogle Scholar
  22. 22.
    J.Y. Jia, Event-shape fluctuations and flow correlations in ultra-relativistic heavy-ion collisions. J. Phys. G 41, 124003 (2014). doi: 10.1088/0954-3899/41/12/124003 CrossRefGoogle Scholar
  23. 23.
    B.H. Alver, C. Gombeaud, M. Luzum et al., Triangular flow in hydrodynamics and transport theory. Phys. Rev. C 82, 034913 (2010). doi: 10.1103/PhysRevC.82.034913 CrossRefGoogle Scholar
  24. 24.
    K. Aamodt, B. Abelev, A. Abrahantes et al., Higher harmonic anisotropic flow measurements of charged particles in Pb–Pb collisions at \(\sqrt{s_{NN}} \) = 2.76 TeV. Phys. Rev. Lett. 107, 03230 (2011). doi: 10.1103/PhysRevLett.107.032301 CrossRefGoogle Scholar
  25. 25.
    F.G. Gardim, F. Grassi, M. Luzum et al., Mapping the hydrodynamic response to the initial geometry in heavy-ion collisions. Phys. Rev. C 85, 024908 (2012). doi: 10.1103/PhysRevC.85.024908 CrossRefGoogle Scholar
  26. 26.
    G. Aad, H.M. Gray, Z. Marshall, Measurement of the azimuthal anisotropy for charged particle production in \(\sqrt{s_{NN}}=2.76\) TeV lead-lead collisions with the ATLAS detector. Phys. Rev. C 86, 014907 (2012). doi: 10.1103/PhysRevC.86.014907 CrossRefGoogle Scholar
  27. 27.
    M. Luzum, J.Y. Ollitrault, Extracting the shear viscosity of the quark–gluon plasma from flow in ultra-central heavy-ion collisions. Nucl. Phys. A 904–905, 377c–380c (2013). doi: 10.1016/j.nuclphysa.2013.02.028 CrossRefGoogle Scholar
  28. 28.
    A. Rizzi, R. Erbacher, Y. Weng, Studies of azimuthal dihadron correlations in ultra-central PbPb collisions at \(\sqrt{s_{NN}} =\) 2.76 TeV. JHEP 02, 088 (2014). doi: 10.1007/JHEP02(2014)088 Google Scholar
  29. 29.
    G. Aad, M. Barbero, C.P. Bee, Measurement of the distributions of event-by-event flow harmonics in lead–lead collisions at = 2.76 TeV with the ATLAS detector at the LHC. JHEP 11, 183 (2013). doi: 10.1007/JHEP11(2013)183 CrossRefGoogle Scholar
  30. 30.
    C. Gale, S.Y. Jeon, B. Schenke et al., Event-by-event anisotropic flow in heavy-ion collisions from combined Yang–Mills and viscous fluid dynamics. Phys. Rev. Lett. 110, 012302 (2013). doi: 10.1103/PhysRevLett.110.012302 CrossRefGoogle Scholar
  31. 31.
    G. Aad, B. Abbott, J. Abdallah et al., Measurement of event-plane correlations in \(\sqrt{s_{NN}}=2.76\) TeV lead-lead collisions with the ATLAS detector. Phys. Rev. C 90, 024905 (2014). doi: 10.1103/PhysRevC.90.024905 CrossRefGoogle Scholar
  32. 32.
    Z. Qiu, U. Heinz, Hydrodynamic event-plane correlations in Pb+Pb collisions at \(\sqrt{s}=2.76\)ATeV. Phys. Lett. B 717, 261–265 (2012). doi: 10.1016/j.physletb.2012.09.030 CrossRefGoogle Scholar
  33. 33.
    G. Aad, B. Abbott, J. Abdallah et al., Measurement of the correlation between flow harmonics of different order in lead–lead collisions at \(\sqrt{s_{NN}} \)= 2.76 TeV with the ATLAS detector. Phys. Rev. C 92, 034903 (2015). doi: 10.1103/PhysRevC.92.034903 CrossRefGoogle Scholar
  34. 34.
    J. Adam, D. Adamová, M.M. Aggarwal et al., Correlated event-by-event fluctuations of flow harmonics in Pb–Pb collisions at \(\sqrt{s_{\rm NN}}=2.76\) TeV (2016), arXiv: 1604.07663
  35. 35.
    G. Giacalone, L. Yan, J. Noronha-Hostler et al., Symmetric cumulants and event-plane correlations in Pb + Pb collisions. Phys. Rev. C 94, 014906 (2016). doi: 10.1103/PhysRevC.94.014906 CrossRefGoogle Scholar
  36. 36.
    X.R. Zhu, Y. Zhou, H.J. Xu et al., Correlations of flow harmonics in 2.76 A TeV Pb–Pb collisions (2016), arXiv: 1608.05305
  37. 37.
    J. Qian, U. Heinz, Hydrodynamic flow amplitude correlations in event-by-event fluctuating heavy-ion collisions. Phys. Rev. C 94, 024910 (2016). doi: 10.1103/PhysRevC.94.024910 CrossRefGoogle Scholar
  38. 38.
    U. Heinz, Z. Qiu, C. Shen, Fluctuating flow angles and anisotropic flow measurements. Phys. Rev. C 87, 034913 (2013). doi: 10.1103/PhysRevC.87.034913 CrossRefGoogle Scholar
  39. 39.
    F.G. Gardim, F. Grassi, M. Luzum et al., Breaking of factorization of two-particle correlations in hydrodynamics. Phys. Rev. C 87, 031901 (2013). doi: 10.1103/PhysRevC.87.031901 CrossRefGoogle Scholar
  40. 40.
    V. Khachatryan, A.M. Sirunyan, A. Tumasyan et al., Evidence for transverse momentum and pseudorapidity dependent event plane fluctuations in PbPb and pPb collisions. Phys. Rev. C 92, 034911 (2015). doi: 10.1103/PhysRevC.92.034911 CrossRefGoogle Scholar
  41. 41.
    S. chatrchyan, V. Khachatryan, A.M. Sirunyan, Observation of long-range near-side angular correlations in proton–lead collisions at the LHC. Phys. Lett. B 718, 795–814 (2013). doi: 10.1016/j.physletb.2012.11.025 CrossRefGoogle Scholar
  42. 42.
    B. Abelev, J. Adam, D. Adamova, et al., Long-range angular correlations on the near and away side in \(p\)–Pb collisions at \(\sqrt{s_{NN}}=5.02\) TeV. Phys. Lett. B 719, 29–41 (2013). doi: 10.1016/j.physletb.2013.01.012 CrossRefGoogle Scholar
  43. 43.
    G. Aad, T. Abajyan, B. Abbott et al., Measurement with the ATLAS detector of multi-particle azimuthal correlations in p+Pb collisions at \(\sqrt{s_{NN}}=\) 5.02 TeV. Phys. Lett. B 725, 60–78 (2013). doi: 10.1016/j.physletb.2013.06.057 CrossRefGoogle Scholar
  44. 44.
    V. Khachatryan, A.M. Sirunyan, A. Tumasyan et al., Evidence for collective multiparticle correlations in p–Pb collisions. Phys. Rev. Lett. 115, 012301 (2015). doi: 10.1103/PhysRevLett.115.012301 CrossRefGoogle Scholar
  45. 45.
    B. Abelev, J. Adam, D. Adamova et al., Long-range angular correlations on the near and away side in \(p\)-Pb collisions at \(\sqrt{s_{NN}}=5.02\) TeV. Phys. Rev. C 90, 054901 (2014). doi: 10.1103/PhysRevC.90.054901 CrossRefGoogle Scholar
  46. 46.
    V. Khachatryan, A.M. Sirunyan, A. Tumasyan et al., Long-range angular correlations of \({\uppi }\), K and p in p–Pb collisions at \(\sqrt{s_{\rm NN}}\) = 5.02 TeV. Phys. Lett. B 726, 164–177 (2013). doi: 10.1016/j.physletb.2013.08.024 CrossRefGoogle Scholar
  47. 47.
    V. Khachatryan, A.M. Sirunyan, A. Tumasyan et al., Long-range two-particle correlations of strange hadrons with charged particles in pPb and PbPb collisions at LHC energies. Phys. Lett. B 742, 200–224 (2015). doi: 10.1016/j.physletb.2015.01.034 CrossRefGoogle Scholar
  48. 48.
    P. Bozek, Collective flow in p–Pb and d–Pd collisions at TeV energies. Phys. Rev. C 85, 014911 (2012). doi: 10.1103/PhysRevC.85.014911 CrossRefGoogle Scholar
  49. 49.
    P. Bozek, W. Broniowski, Correlations from hydrodynamic flow in p–Pb collisions. Phys. Lett. B 718, 1557–1561 (2013). doi: 10.1016/j.physletb.2012.12.051 CrossRefGoogle Scholar
  50. 50.
    P. Bozek, W. Broniowski, G. Torrieri, Mass hierarchy in identified particle distributions in proton–lead collisions. Phys. Rev. Lett. 111, 172303 (2013). doi: 10.1103/PhysRevLett.111.172303 CrossRefGoogle Scholar
  51. 51.
    A. Bzdak, B. Schenke, P. Tribedy et al., Initial state geometry and the role of hydrodynamics in proton–proton, proton–nucleus and deuteron–nucleus collisions. Phys. Rev. C 87, 064906 (2013). doi: 10.1103/PhysRevC.87.064906 CrossRefGoogle Scholar
  52. 52.
    G.Y. Qin, B. Müller, Elliptic and triangular flow anisotropy in deuteron–gold collisions at \(\sqrt{s_{NN}}=200\) GeV at RHIC and in proton–lead collisions at \(\sqrt{s_{NN}}=5.02\) TeV at the LHC. Phys. Rev. C 89, 044902 (2014). doi: 10.1103/PhysRevC.89.044902 CrossRefGoogle Scholar
  53. 53.
    K. Werner, M. Bleicher, B. Guiot et al., Evidence for flow from hydrodynamic simulations of \(p\)–Pb collisions at 5.02 TeV from \(\nu _2\) mass splitting. Phys. Rev. Lett. 112, 232301 (2014). doi: 10.1103/PhysRevLett.112.232301 CrossRefGoogle Scholar
  54. 54.
    B. Schenke, R. Venugopalan, Eccentric protons? Sensitivity of flow to system size and shape in p+p, p+Pb and Pb+Pb collisions. Phys. Rev. Lett. 113, 102301 (2014). doi: 10.1103/PhysRevLett.113.102301 CrossRefGoogle Scholar
  55. 55.
    S. Chatrchyan, V. Khachatryan, A.M. Sirunyan et al., Observation of long-range near-side angular correlations in proton–proton collisions at the LHC. JHEP 09, 091 (2010). doi: 10.1007/JHEP09(2010)091 Google Scholar
  56. 56.
    W. Li, Observation of a ’Ridge’ correlation structure in high multiplicity proton–proton collisions: a brief review. Mod. Phys. Lett. A 27, 1230018 (2012). doi: 10.1142/S0217732312300182 CrossRefGoogle Scholar
  57. 57.
    G. Aad, B. Abbott, J. Abdallah et al., Observation of long-range elliptic azimuthal anisotropies in \(\sqrt{s}=\)13 and 2.76 TeV \(pp\) collisions with the ATLAS detector. Phys. Rev. Lett. 116, 172301 (2016). doi: 10.1103/PhysRevLett.116.172301 CrossRefGoogle Scholar
  58. 58.
    V. Khachatryan, A.M. Sirunyan, A. Tumasyan et al., Measurement of long-range near-side two-particle angular correlations in pp collisions at \(\sqrt{s} =\) 13 TeV. Phys. Rev. Lett. 116, 172302 (2016). doi: 10.1103/PhysRevLett.116.172302 CrossRefGoogle Scholar
  59. 59.
    V. Khachatryan, A.M. Sirunyan, A. Tumasyan et al., Evidence for collectivity in pp collisions at the LHC (2016), arXiv: 1606.06198
  60. 60.
    K. Dusling, W. Li, B. Schenke, Novel collective phenomena in high-energy proton–proton and proton–nucleus collisions. Int. J. Mod. Phys. E 25, 1630002 (2016). doi: 10.1142/S0218301316300022 CrossRefGoogle Scholar
  61. 61.
    D.A. Teaney, Viscous hydrodynamics and the quark gluon plasma (2009), arXiv: nucl-th0905.2433
  62. 62.
    P. Romatschke, New developments in relativistic viscous hydrodynamics. Int. J. Mod. Phys. E 19, 1–53 (2010). doi: 10.1142/S0218301310014613 CrossRefGoogle Scholar
  63. 63.
    P. Huovinen, Hydrodynamics at RHIC and LHC: what have we learned? Int. J. Mod. Phys. E 22, 1330029 (2013). doi: 10.1142/S0218301313300294 CrossRefGoogle Scholar
  64. 64.
    P. Romatschke, U. Romatschke, Viscosity information from relativistic nuclear collisions: how perfect is the fluid observed at RHIC? Phys. Rev. Lett. 99, 172301 (2007). doi: 10.1103/PhysRevLett.99.172301 CrossRefGoogle Scholar
  65. 65.
    M. Luzum, P. Romatschke, Conformal relativistic viscous hydrodynamics: applications to RHIC results at s(NN)**(1/2) = 200-GeV. Phys. Rev. C 78, 034915 (2008). doi: 10.1103/PhysRevC.78.034915 CrossRefGoogle Scholar
  66. 66.
    H.C. Song, U.W. Heinz, Suppression of elliptic flow in a minimally viscous quark–gluon plasma. Phys. Lett. B 658, 279–283 (2008). doi: 10.1016/j.physletb.2007.11.019 CrossRefGoogle Scholar
  67. 67.
    H.C. Song, U.W. Heinz, Causal viscous hydrodynamics in 2+1 dimensions for relativistic heavy-ion collisions. Phys. Rev. C 77, 064901 (2008). doi: 10.1103/PhysRevC.77.064901 CrossRefGoogle Scholar
  68. 68.
    H.C. Song, Causal viscous hydrodynamics for relativistic heavy ion collisions, Ph.D. thesis, Ohio State U, 2009,, arXiv: 0908.3656
  69. 69.
    K. Dusling, D. Teaney, Simulating elliptic flow with viscous hydrodynamics. Phys. Rev. C 77, 034905 (2008). doi: 10.1103/PhysRevC.77.034905 CrossRefGoogle Scholar
  70. 70.
    D. Molnar, P. Huovinen, Dissipative effects from transport and viscous hydrodynamics. J. Phys. G 35, 104125 (2008). doi: 10.1088/0954-3899/35/10/104125 CrossRefGoogle Scholar
  71. 71.
    P. Bozek, Bulk and shear viscosities of matter created in relativistic heavy-ion collisions. Phys. Rev. C 81, 034909 (2010). doi: 10.1103/PhysRevC.81.034909 CrossRefGoogle Scholar
  72. 72.
    A.K. Chaudhuri, Centrality dependence of elliptic flow and QGP viscosity. J. Phys. G 37, 075011 (2010). doi: 10.1088/0954-3899/37/7/075011 CrossRefGoogle Scholar
  73. 73.
    B. Schenke, S. Jeon, C. Gale, Elliptic and triangular flow in event-by-event (3+1)D viscous hydrodynamics. Phys. Rev. Lett. 106, 042301 (2011). doi: 10.1103/PhysRevLett.106.042301 CrossRefGoogle Scholar
  74. 74.
    W. Israel, Nonstationary irreversible thermodynamics: a causal relativistic theory. Ann. Phys. 100, 310–331 (1976). doi: 10.1016/0003-4916(76)90064-6 MathSciNetCrossRefGoogle Scholar
  75. 75.
    A. Muronga, D.H. Rischke, Evolution of hot, dissipative quark matter in relativistic nuclear collisions (2004), arXiv: nucl-th/0407114
  76. 76.
    R. Baier, P. Romatschke, U.A. Wiedemann, Dissipative hydrodynamics and heavy ion collisions. Phys. Rev. C 73, 064903 (2006). doi: 10.1103/PhysRevC.73.064903 CrossRefGoogle Scholar
  77. 77.
    R. Baier, P. Romatschke, D.T. Son et al., Relativistic viscous hydrodynamics, conformal invariance, and holography. JHEP 04, 100 (2008). doi: 10.1088/1126-6708/2008/04/100 MathSciNetzbMATHCrossRefGoogle Scholar
  78. 78.
    B. Betz, D. Henkel, D.H. Rischke, From kinetic theory to dissipative fluid dynamics. Prog. Part. Nucl. Phys. 62, 556–561 (2009). doi: 10.1016/j.ppnp.2008.12.018 CrossRefGoogle Scholar
  79. 79.
    G.S. Denicol, H. Niemi, E. Molnar et al., Derivation of transient relativistic fluid dynamics from the Boltzmann equation. Phys. Rev. D 85, 114047 (2012). doi: 10.1103/PhysRevD.85.114047 CrossRefGoogle Scholar
  80. 80.
    G.S. Denicol, E. Molnar, H. Niemi et al., Derivation of fluid dynamics from kinetic theory with the 14-moment approximation. Eur. Phys. J. A 48, 170 (2012). doi: 10.1140/epja/i2012-12170-x CrossRefGoogle Scholar
  81. 81.
    M. Martinez, M. Strickland, Dissipative dynamics of highly anisotropic systems. Nucl. Phys. A 848, 183–197 (2010). doi: 10.1016/j.nuclphysa.2010.08.011 CrossRefGoogle Scholar
  82. 82.
    W. Florkowski, R. Ryblewski, Highly-anisotropic and strongly-dissipative hydrodynamics for early stages of relativistic heavy-ion collisions. Phys. Rev. C 83, 034907 (2011). doi: 10.1103/PhysRevC.83.034907 CrossRefGoogle Scholar
  83. 83.
    S. Jeon, U. Heinz, Introduction to hydrodynamics, in Quark–Gluon Plasma 5, edited by X.-N. Wang (2016) pp. 131–187. doi: 10.1142/9789814663717_0003
  84. 84.
    M.A. Stephanov, Non-Gaussian fluctuations near the QCD critical point. Phys. Rev. Lett. 102, 032301 (2009). doi: 10.1103/PhysRevLett.102.032301 CrossRefGoogle Scholar
  85. 85.
    M.A. Stephanov, On the sign of kurtosis near the QCD critical point. Phys. Rev. Lett. 107, 052301 (2011). doi: 10.1103/PhysRevLett.107.052301 CrossRefGoogle Scholar
  86. 86.
    L.J. Jiang, P.F. Li, H.C. Song, Correlated fluctuations near the QCD critical point. Phys. Rev. C 94, 024918 (2016). doi: 10.1103/PhysRevC.94.024918 CrossRefGoogle Scholar
  87. 87.
    L.J. Jiang, P.F. Li, H.C. Song, Multiplicity fluctuations of net protons on the hydrodynamic freeze-out surface. Nucl. Phys. A 956, 360–364 (2016). doi: 10.1016/j.nuclphysa.2016.01.034 CrossRefGoogle Scholar
  88. 88.
    M. Martinez, R. Ryblewski, M. Strickland, Boost-invariant (2+1)-dimensional anisotropic hydrodynamics. Phys. Rev. C 85, 064913 (2012). doi: 10.1103/PhysRevC.85.064913 CrossRefGoogle Scholar
  89. 89.
    W. Florkowski, R. Ryblewski, M. Strickland, Anisotropic hydrodynamics for rapidly expanding systems. Nucl. Phys. A 916, 249–259 (2013). doi: 10.1016/j.nuclphysa.2013.08.004 CrossRefGoogle Scholar
  90. 90.
    R. Ryblewski, W. Florkowski, Highly-anisotropic hydrodynamics in 3+1 space-time dimensions. Phys. Rev. C 85, 064901 (2012). doi: 10.1103/PhysRevC.85.064901 CrossRefGoogle Scholar
  91. 91.
    D. Bazow, U.W. Heinz, M. Strickland, Second-order (2+1)-dimensional anisotropic hydrodynamics. Phys. Rev. C 90, 054910 (2014). doi: 10.1103/PhysRevC.90.054910 CrossRefGoogle Scholar
  92. 92.
    D. Bazow, U.W. Heinz, M. Martinez, Nonconformal viscous anisotropic hydrodynamics. Phys. Rev. C 91, 064903 (2015). doi: 10.1103/PhysRevC.91.064903 CrossRefGoogle Scholar
  93. 93.
    M. Strickland, Recent progress in anisotropic hydrodynamics 2016, arXiv: 1611.05056
  94. 94.
    K. Paech, H. Stoecker, A. Dumitru, Hydrodynamics near a chiral critical point. Phys. Rev. C 68, 044907 (2003). doi: 10.1103/PhysRevC.68.044907 CrossRefGoogle Scholar
  95. 95.
    M. Nahrgang, S. Leupold, C. Herold et al., Nonequilibrium chiral fluid dynamics including dissipation and noise. Phys. Rev. C 84, 024912 (2011). doi: 10.1103/PhysRevC.84.024912 CrossRefGoogle Scholar
  96. 96.
    M. Nahrgang, S. Leupold, M. Bleicher, Equilibration and relaxation times at the chiral phase transition including reheating. Phys. Lett. B 711, 109–116 (2012). doi: 10.1016/j.physletb.2012.03.059 CrossRefGoogle Scholar
  97. 97.
    C. Herold, M. Nahrgang, I. Mishustin et al., Chiral fluid dynamics with explicit propagation of the Polyakov loop. Phys. Rev. C 87, 014907 (2013). doi: 10.1103/PhysRevC.87.014907 CrossRefGoogle Scholar
  98. 98.
    C. Herold, M. Nahrgang, Y. Yan et al., Dynamical net-proton fluctuations near a QCD critical point. Phys. Rev. C 93, 021902 (2016). doi: 10.1103/PhysRevC.93.021902 CrossRefGoogle Scholar
  99. 99.
    G.S. Denicol, H. Niemi, I. Bouras et al., Solving the heat-flow problem with transient relativistic fluid dynamics. Phys. Rev. D 89, 074005 (2014). doi: 10.1103/PhysRevD.89.074005 CrossRefGoogle Scholar
  100. 100.
    P. Huovinen, P. Petreczky, QCD equation of state and hadron resonance gas. Nucl. Phys. A 837, 26–53 (2010). doi: 10.1016/j.nuclphysa.2010.02.015 CrossRefGoogle Scholar
  101. 101.
    C. Shen, U. Heinz, P. Huovinen et al., Systematic parameter study of hadron spectra and elliptic flow from viscous hydrodynamic simulations of Au+Au collisions at \(\sqrt{s_{NN}}=200\) GeV. Phys. Rev. C 82, 054904 (2010). doi: 10.1103/PhysRevC.82.054904 CrossRefGoogle Scholar
  102. 102.
    P.F. Kolb, J. Sollfrank, U.W. Heinz, Anisotropic transverse flow and the quark hadron phase transition. Phys. Rev. C 62, 054909 (2000). doi: 10.1103/PhysRevC.62.054909 CrossRefGoogle Scholar
  103. 103.
    D. Kharzeev, M. Nardi, Hadron production in nuclear collisions at RHIC and high density QCD. Phys. Lett. B 507, 121–128 (2001). doi: 10.1016/S0370-2693(01)00457-9 CrossRefGoogle Scholar
  104. 104.
    M.L. Miller, K. Reygers, S.J. Sanders et al., Glauber modeling in high energy nuclear collisions. Annu. Rev. Nucl. Part. Sci. 57, 205–243 (2007). doi: 10.1146/annurev.nucl.57.090506.123020 CrossRefGoogle Scholar
  105. 105.
    H.-J. Drescher, Y. Nara, Effects of fluctuations on the initial eccentricity from the color glass condensate in heavy ion collisions. Phys. Rev. C 75, 034905 (2007). doi: 10.1103/PhysRevC.75.034905 CrossRefGoogle Scholar
  106. 106.
    T. Hirano, Y. Nara, Eccentricity fluctuation effects on elliptic flow in relativistic heavy ion collisions. Phys. Rev. C 79, 064904 (2009). doi: 10.1103/PhysRevC.79.064904 CrossRefGoogle Scholar
  107. 107.
    R.S. Bhalerao, A. Jaiswal, S. Pal, Collective flow in event-by-event partonic transport plus hydrodynamics hybrid approach. Phys. Rev. C 92, 014903 (2015). doi: 10.1103/PhysRevC.92.014903 CrossRefGoogle Scholar
  108. 108.
    L.G. Pang, Q. Wang, X.N. Wang, Effects of initial flow velocity fluctuation in event-by-event (3+1)D hydrodynamics. Phys. Rev. C 86, 024911 (2012). doi: 10.1103/PhysRevC.86.024911 CrossRefGoogle Scholar
  109. 109.
    H.J. Xu, Z.P. Li, H.C. Song, High-order flow harmonics of identified hadrons in 2.76A TeV Pb + Pb collisions. Phys. Rev. C 93, 064905 (2016). doi: 10.1103/PhysRevC.93.064905 CrossRefGoogle Scholar
  110. 110.
    B. Schenke, P. Tribedy, R. Venugopalan, Event-by-event gluon multiplicity, energy density, and eccentricities in ultrarelativistic heavy-ion collisions. Phys. Rev. C 86, 034908 (2012). doi: 10.1103/PhysRevC.86.034908 CrossRefGoogle Scholar
  111. 111.
    R. Paatelainen, K.J. Eskola, H. Niemi et al., Fluid dynamics with saturated minijet initial conditions in ultrarelativistic heavy-ion collisions. Phys. Lett. B 731, 126–130 (2014). doi: 10.1016/j.physletb.2014.02.018 CrossRefGoogle Scholar
  112. 112.
    H. Niemi, K.J. Eskola, 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, 024907 (2016). doi: 10.1103/PhysRevC.93.024907 CrossRefGoogle Scholar
  113. 113.
    J.S. Moreland, J.E. Bernhard, S.A. Bass, Alternative ansatz to wounded nucleon and binary collision scaling in high-energy nuclear collisions. Phys. Rev. C 92, 011901 (2015). doi: 10.1103/PhysRevC.92.011901 CrossRefGoogle Scholar
  114. 114.
    J. Liu, C. Shen, U. Heinz, Pre-equilibrium evolution effects on heavy-ion collision observables. Phys. Rev. C 91, 064906 (2015). doi: 10.1103/PhysRevC.92.049904 CrossRefGoogle Scholar
  115. 115.
    K. Werner, lu Karpenko, T. Pierog, Evidence for hydrodynamic evolution in proton-proton scattering at 900 GeV. Phys. Rev.C 83, 044915 (2011). doi: 10.1103/PhysRevC.83.044915 CrossRefGoogle Scholar
  116. 116.
    H. Petersen, M. Bleicher, Ideal hydrodynamics and elliptic flow at SPS energies: importance of the initial conditions. Phys. Rev. C 79, 054904 (2009). doi: 10.1103/PhysRevC.79.054904 CrossRefGoogle Scholar
  117. 117.
    H. Petersen, J. Steinheimer, G. Burau et al., Elliptic flow in an integrated (3+1)d microscopic + macroscopic approach with fluctuating initial conditions. Eur. Phys. J. C 62, 31–36 (2009). doi: 10.1140/epjc/s10052-009-0921-6 CrossRefGoogle Scholar
  118. 118.
    B. Schenke, S. Schlichting, 3D glasma initial state for relativistic heavy ion collisions. Phys. Rev. C 94, 044907 (2016). doi: 10.1103/PhysRevC.94.044907 CrossRefGoogle Scholar
  119. 119.
    F. Cooper, G. Frye, Phys. Rev. D 10, 186 (1974)CrossRefGoogle Scholar
  120. 120.
    T. Hirano, M. Gyulassy, Perfect fluidity of the quark gluon plasma core as seen through its dissipative hadronic corona. Nucl. Phys. A 769, 71–94 (2006). doi: 10.1016/j.nuclphysa.2006.02.005 CrossRefGoogle Scholar
  121. 121.
    H.C. Song, S.A. Bass, U. Heinz, Viscous QCD matter in a hybrid hydrodynamic+Boltzmann approach. Phys. Rev. C 83, 024912 (2011). doi: 10.1103/PhysRevC.83.024912 CrossRefGoogle Scholar
  122. 122.
    S. Ryu, S. Jeon, C. Gale et al., MUSIC with the UrQMD afterburner. Nucl. Phys. A 904–905, 389c–392c (2013). doi: 10.1016/j.nuclphysa.2013.02.031 CrossRefGoogle Scholar
  123. 123.
    lu A. Karpenko, M. Bleicher, P. Huovinen, 3+1 dimensional viscous hydrodynamics at high baryon densities. J. Phys. Conf. Ser. 503, 012040 (2014). doi: 10.1088/1742-6596/503/1/012040 CrossRefGoogle Scholar
  124. 124.
    H.T. Ding, F. Karsch, S. Mukherjee, Thermodynamics of strong-interaction matter from Lattice QCD. Int. J. Mod. Phys. E 24, 1530007 (2015). doi: 10.1142/S0218301315300076 zbMATHCrossRefGoogle Scholar
  125. 125.
    K. Dusling, T. Schäfer, Bulk viscosity, particle spectra and flow in heavy-ion collisions. Phys. Rev. C 85, 044909 (2012). doi: 10.1103/PhysRevC.85.044909 CrossRefGoogle Scholar
  126. 126.
    J. Noronha-Hostler, G.S. Denicol, J. Noronha et al., Bulk viscosity effects in event-by-event relativistic hydrodynamics. Phys. Rev. C 88, 044916 (2013). doi: 10.1103/PhysRevC.88.044916 CrossRefGoogle Scholar
  127. 127.
    S.A. Bass, M. Belkacem, M. Bleicher et al., Microscopic models for ultrarelativistic heavy ion collisions. Prog. Part. Nucl. Phys. 41, 255–369 (1998). doi: 10.1016/S0146-6410(98)00058-1 CrossRefGoogle Scholar
  128. 128.
    M. Bleicher, E. Zabrodin, C. Spieles, Relativistic hadron hadron collisions in the ultrarelativistic quantum molecular dynamics model. J. Phys. G 25, 1859–1896 (1999). doi: 10.1088/0954-3899/25/9/308 CrossRefGoogle Scholar
  129. 129.
    H.C. Song, S. Bass, U.W. Heinz, Spectra and elliptic flow for identified hadrons in 2.76A TeV Pb + Pb collisions. Phys. Rev. C 89, 034919 (2014). doi: 10.1103/PhysRevC.89.034919 CrossRefGoogle Scholar
  130. 130.
    U. Heinz, C. Shen, H.C. Song, The viscosity of quark–gluon plasma at RHIC and the LHC. AIP Conf. Proc. 1441, 766–770 (2012). doi: 10.1063/1.3700674 CrossRefGoogle Scholar
  131. 131.
    H.C. Song, QGP viscosity at RHIC and the LHC—a 2012 status report, A904–905, 114c–121c (2013). doi: 10.1016/j.nuclphysa.2013.01.052
  132. 132.
    P. Bozek, Flow and interferometry in 3+1 dimensional viscous hydrodynamics. Phys. Rev. C 85, 034901 (2012). doi: 10.1103/PhysRevC.85.034901 CrossRefGoogle Scholar
  133. 133.
    J. Vredevoogd, S. Pratt, Viscous hydrodynamics and relativistic heavy ion collisions. Phys. Rev. C 85, 044908 (2012). doi: 10.1103/PhysRevC.85.044908 CrossRefGoogle Scholar
  134. 134.
    C. Nonaka, Y. Akamatsu, M. Takamoto, Study of higher harmonics based on (3+1)-d relativistic viscous hydrodynamics. Nucl. Phys. A 904–905, 405c–408c (2013). doi: 10.1016/j.nuclphysa.2013.02.035 CrossRefGoogle Scholar
  135. 135.
    L. Del Zanna, V. Chandra, G. Inghirami et al., Relativistic viscous hydrodynamics for heavy-ion collisions with ECHO-QGP. Eur. Phys. J. C 73, 2524 (2013). doi: 10.1140/epjc/s10052-013-2524-5 CrossRefGoogle Scholar
  136. 136.
    lu Karpenko, P. Huovinen, M. Bleicher, A 3+1 dimensional viscous hydrodynamic code for relativistic heavy ion collisions. Comput. Phys. Commun. 185, 3016–3027 (2014). doi: 10.1016/j.cpc.2014.07.010 zbMATHCrossRefGoogle Scholar
  137. 137.
    H. Petersen, G.Y. Qin, S.A. Bass et al., Triangular flow in event-by-event ideal hydrodynamics in Au+Au collisions at \(\sqrt{s_{\rm NN}}=200A\) GeV. Phys. Rev. C 82, 041901 (2010). doi: 10.1103/PhysRevC.82.041901 CrossRefGoogle Scholar
  138. 138.
    G.Y. Qin, H. Petersen, S.A. Bass et al., Translation of collision geometry fluctuations into momentum anisotropies in relativistic heavy-ion collisions. Phys. Rev. C 82, 064903 (2010). doi: 10.1103/PhysRevC.82.064903 CrossRefGoogle Scholar
  139. 139.
    H. Holopainen, H. Niemi, K.J. Eskola, Event-by-event hydrodynamics and elliptic flow from fluctuating initial state. Phys. Rev. C 83, 034901 (2011). doi: 10.1103/PhysRevC.83.034901 CrossRefGoogle Scholar
  140. 140.
    Z. Qiu, U.W. Heinz, Event-by-event shape and flow fluctuations of relativistic heavy-ion collision fireballs. Phys. Rev. C 84, 024911 (2011). doi: 10.1103/PhysRevC.84.024911 CrossRefGoogle Scholar
  141. 141.
    C. Shen, Z. Qiu, H.C. Song et al., The iEBE-VISHNU code package for relativistic heavy-ion collisions. Comput. Phys. Commun. 199, 61–85 (2016). doi: 10.1016/j.cpc.2015.08.039 MathSciNetCrossRefGoogle Scholar
  142. 142.
    D. Bazow, U.W. Heinz, M. Strickland, Massively parallel simulations of relativistic fluid dynamics on graphics processing units with CUDA (2016), arXiv: 1608.06577
  143. 143.
    A.M. Poskanzer, S.A. Voloshin, Methods for analyzing anisotropic flow in relativistic nuclear collisions. Phys. Rev. C 58, 1671–1678 (1998). doi: 10.1103/PhysRevC.58.1671 CrossRefGoogle Scholar
  144. 144.
    M. Luzum, J.-Y. Ollitrault, Eliminating experimental bias in anisotropic-flow measurements of high-energy nuclear collisions. Phys. Rev. C 87, 044907 (2013). doi: 10.1103/PhysRevC.87.044907 CrossRefGoogle Scholar
  145. 145.
    A. Bilandzic, R. Snellings, S. Voloshin, Flow analysis with cumulants: direct calculations. Phys. Rev. C 83, 044913 (2011). doi: 10.1103/PhysRevC.83.044913 CrossRefGoogle Scholar
  146. 146.
    A. Bilandzic, C.H. Christensen, K. Gulbrandsen et al., Generic framework for anisotropic flow analyses with multiparticle azimuthal correlations. Phys. Rev. C 89, 064904 (2014). doi: 10.1103/PhysRevC.89.064904 CrossRefGoogle Scholar
  147. 147.
    R.S. Bhalerao, M. Luzum, J.Y. Ollitrault, Determining initial-state fluctuations from flow measurements in heavy-ion collisions. Phys. Rev. C 84, 034910 (2011). doi: 10.1103/PhysRevC.84.034910 CrossRefGoogle Scholar
  148. 148.
    H.C. Song, S.A. Bass, U. Heinz et al., 200 A GeV Au+Au collisions serve a nearly perfect quark–gluon liquid. Phys. Rev. Lett. 106, 192301 (2011). doi: 10.1103/PhysRevLett.106.192301 CrossRefGoogle Scholar
  149. 149.
    J.-Y. Ollitrault, A.M. Poskanzer, S.A. Voloshin, Effect of flow fluctuations and nonflow on elliptic flow methods. Phys. Rev. C 80, 014904 (2009). doi: 10.1103/PhysRevC.80.014904 CrossRefGoogle Scholar
  150. 150.
    B. Abelev, L. Aphecetche, G. Batigne, Elliptic flow of identified hadrons in Pb–Pb collisions at \( \sqrt{s_{\rm NN}}=2.76 \) TeV. JHEP 06, 190 (2015). doi: 10.1007/JHEP06(2015)190 Google Scholar
  151. 151.
    N. Mohammadi, Higher harmonic anisotropic flow of identified particles in Pb–Pb collisions with the ALICE detector. Nucl. Phys. A 956, 304–307 (2016). doi: 10.1016/j.nuclphysa.2016.03.031 CrossRefGoogle Scholar
  152. 152.
    H.C. Song, U.W. Heinz, Extracting the QGP viscosity from RHIC data—a status report from viscous hydrodynamics. J. Phys. G 36, 064033 (2009). doi: 10.1088/0954-3899/36/6/064033 CrossRefGoogle Scholar
  153. 153.
    H.C. Song, S.A. Bass, U. Heinz et al., Hadron spectra and elliptic flow for 200 A GeV Au+Au collisions from viscous hydrodynamics coupled to a Boltzmann cascade. Phys. Rev. C 83, 054910 (2011). doi: 10.1103/PhysRevC.83.054910 CrossRefGoogle Scholar
  154. 154.
    H.C. Song, S.A. Bass, U. Heinz, Elliptic flow in 200 A GeV Au+Au collisions and 2.76 A TeV Pb+Pb collisions: insights from viscous hydrodynamics + hadron cascade hybrid model. Phys. Rev. C 83, 054912 (2011). doi: 10.1103/PhysRevC.83.054912 CrossRefGoogle Scholar
  155. 155.
    X.G. Zhu, F.L. Meng, H.C. Song et al., Hybrid model approach for strange and multistrange hadrons in 2.76A TeV Pb+Pb collisions. Phys. Rev. C 91, 034904 (2015). doi: 10.1103/PhysRevC.91.034904 CrossRefGoogle Scholar
  156. 156.
    J. Adam, D. Adamová, M.M. Aggarwal, Higher harmonic flow coefficients of identified hadrons in Pb–Pb collisions at \(\sqrt{s_{\rm NN}}\) = 2.76 TeV. JHEP 09, 164 (2016). doi: 10.1007/JHEP09(2016)164 CrossRefGoogle Scholar
  157. 157.
    G. Torrieri, I. Mishustin, Instability of boost-invariant hydrodynamics with a QCD inspired bulk viscosity. Phys. Rev. C 78, 021901 (2008). doi: 10.1103/PhysRevC.78.021901 CrossRefGoogle Scholar
  158. 158.
    K. Rajagopal, N. Tripuraneni, Bulk viscosity and cavitation in boost-invariant hydrodynamic expansion. JHEP 03, 018 (2010). doi: 10.1007/JHEP03(2010)018 zbMATHCrossRefGoogle Scholar
  159. 159.
    H.C. Song, U.W. Heinz, Interplay of shear and bulk viscosity in generating flow in heavy-ion collisions. Phys. Rev. C 81, 024905 (2010). doi: 10.1103/PhysRevC.81.024905 CrossRefGoogle Scholar
  160. 160.
    H.C. Song, U.W. Heinz, Viscous hydrodynamics with bulk viscosity: uncertainties from relaxation time and initial conditions. Nucl. Phys. A 830, 467C–470C (2009). doi: 10.1016/j.nuclphysa.2009.10.041 CrossRefGoogle Scholar
  161. 161.
    A. Monnai, T. Hirano, Effects of bulk viscosity at freezeout. Phys. Rev. C 80, 054906 (2009). doi: 10.1103/PhysRevC.80.054906 CrossRefGoogle Scholar
  162. 162.
    G.S. Denicol, T. Kodama, T. Koide et al., Effect of bulk viscosity on elliptic flow near QCD phase transition. Phys. Rev. C 80, 064901 (2009). doi: 10.1103/PhysRevC.80.064901 CrossRefGoogle Scholar
  163. 163.
    J. Noronha-Hostler, J. Noronha, F. Grassi, Bulk viscosity-driven suppression of shear viscosity effects on the flow harmonics at energies available at the BNL relativistic heavy ion collider. Phys. Rev. C 90, 034907 (2014). doi: 10.1103/PhysRevC.90.034907 CrossRefGoogle Scholar
  164. 164.
    S. Ryu, J.-F. Paquet, C. Shen et al., Importance of the bulk viscosity of QCD in ultrarelativistic heavy-ion collisions. Phys. Rev. Lett. 115, 132301 (2015). doi: 10.1103/PhysRevLett.115.132301 CrossRefGoogle Scholar
  165. 165.
    R.A. Soltz, I. Garishvili, M. Cheng et al., Constraining the initial temperature and shear viscosity in a hybrid hydrodynamic model of \(\sqrt{s_{NN}} \)= 200 GeV Au+Au collisions using pion spectra, elliptic flow, and femtoscopic radii. Phys. Rev. C 87, 044901 (2013). doi: 10.1103/PhysRevC.87.044901 CrossRefGoogle Scholar
  166. 166.
    J.E. Bernhard, P.W. Marcy, C.F. Coleman-Smith et al., Quantifying properties of hot and dense QCD matter through systematic model-to-data comparison. Phys. Rev. C 91, 054910 (2015). doi: 10.1103/PhysRevC.91.054910 CrossRefGoogle Scholar
  167. 167.
    J.E. Bernhard, J.S. Moreland, S.A. Bass et al., 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). doi: 10.1103/PhysRevC.94.024907 CrossRefGoogle Scholar
  168. 168.
    P. Danielewicz, M. Gyulassy, Dissipative phenomena in quark gluon plasmas. Phys. Rev. D 31, 53–62 (1985). doi: 10.1103/PhysRevD.31.53 CrossRefGoogle Scholar
  169. 169.
    G. Policastro, D.T. Son, A.O. Starinets, The shear viscosity of strongly coupled N = 4 supersymmetric Yang–Mills plasma. Phys. Rev. Lett. 87, 081601 (2001). doi: 10.1103/PhysRevLett.87.081601 CrossRefGoogle Scholar
  170. 170.
    P. Kovtun, D.T. Son, A.O. Starinets, Viscosity in strongly interacting quantum field theories from black hole physics. Phys. Rev. Lett. 94, 111601 (2005). doi: 10.1103/PhysRevLett.94.111601 CrossRefGoogle Scholar
  171. 171.
    B. Abelev, J. Adam, D. Adamova, Centrality dependence of \(\pi \), K, p production in Pb–Pb collisions at \(\sqrt{s_{NN}}\) = 2.76 TeV. Phys. Rev. C 88, 044910 (2013). doi: 10.1103/PhysRevC.88.044910 CrossRefGoogle Scholar
  172. 172.
    J. Auvinen, J.E. Bernhard, S.A. Bass, Systematic extraction of QGP properties (2016), arXiv: 1610.00590
  173. 173.
    B. Alver, G. Roland, Collision geometry fluctuations and triangular flow in heavy-ion collisions. Phys. Rev. C 81, 054905 (2010). doi: 10.1103/PhysRevC.82.039903 CrossRefGoogle Scholar
  174. 174.
    A. Adare, S. Afanasiev, C. Aidala et al., Measurements of higher-order flow harmonics in Au+Au collisions at \(\sqrt{s_{NN}} = 200\) GeV. Phys. Rev. Lett. 107, 252301 (2011). doi: 10.1103/PhysRevLett.107.252301 CrossRefGoogle Scholar
  175. 175.
    L. Adamczyk, J.K. Adkins, G. Agakishiev et al., Third harmonic flow of charged particles in Au+Au collisions at \(\sqrt{s_{NN}} = 200\) GeV. Phys. Rev. C 88, 014904 (2013). doi: 10.1103/PhysRevC.88.014904 CrossRefGoogle Scholar
  176. 176.
    A. Adare, C. Aidala, N.N. Ajitanand et al., Harmonic decomposition of two-particle angular correlations in Pb–Pb collisions at \(\sqrt{s_{NN}}=\) 2.76 TeV. Phys. Lett. B 708, 249–264 (2012). doi: 10.1016/j.physletb.2012.01.060 CrossRefGoogle Scholar
  177. 177.
    Y. Zhou, Searches for \(p_{\rm T}\) dependent fluctuations of flow angle and magnitude in Pb–Pb and p–Pb collisions. Nucl. Phys. A 931, 949–953 (2014). doi: 10.1016/j.nuclphysa.2014.08.068 CrossRefGoogle Scholar
  178. 178.
    S.A. Voloshin, A.M. Poskanzer, A.H. Tang et al., Elliptic flow in the Gaussian model of eccentricity fluctuations. Phys. Lett. B 659, 537–541 (2008). doi: 10.1016/j.physletb.2007.11.043 CrossRefGoogle Scholar
  179. 179.
    W. Broniowski, P. Bozek, M. Rybczynski, Fluctuating initial conditions in heavy-ion collisions from the Glauber approach. Phys. Rev. C 76, 054905 (2007). doi: 10.1103/PhysRevC.76.054905 CrossRefGoogle Scholar
  180. 180.
    L. Yan, J.Y. Ollitrault, A.M. Poskanzer, Eccentricity distributions in nucleus–nucleus collisions. Phys. Rev. C 90, 024903 (2014). doi: 10.1103/PhysRevC.90.024903 CrossRefGoogle Scholar
  181. 181.
    Y. Zhou, K. Xiao, Z. Feng et al., Anisotropic distributions in a multiphase transport model. Phys. Rev. C 93, 034909 (2016). doi: 10.1103/PhysRevC.93.034909 CrossRefGoogle Scholar
  182. 182.
    D. Teaney, L. Yan, Event-plane correlations and hydrodynamic simulations of heavy ion collisions. Phys. Rev. C 90, 024902 (2014). doi: 10.1103/PhysRevC.90.024902 CrossRefGoogle Scholar
  183. 183.
    L.G. Pang, G.Y. Qin, V. Roy et al., Longitudinal decorrelation of anisotropic flows in heavy-ion collisions at the CERN large hadron collider. Phys. Rev. C 91, 044904 (2015). doi: 10.1103/PhysRevC.91.044904 CrossRefGoogle Scholar
  184. 184.
    L.G. Pang, H. Petersen, G.Y. Qin et al., Decorrelation of anisotropic flow along the longitudinal direction. Eur. Phys. J. A 52, 97 (2016). doi: 10.1140/epja/i2016-16097-x CrossRefGoogle Scholar
  185. 185.
    K. Xiao, L. Yi, F. Liu et al., Factorization of event-plane correlations over transverse momentum in relativistic heavy ion collisions in a multiphase transport model. Phys. Rev. C 94, 024905 (2016). doi: 10.1103/PhysRevC.94.024905 CrossRefGoogle Scholar
  186. 186.
    G.-L. Ma, Z.-W. Lin, Predictions for \(\sqrt{s_{NN}}=5.02\) TeV Pb+Pb collisions from a multi-phase transport model. Phys. Rev. C 93, 054911 (2016). doi: 10.1103/PhysRevC.93.054911 CrossRefGoogle Scholar
  187. 187.
    Y. Zhou, Review of anisotropic flow correlations in ultrarelativistic heavy-ion collisions. Adv. High Energy Phys. 2016, 9365637 (2016). doi: 10.1155/2016/9365637 CrossRefGoogle Scholar
  188. 188.
    R.S. Bhalerao, J.Y. Ollitrault, S. Pal, Event-plane correlators. Phys. Rev. C 88, 024909 (2013). doi: 10.1103/PhysRevC.88.024909 CrossRefGoogle Scholar
  189. 189.
    J. Schukraft, A. Timmins, S.A. Voloshin, Ultra-relativistic nuclear collisions: event shape engineering. Phys. Lett. B 719, 394–398 (2013). doi: 10.1016/j.physletb.2013.01.045 CrossRefGoogle Scholar
  190. 190.
    D. Teaney, L. Yan, Non linearities in the harmonic spectrum of heavy ion collisions with ideal and viscous hydrodynamics. Phys. Rev. C 86, 044908 (2012). doi: 10.1103/PhysRevC.86.044908 CrossRefGoogle Scholar
  191. 191.
    D. Teaney, L. Yan, Non-linear flow response and reaction plane correlations. Nucl. Phys. A 904–905, 365c–368c (2013). doi: 10.1016/j.nuclphysa.2013.02.025 CrossRefGoogle Scholar
  192. 192.
    R.S. Bhalerao, J.-Y. Ollitrault, S. Pal, Characterizing flow fluctuations with moments. Phys. Lett. B 742, 94–98 (2015). doi: 10.1016/j.physletb.2015.01.019 CrossRefGoogle Scholar
  193. 193.
    L. Yan, J.Y. Ollitrault, \(\nu _{4}, \nu _{5}, \nu _{6}, \nu _{7}\): nonlinear hydrodynamic response versus LHC data. Phys. Lett. B 744, 82–87 (2015). doi: 10.1016/j.physletb.2015.03.040 CrossRefGoogle Scholar
  194. 194.
    Y. Zhou (for the ALICE Collaboration), in Quark Matter (2017)Google Scholar
  195. 195.
    S. Tuo (for the CMS Collaboration), in Quark Matter (2017)Google Scholar
  196. 196.
    W. Adam, T. Bergauer, M. Dragicevic et al., Multiplicity and transverse momentum dependence of two- and four-particle correlations in pPb and PbPb collisions. Phys. Lett. B 724, 213–240 (2013). doi: 10.1016/j.physletb.2013.06.028 CrossRefGoogle Scholar
  197. 197.
    K. Dusling, R. Venugopalan, Azimuthal collimation of long range rapidity correlations by strong color fields in high multiplicity hadron-hadron collisions. Phys. Rev. Lett. 108, 262001 (2012). doi: 10.1103/PhysRevLett.108.262001 CrossRefGoogle Scholar
  198. 198.
    K. Dusling, R. Venugopalan, Evidence for BFKL and saturation dynamics from dihadron spectra at the LHC. Phys. Rev. D 87, 051502 (2013). doi: 10.1103/PhysRevD.87.051502 CrossRefGoogle Scholar
  199. 199.
    K. Dusling, R. Venugopalan, Explanation of systematics of CMS p+Pb high multiplicity di-hadron data at \(\sqrt{s}_{\rm NN} = 5.02\) TeV. Phys. Rev. D 87, 054014 (2013). doi: 10.1103/PhysRevD.87.054014 CrossRefGoogle Scholar
  200. 200.
    K. Dusling, R. Venugopalan, Comparison of the color glass condensate to dihadron correlations in proton–proton and proton–nucleus collisions. Phys. Rev. D 87, 094034 (2013). doi: 10.1103/PhysRevD.87.094034 CrossRefGoogle Scholar
  201. 201.
    K. Dusling, R. Venugopalan, Azimuthal anisotropy from color glass condensates in proton–nucleus collisions. Nucl. Phys. A 931, 283–287 (2014). doi: 10.1016/j.nuclphysa.2014.09.024 CrossRefGoogle Scholar
  202. 202.
    A. Kovner, M. Lublinsky, Angular and long range rapidity correlations in particle production at high energy. Int. J. Mod. Phys. E 22, 1330001 (2013). doi: 10.1142/S0218301313300014 CrossRefGoogle Scholar
  203. 203.
    A. Dumitru, A.V. Giannini, Initial state angular asymmetries in high energy p+A collisions: spontaneous breaking of rotational symmetry by a color electric field and C-odd fluctuations. Nucl. Phys. A 933, 212–228 (2015). doi: 10.1016/j.nuclphysa.2014.10.037 CrossRefGoogle Scholar
  204. 204.
    A. Dumitru, V. Skokov, Anisotropy of the semiclassical gluon field of a large nucleus at high energy. Phys. Rev. D 91, 074006 (2015). doi: 10.1103/PhysRevD.91.074006 CrossRefGoogle Scholar
  205. 205.
    J. Noronha, A. Dumitru, Azimuthal asymmetries in high-energy collisions of protons with holographic shockwaves. Phys. Rev. D 89, 094008 (2014). doi: 10.1103/PhysRevD.89.094008 CrossRefGoogle Scholar
  206. 206.
    A. Bzdak, G.L. Ma, Elliptic and triangular flow in \(p\)+Pb and peripheral Pb+Pb collisions from parton scatterings. Phys. Rev. Lett. 113, 252301 (2014). doi: 10.1103/PhysRevLett.113.252301 CrossRefGoogle Scholar
  207. 207.
    G.L. Ma, A. Bzdak, Long-range azimuthal correlations in proton–proton and proton–nucleus collisions from the incoherent scattering of partons. Phys. Lett. B 739, 209–213 (2014). doi: 10.1016/j.physletb.2014.10.066 CrossRefGoogle Scholar
  208. 208.
    P. Bozek, A. Bzdak, G.L. Ma, Rapidity dependence of elliptic and triangular flow in proton–nucleus collisions from collective dynamics. Phys. Lett. B 748, 301–305 (2015). doi: 10.1016/j.physletb.2015.06.007 CrossRefGoogle Scholar
  209. 209.
    J.D. Orjuela Koop, A. Adare, D. McGlinchey et al., Azimuthal anisotropy relative to the participant plane from a multiphase transport model in central p + Au, d + Au, and \(^{3}\)He + Au collisions at \(\sqrt{s_{NN}}=200\) GeV. Phys. Rev. C 92, 054903 (2015). doi: 10.1103/PhysRevC.92.054903 CrossRefGoogle Scholar
  210. 210.
    H.L. Li, L. He, Z.W. Lin et al., Origin of the mass splitting of azimuthal anisotropies in a multi-phase transport model (2016), arXiv: 1604.07387
  211. 211.
    Y. Zhou, X.R. Zhu, P.F. Li et al., Investigation of possible hadronic flow in \(\sqrt{s_{NN}} = 5.02\) TeV \(p-Pb\) collisions. Phys. Rev. C 91, 064908 (2015). doi: 10.1103/PhysRevC.91.064908 CrossRefGoogle Scholar
  212. 212.
    P.M. Chesler, Colliding shock waves and hydrodynamics in small systems. Phys. Rev. Lett. 115, 241602 (2015). doi: 10.1103/PhysRevLett.115.241602 CrossRefGoogle Scholar
  213. 213.
    P.M. Chesler, How big are the smallest drops of quark–gluon plasma? JHEP 03, 146 (2016). doi: 10.1007/JHEP03(2016)146 MathSciNetCrossRefGoogle Scholar
  214. 214.
    P. Bozek, W. Broniowski, Collective dynamics in high-energy proton–nucleus collisions. Phys. Rev. C 88, 014903 (2013). doi: 10.1103/PhysRevC.88.014903 CrossRefGoogle Scholar
  215. 215.
    H. Mäntysaari, B. Schenke, Evidence of strong proton shape fluctuations from incoherent diffraction. Phys. Rev. Lett. 117, 052301 (2016). doi: 10.1103/PhysRevLett.117.052301 CrossRefGoogle Scholar
  216. 216.
    H. Mantysaari, B. Schenke, Revealing proton shape fluctuations with incoherent diffraction at high energy. Phys. Rev. D 94, 034042 (2016). doi: 10.1103/PhysRevD.94.034042 CrossRefGoogle Scholar
  217. 217.
    A. Adare, C. Aidala, N.N. Ajitanand et al., Quadrupole anisotropy in dihadron azimuthal correlations in central \(d+\)Au collisions at \(\sqrt{s_{NN}} \)  = 200 GeV. Phys. Rev. Lett. 111, 212301 (2013). doi: 10.1103/PhysRevLett.111.212301 CrossRefGoogle Scholar
  218. 218.
    A. Adare, C. Aidala, N.N. Ajitanand et al., Measurement of long-range angular correlation and quadrupole anisotropy of pions and (anti)protons in central \(d+\)Au collisions at \(\sqrt{s_{NN}} \) = 200 GeV. Phys. Rev. Lett. 114, 192301 (2015). doi: 10.1103/PhysRevLett.114.192301 CrossRefGoogle Scholar
  219. 219.
    L. Adamczyk, J.K. Adkins, G. Agakishiev et al., Long-range pseudorapidity dihadron correlations in \(d\)+Au collisions at \(\sqrt{s_{\rm NN}}=200\) GeV. Phys. Lett. B 747, 265–271 (2015). doi: 10.1016/j.physletb.2015.05.075 CrossRefGoogle Scholar
  220. 220.
    A. Adare, S. Afanasiev, C. Aidala et al., Measurements of elliptic and triangular flow in high-multiplicity \(^{3}\)He\(+\)Au collisions at \(\sqrt{s_{NN}}=200\) GeV. Phys. Rev. Lett. 115, 142301 (2015). doi: 10.1103/PhysRevLett.115.142301 CrossRefGoogle Scholar
  221. 221.
    J.D. Orjuela Koop, R. Belmont, P. Yin et al., Exploring the beam energy dependence of flow-like signatures in small system \(d+\)Au collisions. Phys. Rev. C 93, 044910 (2016). doi: 10.1103/PhysRevC.93.044910 CrossRefGoogle Scholar
  222. 222.
    P. Bozek, W. Broniowski, Hydrodynamic modeling of \(^3\)He-Au collisions at \(\sqrt{s_{NN}} \) = 200 GeV. Phys. Lett. B 747, 135–138 (2015). doi: 10.1016/j.physletb.2015.05.068 CrossRefGoogle Scholar
  223. 223.
    P. Romatschke, Light–heavy ion collisions: a window into pre-equilibrium QCD dynamics? Eur. Phys. J. C 75, 305 (2015). doi: 10.1140/epjc/s10052-015-3509-3 CrossRefGoogle Scholar
  224. 224.
    J. Adam, D. Adamov a, M.M. Aggarwal, Two-pion femtoscopy in p–Pb collisions at \(\sqrt{s_{{\rm NN}}}=5.02\) TeV. Phys. Rev. C 91, 034906 (2015). doi: 10.1103/PhysRevC.91.034906 CrossRefGoogle Scholar
  225. 225.
    P. Bozek, Femtoscopy analysis of d–Au interactions at \(\sqrt{s}=200\) GeV. Phys. Rev. C 90, 064913 (2014). doi: 10.1103/PhysRevC.90.064913 CrossRefGoogle Scholar
  226. 226.
    V.M. Shapoval, P. Braun-Munzinger, lu Karpenko, Femtoscopic scales in \(p+p\) and \(p+\)Pb collisions in view of the uncertainty principle. Phys. Lett. B 725, 139–147 (2013). doi: 10.1016/j.physletb.2013.07.002 CrossRefGoogle Scholar
  227. 227.
    H. Niemi, G.S. Denicol, How large is the Knudsen number reached in fluid dynamical simulations of ultrarelativistic heavy ion collisions? (2014), arXiv: 1404.7327
  228. 228.
    B. Schenke, S. Schlichting, R. Venugopalan, Azimuthal anisotropies in p\(+\)Pb collisions from classical YangšCMills dynamics. Phys. Lett. B 747, 76–82 (2015). doi: 10.1016/j.physletb.2015.05.051 CrossRefGoogle Scholar
  229. 229.
    H.L. Li, L. He, Z.W. Lin et al., Origin of the mass splitting of elliptic anisotropy in a multiphase transport model. Phys. Rev. C 93, 051901 (2016). doi: 10.1103/PhysRevC.93.051901 CrossRefGoogle Scholar
  230. 230.
    H. Petersen, M. Bleicher, S.A. Bass et al., UrQMD v2.3: changes and Comparisons (2008), arXiv: 0805.0567
  231. 231.
    P. Romatschke, Collective flow without hydrodynamics: simulation results for relativistic ion collisions. Eur. Phys. J. C 75, 429 (2015). doi: 10.1140/epjc/s10052-015-3646-8 CrossRefGoogle Scholar
  232. 232.
    A. Dumitru, K. Dusling, F. Gelis et al., The Ridge in proton–proton collisions at the LHC. Phys. Lett. B 697, 21–25 (2011). doi: 10.1016/j.physletb.2011.01.024 CrossRefGoogle Scholar
  233. 233.
    E. Levin, A.H. Rezaeian, The Ridge from the BFKL evolution and beyond. Phys. Rev. D 84, 034031 (2011). doi: 10.1103/PhysRevD.84.034031 CrossRefGoogle Scholar
  234. 234.
    P. Tribedy, R. Venugopalan, QCD saturation at the LHC: comparisons of models to p + p and A + A data and predictions for p + Pb collisions. Phys. Lett. B 710, 125–133 (2012). doi: 10.1016/j.physletb.2012.02.047 CrossRefGoogle Scholar
  235. 235.
    P. Bozek, Elliptic flow in proton–proton collisions at \(\sqrt{S} = 7\) TeV. Eur. Phys. J. C 71, 1530 (2011). doi: 10.1140/epjc/s10052-010-1530-0 CrossRefGoogle Scholar
  236. 236.
    K. Werner, lu Karpenko, T. Pierog, The `Ridge’ in proton–proton scattering at 7 TeV. Phys. Rev. Lett. 106, 122004 (2011). doi: 10.1103/PhysRevLett.106.122004 CrossRefGoogle Scholar
  237. 237.
    B. Schenke, S. Schlichting, P. Tribedy et al., Mass ordering of spectra from fragmentation of saturated gluon states in high multiplicity proton–proton collisions. Phys. Rev. Lett. 117, 162301 (2016). doi: 10.1103/PhysRevLett.117.162301 CrossRefGoogle Scholar
  238. 238.
    A. Milov (for the ATLAS Collaboration), in Hard Probe (2016)Google Scholar
  239. 239.
    K. Gajdosova (for the ALICE Collaboration), in Quark Matter (2017)Google Scholar
  240. 240.
    M. Zhou (for the ATLAS Collaboration), in Quark Matter (2017)Google Scholar
  241. 241.
    J. Jia, M. Zhou, A. Trzupek, arXiv:1701.03830 [nucl-th] (2017)
  242. 242.
    M. Guilbaud (for the CMS Collaboration), in Quark Matter (2017)Google Scholar

Copyright information

© Shanghai Institute of Applied Physics, Chinese Academy of Sciences, Chinese Nuclear Society, Science Press China and Springer Science+Business Media Singapore 2017

Authors and Affiliations

  • Huichao Song
    • 1
    • 2
    • 3
  • You Zhou
    • 4
  • Katarína Gajdošová
    • 4
  1. 1.Department of Physics and State Key Laboratory of Nuclear Physics and TechnologyPeking UniversityBeijingChina
  2. 2.Collaborative Innovation Center of Quantum MatterBeijingChina
  3. 3.Center for High Energy PhysicsPeking UniversityBeijingChina
  4. 4.Niels Bohr InstituteUniversity of CopenhagenCopenhagenDenmark

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