Skip to main content

Non-linear flow modes of identified particles in Pb-Pb collisions at \( \sqrt{s_{\mathrm{NN}}} \) = 5.02 TeV

A preprint version of the article is available at arXiv.

Abstract

The pT-differential non-linear flow modes, v4,22, v5,32, v6,33 and v6,222 for π±, K±, \( {\mathrm{K}}_{\mathrm{S}}^0 \) , p + \( \overline{\mathrm{p}} \), Λ + \( \overline{\Lambda} \) and ϕ-meson have been measured for the first time at \( \sqrt{s_{\mathrm{NN}}} \) = 5.02 TeV in Pb-Pb collisions with the ALICE detector at the Large Hadron Collider. The results were obtained with a multi-particle technique, correlating the identified hadrons with reference charged particles from a different pseudorapidity region. These non-linear observables probe the contribution from the second and third order initial spatial anisotropy coefficients to higher flow harmonics. All the characteristic features observed in previous pT-differential anisotropic flow measurements for various particle species are also present in the non-linear flow modes, i.e. increase of magnitude with increasing centrality percentile, mass ordering at low pT and particle type grouping in the intermediate pT range. Hydrodynamical calculations (iEBE-VISHNU) that use different initial conditions and values of shear and bulk viscosity to entropy density ratios are confronted with the data at low transverse momenta. These calculations exhibit a better agreement with the anisotropic flow coefficients than the non-linear flow modes. These observations indicate that non-linear flow modes can provide additional discriminatory power in the study of initial conditions as well as new stringent constraints to hydrodynamical calculations.

References

  1. S. Borsányi et al., The QCD equation of state with dynamical quarks, JHEP 11 (2010) 077 [arXiv:1007.2580] [INSPIRE].

  2. T. Bhattacharya et al., QCD Phase Transition with Chiral Quarks and Physical Quark Masses, Phys. Rev. Lett. 113 (2014) 082001 [arXiv:1402.5175] [INSPIRE].

  3. E.V. Shuryak, Theory and phenomenology of the QCD vacuum, Phys. Rept. 115 (1984) 151 [INSPIRE].

    ADS  Article  Google Scholar 

  4. J. Cleymans, R.V. Gavai and E. Suhonen, Quarks and Gluons at High Temperatures and Densities, Phys. Rept. 130 (1986) 217 [INSPIRE].

    ADS  Article  Google Scholar 

  5. S.A. Bass, M. Gyulassy, H. Stoecker and W. Greiner, Signatures of quark gluon plasma formation in high-energy heavy ion collisions: A Critical review, J. Phys. G 25 (1999) R1 [hep-ph/9810281] [INSPIRE].

  6. M. Miller and R. Snellings, Eccentricity fluctuations and its possible effect on elliptic flow measurements, nucl-ex/0312008 [INSPIRE].

  7. R.S. Bhalerao and J.-Y. Ollitrault, Eccentricity fluctuations and elliptic flow at RHIC, Phys. Lett. B 641 (2006) 260 [nucl-th/0607009] [INSPIRE].

  8. PHOBOS collaboration, Importance of correlations and fluctuations on the initial source eccentricity in high-energy nucleus-nucleus collisions, Phys. Rev. C 77 (2008) 014906 [arXiv:0711.3724] [INSPIRE].

  9. B. Alver and G. Roland, Collision geometry fluctuations and triangular flow in heavy-ion collisions, Phys. Rev. C 81 (2010) 054905 [Erratum ibid. C 82 (2010) 039903] [arXiv:1003.0194] [INSPIRE].

  10. B.H. Alver, C. Gombeaud, M. Luzum and J.-Y. Ollitrault, Triangular flow in hydrodynamics and transport theory, Phys. Rev. C 82 (2010) 034913 [arXiv:1007.5469] [INSPIRE].

  11. PHOBOS collaboration, System size, energy and pseudorapidity dependence of directed and elliptic flow at RHIC, Nucl. Phys. A 774 (2006) 523 [nucl-ex/0510031] [INSPIRE].

  12. S.A. Voloshin, Toward the energy and the system size dependece of elliptic flow: Working on flow fluctuations, in 22nd Winter Workshop on Nuclear Dynamics (WWND 2006) La Jolla, California, March 11-19, 2006, 2006, nucl-th/0606022 [INSPIRE].

  13. ALICE collaboration, Centrality dependence of the charged-particle multiplicity density at midrapidity in Pb-Pb collisions at \( \sqrt{s_{\mathrm{NN}}} \)= 5.02 TeV, Phys. Rev. Lett. 116 (2016) 222302 [arXiv:1512.06104] [INSPIRE].

  14. S. Voloshin and Y. Zhang, Flow study in relativistic nuclear collisions by Fourier expansion of Azimuthal particle distributions, Z. Phys. C 70 (1996) 665 [hep-ph/9407282] [INSPIRE].

  15. STAR collaboration, Particle type dependence of azimuthal anisotropy and nuclear modification of particle production in Au + Au collisions at \( \sqrt{s_{\mathrm{NN}}} \) = 200 GeV, Phys. Rev. Lett. 92 (2004) 052302 [nucl-ex/0306007] [INSPIRE].

  16. STAR collaboration, Mass, quark-number and \( \sqrt{s_{NN}} \)dependence of the second and fourth flow harmonics in ultra-relativistic nucleus-nucleus collisions, Phys. Rev. C 75 (2007) 054906 [nucl-ex/0701010] [INSPIRE].

  17. PHENIX collaboration, Elliptic flow of identified hadrons in Au+Au collisions at \( \sqrt{s_{\mathrm{NN}}} \) = 200 GeV, Phys. Rev. Lett. 91 (2003) 182301 [nucl-ex/0305013] [INSPIRE].

  18. PHENIX collaboration, Scaling properties of azimuthal anisotropy in Au+Au and Cu+Cu collisions at \( \sqrt{s_{\mathrm{NN}}} \) = 200 GeV, Phys. Rev. Lett. 98 (2007) 162301 [nucl-ex/0608033] [INSPIRE].

  19. PHOBOS collaboration, Event-by-Event Fluctuations of Azimuthal Particle Anisotropy in Au + Au Collisions at \( \sqrt{s_{NN}} \) = 200 GeV, Phys. Rev. Lett. 104 (2010) 142301 [nucl-ex/0702036] [INSPIRE].

  20. PHENIX collaboration, Flow measurements via two particle azimuthal correlations in Au+Au collisions at \( \sqrt{s_{\mathrm{NN}}} \) = 130 GeV, Phys. Rev. Lett. 89 (2002) 212301 [nucl-ex/0204005] [INSPIRE].

  21. STAR collaboration, Elliptic flow of identified hadrons in Au+Au collisions at \( \sqrt{s_{NN}} \) = 7.762.4 GeV, Phys. Rev. C 88 (2013) 014902 [arXiv:1301.2348] [INSPIRE].

  22. PHENIX collaboration, Saturation of azimuthal anisotropy in Au + Au collisions at \( \sqrt{s_{\mathrm{NN}}} \) = 62 GeV to 200 GeV, Phys. Rev. Lett. 94 (2005) 232302 [nucl-ex/0411040] [INSPIRE].

  23. PHENIX collaboration, Systematic Studies of Elliptic Flow Measurements in Au+Au Collisions at \( \sqrt{s} \) = 200 GeV, Phys. Rev. C 80 (2009) 024909 [arXiv:0905.1070] [INSPIRE].

  24. PHENIX collaboration, Measurements of Higher-Order Flow Harmonics in Au+Au Collisions at \( \sqrt{s_{NN}} \) = 200 GeV, Phys. Rev. Lett. 107 (2011) 252301 [arXiv:1105.3928] [INSPIRE].

  25. STAR collaboration, Elliptic flow in Au + Au collisions at \( \sqrt{s_{\mathrm{NN}}} \) = 130 GeV, Phys. Rev. Lett. 86 (2001) 402 [nucl-ex/0009011] [INSPIRE].

  26. STAR collaboration, Identified particle elliptic flow in Au + Au collisions at \( \sqrt{s_{\mathrm{NN}}} \) = 130 GeV, Phys. Rev. Lett. 87 (2001) 182301 [nucl-ex/0107003] [INSPIRE].

  27. STAR collaboration, Azimuthal anisotropy and correlations in the hard scattering regime at RHIC, Phys. Rev. Lett. 90 (2003) 032301 [nucl-ex/0206006] [INSPIRE].

  28. STAR collaboration, Elliptic flow from two and four particle correlations in Au+Au collisions at \( \sqrt{s_{\mathrm{NN}}} \) = 130 GeV, Phys. Rev. C 66 (2002) 034904 [nucl-ex/0206001] [INSPIRE].

  29. STAR collaboration, Azimuthal anisotropy at RHIC: The First and fourth harmonics, Phys. Rev. Lett. 92 (2004) 062301 [nucl-ex/0310029] [INSPIRE].

  30. STAR collaboration, Azimuthal anisotropy and correlations at large transverse momenta in p+p and Au+Au collisions at \( \sqrt{s_{\mathrm{NN}}} \) = 200 GeV, Phys. Rev. Lett. 93 (2004) 252301 [nucl-ex/0407007] [INSPIRE].

  31. STAR collaboration, Azimuthal anisotropy in Au+Au collisions at \( \sqrt{s_{\mathrm{NN}}} \) = 200 GeV, Phys. Rev. C 72 (2005) 014904 [nucl-ex/0409033] [INSPIRE].

  32. ALICE collaboration, Elliptic flow of charged particles in Pb-Pb collisions at 2.76 TeV, Phys. Rev. Lett. 105 (2010) 252302 [arXiv:1011.3914] [INSPIRE].

  33. ALICE collaboration, Higher harmonic anisotropic flow measurements of charged particles in Pb-Pb collisions at \( \sqrt{s_{NN}} \) = 2.76 TeV, Phys. Rev. Lett. 107 (2011) 032301 [arXiv:1105.3865] [INSPIRE].

  34. ALICE collaboration, Anisotropic flow of charged hadrons, pions and (anti-)protons measured at high transverse momentum in Pb-Pb collisions at \( \sqrt{s_{NN}} \) = 2.76 TeV, Phys. Lett. B 719 (2013) 18 [arXiv:1205.5761] [INSPIRE].

  35. CMS collaboration, Azimuthal anisotropy of charged particles at high transverse momenta in PbPb collisions at \( \sqrt{s_{NN}} \) = 2.76 TeV, Phys. Rev. Lett. 109 (2012) 022301 [arXiv:1204.1850] [INSPIRE].

  36. CMS collaboration, Measurement of the elliptic anisotropy of charged particles produced in PbPb collisions at \( \sqrt{s_{NN}} \) = 2.76 TeV, Phys. Rev. C 87 (2013) 014902 [arXiv:1204.1409] [INSPIRE].

  37. ATLAS collaboration, Measurement of the pseudorapidity and transverse momentum dependence of the elliptic flow of charged particles in lead-lead collisions at \( \sqrt{s_{NN}} \) = 2.76 TeV with the ATLAS detector, Phys. Lett. B 707 (2012) 330 [arXiv:1108.6018] [INSPIRE].

  38. ATLAS collaboration, 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 (2012) 014907 [arXiv:1203.3087] [INSPIRE].

  39. ALICE collaboration, Elliptic flow of identified hadrons in Pb-Pb collisions at \( \sqrt{s_{\mathrm{NN}}} \) = 2.76 TeV, JHEP 06 (2015) 190 [arXiv:1405.4632] [INSPIRE].

  40. ALICE collaboration, Higher harmonic flow coefficients of identified hadrons in Pb-Pb collisions at \( \sqrt{s_{\mathrm{NN}}} \) = 2.76 TeV, JHEP 09 (2016) 164 [arXiv:1606.06057] [INSPIRE].

  41. ALICE collaboration, Anisotropic flow of charged particles in Pb-Pb collisions at \( \sqrt{s_{\mathrm{NN}}} \) = 5.02 TeV, Phys. Rev. Lett. 116 (2016) 132302 [arXiv:1602.01119] [INSPIRE].

  42. ALICE collaboration, Anisotropic flow of identified particles in Pb-Pb collisions at \( \sqrt{s_{\mathrm{NN}}} \) = 5.02 TeV, JHEP 09 (2018) 006 [arXiv:1805.04390] [INSPIRE].

  43. CMS collaboration, Measurement of Higher-Order Harmonic Azimuthal Anisotropy in PbPb Collisions at \( \sqrt{s_{NN}} \) = 2.76 TeV, Phys. Rev. C 89 (2014) 044906 [arXiv:1310.8651] [INSPIRE].

  44. ALICE collaboration, Event shape engineering for inclusive spectra and elliptic flow in Pb-Pb collisions at \( \sqrt{s_{\mathrm{NN}}} \) = 2.76 TeV, Phys. Rev. C 93 (2016) 034916 [arXiv:1507.06194] [INSPIRE].

  45. ALICE collaboration, Energy dependence and fluctuations of anisotropic flow in Pb-Pb collisions at \( \sqrt{s_{\mathrm{NN}}} \) = 5.02 and 2.76 TeV, JHEP 07 (2018) 103 [arXiv:1804.02944] [INSPIRE].

  46. ALICE collaboration, Anisotropic flow in Xe-Xe collisions at \( \sqrt{s_{\mathrm{NN}}} \) = 5.44 TeV, Phys. Lett. B 784 (2018) 82 [arXiv:1805.01832] [INSPIRE].

  47. P. Kovtun, D.T. Son and A.O. Starinets, Viscosity in strongly interacting quantum field theories from black hole physics, Phys. Rev. Lett. 94 (2005) 111601 [hep-th/0405231] [INSPIRE].

    ADS  Article  Google Scholar 

  48. H. Niemi, K.J. Eskola, R. Paatelainen and K. Tuominen, Predictions for 5.023 TeV Pb+Pb collisions at the CERN Large Hadron Collider, Phys. Rev. C 93 (2016) 014912 [arXiv:1511.04296] [INSPIRE].

  49. D. Teaney and L. Yan, Triangularity and Dipole Asymmetry in Heavy Ion Collisions, Phys. Rev. C 83 (2011) 064904 [arXiv:1010.1876] [INSPIRE].

  50. D. Teaney and L. Yan, Event-plane correlations and hydrodynamic simulations of heavy ion collisions, Phys. Rev. C 90 (2014) 024902 [arXiv:1312.3689] [INSPIRE].

  51. J. Qian, U. Heinz, R. He and L. Huo, Differential flow correlations in relativistic heavy-ion collisions, Phys. Rev. C 95 (2017) 054908 [arXiv:1703.04077] [INSPIRE].

  52. R.S. Bhalerao, J.-Y. Ollitrault and S. Pal, Characterizing flow fluctuations with moments, Phys. Lett. B 742 (2015) 94 [arXiv:1411.5160] [INSPIRE].

    ADS  Article  Google Scholar 

  53. L. Yan and J.-Y. Ollitrault, ν4, ν5, ν6, ν7: nonlinear hydrodynamic response versus LHC data, Phys. Lett. B 744 (2015) 82 [arXiv:1502.02502] [INSPIRE].

  54. ALICE collaboration, Linear and non-linear flow modes in Pb-Pb collisions at \( \sqrt{s_{\mathrm{NN}}} \) = 2.76 TeV, Phys. Lett. B 773 (2017) 68 [arXiv:1705.04377] [INSPIRE].

  55. ALICE collaboration, Systematic studies of correlations between different order flow harmonics in Pb-Pb collisions at \( \sqrt{s_{\mathrm{NN}}} \) = 2.76 TeV, Phys. Rev. C 97 (2018) 024906 [arXiv:1709.01127] [INSPIRE].

  56. S.A. Voloshin, A.M. Poskanzer and R. Snellings, Collective phenomena in non-central nuclear collisions, Landolt-Bornstein 23 (2010) 293 [arXiv:0809.2949] [INSPIRE].

    ADS  Google Scholar 

  57. S.A. Voloshin, Transverse radial expansion and directed flow, Phys. Rev. C 55 (1997) R1630 [nucl-th/9611038] [INSPIRE].

  58. P. Huovinen, P.F. Kolb, U.W. Heinz, P.V. Ruuskanen and S.A. Voloshin, Radial and elliptic flow at RHIC: Further predictions, Phys. Lett. B 503 (2001) 58 [hep-ph/0101136] [INSPIRE].

  59. S.A. Voloshin, Anisotropic flow, Nucl. Phys. A 715 (2003) 379 [nucl-ex/0210014] [INSPIRE].

  60. D. Molnar and S.A. Voloshin, Elliptic flow at large transverse momenta from quark coalescence, Phys. Rev. Lett. 91 (2003) 092301 [nucl-th/0302014] [INSPIRE].

  61. PHENIX collaboration, Deviation from quark-number scaling of the anisotropy parameter v2 of pions, kaons and protons in Au+Au collisions at \( \sqrt{s_{NN}} \) = 200 GeV, Phys. Rev. C 85 (2012) 064914 [arXiv:1203.2644] [INSPIRE].

  62. X. Zhu, Y. Zhou, H. Xu and H. Song, Correlations of flow harmonics in 2.76A TeV Pb-Pb collisions, Phys. Rev. C 95 (2017) 044902 [arXiv:1608.05305] [INSPIRE].

  63. ALICE collaboration, The ALICE experiment at the CERN LHC, 2008 JINST 3 S08002.

  64. ALICE collaboration, Performance of the ALICE Experiment at the CERN LHC, Int. J. Mod. Phys. A 29 (2014) 1430044 [arXiv:1402.4476] [INSPIRE]

  65. ALICE collaboration, Charged-particle multiplicity density at mid-rapidity in central Pb-Pb collisions at \( \sqrt{s_{NN}} \) = 2.76 TeV, Phys. Rev. Lett. 105 (2010) 252301 [arXiv:1011.3916] [INSPIRE].

  66. J. Alme et al., The ALICE TPC, a large 3-dimensional tracking device with fast readout for ultra-high multiplicity events, Nucl. Instrum. Meth. A 622 (2010) 316 [arXiv:1001.1950] [INSPIRE].

    ADS  Article  Google Scholar 

  67. ALICE collaboration, Performance of the ALICE VZERO system, 2013 JINST 8 P10016 [arXiv:1306.3130] [INSPIRE].

  68. ALICE collaboration, Centrality determination of Pb-Pb collisions at \( \sqrt{s_{NN}} \) = 2.76 TeV with ALICE, Phys. Rev. C 88 (2013) 044909 [arXiv:1301.4361] [INSPIRE].

  69. P. Billoir, Track Fitting With Multiple Scattering: A New Method, Nucl. Instrum. Meth. A 225 (1984) 352 [INSPIRE].

    Article  Google Scholar 

  70. P. Billoir, R. Fruhwirth and M. Regler, Track element merging strategy and vertex fitting in complex modular detectors, Nucl. Instrum. Meth. A 241 (1985) 115 [INSPIRE].

    ADS  Article  Google Scholar 

  71. ALICE collaboration, Centrality dependence of π, K, p production in Pb-Pb collisions at \( \sqrt{s_{NN}} \) = 2.76 TeV, Phys. Rev. C 88 (2013) 044910 [arXiv:1303.0737] [INSPIRE].

  72. Particle Data Group collaboration, Review of particle physics, Phys. Rev. D 98 (2018) 030001 [INSPIRE].

  73. J. Podolanski and R. Armenteros, III. Analysis of V-events, London Edinburgh Dublin Philos. Mag. J. Sci. 45 (1954) 13.

    Article  Google Scholar 

  74. ALICE collaboration, Particle identification in ALICE: a Bayesian approach, Eur. Phys. J. Plus 131 (2016) 168 [arXiv:1602.01392] [INSPIRE].

  75. A. Bilandzic, C.H. Christensen, K. Gulbrandsen, A. Hansen and Y. Zhou, Generic framework for anisotropic flow analyses with multiparticle azimuthal correlations, Phys. Rev. C 89 (2014) 064904 [arXiv:1312.3572] [INSPIRE].

  76. V. Pacik, Investigation of azimuthal anisotropy using multi-particle correlations of identified hadrons at the LHC with ALICE detector, Ph.D. Thesis, Copenhagen University, Copenhagen Denmark (2020), CERN-THESIS-2020-007 (2020).

  77. R. Barlow, Systematic errors: Facts and fictions, in Advanced Statistical Techniques in Particle Physics. Proceedings of Conference, Durham U.K. (2002), pg. 134, http://www.ippp.dur.ac.uk/Workshops/02/statistics/proceedings//barlow.pdf [hep-ex/0207026] [INSPIRE].

  78. C. Shen, U. Heinz, P. Huovinen and H. Song, Radial and elliptic flow in Pb+Pb collisions at the Large Hadron Collider from viscous hydrodynamic, Phys. Rev. C 84 (2011) 044903 [arXiv:1105.3226] [INSPIRE].

  79. H.-j. Xu, Z. Li and H. Song, High-order flow harmonics of identified hadrons in 2.76A TeV Pb+Pb collisions, Phys. Rev. C 93 (2016) 064905 [arXiv:1602.02029] [INSPIRE].

  80. S. McDonald, C. Shen, F. Fillion-Gourdeau, S. Jeon and C. Gale, Hydrodynamic predictions for Pb+Pb collisions at 5.02 TeV, Phys. Rev. C 95 (2017) 064913 [arXiv:1609.02958] [INSPIRE].

  81. W. Zhao, H.-j. Xu and H. Song, Collective flow in 2.76A TeV and 5.02A TeV Pb+Pb collisions, Eur. Phys. J. C 77 (2017) 645 [arXiv:1703.10792] [INSPIRE].

  82. C. Shen, Z. Qiu, H. Song, J. Bernhard, S. Bass and U. Heinz, The iEBE-VISHNU code package for relativistic heavy-ion collisions, Comput. Phys. Commun. 199 (2016) 61 [arXiv:1409.8164] [INSPIRE].

    ADS  MathSciNet  Article  Google Scholar 

  83. H. Song, S.A. Bass and U. Heinz, Viscous QCD matter in a hybrid hydrodynamic+Boltzmann approach, Phys. Rev. C 83 (2011) 024912 [arXiv:1012.0555] [INSPIRE].

  84. H. Song and U.W. Heinz, Suppression of elliptic flow in a minimally viscous quark-gluon plasma, Phys. Lett. B 658 (2008) 279 [arXiv:0709.0742] [INSPIRE].

    ADS  Article  Google Scholar 

  85. Z.-W. Lin, C.M. Ko, B.-A. Li, B. Zhang and S. Pal, A Multi-phase transport model for relativistic heavy ion collisions, Phys. Rev. C 72 (2005) 064901 [nucl-th/0411110] [INSPIRE].

  86. J.S. Moreland, J.E. Bernhard and S.A. Bass, Alternative ansatz to wounded nucleon and binary collision scaling in high-energy nuclear collisions, Phys. Rev. C 92 (2015) 011901 [arXiv:1412.4708] [INSPIRE].

  87. J.E. Bernhard, J.S. Moreland, S.A. Bass, J. Liu and U. 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 (2016) 024907 [arXiv:1605.03954] [INSPIRE].

Download references

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

Author information

Authors and Affiliations

Authors