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Perfect Fluidity of the Quark Gluon Plasma in Relativistic Heavy Ion Collisions

Perfect Fluidity of the Quark Gluon Plasma in Relativistic Heavy Ion Collisions. Tetsufumi Hirano Department of Physics, the University of Tokyo hirano @ phys.s.u-tokyo.ac.jp http://tkynt2.phys.s.u-tokyo.ac.jp/~hirano/. KEK-CPWS-HEAP2009. Introduction

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Perfect Fluidity of the Quark Gluon Plasma in Relativistic Heavy Ion Collisions

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  1. Perfect Fluidity of the Quark Gluon Plasma in Relativistic Heavy Ion Collisions Tetsufumi Hirano Department of Physics, the University of Tokyo hirano @ phys.s.u-tokyo.ac.jp http://tkynt2.phys.s.u-tokyo.ac.jp/~hirano/ KEK-CPWS-HEAP2009

  2. Introduction Quark gluon plasma and relativistic heavy ion collisions Time evolution of heavy ion collisions Transverse collective flow Radial flow Elliptic flow Current status of dynamical modeling in heavy ion collisions Summary and Outlook OUTLINE

  3. Where was the Quark Gluon Plasma? History of the Universe History of the matter Nucleosynthesis Hadronization Quark Gluon Plasma (after micro seconds of Big Bang)

  4. Recipes for Quark Gluon Plasma How are colored particles set free from confinement? Compress Heat up hadronic many body system Figure adopted from http://www.bnl.gov/rhic/QGP.htm

  5. Little Bang! front view Relativistic Heavy Ion Collider(2000-) RHIC as a time machine! STAR side view STAR Collision energy Multiple production (N~5000) Heat 100 GeV per nucleon Au(197×100)+Au(197×100)

  6. Big Bang vs. Little Bang beam axis Nearly 1D Hubble expansion* + 2D transverse expansion 3D Hubble expansion Figure adopted from http://www-utap.phys.s.u-tokyo.ac.jp/~sato/index-j.htm *Bjorken(’83)

  7. Big Bang vs. Little Bang  Local thermalization of the QGP is non-trivial in H.I.C. • Collective flow is a key to check whether local thermalization is achieved. See, e.g., Yagi, Hatsuda, Miake, Quark-Gluon Plasma (Cambridge, 2005)

  8. Dynamics of Heavy Ion Collisions Freezeout “Re-confinement” Expansion, cooling Thermalization First contact (two bunches of gluons) Temperature scale 100MeV~1012K Time scale 10fm/c~10-23sec

  9. Jargon: Centrality “Centrality” characterizes a collision and categorizes events. central event peripheral event Participant-Spectator picture is valid

  10. How to Quantify Centrality Npart and Ncoll 197Au+197Au Npart: The number of participants Ncoll: The number of binary collisions Npart and Ncoll as a function of impact parameter PHENIX: Correlation btw. BBC and ZDC signals

  11. Estimated Energy Density at RHIC Well above ec from lattice simulations in central collision at RHIC ec from lattice PHENIX(’05)

  12. M.Cheng et al., PRD77,014511 (’08) QGP from the 1st Principle • Equation of state from lattice QCD • A large number of d.o.f. are freed around Tc. • Pseudo-critical temperature Tc: ~150-200 MeV • Typical energy density scale of transition : ~1 GeV/fm3 • Not available for time evolution

  13. Transverse* Collective Flow * “Transverse”: a direction perpendicular to the collision axis.

  14. Radial Flow (Azimuthally Averaged Flow) Blast wave model (thermal+boost) Driving force of flow pressure gradient In general, flow is sensitive to EOS Inside: high pressure Outside: vacuum (P=0) Sollfrank et al.(’93)

  15. Blue-Shifted Spectra p p Au d Au Au pp & dAu: Power-law Au+Au: Convex to Power law O.Barannikova, talk at QM05 Consistent with the thermal+boost picture

  16. What is Elliptic Flow? Ollitrault (’92) How does the system respond to spatial anisotropy? No secondary interaction Hydro behavior y f x INPUT Spatial Anisotropy 2v2 Interaction among produced particles dN/df dN/df OUTPUT Momentum Anisotropy f 0 2p f 0 2p

  17. Time Evolution of v2 from a Parton Cascade Model Zhang et al.(’99) ideal hydro limit v2 : Ideal hydro : strongly interacting system b = 7.5fm t(fm/c) generated through secondary collisions saturated in the early stage sensitive to cross section (~1/m.f.p.~1/viscosity) v2 is

  18. Arrival at Hydrodynamic Limit y x Experimental data reach hydrodynamic limit curve for the first time at RHIC.

  19. Current Status of Dynamical Modeling In Relativistic Heavy Ion Collisions

  20. Strategy to Attack QGP Problem • The first principle (QuantumChromo Dynamics) • Inputs to phenomenology (lattice QCD) Complexity of QCD Non-linear interactions of gluons Strong coupling Many body system Color confinement • Phenomenology (hydrodynamics) • Experimental data • @ Relativistic Heavy Ion Collider • 200+ papers from 4 collaborations • since 2000

  21. 3D Ideal Hydro Simulation in Au+Au Collisions with b=7.2fm @ 100 GeV/n Higher quality animation is available at Caveat: Camera angle keeps changing.

  22. … 20-30% 10-20% 0-10% Multi-Module Modeling (1) hadron gas • Initial condition • Glauber • Color Glass Condensate • EPOS time QGP fluid collision axis 0 Au Au H.J.Drescher and Y.Nara (2007), K.Werner et al.(2006)

  23. Details of Initial Conditions • Glauber model • Conventional initial • conditions • Announcement of • discovery was made • in comparison of • results from Glauber • with data. • Initial entropy • distribution is prop. • to Npart • Color Glass • Condensate • Natural picture • based on QCD • at very high collision • energies. • EPOS • Phenomenological • implication of parton • ladder ~ string. • Application to air • shower simulation • for high energy • cosmic rays.

  24. Multi-Module Modeling (2) hadron gas • Ideal Hydrodynamics* • Initial time 0.6fm/c • Model EoS • lattice-based# • 1st order time QGP fluid collision axis 0 Au Au *T.Hirano(2002), #Lattice part : M.Cheng et al. (2008)

  25. Relativistic Hydrodynamic Equations for a Perfect Fluid e : energy density, P : pressure, : four velocity Energy Momentum Baryon number

  26. Multi-Module Modeling (3) hadron gas • Hadronic afterburner • Hadronic transport • model (JAM, UrQMD) • Kinetic theory of • hadron gases including • all resonances • Switching temperature • T=160 MeV (169MeV) time QGP fluid collision axis 0 Au Au

  27. Transverse Plane Kinetic evolution of hadron gas y x Perfect fluid evolution of QGP Initial condition QGP fluid surrounded by hadron gas

  28. pT Spectra for Pions and Protons Glauber/CGC + Ideal Hydro + JAM Hybrid model works well up to pT~1.5 GeV/c (1st order, dotted) and 2-3 GeV/c (lattice-based, solid)

  29. TH et al. (’06). Centrality Dependence of Elliptic Flow • Discovery of “Large” v2 at RHIC • v2 data are comparable with (naive) hydro results for the first time. • Hadronic cascade models cannot reproduce data. • This is the first time for ideal • hydro at work in H.I.C. •  Strong motivation to develop hydro-based analysis tools. Glauber + Ideal Hydro Result from a hadronic cascade (JAM) (Courtesy of M.Isse)

  30. TH et al, (in prepation) Centrality Dependence of Elliptic Flow 197Au+197Au 63Cu+63Cu Glauber/CGC + Ideal Hydro + JAM • 1st order phase transition is unlikely from data since • viscosity reduces v2 largely. • How perfect?  Depends on initial model.

  31. Effects of Viscosity • A tiny kinetic viscosity • leads to large reduction • of elliptic flow coefficients. • Elliptic flow is sufficiently • sensitive to constrain EoS, • transport coefficients, and • initial conditions. Glauber + Viscous Hydro Figure taken from M.Luzum and P.Romatschke, arXiv:0804.4015

  32. Pseudorapidity Dependence of Elliptic Flow Coefficient QGP fluid+hadron gas QGP+hadron fluids QGP only T.Hirano et al.,Phys.Lett.B636(2006)299. Not boost invariant Suppression in forward and backward rapidity

  33. pT Dependence of Elliptic Flow Au+Au 200 GeV • Glauber+ Ideal hydro with • lattice(-motivated) EoS + • hadronic cascade • Viscosity would be needed for • better description.

  34. Results from EPOS Initial Conditions K.Werner et al. (2009) EPOS + Ideal Hydro + UrQMD Reasonably reproduce rapidity dependence

  35. Summary & Outlook • Elliptic flow pattern observed at RHIC is described reasonably well by hydro-based models. • Hydro model at work for the first time in H.I.C. • Hadron-based kinetic theory cannot reproduce flow pattern. • Systematic studies are undergoing: • Effects of viscosity  Constraint of EOS and transport coefficients • Understanding of initial pre-thermalization stage

  36. TH(’02); TH and K.Tsuda(’02); TH et al. (’06). Pseudorapidity Dependence of v2 QGP+hadron • v2 data are comparable with hydro results again around h=0 • Not a QGP gas  sQGP • Nevertheless, large discrepancy in forward/backward rapidity • See next slides QGP only h=0 h<0 h>0

  37. T.Hirano and M.Gyulassy,Nucl.Phys.A769 (2006)71. Hadron Gas Instead of Hadron Fluid A QGP fluid surrounded by hadronic gas “Reynolds number” QGP core Matter proper part: (shear viscosity) (entropy density) big in Hadron small in QGP QGP: Liquid (hydro picture) Hadron: Gas (particle picture)

  38. Importance of Hadronic “Corona” • Boltzmann Eq. for hadrons instead of hydrodynamics • Including viscosity through finite mean free path QGP fluid+hadron gas QGP+hadron fluids QGP only • Suggesting rapid increase of entropy density • Deconfinement makes hydro work at RHIC!? •  Signal of QGP!? T.Hirano et al.,Phys.Lett.B636(2006)299.

  39. Sensitivity to Initial Conditions Novel initial conditions from “Color Glass Condensate” lead to large eccentricity. Hirano and Nara(’04), Hirano et al.(’06) Kuhlman et al.(’06), Drescher et al.(’06) Need viscosity even in QGP!

  40. How to Quantify Centrality y Thickness function: Gold nucleus: r0=0.17 fm-3 R=1.12A1/3-0.86A-1/3 d=0.54 fm x Woods-Saxon nuclear density: # of binary collisions # of participants sin = 42mb @200GeV 1－（survival probability）

  41. Parton Distribution in Proton at Small x • Gluons are dominant at small x. • Small x = High energy • Hadron/Nucleus as a bunch of gluons at high energy x 20!! Bjorken x ~ Fraction of longitudinal momentum in proton Kinematics in gg g

  42. Interplay btw. Emission and Recombination at Small x Linear effect (BFKL) Non-linear effect Figures adopted from E.Iancu and R.Venugopalan, in Quark Gluon Plasma 3 (world scientific)

  43. Non-Linear Evolution and Color Glass Condensate (CGC) Rate eq.* small x high energy *More sophisticated equation (BK or JIMWLK) based on QCD is solved. Figures adopted from K.Itakura, talk at QM2005.

  44. “Phase Diagram” of hadrons • Onset of CGC at RHIC • Some evidences exist. • Test of CGC at LHC • How to describe • perturbative CGC to • non-perturbative QGP? CGC geometrical scaling BFKL non-perturbative region LHC RHIC dilute parton DGLAP 0

  45. Onset of CGC in d+Au Collisions at RHIC midrapidity forward rapidity data BRAHMS Collaboration, white paper y=0,1,2,3 theory (CGC) H.Fujii, talk at RCNP workshop(’07) D.Kharzeev et al., PRD68,094013(’03).

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