1. Perfect Fluid QGP or CGC? Tetsufumi Hirano Institute of Physics, University of Tokyo References: T.Hirano and M.Gyulassy, Nucl.Phys.A 769(2006)71. T.Hirano, U.Heinz, D.Kharzeev, R.Lacey, Y.Nara, Phys.Lett.B 636 (2006)299; work in progress. RIKEN Workshop on "Frontiers in the physics of quark-gluon plasma" RIKEN, Wako, Japan, July 8-9, 2006

2. OUTLINE Dynamical modeling in heavy ion collisions based on ideal hydrodynamics Dynamical modeling in heavy ion collisions based on ideal hydrodynamics Elliptic flow Elliptic flow Results from hydro models Results from hydro models –Dependence on freezeout prescription –Dependence on initialization Summary and Outlook Summary and Outlook

3. Why Hydrodynamics? Static EoS from Lattice QCDEoS from Lattice QCD Finite T,  field theoryFinite T,  field theory Critical phenomenaCritical phenomena Chiral property of hadronChiral property of hadron Dynamic Phenomena in HIC Expansion, FlowExpansion, Flow Space-time evolution ofSpace-time evolution of thermodynamic variables thermodynamic variables Once one accepts local thermalization ansatz, life becomes very easy. Energy-momentum: Conserved number:

4. Three Inputs for Hydrodynamic Models Final stage: Free streaming particles  Need decoupling prescription Intermediate stage: Hydrodynamics can be valid as far as local thermalization is achieved.  Need EoS P(e,n) Initial stage: Particle production, pre-thermalization, instability?  Instead, initial conditions are put for hydro simulations. Need modeling (1) EoS, (2) Initial cond., and (3) Decoupling 0 z t

5. 1. Equation of state 2. Initial condition 3. Freezeout Caveats on Hydrodynamic Results Observables Systematic studies are needed! Cover 2nd and 3rd topics in this talk Future: To determine EOS from data!

6. What is Elliptic Flow? How does the system respond to spatial anisotropy? Ollitrault (’92) Hydro behavior Spatial Anisotropy Momentum Anisotropy INPUT OUTPUT Interaction among produced particles dN/d   No secondary interaction 0 22 dN/d   0 22 2v22v2 x y 

7. Elliptic Flow from a Kinetic Theory b = 7.5fm Time evolution of v 2 generated through secondary collisions generated through secondary collisions saturated in the early stage saturated in the early stage sensitive to cross section (~m.f.p.~viscosity) sensitive to cross section (~m.f.p.~viscosity) Gluons uniformly distributed Gluons uniformly distributed in the overlap region dN/dy ~ 300 for b = 0 fm dN/dy ~ 300 for b = 0 fm Thermal distribution with Thermal distribution with T = 500 MeV v 2 is Zhang et al.(’99) View from collision axis ideal hydro limit t(fm/c) v2v2

9. Basis of the Announcement PHENIX(’03)STAR(’02) Multiplicity dependence p T dependence and mass ordering Hydro results: Huovinen, Kolb, Heinz,…

10. Sensitivity to Different Assumptions in Early/Late Stages Glauber-type Color Glass Condensate Sudden freezeout Discovery of “Perfect Liquid” ? Hadronic rescattering ?? InitialCondition Freezeout

11. Dependence on Freezeout Prescription T.Hirano and M.Gyulassy, Nucl.Phys.A 769(2006)71.

12. Classification of Hydro Models TcTc QGP phase Hadron phase  P artial C hemical E quilibrium EOS Model PCE: Hirano, Teaney, Kolb… Model HC: Teaney, Shuryak, Bass, Dumitru, … T ch T th H adronic C ascade C hemical E quilibrium EOS T th Model CE: Kolb, Huovinen, Heinz, Hirano… Perfect Fluid of QGP T ~1 fm/c ~3 fm/c ~10-15 fm/c ideal hydrodynamics

13. v 2 (p T ) for Different Freezeout Prescriptions 2000 (Heinz, Huovinen, Kolb…) Ideal hydro w/ chem.eq.hadrons 2002 (TH,Teaney,Kolb…) +Chemical freezeout 2002 (Teaney…) +Dissipation in hadron phase 2005 (BNL) “RHIC serves the perfect liquid.” 20-30% Why so different/similar?

14. Accidental Reproduction of v 2 (p T ) pTpT v 2 (p T ) v2v2 pTpT v 2 (p T ) v2v2 pTpT v 2 (p T ) v2v2 Chemical Eq. Chemical F.O. At hadronization CE: increase CFO: decrease freezeout

15. Why behaves differently? Chemical Freezeout Chemical Freezeout Chemical Equilibrium Chemical Equilibrium Mean E T decreases due to pdV work For a more rigorous discussion, see TH and M.Gyulassy, NPA769(2006)71 MASS energy KINETIC energy E T per particle increases in chemical equilibrium.  This effect delays cooling of the system like a viscous fluid.  Chemical equilibrium imitates viscosity at the cost of particle yield!  Hydro+Cascade is the only model to reproduce v 2 (p T )!!!

16. (CGC +)QGP Hydro+Hadronic Cascade 0 z t (Option) Color Glass Condensate sQGP core (Full 3D Ideal Hydro) HadronicCorona(Cascade,JAM) TH et al.(’05-)

17. v 2 (p T ) for identified hadrons from QGP Hydro + Hadronic Cascade Mass dependence is o.k. Note: First result was obtained by Teaney et al. 20-30% Proton Pion Mass splitting/ordering comes from hadronic rescattering.  Not a direct signature of perfect fluid QGP

18. v 2 (N part ) and v 2 (eta) Significant Hadronic Viscous Effects at Small Multiplicity at Small Multiplicity!

19. Summary So Far When we employ Glauber-type initial conditions, hadronic dissipation is indispensable. When we employ Glauber-type initial conditions, hadronic dissipation is indispensable. Spectra and elliptic flow are consistent with a picture “perfect fluid QGP core and dissipative hadronic corona” Spectra and elliptic flow are consistent with a picture “perfect fluid QGP core and dissipative hadronic corona”

20. Dependence on Initialization of Hydro T.Hirano, U.Heinz, D.Kharzeev, R.Lacey, Y.Nara, Phys.Lett.B 636 (2006)299; work in progress.

21. (1) Glauber and (2) CGC Hydro Initial Conditions Which Clear the First Hurdle Glauber modelGlauber model N part :N coll = 85%:15% N part :N coll = 85%:15% CGC modelCGC model Matching I.C. via e(x,y,  ) Matching I.C. via e(x,y,  ) Centrality dependence Rapidity dependence

22. v 2 (N part ) from QGP Hydro + Hadronic Cascade Glauber: Early thermalization Early thermalization Mechanism? Mechanism? CGC: No perfect fluid? No perfect fluid? Additional viscosity Additional viscosity is required in QGP Importance of better understanding of initial condition TH et al.(’06)

23. Large Eccentricity from CGC Initial Condition x y Pocket formula (ideal hydro): v 2 ~ 0.2  @ RHIC energies v 2 ~ 0.2  @ RHIC energies Ollitrault(’92) Hirano and Nara(’04), Hirano et al.(’06) Kuhlman et al.(’06), Drescher et al.(’06)

24. v 2 (p T ) and v 2 (eta) from CGC initial conditions v 2 (model) > v 2 (data) 20-30%

25. Summary and Outlook Much more studies needed for initial states Much more studies needed for initial states Still further needed to investigate EOS dependence Still further needed to investigate EOS dependence FAKE!

26. Summary and Outlook (contd.) What have we discovered at RHIC? What have we discovered at RHIC? What leads to large v 2 at RHIC? What leads to large v 2 at RHIC? Perfect fluid QGP or CGC? To be or not to be (consistent with hydro), that is the question! To be or not to be (consistent with hydro), that is the question!

27. Excitation Function of v2 Hadronic Dissipation is huge at SPS.is huge at SPS. still affects v2 at RHIC.still affects v2 at RHIC. is almost negligible at LHC.is almost negligible at LHC.

28. Intermediate Stage: Equation of State Latent heat Lattice QCD predicts cross over phase transition. Nevertheless, energy density explosively increases in the vicinity of T c.  Looks like 1 st order. Lattice QCD simulations Typical EoS in hydro models H: resonance gas(RG) p=e/3 Q: QGP+RG F.Karsch et al. (’00) P.Kolb and U.Heinz(’03) Recent lattice results at finite T

29. Initial Stage: Initial Condition Transverse plane Reaction plane Energy density distribution Parameterization/model-calculation to reproduce (dN/d  )/(N part /2) and dN/d 

30. Final Stage: Freezeout (1) Sudden freezeout (2) Transport of hadrons via Boltzman eq. (hybrid) Continuum approximation no longer valid at the late stage  Molecular dynamic approach for hadrons ( ,K,p,…) 0 z t 0 z t At T=T f, =0 (ideal fluid) =0 (ideal fluid)  =infinity (free stream) T=TfT=Tf QGP fluid Hadron fluid QGP fluid

31. Source Function from 3D Hydro + Cascade Blink: Ideal Hydro, Kolb and Heinz (2003) Caveat: No resonance decays in ideal hydro How much the source function differs from ideal hydro in Configuration space?

32. Non-Gaussian Source? x y p x = 0.5GeV/c

33. Viscosity from a Kinetic Theory See, e.g. Danielewicz&Gyulassy(’85) For ultra-relativistic particles, the shear viscosity is Ideal hydro:  0  0 shear viscosity  0 Transport cross section

34. Viscosity and Entropy 1+1D Bjorken flow Bjorken(’83)1+1D Bjorken flow Bjorken(’83) Baym(’84)Hosoya,Kajantie(’85)Danielewicz,Gyulassy(’85)Gavin(’85)Akase et al.(’89)Kouno et al.(’90)… (Ideal) (Viscous) Reynolds numberReynolds number  : shear viscosity (MeV/fm 2 ), s : entropy density (1/fm 3 ) where  /s is a good dimensionless measure (in the natural unit) to see viscous effects. R>>1  Perfect fluid Iso, Mori, Namiki (’59)

35. Why QGP Fluid + Hadron Gas Works? TH and Gyulassy (’06) ! Absolute value of viscosityAbsolute value of viscosity Its ratio to entropy densityIts ratio to entropy density Rapid increase of entropy density can make hydro work at RHIC. Deconfinement Signal?!  : shear viscosity, s : entropy density Kovtun,Son,Starinets(’05)

36. Temperature Dependence of  /s We propose a possible scenario:We propose a possible scenario: Kovtun, Son, Starinets(‘05) Danielewicz&Gyulassy(’85) Shear Viscosity in Hadron GasShear Viscosity in Hadron Gas Assumption:  /s at T c in the sQGP is 1/4 Assumption:  /s at T c in the sQGP is 1/4  No big jump in viscosity at T c !

37. Digression (Dynamical) Viscosity  : ~1.0x10 -3 [Pa s] (Water 20 ℃ ) ~1.0x10 -3 [Pa s] (Water 20 ℃ ) ~1.8x10 -5 [Pa s] (Air 20 ℃ ) ~1.8x10 -5 [Pa s] (Air 20 ℃ ) Kinetic Viscosity  : ~1.0x10 -6 [m 2 /s] (Water 20 ℃ ) ~1.0x10 -6 [m 2 /s] (Water 20 ℃ ) ~1.5x10 -5 [m 2 /s] (Air 20 ℃ ) ~1.5x10 -5 [m 2 /s] (Air 20 ℃ ) [Pa] = [N/m 2 ] Non-relativistic Navier-Stokes eq. (a simple form) Neglecting external force and assuming incompressibility.  water >  air BUT water  air BUT water < air

38. A Bigger Picture in Heavy Ion Collisions Proper time Transverse momentum CGC Geometric Scaling Shattering CGC Hydrodynamics viscosity?viscosity? non chem. eq.?non chem. eq.? Parton energy loss InelasticInelastic ElasticElastic Hadroniccascade Low p T High p T RecombinationCoalescence “DGLAP region” (N)LOpQCD Before collisions PartonproductionPre-equilibrium “Perfect” fluid QGP or GP Dissipativehadrongas Fragmentation Interaction Intermediate p T Instability?Equilibration?

39. Differential Elliptic Flow Develops in the Hadron Phase? T.H. and K.Tsuda (’02) Kolb and Heinz(’04) Is v 2 (p T ) really sensitive to the late dynamics? 0.4 0.6 0.8 0.2 0 0.4 0.6 0.8 0.2 0 1.0 140MeV 100MeV transverse momentum (GeV/c)

40. Mean p T is the Key Slope of v 2 (p T ) ~ v 2 / Response to decreasing T th (or increasing  ) v2v2v2v2 PCE CE v 2 / v 2 / <pT><pT><pT><pT>    Generic feature!

41. Ideal QGP Fluid + Dissipative Hadron Gas Models (1+1)D with Bjorken flow (2+1)D with Bjorken flow Full (3+1)D UrQMD A.Dumitru et al., PLB460,411(1999); PRC60,021902(1999); S.Bass and A.Dumitru, PRC61,064909(2000). N/A C.Nonaka and S.Bass, nucl-th/0510038. RQMDN/A D.Teaney et al., PRL86,4783(2001), nucl-th/0110037; D.Teaney, nucl-th/0204023. N/A JAMN/AN/A TH, U.Heinz, D.Kharzeev, R.Lacey, and Y.Nara, PLB636,299(2006). hydro cascade

42. p T Spectra for identified hadrons from QGP Hydro+Hadronic Cascade Caveat: Other components such as recombination and fragmentation should appear in the intermediate-high p T regions. dN/dy and dN/dp T are o.k. by hydro+cascade.

43. Discussions: Hadronic Dissipation Hybrid Model: Hybrid Model: QGP Fluid + Hadronic Gas + Glauber I.C. Hydro Model: Hydro Model: QGP Fluid + Hadronic Fluid + Glauber I.C. Comparison  Try to draw information on hadron gas Key technique in hydro: Partial chemical equilibrium in hadron phasePartial chemical equilibrium in hadron phase Particle ratio fixed at T chParticle ratio fixed at T ch  Chemical equilibrium changes dynamics. TH and K.Tsuda(’02),TH and M.Gyulassy(’06) TH and K.Tsuda(’02),TH and M.Gyulassy(’06)

44. Hadronic Dissipation Suppresses Differential Elliptic Flow Difference comes from dissipation only in the hadron phase Caveat: Chemically frozen hadronic fluid is essential in differential elliptic flow. (TH and M.Gyulassy (’06)) Relevant parameter:  s Relevant parameter:  s  Teaney(’03) Teaney(’03) Dissipative effect is not soDissipative effect is not so large due to small expansion rate (1/tau ~ 0.05-0.1 fm -1 )