1. What can we learn from hydrodynamic analysis of elliptic flow? Tetsufumi Hirano Dept. of Physics, Columbia Univ. T.H. and M.Gyulassy, nucl-th/0506049 T.H., Y.Nara et al., work in progress. Quark Matter 2005, August 4-9, Budapest, Hungary

2. Outline 1.Perfect fluidity of sQGP core and highly dissipative hadronic corona 2.CGC + full 3D hydro + cascade 3.Hydrodynamic analysis suggests even a signal of DECONFINEMENT?! DECONFINEMENT?!

4. Bases of the Discovery Integrated elliptic flow NA49(’03) PHENIX white paper Differential elliptic flow Our claims: 1. Ideal hydrodynamics accidentally reproduces these data! 2. Nevertheless, “perfect fluidity of the sQGP” statement and early thermalization still hold. WHY!!!???

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

6. PHENIX white paper, NPA757,184(2005) Are hydro results consistent? If not, what does it mean? elliptic flow p T spectra p  P artial CE C hem. E q. H adronic C ascade

7. Differential Elliptic Flow Develops in the Hadron Phase? T.H. and K.Tsuda (’02) Kolb and Heinz(’04) 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)

8. Mean p T is the Key Response to decreasing T th (or increasing  ) v2v2 PCE CE v 2 / <pT><pT> 

9. Cancel between v 2 and Cancel between v 2 and 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

10. 1.Why mean p T behaves so differently? 2. Why CE result ~ HC result? P artial CE C hem. E q. H adronic C ascade PHENIX white paper, NPA757,184(2005)

11. Intuitive Picture Chemical Freezeout Chemical Freezeout Chemical Equilibrium Chemical Equilibrium Mean E T decreases due to pdV work For a more rigorous discussion, see T.H. and M.Gyulassy, nucl-th/0506049 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!!!

12. Summary of Hydro Results Models for Hadron Phase v2(pT,m)v2(pT,m) p T spectra Yield or ratio Viscous effect Caveat Chemical Equilibrium Y es Y es *NoNo NoNo * P (Pbar) yields << exp. data Partial Chemical Equilibrium NoNo Y es *Y es NoNo *Only low p T for pions Hadronic Cascade Y es Y es * *Kinetic approach Boundary (QGP  hadron) “No-Go theorem” Ruled out! WINNER for hydro race at RHIC !  Hybrid model (Ideal QGP fluid + dissipative hadron gas)

13. CGC + Full 3D Hydro + Cascade 0 z t Color Glass Condensate sQGP core (Full 3D Hydro) Hadronic Corona (Cascade)

14. CGC + Full 3D Hydro + Hadronic Cascade PHOBOS data: “Triangle shape” prop. to dN/d  T th =100MeV: “Trapezoidal shape” Typical hydro result T th =169MeV: Triangle shape! Just after hadronization CGC+hydro+cascade: Good agreement! Perfect fluid sQGP core + dissipative hadronic corona picture works as well in forward region!

15. What Have We Learned? T.H. and M.Gyulassy (’05) ! Absolute value of viscosityIts ratio to entropy density What makes this sudden behavior?  : shear viscosity, s : entropy density

16. Conclusion Critical data harvested at RHIC 1.Particle ratio (Particle yield) 2.p T spectra 3.v 2, v 2 (p T ), and v 2 (  ) Nearly perfect fluidity of the sQGP core AND Highly dissipative hadronic corona  DECONFINEMENT!? Hydrodynamic analyses

17. BONUS SLIDES!

18. T th <T ch Chemical parameters  particle ratio Thermal parameters  p t spectra Statistical model T ch >T th (conventional) hydro T ch =T th No reproduction of ratio and spectra simultaneously

19. Many people don’t know this… P.Huovinen, QM2002 proceedings

20. Extension of Parameter Space ii Introduction of chemical potential for each hadron! Single T f in hydro Hydro works? Both ratio and spectra?

21. Chemical Potential & EoS EOS Example of chem. potential Partial chemical equilibrium (PCE) Expansion dynamics is changed (or not)? T.H. and K.Tsuda(’02) 

22. Does Dynamics change? Model PCE Model CE Contour(T=const.) T(  ) at origin T.H. and K.Tsuda(’02) (T th ) 

23. p T Spectra How to fix T th in conventional hydro Response to p T slope Spectrum harder with decreasing T th Up to how large p T ? T th independence of slope in chemically frozen hydro No way to fix T th Suggests necessity of (semi)hard components Charged hadrons in AuAu 130AGeV C hemical E quilibrium P artial C hemical E quilibrium T.H. and K.Tsuda (’02)

24. Why behaves differently? Simplest case: Pion gas Longitudinal expansion  pdV work! dE T /dy should decrease with decreasing T th.  dN/dy should so. CFO: dS/dy = const.  dN/dy = const.  MUST decreases CE: dS/dy = const.  dN/dy decreases (mass effect)  can increase as long as dN/dy decreases. Result from the 1 st law of thermodynamics & Bjorken flow dE T /dy proper time ideal hydro

25. QGP Fuzzy image if focus is not adjusted yet. QGP QGP Wanna see this? Fine-tune the “hadronic” focus! focus: hadron corona The importance of the dissipative hadronic corona to understand “perfect fluid” sQGP core!

26. The End of 50-Year-Old Ideal, Chem. Eq. Hadronic Fluid After the famous Landau’s paper (1953), ideal and chemical equilibrium hadronic hydrodynamics has been exploited for a long time. However, the model may not be used when chemical freezeout happens earlier than thermal freezeout since it accidentally reproduces p T spectra and v 2 (p T ) at the cost of particle yields.

27. A Long Long Time Ago… …we obtain the value R (Reynolds number)=1~10… Thus we may infer that the assumption of the perfect fluid is not so good as supposed by Landau. Digression

28. 1. Ideal hydrodynamics reproduce v 2 (p T ) remarkably well, but not HBT radii. TRUE FALSE 2. v 2 (p T ) is not sensitive to the late hadronic stage. TRUE FALSE TRUE: Ideal Hydrodynamics reproduces neither v 2 (p T ) nor HBT radii at RHIC. TRUE: v 2 (p T ) depends on thermal equilibrium, chemical equilibrium, and viscous effects in the hadron phase. Check Sheet for Prevailing Opinion X X

29. FAQ 1.We cannot say “Hydro works very well at RHIC” anymore?  Yes/No. Only a hydro+cascade model does a good job.  Nevertheless, HBT puzzle!  QGP as a perfect fluid. Hadron as a viscous fluid. 2. Why ideal hydro can be used for chemically frozen hydro?  We can show from AND.  One has to distinguish “chemical freeze out” from “chemical non-equilibrium”.

30. Finite Mean Free Path & Viscosity See, e.g. Danielewicz&Gyulassy(1985) For ultra-relativistic particles, the shear viscosity is Ideal hydro:  0  shear viscosity  0 Transport cross section

31. Toward a Unified Model in H.I.C. T.H. and Y.Nara (’02-) Proper time Transverse momentum CGC (a la KLN) Color Quantum Fluid (Q S 2 <k T 2 <Q S 4 /  2 ) (x-evolution eq.) Shattering CGC (k T factorization) Hydrodynamics (full 3D hydro) Parton energy loss (a la Gyulassy-Levai-Vitev) Hadroniccascade(JAM) Low p T High p T Recombination Collinear factorized Parton distribution (CTEQ) LOpQCD(PYTHIA) Nuclear wave function Parton distribution Parton production (dissipative process?) QGP Hadron gas Fragmentation (MV model on 2D lattice) (classical Yang-Mills on 2D lattice) Jet quenching Intermediate p T important in forward region? Not covered in this talk

32. Importance of Thermalization Stage at RHIC CGC + hydro + cascade agreement only up to 15~20% centrality (impact parameter ~5fm) Centrality dependence of thermalization time Semi-central to peripheral collisions:  Not interpreted only by hadronic dissipation  Important to understand pre-thermalization stage

33. Initial Eccentricity CGC initial condition gives ~25% larger initial eccentricity than participant or binary collision scaling.

34. Viscosity and Entropy 1+1D Bjorken flow (Ideal) (Viscous) Reynolds number  : shear viscosity (MeV/fm 2 ) s : entropy density (1/fm 3 ) where  /s is a good dimensionless measure to see viscous effects. R>>1  Perfect fluid

35. Large radial flow reduces v 2 for protons Radial flow pushes protons to high p T regions Low p T protons are likely to come from fluid elements with small radial flow Even for positive elliptic flow of matter, v 2 for heavy particles can be negative in low p T regions! High pT protons Low pT protons x y pTpT Blast wave peak depends on 

36. v 2 (p T ) Stalls in Hadron Phase? D.Teaney(’02) Pb+Pb, SPS 17 GeV, b=6 fm Hadronic rescattering via RQMD does not change v 2 (p T ) for  ! Solid lines are guide to eyes Mechanism for stalling v 2 (p T ) Hydro (chem. eq.): Cancellation between v 2 and  Effect of EoS Hydro+RQMD: Effective viscosity  Effect of finite