1. What can we learn from hydrodynamic analysis at RHIC? Tetsufumi Hirano Dept. of Physics, Columbia Univ. Workshop on Quark-Gluon-Plasma Thermalization August 10-12, TU Wien, Vienna, Austria T.H. and M.Gyulassy, nucl-th/0506049 T.H., Y.Nara et al., in preparation.

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. Basis of the Announcement Integrated elliptic flow NA49(’03) PHENIX white paper Differential elliptic flow Common initial time in hydro ~ 0.6-1.0 fm/c A big surprise! Our claims: 1. Ideal hydrodynamics accidentally reproduces these data! 2. Nevertheless, “perfect fluidity of the sQGP” statement still holds. WHY!!!???

5. 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, Nonaka… 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

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) 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)

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

9. 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

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. Chem. Eq. Imitates Viscosity! Model PCE Model CE Contour(T=const.) T(  ) at origin T.H. and K.Tsuda(’02) (T th ) 

13. 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) by Teaney, Lauret, and Shuryak

14. 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 in a way that it imitates viscosity.

15. 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

16. Summary 1 Critical data harvested at RHIC 1.Particle ratio (Particle yield) 2.p T spectra 3.v 2 AND v 2 (p T ) Nearly perfect fluidity of the sQGP core AND Highly dissipative hadronic corona Hydrodynamic analyses

17. Results from CGC + full 3D hydro + hadronic cascade Part 2

18. Toward a Unified Model in H.I.C. 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 T.H. and Y.Nara, PRC66(’02)041901, 68(’03)064902, 69(’04)034908, PRL91(’03)082301, NPA743(’04)305

19. CGC + Full 3D Hydro + Cascade 0 z t Color Glass Condensate sQGP core (Full 3D Hydro) Hadronic Corona (Cascade, JAM) c.f. Recent similar approach by Nonaka and Bass (DNP04,QM05)

20. v 2 (  ) from 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 in forward region!

21. CGC+Hydro+Cascade in Cu+Cu Collisions The effect of rescattering is seen especially near midrapidity.

22. Predictions for LHC from CGC+Hydro+Cascade No jet components Need to estimate systematic error from Cooper-Frye formula Monotonic increase is consistent with previous work by Teaney et al.

23. Early Thermalization in Peripheral Collisions at RHIC? CGC + hydro + cascade agreement only up to 15~20% centrality (impact parameter ~5fm) Centrality dependence of thermalization time?  Common  0 =0.6fm/c Semi-central to peripheral collisions:  Not interpreted only by hadronic dissipation  Important to understand pre-thermalization stage  Imcomplete thermalization? (Talk by Borghini)

24. Does the hydrodynamic agreement with experimental data suggest even DECONFINEMENT?! DECONFINEMENT?! hydro+cascade Part 3

25. 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 Iso, Mori, Namiki (1959)

26. 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

27. Summary The sQGP core + the dissipative hadronic corona picture can be established through careful comparison of current hydro results with high precision RHIC data. This picture is confirmed in forward rapidity region by using a “cutting edge” hybrid model (CGC + full 3D hydro + hadronic cascade). This picture is manifestation of the sudden change of entropy density at T c, namely deconfinement!