1. Perfect Fluidity of QGP at RHIC? Tetsufumi Hirano Institute of Physics University of Tokyo Komaba, Tokyo 153-8902, Japan 平野哲文 东京大学 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.

2. OUTLINE “RHIC serves the perfect liquid” “RHIC serves the perfect liquid” Elliptic flow Elliptic flow Results from hydro + cascade model Results from hydro + cascade model Ratio of viscosity to entropy Ratio of viscosity to entropy Summary Summary

4. What is “Perfect Liquid”? A possibility of “Perfect Liquid QGP” is intriguing. In this context, a lot of people say, “QGP viscosity is small”. “QGP viscosity is small”. Viscosity is “small” in comparison with …, what??? I will discuss this issue later.

5. 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 

6. 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

7. Hydro Meets Data for the First Time at RHIC: “Current” Three Pillars 1. Perfect Fluid (s)QGP Core Ideal hydro description of the QGP phaseIdeal hydro description of the QGP phase Necessary to gain integrated v 2Necessary to gain integrated v 2 2. Dissipative Hadronic Corona Boltzmann description of the hadron phaseBoltzmann description of the hadron phase Necessary to gain enough radial flowNecessary to gain enough radial flow Necessary to fix particle ratio dynamicallyNecessary to fix particle ratio dynamically 3. Glauber Type Initial Condition Diffuseness of initial geometryDiffuseness of initial geometry TH&Gyulassy(’06),TH,Heinz,Kharzeev,Lacey,Nara(’06) A Lack of each pillar leads to discrepancy!

8. (CGC +)QGP Hydro+Hadronic Cascade 0 z t (Option) Color Glass Condensate sQGP core (Full 3D Ideal Hydro) HadronicCorona(Cascade,JAM) c.f. Similar approach by Nonaka and Bass (DNP04,QM05) TH et al.(’05-) 0.6fm/c

9. (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

10. 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.

11. 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 Result of JAM: Courtesy of M.Isse TH et al.(’06)

12. 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)

13. v 2 (p T ) for identified hadrons Glauber type initial condition CGC initial condition Mass dependence is o.k. v 2 (model) > v 2 (data)

14. 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)

15. 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)

16. 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

17. Summary Perfect Fluid QGP + Dissipative Hadron + Glauber initial conditions does a good job. Perfect Fluid QGP + Dissipative Hadron + Glauber initial conditions does a good job. –Manifestation of deconfinement? CGC initial conditions spoil this agreement. CGC initial conditions spoil this agreement. Viscous QGP may compensate “CGC effect”. Viscous QGP may compensate “CGC effect”. Importance of better understanding initial conditions. Importance of better understanding initial conditions. To be or not to be (consistent with hydro), that is THE question. -- Anonymous

18. QGP mixed hadron Energy density in the transverse plane at midrapidity Energy in (four-)velocity plane at midrapidity Thank you! TH&Gyulassy(’06)

19. 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

20. 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.

21. A Final Piece of RHIC Jigsaw Puzzle? A much better understanding of initial condition is of initial condition is desperately needed. desperately needed. Glauber or CGC Or any other possible scenarios based on non-equilibrium models, instabilities, etc. for thermalization / isotropization mechanism. Distinguish via 3D jet tomography Adil, Gyulassy and TH (’06)

22. Results from Hydro + Cascade (III) Glauber-BGKCGC

23. v 2 (p T ) from Hydro: Past, Present and Future 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.” 2004-2005 (TH,Gyulassy) Mechanism of v 2 (p T ) slope 2005-2006(TH,Heinz,Nara,…) +Color glass condensate Future “To be or not to be (consistent with hydro), that is THE question” -- anonymous -- anonymous History of differential elliptic flow ~History of development of hydro ~History of removing ambiguity in hydro 20-30% XXXXXXXXXXXXXX ????????????????? XXXXXXXXXXXXXX

24. 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 !

25. 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, PLB636299(2006). hydro cascade