1. Flow and Collective Phenomena in Nucleus-Nucleus Collisions Huan Z Huang Department of Physics and Astronomy University of California, Los Angeles Department of Engineering Physics Tsinghua University

2. Ultra Relativistic Heavy Ion Collisions QuarkGluonPlasma Quark Gluon Plasma

3. -4.8, 0.66, 2.86, 9.39, 18.48, 35.96 In Pictures

4. Evolution 1) Initial Condition - baryon transfer - E T production - partons dof 2) System Evolves - parton/hadron expansion 3) Bulk Freeze-out - hadrons dof - interactions stop ? ? ? ? ? ? J/  D  K*  ,   K  p  d, HBT v 2 saturates  T saturates Q2Q2 time

5. Inspiration from Hydrodynamics H. Stöcker, J.A. Maruhn, and W. Greiner, PRL 44, 725 (1980) U Ne

6. Discovery of Collective Flow Plastic Ball, Gustafsson et al., PRL 52, 1590 (1984) Non-zero flow angle distribution for Nb, but not Ca dN/dcos  Bevalac 400 MeV/A

7. bounce squeeze Squeeze-out

8. Transverse Plane y x Anisotropic Flow as a function of rapidity around the beam axis

9. Geometry of Nucleus-Nucleus Collisions N part – No of participant nucleons N binary – No of binary nucleon-nucleon collisions cannot be directly measured at RHIC estimated from Woods-Saxon geometry

10.  = 0 0.5 Infinite Nuclear Collision Evolution Epoches Chemical Freeze-out --- formation of hadrons Kinetic Freeze-out --- Interaction ceases

11. Radial Flow Partonic: parton-parton scattering, QGP EOS Hadronic: hadron-hadron scattering, hadron gas

12. Pressure, Flow, … Matter flows – all particles have the same collective velocity: I.Bearden et al, Phys. Rev. Lett. 78, 2080(1997).

13. Pressure, Flow, … Thermodynamic identity  – entropy p – pressure U – energy V – volume  = k B T, thermal energy per dof In nuclear collisions, density distribution and pressure will lead:  pressure gradient  flow – integrated effects  number of degree of freedom  Equation of State (EOS)

14. Hydrodynamic Basics Hydrodynamic Basics f(x,p): phase space distribution function - information on dynamics T   energy-momentum tensor idea hydrodynamics u  : 4-velocity,  Lorentz factor K.J. Eskola, et al., nucl-th/9705015 L. Ch, ISBN- ----------------------------------------------- - Initial conditions (?) - EOS (?) - Freeze-out conditions (?)  Hydrodynamics solutions

15. Bag Model Equation of State Two Flavor Quarks (up, down) Degeneracy factors: quarks  Q = (3 color)x(2 flavor)x(2 helicity)=12 gluons  G = (8 color)x(2 helicity) = 16 Bag Constant:(E/V) vac = +B Free quarks and gluons:

16. Bag Model EOS Free quark and gluons in a bag: 3 (p+B) =  – B (B bag constant) 1)At finite baryon density  B =2k F 2 /3  2 and zero T 3(p+B) =  -B = 3k F 4 /2  2 Fermi pressure keeps the bubble from collapsing 2) At finite T and vanishing baryon density  B =0 3(p+B) =  -B = 37  2 (k B T) 4 /30 Thermal pressure keeps the bubble from collapsing

17. EOS of Nucleon DOF @T=0

18. Mix Hadrons and the QGP

19. QCD on Lattice Lattice calculations predict T C ~ 170 MeV 1) Large increase in  ! 2) Not reach idea non-interaction S. Boltzmann limit !  many body interactions  Collective modes  Quasi-particles are necessary 3) T C ~ 170 MeV robust! Z. Fordor et al, JHEP 0203:014(02) Z. Fodor et al, hep-lat/0204001 C.R. Allton et al, hep-lat/0204010 F. Karsch, Nucl. Phys. A698, 199c(02).

20. Sample QGP EOS Latent Heat 0.4 GeV Latent Heat 0.8 GeV Resonant Gas

21. Collision Dynamics

22. Final Spectra Reflect the Kinetic Freeze-out

23. Final State Hadronic Rescattering important

24. Elliptic Flow Reaction plane x z y

25. Initial Geometry Important Eccentricity =

26. Time Evolution of the Asymmetry

27. Elliptic Flow v 2 and Early Dynamics Coordinate space: initial asymmetry Momentum space: final asymmetry pypy pxpx x y dN/d  1 + 2v 2 cos2  Pressure induced flow + Surface emission pattern + Final state rescattering –

28. V 2 and the Early Stage EOS

29. Elliptic Flow: ultra-cold Fermi-Gas Li-atoms released from an optical trap exhibit elliptic flow analogous to what is observed in ultra- relativistic heavy-ion collisions  Elliptic flow is a general feature of strongly interacting systems!

30. y Dynamical Origin of Elliptic Flow STAR Preliminary Au+Au 200 GeV V 2 in the high p T region: should large parton energy loss lead to surface emission pattern ?! Particle Dependence of v 2 ? Collective Pressure High pressure gradient Large expansion velocity Small expansion velocity p T dependent ! Surface Geometrical Phase Space Surface Emission Pattern High particle density Low particle density p T independent ! or p T dependence may come from surface thickness (p T ) x

31. Three p T Regions STAR PHENIX LOW INTERMEDIATEHIGH

32. Hydro calculations break-down at higher p T (as expected). How is v 2 established at p T above 2 GeV/c? Why is baryon v 2 so large? PRL 92 (2004) 052302; PRL 91 (2003) 182301 Elliptic Flow v 2

33. 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 

34. Multi-strange hadrons, ,  and , are expected to have smaller hadronic x- sections.  and  v 2 values are large: apparently independent hadronic x-section. Consistant with the creation of v 2 before hadron formation. STAR Preliminary; PRL 91 (2003) 182301 Multi-strange Baryon v 2

35.  meson flow  meson (s-sbar) state! Jinhui Chen Guoliang Ma SINAP

36. Constituent Quark Degree of Freedom K S – two quark coalescence  – three quark coalescence from the partonic matter surface?! Particle v 2 may be related to quark matter anisotropy !! p T < 1 GeV/c may be affected by hydrodynamic flow ! Hadronization Scheme for Bulk Partonic Matter: Quark Coalescence – (ALCOR-J.Zimanyi et al, AMPT-Lin et al, Rafelski+Danos, Molnar+Voloshin …..) Quark Recombination – (R.J. Fries et al, R. Hwa et al)

37. Multi-Parton Dynamics for Bulk Matter Hadronization Essential difference: Traditional fragmentation  particle properties mostly determined by the leading quark ! Emerging picture from RHIC data (R AA /R CP and v 2 )  all constituent quarks are almost equally important in determining particle properties ! v 2 of hadron comes from v 2 of all constituent quarks ! The fact that in order to explain the v 2 of hadrons individual constituent quarks (n=2-meson,3-baryon) must have a collective elliptic flow v 2 and the hadron v 2 is the sum of quark v 2  Strong Evidence for Deconfiement !

38. Implication of the Experimental Observation 1) At the moment of hadronization in nucleus-nucleus collisions at RHIC the dominant degrees of freedom is related to number of constituent (valence) quarks. 2) These ‘constituent quarks’ exhibit an angular anisotropy resulting from collective interactions. 3) Hadrons seem to be formed from coalescence or recombination of the ‘constituent quarks’, and the hadron properties are determined by the sum of ‘constituent quarks’. Is this picture consistent with recent LQCD on spectral function calculations near T c ?

39. Recombination Model Including Hadron Structure Muller et al nucl-th/0503003

40. Constituent Quark Number Scaling Systematic particle dependence from internal structure

41. Heavy Quark Flow Heavy Quark Energy Loss, Elliptic Flow, B and D Contributions -- outstanding issues in heavy ion physics !!

43. Quark-Gluon Fluid Experimental Indications: Hydrodynamic Description of Bulk Particle Properties – v 2 and Spectra Shape – Successful. Hydrodynamic Calculation – Ideal Fluid. v 2 saturation and coalescence picture. Uncertainties – uniqueness for hydro calculation? -- Initial conditions ? Theoretical Understanding: How come a strongly coupled quark-gluon matter has small viscosity? Hadronization in hydrodynamic calculation? Equilibration condition? Hadronic stage radial flow?

44. Quark Cluster Formation from Strongly Interacting Partonic Matter Volcanic mediate p T – Spatter (clumps)   Strangeness enhancement from QGP is most prominent in the region where particle formation from quark coalescence is dominant !

45. p T Scales and Physical Processes R CP Three P T Regions: -- Fragmentation -- multi-parton dynamics (recombination or coalescence or …) -- Hydrodynamics (constituent quarks ? parton dynamics from gluons to constituent quarks? )

46. The END