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Flow and Collective Phenomena in Nucleus-Nucleus Collisions

Flow and Collective Phenomena in Nucleus-Nucleus Collisions. Huan Z Huang Department of Physics and Astronomy University of California, Los Angeles. Ultra Relativistic Heavy Ion Collisions. Quark Gluon Plasma. In Pictures. -4.8, 0.66, 2.86, 9.39, 18.48, 35.96. 1) Initial Condition

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Flow and Collective Phenomena in Nucleus-Nucleus Collisions

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

  2. Ultra Relativistic Heavy Ion Collisions QuarkGluonPlasma

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

  4. 1) Initial Condition - baryon transfer - ET production - partons dof 2) System Evolves - parton/hadron expansion 3) Bulk Freeze-out - hadrons dof - interactions stop Evolution J/y, D W K* X F,L p, K D, p d, HBT Q2 ? v2 saturates ? ? ? ? ? bT saturates time

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

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

  7. bounce squeeze squeeze Squeeze-out

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

  9. Number of Participants Impact Parameter Geometry of Nucleus-Nucleus Collisions Npart – No of participant nucleons Nbinary – No of binary nucleon-nucleon collisions cannot be directly measured at RHIC estimated from Woods-Saxon geometry

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

  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 t = kBT, 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 f(x,p): phase space distribution function - information on dynamics Tmn : energy-momentum tensor idea hydrodynamics umn: 4-velocity, g: 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 gQ = (3 color)x(2 flavor)x(2 helicity)=12 gluons gG = (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) = e – B (B bag constant) • At finite baryon density rB=2kF2/3p2 and zero T • 3(p+B) = e-B = 3kF4/2p2 • Fermi pressure keeps the bubble from collapsing • 2) At finite T and vanishing baryon density rB=0 • 3(p+B) = e-B = 37p2(kBT)4/30 • Thermal pressure keeps the bubble from collapsing

  17. EOS of Nucleon DOF @T=0 QHD-I Quantum Hydrodynamics

  18. Mix Hadrons and the QGP

  19. QCD on Lattice • 1) Large increase in  ! • 2) Not reach idea non-interaction • S. Boltzmann limit ! • many body interactions • Collective modes • Quasi-particles are necessary 3) TC~ 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). Lattice calculations predict TC ~ 170 MeV

  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. z Reaction plane y x Elliptic Flow

  25. Initial Geometry Important Eccentricity =

  26. Time Evolution of the Asymmetry

  27. y Elliptic Flow v2 and Early Dynamics Coordinate space: initial asymmetry Momentum space: final asymmetry py Pressure induced flow + Surface emission pattern + Final state rescattering – px x dN/d 1 + 2v2 cos2(f)

  28. V2 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 Small expansion velocity Collective Pressure High pressure gradient Large expansion velocity pT dependent ! Low particle density Surface Geometrical Phase Space Surface Emission Pattern High particle density pT independent ! or pT dependence may come from surface thickness (pT) Dynamical Origin of Elliptic Flow STAR Preliminary Au+Au 200 GeV x V2 in the high pT region: should large parton energy loss lead to surface emission pattern ?! Particle Dependence of v2 ?

  31. STAR PHENIX Three pT Regions LOW INTERMEDIATE HIGH

  32. Elliptic Flow v2 PRL 92 (2004) 052302; PRL 91 (2003) 182301 Hydro calculations break-down at higher pT (as expected). How is v2 established at pT above 2 GeV/c? Why is baryon v2 so large?

  33. Large radial flow reduces v2 for protons Blast wave peak depends on f High pT protons x y pT • Radial flow pushes protons to high pT regions • Low pT protons are likely to come from fluid elements with small radial flow Low pT protons Even for positive elliptic flow of matter, v2 for heavy particles can be negative in low pT regions!

  34. Multi-strange Baryon v2 Multi-strange hadrons, ,  and , are expected to have smaller hadronic x-sections.  and  v2 values are large: apparently independent hadronic x-section. Consistant with the creation of v2 before hadron formation. STAR Preliminary; PRL 91 (2003) 182301

  35. F meson flow f meson (s-sbar) state! Jinhui Chen Guoliang Ma SINAP

  36. Constituent Quark Degree of Freedom Hadronization Scheme for Bulk Partonic Matter: • KS – two quark coalescence • – three quark coalescence from the partonic matter surface?! Particle v2 may be related to quark matter anisotropy !! pT < 1 GeV/c may be affected by hydrodynamic flow ! 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 (RAA/RCP and v2)  all constituent quarks are almost equally important in determining particle properties ! v2 of hadron comes from v2 of all constituent quarks ! The fact that in order to explain the v2 of hadrons individual constituent quarks (n=2-meson,3-baryon) must have a collective elliptic flow v2 and the hadron v2 is the sum of quark v2  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 Tc ?

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

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

  41. Eccentricity Scaling(?) STAR Identified Particles PHENIX Au+Au,Cu+Cu Charged hadrons! Central collisions  Higher energy density Stronger hydro flow  How is it manifested?

  42. Hydrodynamics at RHIC – Coincidence or Physics ? LHC – new testing ground !

  43. (no) Scaling in Hydro Model No scaling is observed in the non-viscous hydrodynamic model predictions. Realistic calculations with viscosity are necessary! - STAR data: PRC 72, 014904, 2005 arXiv:0801.3466v1 - Non-viscous hydrodynamic results: P. Huovinen, private communications 2007 - D. Teaney, J. Lauret, and E.Shuryak, nucl-th/0110037 - T. Hirano et al. Phy. Lett. B636, 299 (06); J. Phys. G34 S879(07); arXiv: 0710.5795

  44. Quark-Gluon Fluid Experimental Indications: Hydrodynamic Description of Bulk Particle Properties – v2 and Spectra Shape – Successful. Hydrodynamic Calculation – Ideal Fluid. v2 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?

  45. Volcanic mediate pT – Spatter (clumps) Quark Cluster Formation from Strongly Interacting Partonic Matter L X W Strangeness enhancement from QGP is most prominent in the region where particle formation from quark coalescence is dominant !

  46. pT Scales and Physical Processes RCP Three PT Regions: -- Fragmentation -- multi-parton dynamics (recombination or coalescence or …) -- Hydrodynamics (constituent quarks ? parton dynamics from gluons to constituent quarks? ) -- Important to measure the scale for heavy Q !

  47. The END

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