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Perfect Fluid QGP or CGC?

“RHIC Physics in the Context of the Standard Model” RBRC workshop on Heavy Ion Physics. Perfect Fluid QGP or CGC?. Tetsufumi Hirano* Institute of Physics, University of Tokyo. * Visiting scientist at RBRC. References: T.Hirano and M.Gyulassy, Nucl.Phys.A 769 (2006)71.

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Perfect Fluid QGP or CGC?

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  1. “RHIC Physics in the Context of the Standard Model” RBRC workshop on Heavy Ion Physics Perfect Fluid QGP or CGC? Tetsufumi Hirano* Institute of Physics, University of Tokyo * Visiting scientist at RBRC 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; work in progress.

  2. OUTLINE • Dynamical modeling in heavy ion collisions based on ideal hydrodynamics • Elliptic flow and perfect fluid • Results from hydro models • Dependence on freezeout prescription • Dependence on initialization • Summary and Outlook

  3. Why Hydrodynamics? • Static • EoS from Lattice QCD • Finite T, m field theory • Critical phenomena • Chiral property of hadron Once one accepts local thermalization ansatz, life becomes very easy. Energy-momentum: Conserved number: • Dynamic Phenomena in HIC • Expansion, Flow • Space-time evolution of • thermodynamic variables A possible mechanism of apparent thermalization  Talk by Y.Nara

  4. Three Inputs for Hydrodynamic Models Final stage: Free streaming particles  Need decoupling prescription t Intermediate stage: Hydrodynamics can be valid as far as local thermalization is achieved.  Need EoS P(e,n) z • Initial stage: • Particle production, • pre-thermalization, instability? • Instead, initial conditions are put for hydro simulations. 0 Need modeling (1) EoS, (2) Initial cond., and (3) Decoupling

  5. Intermediate Stage: Equation of State Typical EoS in hydro models Lattice QCD simulations H: resonance gas(RG) Q: QGP+RG P.Kolb and U.Heinz(’03) F.Karsch et al. (’00) p=e/3 Recent lattice results at finite T  Talk by Y.Aoki Latent heat Lattice QCD predicts cross over phase transition. Nevertheless, energy density explosively increases in the vicinity of Tc.  Looks like 1st order.

  6. Initial Stage: Initial Condition Energy density distribution Transverse plane Reaction plane Parameterization/model-calculation to reproduce (dN/dh)/(Npart/2) and dN/dh

  7. Final Stage: Freezeout (1) Sudden freezeout (2) Transport of hadrons via Boltzman eq. (hybrid) T=Tf t t Hadron fluid QGP fluid QGP fluid z z 0 0 Continuum approximation no longer valid at the late stage Molecular dynamic approach for hadrons (p,K,p,…) At T=Tf, l=0 (ideal fluid)  l=infinity (free stream)

  8. Caveats on Hydrodynamic Results • Obviously, final results depend on • modeling of • Equation of state • Initial condition • Freezeout • So it is indispensable to check sensitivity • of conclusion to model assumptions and • try to reduce model parameters. • In this talk, I will cover 2 and 3.

  9. What is Elliptic Flow? Ollitrault (’92) How does the system respond to spatial anisotropy? No secondary interaction Hydro behavior y f x INPUT Spatial Anisotropy 2v2 Interaction among produced particles dN/df dN/df OUTPUT Momentum Anisotropy 0 f 2p 0 f 2p

  10. Elliptic Flow from a Kinetic Theory ideal hydro limit Zhang et al.(’99) View from collision axis Time evolution of v2 b = 7.5fm v2 • Gluons uniformly distributed • in the overlap region • dN/dy ~ 300 for b = 0 fm • Thermal distribution with • T = 500 MeV t(fm/c) generated through secondary collisions saturated in the early stage sensitive to cross section (~m.f.p.~viscosity) v2 is

  11. Basis of the Announcement STAR(’02) PHENIX(’03) pT dependence and mass ordering Multiplicity dependence Hydro results: Huovinen, Kolb, Heinz,…

  12. Sensitivity to Different Assumptions in Early/Late Stages Initial Condition Freezeout

  13. Dependence on Freezeout Prescription T.Hirano and M.Gyulassy, Nucl.Phys.A 769(2006)71.

  14. Classification of Hydro Models Model CE: Kolb, Huovinen, Heinz, Hirano… Model PCE: Hirano, Teaney, Kolb… Model HC: Teaney, Shuryak, Bass, Dumitru, … T ~1 fm/c QGP phase Perfect Fluid of QGP Tc ~3 fm/c Chemical Equilibrium EOS Partial Chemical Equilibrium EOS Tch Hadronic Cascade Hadron phase Tth Tth ~10-15 fm/c t ideal hydrodynamics

  15. v2(pT) for Different Freezeout Prescriptions 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.” 20-30% Why so different/similar?

  16. Accidental Reproduction of v2(pT) v2(pT) v2(pT) At hadronization Chemical Eq. v2 v2 freezeout <pT> <pT> pT pT v2(pT) Chemical F.O. CE: increase CFO: decrease v2 <pT> pT

  17. Why <pT> behaves differently? Mean ET decreases due to pdV work • ETper 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!  Hydro+Cascade is the only model to reproduce v2(pT)!!! Chemical Freezeout MASS energy KINETIC energy Chemical Equilibrium For a more rigorous discussion, see TH and M.Gyulassy, NPA769(2006)71

  18. v2(pT) for identified hadronsfrom QGP Hydro + Hadronic Cascade Pion 20-30% Proton Mass dependence is o.k. Note: First result was obtained by Teaney et al. Mass splitting/ordering comes from hadronic rescattering. Not a direct signature of perfect fluid QGP

  19. v2(Npart) and v2(eta) Significant Hadronic Viscous Effects at Small Multiplicity!

  20. Summary So Far • When we employ Glauber-type initial conditions, hadronic dissipation is indispensable. • Perfect fluid QGP core and dissipative hadronic corona

  21. Dependence on Initialization of Hydro T.Hirano, U.Heinz, D.Kharzeev, R.Lacey, Y.Nara, Phys.Lett.B 636 (2006)299; work in progress.

  22. (1) Glauber and (2) CGC Hydro Initial Conditions Which Clear the First Hurdle Centrality dependence Rapidity dependence • Glauber model • Npart:Ncoll = 85%:15% • CGC model • Matching I.C. via e(x,y,h) Details on CGC  Talk by K.Itakura

  23. TH et al.(’06) v2(Npart) from QGP Hydro + Hadronic Cascade • Glauber: • Early thermalization • Mechanism? • CGC: • No perfect fluid? • Additional viscosity • is required in QGP Importance of better understanding of initial condition

  24. Large Eccentricity from CGC Initial Condition Hirano and Nara(’04), Hirano et al.(’06) Kuhlman et al.(’06), Drescher et al.(’06) y x Pocket formula (ideal hydro): v2 ~ 0.2e @ RHIC energies Ollitrault(’92)

  25. v2(pT) and v2(eta) from CGC initial conditions 20-30% v2(model) > v2(data)

  26. Summary and Outlook • Much more studies needed for initial states • Still further needed to investigate EOS dependence • To be or not to be (consistent with hydro), that is the question! FAKE!

  27. Acknowledgement Miklos is supposed to attend this workshop but cannot come. I really appreciate his continuous encouragement to my work. Get well soon completely, Miklos!

  28. Excitation Function of v2 • Hadronic Dissipation • is huge at SPS. • still affects v2 at RHIC. • is almost negligible at LHC.

  29. Source Function from 3D Hydro + Cascade How much the source function differs from ideal hydro in Configuration space? Blink: Ideal Hydro, Kolb and Heinz (2003) Caveat: No resonance decays in ideal hydro

  30. Non-Gaussian Source? y px= 0.5GeV/c x

  31. Viscosity from a Kinetic Theory See, e.g. Danielewicz&Gyulassy(’85) For ultra-relativistic particles, the shear viscosity is Ideal hydro: l 0 shear viscosity  0 Transport cross section

  32. Viscosity and Entropy • Reynolds number Iso, Mori, Namiki (’59) R>>1 Perfect fluid where • 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) h: shear viscosity (MeV/fm2), s : entropy density (1/fm3) h/s is a good dimensionless measure (in the natural unit) to see viscous effects.

  33. Why QGP Fluid + Hadron Gas Works? h: shear viscosity, s : entropy density TH and Gyulassy (’06) Kovtun,Son,Starinets(’05) • Absolute value of viscosity • Its ratio to entropy density ! Rapid increase of entropy density can make hydro work at RHIC. Deconfinement Signal?!

  34. Temperature Dependence ofh/s • Shear Viscosity in Hadron Gas Danielewicz&Gyulassy(’85) • Assumption:h/s at Tc in the sQGP is 1/4p Kovtun, Son, Starinets(‘05) No big jump in viscosity at Tc! • We propose a possible scenario:

  35. Digression [Pa] = [N/m2] (Dynamical) Viscosity h: ~1.0x10-3 [Pa s] (Water20℃) ~1.8x10-5 [Pa s] (Air 20℃) Kinetic Viscosity n=h/r: ~1.0x10-6 [m2/s] (Water20℃) ~1.5x10-5 [m2/s] (Air20℃) hwater > hair BUT nwater < nair Non-relativistic Navier-Stokes eq. (a simple form) Neglecting external force and assuming incompressibility.

  36. A Bigger Picture in Heavy Ion Collisions Before collisions Geometric Scaling CGC “DGLAP region” Parton production Pre- equilibrium Transverse momentum Shattering CGC (N)LOpQCD Instability? Equilibration? • Parton energy loss • Inelastic • Elastic Interaction “Perfect” fluid QGP or GP • Hydrodynamics • viscosity? • non chem. eq.? Recombination Coalescence Dissipative hadron gas Hadronic cascade Fragmentation Proper time Low pT Intermediate pT High pT

  37. Differential Elliptic Flow Developsin the Hadron Phase? Kolb and Heinz(’04) Is v2(pT) really sensitive to the late dynamics? 100MeV T.H. and K.Tsuda (’02) 140MeV 0.8 1.0 0.2 0.6 0 0.4 0.8 0.2 0.6 0 0.4 transverse momentum (GeV/c)

  38. Mean pT is the Key Generic feature! t t Slope of v2(pT) ~ v2/<pT> Response todecreasing Tth (or increasing t) v2 <pT> v2/<pT> CE PCE t

  39. TH et al.(’05-) (CGC +)QGP Hydro+Hadronic Cascade Hadronic Corona (Cascade, JAM) t sQGP core (Full 3D Ideal Hydro) z 0 (Option) Color Glass Condensate

  40. Ideal QGP Fluid + Dissipative Hadron Gas Models hydro cascade

  41. TH&Gyulassy(’06),TH,Heinz,Kharzeev,Lacey,Nara(’06) Hydro Meets Data for the First Time at RHIC: “Current” Three Pillars • Perfect Fluid (s)QGP Core • Ideal hydro description of the QGP phase • Necessary to gain integrated v2 • Dissipative Hadronic Corona • Boltzmann description of the hadron phase • Necessary to gain enough radial flow • Necessary to fix particle ratio dynamically • Glauber Type Initial Condition • Diffuseness of initial geometry A Lack of each pillar leads to discrepancy!

  42. pT Spectra for identified hadronsfrom QGP Hydro+Hadronic Cascade dN/dy and dN/dpT are o.k. by hydro+cascade. Caveat: Other components such as recombination and fragmentation should appear in the intermediate-high pT regions.

  43. Discussions: Hadronic Dissipation • Hybrid Model: QGP Fluid + Hadronic Gas + Glauber I.C. • Hydro Model: QGP Fluid + Hadronic Fluid + Glauber I.C. ComparisonTry to draw information on hadron gas • Key technique in hydro: • Partial chemical equilibrium in hadron phase • Particle ratio fixed at Tch • Chemical equilibrium changes dynamics. TH and K.Tsuda(’02),TH and M.Gyulassy(’06)

  44. Hadronic Dissipation Suppresses Differential Elliptic Flow Difference comes from dissipation only in the hadron phase • Relevant parameter: Gs/t • Teaney(’03) • Dissipative effect is not so • large due to small expansion • rate (1/tau ~ 0.05-0.1 fm-1) Caveat: Chemically frozen hadronic fluid is essential in differential elliptic flow. (TH and M.Gyulassy (’06))

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