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Perfect Fluid QGP or CGC?

Perfect Fluid QGP or CGC?. Tetsufumi Hirano Institute of Physics, University of Tokyo. 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. Seminar@RCNP, 7/27/2006. OUTLINE.

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Perfect Fluid QGP or CGC?

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  1. Perfect Fluid QGP or CGC? Tetsufumi Hirano Institute of Physics, University of Tokyo 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. Seminar@RCNP, 7/27/2006

  2. OUTLINE • Introduction • Basic checks • 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. Introduction What is the matter where our building block plays a fundamental role? What is the origin of matter? Confinement Quark Gluon Plasma Matter Particle: quark Gauge Particle: gluon Dynamics : QCD Matter form : QGP Quarks, Leptons +Gauge particles

  4. Two Faces of QCD Strong coupling “constant” q-qbar potential F.Karsch and E.Laermann S. Eidelman et al. Color confinement Asymptotic freedom Low energy scale  High energy scale ???  perturbation  OK!

  5. QGP Recipe • Adding pressure  Pushing up chemical potential scale • Adding heat  Pushing up temperature scale

  6. QGP from 1st principle calculations • Critical temperature • Tc ~170MeV ~2x1012K ! • ec ~0.3-1.3GeV/fm3 • Rapid increase around Tc Karsch et al. Normalized temperature Stefan-Boltzmann law (energy density)∝(d.o.f.)x(temperature)4 Hadron phase(p): 3  QGP: 37 (color, flavor…)

  7. Matter Evolved with Our Universe QGP Hadronization Nucleosynthesis QGP study Understanding early universe

  8. Little Bang! Relativistic Heavy Ion Collider(2000-) RHIC as a time machine! front view STAR side view STAR Collision energy Multiple production Heat 100 GeV per nucleon Au(197×100)+Au(197×100)

  9. Physics of the QGP • Matter governed by QCD, not QED • High energy density/temperature frontier Toward an ultimate matter (Maximum energy density/temperature) • Reproduction of QGP in H.I.C. Reproduction of early universe on the Earth • Understanding the origin of matter which evolves with our universe

  10. BASIC CHECKSAS AN INTRODUCTION

  11. Basic Checks (I): Energy Density Bjorken energy density t: proper time y: rapidity R: effective transverse radius mT: transverse mass Bjorken(’83)

  12. Critical Energy Density from Lattice Stolen from Karsch(PANIC05).

  13. Centrality Dependence of Energy Density Well above ec from lattice in central collision at RHIC, if assuming t=1fm/c. ec from lattice PHENIX(’05)

  14. CAVEATS (I) • Just a necessary condition in the sense that temperature (or pressure) is not measured. (Just a firework?) • How to estimate tau? • If the system is thermalized, the actual energy density is larger due to pdV work. • Boost invariant? • Averaged over transverse area. Effect of thickness? How to estimate area? Gyulassy, Matsui(’84) Ruuskanen(’84)

  15. Basic Checks (II): Chemical Eq. direct Resonance decay Two fitting parameters: Tch, mB

  16. Amazing fit! T=177MeV, mB = 29 MeV Close to Tc from lattice

  17. CAVEATS (II) • Even e+e- or pp data can be fitted well! See, e.g., Becattini&Heinz(’97) • What is the meaning of fitting parameters? See, e.g., Rischke(’02),Koch(’03) • Why so close to Tc? • No chemical eq. in hadron phase!? • Essentially dynamical problem! Expansion rate  Scattering rate (Process dependent) see, e.g., U.Heinz, nucl-th/0407067

  18. Statistical Model Fitting to ee&pp Becattini&Heinz(’97) Phase space dominance? “T” prop to E/N? See, e.g., Rischke(’02),Koch(’03)

  19. Basic Checks (III): Radial Flow Blast wave model (thermal+boost) Driving force of flow: Inside: high pressure Outside: vacuum (p=0) pressure gradient Sollfrank et al.(’93) Spectrum for heavier particles is a good place to see radial flow.

  20. Spectrum change is seen in AA! Power law in pp & dAu Convex to Power law in Au+Au • “Consistent” with thermal + boost picture • Pressure can be built up in AA O.Barannikova, talk at QM05

  21. CAVEATS (III) • Finite radial flow even in pp collisions? • (T,vT)~(140MeV,0.2) • Is blast wave reliable quantitatively? • Not necessary to be thermalized completely • Results from hadronic cascade models. • How is radial flow generated dynamically? • Consistency? • Chi square minimum located a different point for f and W • Separate f.o. due to strong expansion. Time scale: micro sec. in early universe  10-23 (10 yocto) sec. in H.I.C. • Flow profile? Freezeout hypersurface? Sudden freezeout?

  22. Basic Checks  Necessary Conditions to Study QGP at RHIC • Energy density can be well above ec. • tau? thermalized? • “Temperature” can be extracted. (particle ratio) • e+e- and pp? Why freezeout happens so close to Tc • Pressure can be built up. (pT spectra) • Completely thermalized? Importance of Systematic Study based on Dynamical Framework

  23. Dynamics of Heavy Ion Collisions Freezeout “Re-confinement” Expansion, cooling Thermalization First contact (two bunches of gluons) Temperature scale 100MeV~1012K Time scale 10fm/c~10-23sec

  24. 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

  25. 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

  26. 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 Latent heat Lattice QCD predicts cross over phase transition. Nevertheless, energy density explosively increases in the vicinity of Tc.  Looks like 1st order.

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

  28. 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)

  29. 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.

  30. 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

  31. 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

  32. Basis of the Announcement STAR(’02) PHENIX(’03) response = (output)/(input) pT dependence and mass ordering Multiplicity dependence Hydro results: Huovinen, Kolb, Heinz,…

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

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

  35. 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

  36. Chemically Frozen Hadron Phase • Statistical model • Tch>Tth • (conventional) hydro • Tch=Tth • No reproduction • of ratio and spectra • simultaneously Chemical parameters  particle ratio Thermal parameters pt spectra

  37. Nobody knows this fact… P.Huovinen, QM2002 proceedings

  38. Extension of Phase Diagram • Single Tf in hydro • Hydro works? • Both ratio and • spectra? Introduction of chemical potential for each hadron! mi

  39. 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?

  40. 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)

  41. 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

  42. 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

  43. 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

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

  45. 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

  46. v2(pT) for identified hadronsfrom QGP Hydro + Hadronic Cascade 20-30% Mass dependence is o.k. Note: First result was obtained by Teaney et al.

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

  48. 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.

  49. 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?!

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