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. 7/27/2006

OUTLINE Introduction Introduction Basic checks Basic checks Dynamical modeling in heavy ion collisions based on ideal hydrodynamics Dynamical modeling in heavy ion collisions based on ideal hydrodynamics Elliptic flow and perfect fluid Elliptic flow and perfect fluid Results from hydro models Results from hydro models –Dependence on freezeout prescription –Dependence on initialization Summary and Outlook Summary and Outlook

Introduction What is the origin of matter? What is the matter where our building block plays a fundamental role? Matter Particle: quark Gauge Particle: gluon Dynamics : QCD Matter form : QGP Quarks, Leptons +Gauge particles ConfinementQuark Gluon Plasma

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

QGP Recipe 1.Adding pressure  Pushing up chemical potential scale 2.Adding heat  Pushing up temperature scale

QGP from 1 st principle calculations Critical temperature T c ~170MeV ~2x10 12 K !  c ~ GeV/fm 3 Rapid increase around T c Karsch et al. Stefan-Boltzmann law (energy density) ∝ (d.o.f.)x(temperature) 4 Hadron phase(  ): 3  QGP: 37 (color, flavor…) Normalized temperature

QGPHadronizationNucleosynthesis Matter Evolved with Our Universe QGP study Understanding early universe

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

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

BASIC CHECKS AS AN INTRODUCTION

Basic Checks (I): Energy Density Bjorken energy density  : proper time y: rapidity R: effective transverse radius m T : transverse mass Bjorken(’83)

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

Centrality Dependence of Energy Density PHENIX(’05)  c from lattice Well above  c from lattice in central collision at RHIC, if assuming  =1fm/c.

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

Basic Checks (II): Chemical Eq. Two fitting parameters: T ch,  B direct Resonance decay

Amazing fit! T=177MeV,  B = 29 MeV Close to T c from lattice

CAVEATS (II) Even e + e - or pp data can be fitted well! 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) What is the meaning of fitting parameters? See, e.g., Rischke(’02),Koch(’03) Why so close to T c ? Why so close to T c ?  No chemical eq. in hadron phase!?  Essentially dynamical problem! Expansion rate  Scattering rate (Process dependent) (Process dependent) see, e.g., U.Heinz, nucl-th/

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

Basic Checks (III): Radial Flow Spectrum for heavier particles is a good place to see 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 change is seen in AA! O.Barannikova, talk at QM05 Power law in pp & dAu Convex to Power law in Au+Au “Consistent” with thermal + boost picture“Consistent” with thermal + boost picture Pressure can be built up in AAPressure can be built up in AA

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

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

Dynamics of Heavy Ion Collisions Time scale 10fm/c~ sec Temperature scale 100MeV~10 12 K Freezeout “Re-confinement” Expansion, cooling Thermalization First contact (two bunches of gluons)

Why Hydrodynamics? Static EoS from Lattice QCDEoS from Lattice QCD Finite T,  field theoryFinite T,  field theory Critical phenomenaCritical phenomena Chiral property of hadronChiral property of hadron Dynamic Phenomena in HIC Expansion, FlowExpansion, Flow Space-time evolution ofSpace-time evolution of thermodynamic variables thermodynamic variables Once one accepts local thermalization ansatz, life becomes very easy. Energy-momentum: Conserved number:

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

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

Initial Stage: Initial Condition Transverse plane Reaction plane Energy density distribution Parameterization/model-calculation to reproduce (dN/d  )/(N part /2) and dN/d 

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

Obviously, final results depend on Obviously, final results depend on modeling of 1.Equation of state 2.Initial condition 3.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. Caveats on Hydrodynamic Results

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 

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

Basis of the Announcement PHENIX(’03)STAR(’02) Multiplicity dependence p T dependence and mass ordering Hydro results: Huovinen, Kolb, Heinz,… response = (output)/(input)

Sensitivity to Different Assumptions in Early/Late Stages Glauber-type Color Glass Condensate Sudden freezeout Discovery of “Perfect Liquid” ? Hadronic rescattering ?? InitialCondition Freezeout

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

Classification of Hydro Models TcTc QGP phase Hadron phase  P artial C hemical E quilibrium EOS Model PCE: Hirano, Teaney, Kolb… Model HC: Teaney, Shuryak, Bass, Dumitru, … T ch T th H adronic C ascade C hemical E quilibrium EOS T th Model CE: Kolb, Huovinen, Heinz, Hirano… Perfect Fluid of QGP T ~1 fm/c ~3 fm/c ~10-15 fm/c ideal hydrodynamics

Chemically Frozen Hadron Phase Chemical parameters  particle ratio Thermal parameters  p t spectra Statistical model T ch >T th (conventional) hydro T ch =T th No reproduction of ratio and spectra simultaneously

Nobody knows this fact… P.Huovinen, QM2002 proceedings

Extension of Phase Diagram ii Introduction of chemical potential for each hadron! Single T f in hydro Hydro works? Both ratio and spectra?

v 2 (p T ) 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?

Differential Elliptic Flow Develops in the Hadron Phase? T.H. and K.Tsuda (’02) Kolb and Heinz(’04) Is v 2 (p T ) really sensitive to the late dynamics? MeV 100MeV transverse momentum (GeV/c)

Mean p T is the Key Slope of v 2 (p T ) ~ v 2 / Response to decreasing T th (or increasing  ) v2v2v2v2 PCE CE v 2 / v 2 / <pT><pT><pT><pT>    Generic feature!

Accidental Reproduction of v 2 (p T ) pTpT v 2 (p T ) v2v2 pTpT v 2 (p T ) v2v2 pTpT v 2 (p T ) v2v2 Chemical Eq. Chemical F.O. At hadronization CE: increase CFO: decrease freezeout

Why behaves differently? Chemical Freezeout Chemical Freezeout Chemical Equilibrium Chemical Equilibrium Mean E T decreases due to pdV work For a more rigorous discussion, see TH and M.Gyulassy, NPA769(2006)71 MASS energy KINETIC energy E T per 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 v 2 (p T )!!!

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/ ; nucl- th/ RQMDN/A D.Teaney et al., PRL86,4783(2001), nucl-th/ ; D.Teaney, nucl-th/ N/A JAMN/AN/A TH, U.Heinz, D.Kharzeev, R.Lacey, and Y.Nara, PLB636,299(2006). hydro cascade

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

v 2 (p T ) for identified hadrons from QGP Hydro + Hadronic Cascade Mass dependence is o.k. Note: First result was obtained by Teaney et al %

v 2 (N part ) and v 2 (eta) Significant Hadronic Viscous Effects at Small Multiplicity at Small Multiplicity!

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)

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)

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

Taken from Csernai-Kapusta- McLerran paper

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

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

(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

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 TH et al.(’06)

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) Hirano and Nara(’04), Hirano et al.(’06) Kuhlman et al.(’06), Drescher et al.(’06)

v 2 (p T ) and v 2 (eta) from CGC initial conditions v 2 (model) > v 2 (data) 20-30%

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

Experimental Facts Explosive increase! Hadron and nucleus as a bunch of gluons What happens eventually? Unitarity? Froissart bound?

Interplay between Emission and Recombination Small x gluons come from large x partons (linear effect) Fusion of two gluons (non-linear effect) Figures from Iancu and Venugopalan, QGP3

“Phase Diagram” of Hadron 0 non-perturbative region dilute parton CGC geometrical scaling Q 2 : Size of a probe (resolution) x: Momentum fraction DGLAP BFKL Linear region(s) dilute parton geometrical scaling Non-linear region CGC

Color Glass Condensate (CGC) Color: Gluons are colored Glass: The strong analogy to actual glasses. Disorder Evolve slowly due to Lorentz time duration Condensate: High density of massless gluons Density  ~ 1/  s >>1 Coherence “Characteristic momentum” a.k.a. saturation scale “saturation” Gribov, Levin Ryskin (’83) Mueller, Qiu (’86) Blaizot, Mueller (’87)

A Saturation Model Z~1/mx BFKL eq.:linear  Non-linear evolution is important in high density.

Gluon Production from a Saturation Model Qs2Qs2  kT2kT2 0 1/Q s “saturation scale” Mueller diagram gg  g A la Karzeev and Levin

Results from Kharzeev & Levin Parton-hadron duality (gluon dist.  pion dist.) Unintegrated gluon dist. dilute dense

A Closer Look Reveals Details of Hadronic Matter Stolen from M.Bleicher (The Berkeley School)

How Reliable Quantitatively? Radial flow in pp collisions? central peripheral  Smallrescattering Systemexpands like this trajectory?

Excitation Function of v 2 Hadronic Dissipation is huge at SPS.is huge at SPS. still affects v2 at RHIC.still affects v2 at RHIC. is almost negligible at LHC.is almost negligible at LHC.

v 2 (p T ) for identified hadrons from QGP Hydro + Hadronic Cascade Mass dependence is o.k. Note: First result was obtained by Teaney et al % Proton Pion Mass splitting/ordering comes from hadronic rescattering.  Not a direct signature of perfect fluid QGP

Phi meson as a direct messenger of QGP hadronization Violation of mass ordering in low p T region! Tiny splitting Just after hadronization Final v 2

Phi spectra What happens above p T =1.5GeV/c?

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

Non-Gaussian Source? x y p x = 0.5GeV/c

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

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 !

A Bigger Picture in Heavy Ion Collisions Proper time Transverse momentum CGC Geometric Scaling Shattering CGC Hydrodynamics viscosity?viscosity? non chem. eq.?non chem. eq.? Parton energy loss InelasticInelastic ElasticElastic Hadroniccascade Low p T High p T RecombinationCoalescence “DGLAP region” (N)LOpQCD Before collisions PartonproductionPre-equilibrium “Perfect” fluid QGP or GP Dissipativehadrongas Fragmentation Interaction Intermediate p T Instability?Equilibration?

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.

Discussions: Hadronic Dissipation Hybrid Model: Hybrid Model: QGP Fluid + Hadronic Gas + Glauber I.C. Hydro Model: 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 phasePartial chemical equilibrium in hadron phase Particle ratio fixed at T chParticle ratio fixed at T ch  Chemical equilibrium changes dynamics. TH and K.Tsuda(’02),TH and M.Gyulassy(’06) TH and K.Tsuda(’02),TH and M.Gyulassy(’06)

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