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“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. 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 Why Hydrodynamics? Once one accepts local Static •EoS from Lattice QCD thermalization ansatz, •Finite T, m field theory life becomes very easy. •Critical phenomena •Chiral property of hadron Energy-momentum: Conserved number: Dynamic Phenomena in HIC •Expansion, Flow A possible mechanism of •Space-time evolution of apparent thermalization thermodynamic variables Talk by Y.Nara Three Inputs for Hydrodynamic Models Final stage: Free streaming particles t Need decoupling prescription Intermediate stage: Hydrodynamics can be valid as far as local thermalization is achieved. Need EoS P(e,n) z 0 Initial stage: Particle production, Need modeling pre-thermalization, instability? (1) EoS, (2) Initial cond., Instead, initial conditions and (3) Decoupling are put for hydro simulations. Intermediate Stage: Equation of State Typical EoS in hydro models Lattice QCD simulations P.Kolb and U.Heinz(’03) H: resonance gas(RG) F.Karsch et al. (’00) Q: QGP+RG Recent lattice results at finite T Latent heat Talk by Y.Aoki Lattice QCD predicts cross over phase transition. Nevertheless, energy density explosively increases in the vicinity of Tc. Looks like 1st order. Initial Stage: Initial Condition Energy density distribution Transverse plane Reaction plane Parameterization/model-calculation to reproduce (dN/dh)/(Npart/2) and dN/dh Final Stage: Freezeout (1) Sudden freezeout (2) Transport of hadrons T=Tf via Boltzman eq. (hybrid) t t Hadron fluid QGP fluid QGP fluid z z 0 0 At T=Tf, Continuum approximation no l=0 (ideal fluid) longer valid at the late stage l=infinity (free stream) Molecular dynamic approach for hadrons (p,K,p,…) Caveats on Hydrodynamic Results 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. 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 Interaction among 2v2 produced particles dN/df dN/df OUTPUT Momentum Anisotropy 0 f 2p 0 f 2p Elliptic Flow from a Kinetic Theory Zhang et al.(‟99) ideal hydro limit 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(fm/c) T = 500 MeV generated through secondary collisions v2 is saturated in the early stage sensitive to cross section (~m.f.p.~viscosity) Basis of the Announcement STAR(‟02) PHENIX(‟03) pT dependence Multiplicity dependence and mass ordering Hydro results: Huovinen, Kolb, Heinz,… Sensitivity to Different Assumptions in Early/Late Stages Initial Condition Color Glass Glauber-type Condensate Freezeout ? Sudden Discovery of freezeout “Perfect Liquid” Hadronic rescattering ? ? Dependence on Freezeout Prescription T.Hirano and M.Gyulassy, Nucl.Phys.A 769(2006)71. Classification of Hydro Models Model HC: T Model CE: Model PCE: Teaney, Shuryak, Kolb, Huovinen, Hirano, Teaney, Bass, Dumitru, Heinz, Hirano… Kolb… QGP phase … ~1 fm/c Perfect Fluid of QGP Tc ~3 fm/c Tch Partial Chemical Hadronic Chemical Equilibrium Cascade Equilibrium EOS EOS Tth Tth ~10-15 fm/c t ideal hydrodynamics 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? 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. v2 <p > Why <pT> behaves differently? Mean ET Chemical ET per particle increases decreases Freezeout in chemical equilibrium. due to pdV work This effect delays cooling of the system like a viscous fluid. Chemical equilibrium imitates viscosity MASS energy at the cost of particle yield! Chemical Hydro+Cascade is the only model to Equilibrium KINETIC reproduce v2(pT)!!! energy For a more rigorous discussion, see TH and M.Gyulassy, NPA769(2006)71 v2(pT) for identified hadrons from QGP Hydro + Hadronic Cascade Pion 20-30% Proton Mass dependence is o.k. Mass splitting/ordering comes Note: First result was obtained from hadronic rescattering. by Teaney et al. Not a direct signature of perfect fluid QGP v2(Npart) and v2(eta) Significant Hadronic Viscous Effects at Small Multiplicity! Summary So Far • When we employ Glauber-type initial conditions, hadronic dissipation is indispensable. • 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 Centrality dependence Rapidity dependence •Glauber model Npart:Ncoll = 85%:15% •CGC model Details on CGC Matching I.C. via e(x,y,h) Talk by K.Itakura 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 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) v2(pT) and v2(eta) from CGC initial conditions 20-30% v2(model) > v2(data) 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! 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! Excitation Function of v2 Hadronic Dissipation •is huge at SPS. •still affects v2 at RHIC. •is almost negligible at LHC. 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 Non-Gaussian Source? y p x= 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: l0 shear viscosity 0 Transport cross section 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. 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?! Temperature Dependence of h/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: [Pa] = [N/m2] Digression (Dynamical) Viscosity h: ~1.0x10-3 [Pa s] (Water 20℃) ~1.8x10-5 [Pa s] (Air 20℃) Kinetic Viscosity n=h/r: ~1.0x10-6 [m2/s] (Water 20℃) ~1.5x10-5 [m2/s] (Air 20℃) hwater > hair BUT nwater < nair Non-relativistic Navier-Stokes eq. (a simple form) Neglecting external force and assuming incompressibility. A Bigger Picture in Heavy Ion Collisions QGP or GP production collisions Before CGC Geometric Scaling “DGLAP region” equilibrium Transverse momentum Shattering CGC (N)LOpQCD Dissipative “Perfect” fluid Parton Pre- Instability? Equilibration? Parton energy loss Hydrodynamics •Inelastic Interaction •Elastic •viscosity? •non chem. eq.? Recombination Coalescence hadron Hadronic Proper time Fragmentation gas cascade Low pT Intermediate pT High pT Differential Elliptic Flow Develops in the Hadron Phase? Kolb and Heinz(‟04) Is v2(pT) really sensitive to the late dynamics? T.H. and K.Tsuda (‟02) 100MeV 140MeV 0 0.2 0.4 0.6 0.8 0 0.2 0.4 0.6 0.8 1.0 transverse momentum (GeV/c) Mean pT is the Key Generic feature! t t Slope of v2(pT) ~ v2/<pT> Response to decreasing Tth (or increasing t) v2 <pT> v2/<pT> CE PCE t TH et al.(’05-) (CGC +)QGP Hydro+Hadronic Cascade t Hadronic Corona (Cascade, JAM) sQGP core (Full 3D z Ideal Hydro) 0 (Option) Color Glass Condensate Ideal QGP Fluid + Dissipative Hadron Gas Models hydro (1+1)D with (2+1)D with Full (3+1)D Bjorken flow Bjorken flow cascade UrQMD A.Dumitru et al., PLB460,411(1999); C.Nonaka and S.Bass, nucl-th/0510038. PRC60,021902(1999); S.Bass and A.Dumitru, N/A PRC61,064909(2000). RQMD D.Teaney et al., PRL86,4783(2001), N/A nucl-th/0110037; D.Teaney, N/A nucl-th/0204023. JAM TH, U.Heinz, D.Kharzeev, R.Lacey, N/A N/A and Y.Nara, PLB636,299(2006). TH&Gyulassy(’06),TH,Heinz,Kharzeev,Lacey,Nara(’06) Hydro Meets Data for the First Time at RHIC: “Current” Three Pillars 1. Perfect Fluid (s)QGP Core • Ideal hydro description of the QGP phase • Necessary to gain integrated v2 2. Dissipative Hadronic Corona • Boltzmann description of the hadron phase • Necessary to gain enough radial flow • Necessary to fix particle ratio dynamically 3. Glauber Type Initial Condition • Diffuseness of initial geometry A Lack of each pillar leads to discrepancy! pT Spectra for identified hadrons from 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. Discussions: Hadronic Dissipation • Hybrid Model: QGP Fluid + Hadronic Gas + Glauber I.C. ComparisonTry to draw • Hydro Model: information on hadron gas QGP Fluid + Hadronic Fluid + Glauber I.C. 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) 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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