Spectra and Flow from a Full 3D Hydro+Cascade Model 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. Workshop “How perfect is this matter?” in 2006 RHIC & AGS annual users’ meeting

OUTLINE Dynamical modeling in heavy ion collisions (hydro+cascade) Dynamical modeling in heavy ion collisions (hydro+cascade) Results from OUR hydro + cascade model Results from OUR hydro + cascade model Discussion on hadronic dissipation Discussion on hadronic dissipation Summary Summary

A Bigger Picture 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?

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/ 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

What needed (practically) for Dynamical Modeling in Heavy Ion Collisions Man Power Man Power –Modeling –Coding Computing Power Computing Power Consistency of Results Consistency of Results –Comparison among groups –Need benchmark calculations? –Not exclusive, but supplementary Maintenance of Codes Maintenance of Codes –UrQMD: UrQMD collaboration (Frankfurt) –3D hydro (Lagrange): C.Nonaka (Nagoya) –JAM: Y.Nara (Frankfurt) –3D hydro (Euler): T.Hirano (Tokyo) Previous talk Current talk

(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-) 0.6fm/c

Hydro Meets Data for the First Time at RHIC: “Current” Three Pillars 1. Perfect Fluid (s)QGP Core Ideal hydro description of the QGP phaseIdeal hydro description of the QGP phase Necessary to gain integrated v 2Necessary to gain integrated v 2 2. Dissipative Hadronic Corona Boltzmann description of the hadron phaseBoltzmann description of the hadron phase Necessary to gain enough radial flowNecessary to gain enough radial flow Necessary to fix particle ratio dynamicallyNecessary to fix particle ratio dynamically 3. Glauber Type Initial Condition Diffuseness of initial geometryDiffuseness of initial geometry TH&Gyulassy(’06),TH,Heinz,Kharzeev,Lacey,Nara(’06) A Lack of each pillar leads to discrepancy!

(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

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.

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 Result of JAM: Courtesy of M.Isse 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 ) for identified hadrons from QGP Hydro + Hadronic Cascade Glauber type initial condition CGC initial condition Mass dependence is o.k. v 2 (model) > v 2 (data) 20-30%

v 2 (  ) from QGP Hydro + Hadronic Cascade Glauber-BGKCGC

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)

Hydro ~ Hydro+Cascade for Protons T th ~ 100 MeVT th ~ 100 MeV Shape of spectrumShape of spectrum changes due to radial flow rather than hadronic dissipation for protons. radial flow

Opposite Behavior for Pions Hadronic Fluid (pdV work) Hadronic Gas (Viscous pressure) Green line: Teaney(’03) Caveat: Transverse expansion Non-scaling solution

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 )

Mass Splitting Comes from the Late Hadronic Stage Proton Pion Pion: Generation of v2 in the hadronic stage Proton: Radial flow effects Huovinen et al.(’01) Huovinen et al.(’01) Mass splitting itself is not a direct signature of perfect fluid QGP.

v 2 (  ) from QGP Hydro + Hadronic Cascade Suppression due to hadronic dissipation Glauber-BGK

Excitation Function of v2 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.

Summary An answer to the question, “Whether Perfect Fluid QGP is discovered”, depends on relatively unknown details of the initial state. An answer to the question, “Whether Perfect Fluid QGP is discovered”, depends on relatively unknown details of the initial state. –Perfect fluid QGP or CGC? Hadronic dissipative (rescattering) effects after hadronization of QGP fluids are considered through a hadron cascade model. Hadronic dissipative (rescattering) effects after hadronization of QGP fluids are considered through a hadron cascade model. –Many discrepancy between ideal hydro and data can be interpreted by hadronic dissipation.

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

v 2 (p T ) from Hydro: Past, Present and Future 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.” (TH,Gyulassy) Mechanism of v 2 (p T ) slope (TH,Heinz,Nara,…) +Color glass condensate Future “To be or not to be (consistent with hydro), that is THE question” -- anonymous -- anonymous History of differential elliptic flow ~History of development of hydro ~History of removing ambiguity in hydro 20-30% XXXXXXXXXXXXXX ????????????????? XXXXXXXXXXXXXX

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

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)

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 !

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