Spectra and FlowSpectra and Flowfrom Full 3Dfrom Full 3D

Hydro+Cascade Model Hydro+Cascade Model Tetsufumi HiranoTetsufumi Hirano

Institute of Physics, University of Institute of Physics, University of TokyoTokyo

References:References:T.Hirano and M.Gyulassy, Nucl.Phys.A T.Hirano and M.Gyulassy, Nucl.Phys.A 769769(2006)71.(2006)71.T.Hirano, U.Heinz, D.Kharzeev, R.Lacey, Y.Nara, Phys.Lett.B T.Hirano, U.Heinz, D.Kharzeev, R.Lacey, Y.Nara, Phys.Lett.B 636636 (2006)299.(2006)299.

Workshop “How perfect is this matter?”Workshop “How perfect is this matter?”in 2006 RHIC & AGS annual users’ meetingin 2006 RHIC & AGS annual users’ meeting

OUTLINEOUTLINE

• Dynamical modeling in heavy ion Dynamical modeling in heavy ion collisions (hydro+cascade)collisions (hydro+cascade)

• Results from OUR hydro + cascade Results from OUR hydro + cascade modelmodel

• Discussion on hadronic dissipationDiscussion on hadronic dissipation

• Summary Summary

A Bigger PictureA Bigger PictureP

rope

r tim

eP

rope

r tim

e

Transverse momentumTransverse momentum

CGCCGC Geometric ScalingGeometric Scaling

Shattering CGCShattering CGC

HydrodynamicsHydrodynamics•viscosity?viscosity?•non chem. eq.?non chem. eq.?

Parton energy lossParton energy loss•InelasticInelastic•ElasticElastic

HadronicHadroniccascadecascade

Low pLow pTT High pHigh pTT

RecombinationRecombinationCoalescenceCoalescence

““DGLAP region”DGLAP region”

(N)LOpQCD(N)LOpQCD

Bef

ore

Bef

ore

colli

sion

sco

llisi

ons

Par

ton

Par

ton

prod

uctio

npr

oduc

tion

Pre

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re-

equi

libriu

meq

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rium

““ Per

fect

” flu

idP

erfe

ct”

fluid

QG

P o

r G

PQ

GP

or

GP

Dis

sipa

tive

Dis

sipa

tive

hadr

onha

dron

gas

gas

FragmentationFragmentation

InteractionInteraction

Intermediate pIntermediate pTT

Instability?Instability?Equilibration?Equilibration?

Ideal QGP Fluid Ideal QGP Fluid + Dissipative Hadron Gas + Dissipative Hadron Gas ModelsModels

(1+1)D with(1+1)D with

Bjorken flowBjorken flow(2+1)D with(2+1)D with

Bjorken flowBjorken flowFull (3+1)DFull (3+1)D

UrQMUrQMDD

A.Dumitru et al., A.Dumitru et al., PLB460,411(1999); PLB460,411(1999); PRC60,021902(199PRC60,021902(1999);S.Bass and 9);S.Bass and A.Dumitru, A.Dumitru, PRC61,064909(200PRC61,064909(2000).0).

N/AN/A

C.Nonaka and C.Nonaka and S.Bass, S.Bass,

nucl-th/0510038nucl-th/0510038..

RQMDRQMD

N/AN/A

D.Teaney et al., D.Teaney et al., PRL86,4783(2001), PRL86,4783(2001), nucl-th/0110037nucl-th/0110037;;

D.Teaney, D.Teaney, nucl-th/0204023nucl-th/0204023..

N/AN/A

JAMJAMN/AN/A N/AN/A

TH, U.Heinz, TH, U.Heinz, D.Kharzeev, D.Kharzeev, R.Lacey, and R.Lacey, and Y.Nara, Y.Nara, PLB636,299(2006).PLB636,299(2006).

hydrohydro

cascadecascade

What needed (practically) for What needed (practically) for Dynamical Modeling in Heavy Ion Dynamical Modeling in Heavy Ion CollisionsCollisions• Man PowerMan Power

– ModelingModeling– CodingCoding

• Computing PowerComputing Power• Consistency of ResultsConsistency of Results

– Comparison among groupsComparison among groups– Need benchmark calculations?Need benchmark calculations?– Not exclusive, but supplementary Not exclusive, but supplementary

• Maintenance of CodesMaintenance of Codes– UrQMD: UrQMD collaboration (Frankfurt)UrQMD: UrQMD collaboration (Frankfurt)– 3D hydro (Lagrange): C.Nonaka (Nagoya)3D hydro (Lagrange): C.Nonaka (Nagoya)– JAM: Y.Nara (Frankfurt)JAM: Y.Nara (Frankfurt)– 3D hydro (Euler): T.Hirano (Tokyo)3D hydro (Euler): T.Hirano (Tokyo)

Previous talkPrevious talk

Current talkCurrent talk

(CGC +)QGP Hydro+Hadronic (CGC +)QGP Hydro+Hadronic CascadeCascade

0z

t

(Option)(Option)Color GlassColor GlassCondensateCondensate

sQGP coresQGP core(Full 3D(Full 3DIdeal Hydro)Ideal Hydro)

HadronicHadronicCoronaCorona(Cascade, (Cascade, JAM)JAM)

TH et al.(’05-)TH et al.(’05-)

0.6fm/c0.6fm/c

Hydro Meets Data for the First Time Hydro Meets Data for the First Time at RHIC: “Current” Three Pillarsat RHIC: “Current” Three Pillars

1.1. Perfect Fluid (s)QGP CorePerfect Fluid (s)QGP Core• Ideal hydro description of the QGP phaseIdeal hydro description of the QGP phase• Necessary to gain integrated vNecessary to gain integrated v22

2.2. Dissipative Hadronic CoronaDissipative 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

3.3. Glauber Type Initial ConditionGlauber Type Initial Condition• Diffuseness of initial geometryDiffuseness of initial geometry

TH&Gyulassy(’06),TH,Heinz,Kharzeev,Lacey,Nara(’06)TH&Gyulassy(’06),TH,Heinz,Kharzeev,Lacey,Nara(’06)

A Lack of each pillar leads to discrepancy!A Lack of each pillar leads to discrepancy!

(1) Glauber and (2) CGC Hydro (1) Glauber and (2) CGC Hydro Initial Conditions Which Clear the Initial Conditions Which Clear the First Hurdle First Hurdle

•Glauber modelGlauber model NNpartpart:N:Ncollcoll = 85%:15% = 85%:15%•CGC modelCGC model Matching I.C. via e(x,y,Matching I.C. via e(x,y,))

Centrality dependenceCentrality dependence Rapidity dependenceRapidity dependence

ppTT Spectra for identified Spectra for identified hadronshadronsfrom QGP Hydro+Hadronic from QGP Hydro+Hadronic CascadeCascade

Caveat: Other components such as recombination and Caveat: Other components such as recombination and fragmentation should appear in the intermediate-high pfragmentation should appear in the intermediate-high pTT regions. regions.

dN/dy and dN/dpdN/dy and dN/dpTT are o.k. by hydro+cascade. are o.k. by hydro+cascade.

vv22(N(Npartpart) from ) from QGP Hydro + Hadronic QGP Hydro + Hadronic CascadeCascade

GlauberGlauber:: Early thermalizationEarly thermalization Mechanism? Mechanism? CGCCGC:: No perfect fluid?No perfect fluid? Additional viscosity Additional viscosity

is required in QGPis required in QGP

Importance of better understanding of initial Importance of better understanding of initial conditioncondition

Result of JAM: Courtesy of M.IsseResult of JAM: Courtesy of M.Isse

TH et al.(’06)TH et al.(’06)

Large Eccentricity from CGC Initial Large Eccentricity from CGC Initial ConditionCondition

xx

yy

Pocket formula (ideal hydro):Pocket formula (ideal hydro): vv22 ~ 0.2 ~ 0.2 @ RHIC energies @ RHIC energies

Ollitrault(’92)Ollitrault(’92)

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

vv22(p(pTT) for identified hadrons) for identified hadronsfrom QGP Hydro + Hadronic from QGP Hydro + Hadronic CascadeCascade

Glauber type initial conditionGlauber type initial condition CGC initial conditionCGC initial condition

Mass dependence is o.k.Mass dependence is o.k. vv22(model) > v(model) > v22(data)(data)

20-30% 20-30%

vv22(() from) fromQGP Hydro + Hadronic QGP Hydro + Hadronic CascadeCascade

Glauber-BGK CGC

Discussions: Hadronic Discussions: Hadronic DissipationDissipation• Hybrid Model:Hybrid Model:

QGP Fluid + Hadronic QGP Fluid + Hadronic GasGas + Glauber I.C. + Glauber I.C.

• Hydro Model:Hydro Model:

QGP Fluid + Hadronic QGP Fluid + Hadronic FluidFluid + Glauber I.C. + Glauber I.C.

ComparisonComparisonTry to drawTry to drawinformation on hadron gasinformation on hadron gas

Key technique in hydroKey technique in hydro: : •Partial chemical equilibrium in hadron phasePartial chemical equilibrium in hadron phase•Particle ratio fixed at TParticle ratio fixed at Tchch

Chemical equilibrium changes dynamics. 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 Hydro ~ Hydro+Cascade for ProtonsProtons

•TTthth ~ 100 MeV ~ 100 MeV•Shape of spectrumShape of spectrumchanges due tochanges due toradial flow ratherradial flow ratherthan hadronicthan hadronicdissipation fordissipation forprotons.protons.

radial flow

Opposite Behavior for PionsOpposite Behavior for Pions

Hadronic Hadronic FluidFluid(pdV work)(pdV work)

Hadronic Hadronic GasGas(Viscous pressure)(Viscous pressure)

Green line:Green line:

Teaney(’03)Teaney(’03)Caveat:Caveat:Transverse expansionTransverse expansionNon-scaling solutionNon-scaling solution

Hadronic Dissipation Hadronic Dissipation Suppresses Differential Elliptic Suppresses Differential Elliptic FlowFlow

Difference comes Difference comes from dissipation from dissipation only in the hadron only in the hadron phase phase

Caveat: Chemically frozen hadronic fluid is Caveat: Chemically frozen hadronic fluid is essential in differential elliptic flow. (TH and essential in differential elliptic flow. (TH and M.Gyulassy (’06))M.Gyulassy (’06))

•Relevant parameter: Relevant parameter: ss Teaney(’03)Teaney(’03)•Dissipative effect is not soDissipative effect is not solarge due to small expansion large due to small expansion rate (1/tau ~ 0.05-0.1 fmrate (1/tau ~ 0.05-0.1 fm-1-1))

Mass Splitting Comes from the Mass Splitting Comes from the Late Hadronic StageLate Hadronic Stage

Proton

Pion

Pion: Generation of v2Pion: Generation of v2in the hadronic stagein the hadronic stageProton: Radial flow effectsProton: Radial flow effects Huovinen et al.(’01)Huovinen et al.(’01)

Mass splitting itselfMass splitting itselfis not a direct signatureis not a direct signatureof perfect fluid QGP.of perfect fluid QGP.

vv22(() from) fromQGP Hydro + Hadronic QGP Hydro + Hadronic CascadeCascade

Suppression due tohadronic dissipation

Glauber-BGK

Excitation Function of v2Excitation Function of v2

Hadronic DissipationHadronic 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.

SummarySummary• An answer to the question, “Whether An answer to the question, “Whether

Perfect Fluid QGP is discovered”, Perfect Fluid QGP is discovered”, depends on relatively unknown depends on relatively unknown details of the initial state.details of the initial state.– Perfect fluid QGP or CGC?Perfect fluid QGP or CGC?

• Hadronic dissipative (rescattering) Hadronic dissipative (rescattering) effects after hadronization of QGP effects after hadronization of QGP fluids are considered through a fluids are considered through a hadron cascade model.hadron cascade model.– Many discrepancy between ideal hydro Many discrepancy between ideal hydro

and data can be interpreted by hadronic and data can be interpreted by hadronic dissipation.dissipation.

Source Function from 3D Hydro Source Function from 3D Hydro + Cascade+ Cascade

Blink: Ideal Hydro, Kolb and Heinz (2003)Caveat: No resonance decays in ideal hydro

How much the source functionHow much the source functiondiffers from ideal hydrodiffers from ideal hydroin Configuration space?in Configuration space?

Non-Gaussian Source?Non-Gaussian Source?

x

y

px=0.5GeV/c

vv22(p(pTT) from Hydro: Past, ) from Hydro: Past, Present and FuturePresent and Future

2000 (Heinz, Huovinen, Kolb…)2000 (Heinz, Huovinen, Kolb…)Ideal hydro w/ chem.eq.hadronsIdeal hydro w/ chem.eq.hadrons2002 (TH,Teaney,Kolb…)2002 (TH,Teaney,Kolb…)+Chemical freezeout+Chemical freezeout2002 (Teaney…)2002 (Teaney…)+Dissipation in hadron phase+Dissipation in hadron phase2005 (BNL)2005 (BNL)““RHIC serves the perfect liquid.”RHIC serves the perfect liquid.”2004-2005 (TH,Gyulassy)2004-2005 (TH,Gyulassy)Mechanism of vMechanism of v22(p(pTT) slope) slope2005-2006(TH,Heinz,Nara,…)2005-2006(TH,Heinz,Nara,…)+Color glass condensate+Color glass condensateFutureFuture““To be or not to be (consistentTo be or not to be (consistentwith hydro), that is THE question”with hydro), that is THE question” -- anonymous-- anonymous

History of differential elliptic flowHistory of differential elliptic flow~History of development of hydro~History of development of hydro~History of removing ambiguity in hydro~History of removing ambiguity in hydro

20-30%

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Viscosity from a Kinetic Viscosity from a Kinetic TheoryTheory

See, e.g. Danielewicz&Gyulassy(’85)See, e.g. Danielewicz&Gyulassy(’85)

For ultra-relativistic particles, the shear viscosity isFor ultra-relativistic particles, the shear viscosity is

IdealIdeal hydro: hydro: 00

shear viscosity shear viscosity 0 0Transport cross sectionTransport cross section

Viscosity and EntropyViscosity and Entropy

•1+1D Bjorken flow 1+1D Bjorken flow Bjorken(’83)Bjorken(’83) Baym(’84)Hosoya,Kajantie(’85)Danielewicz,Gyulassy(’85)Gavin(’85)Akase et al.(’89)Kouno et al.(’90)…Baym(’84)Hosoya,Kajantie(’85)Danielewicz,Gyulassy(’85)Gavin(’85)Akase et al.(’89)Kouno et al.(’90)…

(Ideal)(Ideal)

(Viscous)(Viscous)

•Reynolds numberReynolds number

: shear viscosity (MeV/fm: shear viscosity (MeV/fm22), ), s s : entropy density : entropy density (1/fm(1/fm33))

wherewhere

//ss is a good dimensionless measure is a good dimensionless measure(in the natural unit) to see viscous effects.(in the natural unit) to see viscous effects.

RR>>1 >>1 Perfect fluidPerfect fluid

Iso, Mori, Namiki (’59)Iso, Mori, Namiki (’59)

Why QGP Fluid + Hadron Gas Works?Why QGP Fluid + Hadron Gas Works?T

H a

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Gyu

lass

y (’

06)

TH

an

d G

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ssy

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!•Absolute value of viscosityAbsolute value of viscosity •Its ratio to entropy densityIts ratio to entropy density

Rapid increase of entropy density Rapid increase of entropy density cancan

make hydro work at RHIC.make hydro work at RHIC.Deconfinement Signal?!Deconfinement Signal?!

: shear viscosity, : shear viscosity, s s : entropy density: entropy density

Kovtun,Son,Starinets(’05)Kovtun,Son,Starinets(’05)

Temperature Dependence Temperature Dependence ofof /s/s

•We propose a possible scenario:We propose a possible scenario:

Kovtun, Son, Starinets(‘05)Kovtun, Son, Starinets(‘05)

Danielewicz&Gyulassy(’85)Danielewicz&Gyulassy(’85)•Shear Viscosity in Hadron GasShear Viscosity in Hadron Gas

•Assumption:Assumption: /s at T/s at Tcc in the sQGP is 1/4 in the sQGP is 1/4

No big jump in viscosity at Tc!

DigressionDigression(Dynamical) Viscosity (Dynamical) Viscosity :: ~1.0x10~1.0x10-3-3 [Pa s] (Water [Pa s] (Water 20℃)20℃) ~1.8x10~1.8x10-5-5 [Pa s] (Air 20℃) [Pa s] (Air 20℃) Kinetic Viscosity Kinetic Viscosity :: ~1.0x10~1.0x10-6-6 [m [m22/s] (Water/s] (Water 20℃)20℃) ~1.5x10~1.5x10-5-5 [m [m22/s] (Air/s] (Air 20℃) 20℃)

[Pa] = [N/m[Pa] = [N/m22]]

Non-relativistic Navier-Stokes eq. (a simple form)Non-relativistic Navier-Stokes eq. (a simple form)

Neglecting external force and assuming incompressibility.Neglecting external force and assuming incompressibility.

waterwater > > airair BUT BUT waterwater < < airair