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Perfect Fluid QGP Perfect Fluid QGP or CGC? or CGC?
Tetsufumi Hirano*Tetsufumi 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; work in progress.(2006)299; work in progress.
““RHIC Physics in the Context of the Standard Model”RHIC Physics in the Context of the Standard Model”RBRC workshop on Heavy Ion PhysicsRBRC workshop on Heavy Ion Physics
* Visiting scientist at RBRC* Visiting scientist at RBRC
OUTLINEOUTLINE
• Dynamical modeling in heavy ion Dynamical modeling in heavy ion collisions based on ideal collisions based on ideal hydrodynamicshydrodynamics
• Elliptic flow and perfect fluidElliptic flow and perfect fluid
• Results from hydro modelsResults from hydro models– Dependence on freezeout prescriptionDependence on freezeout prescription– Dependence on initializationDependence on initialization
• Summary and OutlookSummary and Outlook
Why Hydrodynamics?Why Hydrodynamics?StaticStatic•EoS from Lattice QCDEoS from Lattice QCD•Finite Finite TT, , field theory field theory•Critical phenomenaCritical phenomena•Chiral property of hadronChiral property of hadron
Dynamic Phenomena in HICDynamic Phenomena in HIC•Expansion, FlowExpansion, Flow•Space-time evolution ofSpace-time evolution of thermodynamic variablesthermodynamic variables
Once one accepts localOnce one accepts localthermalization ansatz,thermalization ansatz,life becomes very easy.life becomes very easy.
A possible mechanism ofA possible mechanism ofapparent thermalizationapparent thermalization
Talk by Y.NaraTalk by Y.Nara
Energy-momentum:Energy-momentum:
Conserved number:Conserved number:
Three Inputs for Hydrodynamic Three Inputs for Hydrodynamic ModelsModels
Final stage:Free streaming particles Need decoupling prescription
Intermediate stage:Hydrodynamics can be validas far as local thermalization isachieved. 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
0z
t
Intermediate Stage: Equation Intermediate Stage: Equation of Stateof State
Latent heat
Lattice QCD predicts cross over phase transition.Nevertheless, energy density explosively increases in the vicinity of Tc. Looks like 1st order.
Lattice QCD simulationsLattice QCD simulations Typical EoS in hydro modelsTypical EoS in hydro models
H: resonance gas(RG)
p=e/3
Q: QGP+RG
F.Karsch
et a
l. (’00
)
P.K
olb
and
U.H
ein
z(’03)
Recent lattice results at finite T Talk by Y.Aoki
Initial Stage: Initial ConditionInitial Stage: Initial Condition
Transverse plane Reaction plane
Energy density distributionEnergy density distribution
Parameterization/model-calculation to reproduce (dN/d)/(Npart/2) and dN/d
Final Stage: FreezeoutFinal Stage: Freezeout(1) (1) Sudden freezeoutSudden freezeout (2) (2) Transport of hadronsTransport of hadrons
via Boltzman eq. (hybrid)via Boltzman eq. (hybrid)
Continuum approximation no Continuum approximation no longer valid at the late stagelonger valid at the late stageMolecular dynamic approach Molecular dynamic approach for hadrons (for hadrons (,K,p,…),K,p,…)
0z
t
0z
t
At At TT==TTff,,=0 (ideal fluid)=0 (ideal fluid) =infinity (free stream)=infinity (free stream)
T=Tf
QGP fluid
Hadron fluid
QGP fluid
Obviously, final results depend onObviously, final results depend onmodeling ofmodeling of
1.1.Equation of stateEquation of state2.2.Initial conditionInitial condition3.3.FreezeoutFreezeout
So it is indispensable to check sensitivitySo it is indispensable to check sensitivityof conclusion to model assumptions andof conclusion to model assumptions andtry to reduce model parameters.try to reduce model parameters.In this talk, I will cover 2 and 3.In this talk, I will cover 2 and 3.
Caveats on Hydrodynamic Caveats on Hydrodynamic ResultsResults
What is Elliptic Flow?What is Elliptic Flow?How does the system respond to spatial anisotropy?How does the system respond to spatial anisotropy?
Ollitrault (’92)Ollitrault (’92)
Hydro behaviorHydro behavior
Spatial AnisotropySpatial Anisotropy
Momentum AnisotropyMomentum Anisotropy
INPUTINPUT
OUTPUTOUTPUT
Interaction amongInteraction amongproduced particlesproduced particles
dN
/d
No secondary interactionNo secondary interaction
0 2
dN
/d
0 2
2v2
x
y
Elliptic Flow from a Kinetic Elliptic Flow from a Kinetic TheoryTheory
b b = 7.5fm= 7.5fmTime evolution of Time evolution of vv22
generated through secondary collisionsgenerated 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 distributedGluons uniformly distributedin the overlap regionin the overlap region• dNdN//dy dy ~ 300 for ~ 300 for b b = 0 fm= 0 fm• Thermal distribution with Thermal distribution with T T = 500 MeV= 500 MeV
vv22 is is
Zhang et al.(’99)Zhang et al.(’99)View from collision axisView from collision axis
ideal hydro limitideal hydro limit
t(fm/c)
v2
Basis of the AnnouncementBasis of the AnnouncementPHENIX(’03)STAR(’02)
Multiplicity dependencepT dependenceand mass ordering
Hydro results: Huovinen, Kolb, Heinz,…
Sensitivity to Different Sensitivity to Different Assumptions in Early/Late Assumptions in Early/Late StagesStages
Glauber-typeGlauber-type Color Glass Color Glass CondensateCondensate
Sudden Sudden freezeoutfreezeout
Discovery ofDiscovery of
““Perfect Perfect Liquid”Liquid”
??Hadronic Hadronic
rescatteringrescattering ?? ??
InitialInitialConditionCondition
FreezeoutFreezeout
Dependence onDependence onFreezeout PrescriptionFreezeout Prescription
T.Hirano and M.Gyulassy, Nucl.Phys.A T.Hirano and M.Gyulassy, Nucl.Phys.A 769769(2006)71.(2006)71.
Classification of Hydro ModelsClassification of Hydro Models
Tc
QG
P p
has
eH
ad
r on
ph a
s e
Partial
Chemical
Equilibrium
EOS
Model PCE:Hirano, Teaney,
Kolb…
Model HC:Teaney, Shuryak,
Bass, Dumitru,…
Tch
Tth
Hadronic
Cascade
Chemical
Equilibrium
EOS
Tth
Model CE:Kolb, Huovinen,Heinz, Hirano…
Perfect Fluid of QGP
T
~1 fm/c
~3 fm/c
~10-15 fm/c
ideal hydrodynamics
vv22(p(pTT) for Different Freezeout ) for Different Freezeout Prescriptions Prescriptions
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.”
20-30%
Why so different/similar?
Accidental Reproduction of Accidental Reproduction of vv22(p(pTT) )
pT
v2(p
T)
<pT>
v2
pT
v2(p
T)
v2
<pT>
pT
v2(p
T)
v2
<pT>
Chemical Eq.
Chemical F.O.
At hadronization
CE: increase
CFO: decrease
freezeout
Why <pWhy <pTT> behaves > behaves differently?differently?ChemicalFreezeoutChemicalFreezeout
Chemical EquilibriumChemical
Equilibrium
Mean ET decreasesdue to pdV work
For a more rigorous discussion, see TH and M.Gyulassy, NPA769(2006)71
MASS energy
KINETICenergy
ET 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 v2(pT)!!!
vv22(p(pTT) for identified hadrons) for identified hadronsfrom QGP Hydro + Hadronic from QGP Hydro + Hadronic CascadeCascade
Mass dependence is o.k.Mass dependence is o.k.Note: First result was obtainedNote: First result was obtainedby Teaney et al.by Teaney et al.
20-30%
Proton
Pion
Mass splitting/ordering comesMass splitting/ordering comesfrom hadronic rescattering.from hadronic rescattering.Not a direct signature ofNot a direct signature ofperfect fluid QGPperfect fluid QGP
vv22(N(Npartpart) and v) and v22(eta)(eta)
Significant Hadronic Viscous EffectsSignificant Hadronic Viscous Effects at Small Multiplicityat Small Multiplicity!
Summary So FarSummary So Far
• When we employ Glauber-type initial When we employ Glauber-type initial conditions, hadronic dissipation is conditions, hadronic dissipation is indispensable.indispensable.
• Perfect fluid QGP core and dissipative Perfect fluid QGP core and dissipative hadronic coronahadronic corona
Dependence onDependence onInitialization of HydroInitialization of Hydro
T.Hirano, U.Heinz, D.Kharzeev, R.Lacey, T.Hirano, U.Heinz, D.Kharzeev, R.Lacey, Y.Nara, Phys.Lett.B Y.Nara, Phys.Lett.B 636636 (2006)299; work (2006)299; work in progress.in progress.
(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
Details on CGC Talk by K.Itakura
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
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) and v) and v22(eta) from CGC (eta) from CGC initial conditionsinitial conditions
vv22(model) > v(model) > v22(data)(data)
20-30%
Summary and OutlookSummary and Outlook
• Much more studies needed for initial Much more studies needed for initial statesstates
• Still further needed to investigate EOS Still further needed to investigate EOS dependencedependence
• To be or not to be (consistent with hydro), To be or not to be (consistent with hydro), that is the question!that is the question!
FAKE!FAKE!
AcknowledgementAcknowledgementMiklos is supposedto attend thisworkshop but cannot come.I really appreciatehis continuousencouragementto my work.
Get well soon completely, Miklos!
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.
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
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
nd
Gyu
lass
y (’
06)
TH
an
d G
yula
ssy
(’0
6)
!•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
A Bigger Picture in Heavy Ion A Bigger Picture in Heavy Ion CollisionsCollisions
Pro
per
time
Pro
per
time
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
-P
re-
equi
libriu
meq
uilib
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?
Differential Elliptic Flow Differential Elliptic Flow DevelopsDevelopsin the Hadron Phase?in the Hadron Phase?
T.H
. and K.T
suda (’02)
Ko
lb a
nd
Hei
nz(
’04)
Is v2(pT) really sensitiveto the late dynamics?
0.4 0.6 0.80.20 0.4 0.6 0.80.20 1.0
140MeV
100MeV
transverse momentum (GeV/c)
Mean pMean pTT is the Key is the Key
Slope of v2(pT) ~ v2/<pT> Response to decreasing Tth
(or increasing )vv22
PCEPCE
CECE
vv22/</<ppTT>><<ppTT>>
Generic Generic feature!feature!
(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-)
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
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!
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.
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)
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))