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Perfect Fluid QGP Perfect Fluid QGP or CGC? or CGC? Tetsufumi HiranoTetsufumi Hirano
Institute of Physics, University of Institute of Physics, University of TokyoTokyoReferences: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, T.Hirano, U.Heinz, D.Kharzeev, R.Lacey, Y.Nara, Y.Nara, Phys.Lett.B Phys.Lett.B 636636 (2006)299; work in progress. (2006)299; work in progress.Seminar@RCNP, 7/27/2006Seminar@RCNP, 7/27/2006
OUTLINEOUTLINE
• IntroductionIntroduction• Basic checksBasic checks• Dynamical modeling in heavy ion collisions Dynamical modeling in heavy ion collisions
based on ideal hydrodynamicsbased on ideal hydrodynamics• 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
IntroductionIntroductionWhat is the origin
of matter?
What is the matterwhere our building block
plays a fundamental role?
Matter Particle: quarkGauge Particle: gluonDynamics : QCDMatter form : QGP
Quarks, Leptons+Gauge particles
ConfinementQuark Gluon Plasma
Two Faces of QCDTwo Faces of QCD
Low energy scale Low energy scale High energy scale High energy scale??? ??? perturbation perturbation OK! OK!
S. Eidelman et al.F.Karsch and E.Laermann
q-qbar potentialq-qbar potentialStrong coupling “constant”Strong coupling “constant”
Color confinement Asymptotic freedom
QGP RecipeQGP Recipe
1. Adding pressure Pushing up chemical potential scale2. Adding heat Pushing up temperature scale
QGP from 1QGP from 1stst principle calculations principle calculations
•Critical temperature Tc ~170MeV ~2x1012K !
c ~0.3-1.3GeV/fm3 •Rapid increase around Tc
Karsch et al.
Stefan-Boltzmann law(energy density)∝(d.o.f.)x(temperature)4
Hadron phase(): 3 QGP: 37 (color, flavor…)
Normalized temperature
QGPQGP
HadronizationHadronization
NucleosynthesisNucleosynthesis
Matter Evolved with Our Matter Evolved with Our Universe Universe
QGP studyQGP study
UnderstandingUnderstandingearly universeearly universe
Little Bang!Little Bang!Relativistic Heavy Ion
Collider(2000-)RHIC as a time machine!
100 GeV per nucleonAu(197×100)+Au(197×100)
Collision energy
Multiple production
Heat
sideview
frontview
STAR
STAR
Physics of the QGPPhysics of the QGP
• Matter governed by QCD, not QEDMatter governed by QCD, not QED
• High energy density/temperature frontier High energy density/temperature frontier Toward an ultimate matter (Maximum Toward an ultimate matter (Maximum
energy density/temperature)energy density/temperature)
• Reproduction of QGP in H.I.C.Reproduction of QGP in H.I.C.Reproduction of early universe on the EarthReproduction of early universe on the Earth
• Understanding the origin of matter which Understanding the origin of matter which evolves with our universeevolves with our universe
BASIC CHECKSBASIC CHECKSAS AN AS AN
INTRODUCTIONINTRODUCTION
Basic Checks (I): Energy Basic Checks (I): Energy DensityDensity
Bjorken energy densityBjorken energy density
: proper time: proper timey: rapidityy: rapidityR: effective transverse radiusR: effective transverse radiusmmTT: transverse mass: transverse mass
Bjorken(’83)Bjorken(’83)
Critical Energy Density from Critical Energy Density from LatticeLattice
Stolen from Karsch(PANIC05).Stolen from Karsch(PANIC05).
Centrality Dependence of Centrality Dependence of Energy DensityEnergy Density
PHENIX(’PHENIX(’0505))
c from lattice
Well aboveWell abovecc from lattice from lattice
in centralin centralcollision at RHIC, collision at RHIC,
if assumingif assuming=1fm/c.=1fm/c.
CAVEATS (I)CAVEATS (I)
• Just a necessary condition in the sense that Just a necessary condition in the sense that temperature (or pressure) is not measured. temperature (or pressure) is not measured. (Just a firework?)(Just a firework?)
• How to estimate tau?How to estimate tau?
• If the system is thermalized, the actual If the system is thermalized, the actual energy density is larger due to pdV work.energy density is larger due to pdV work.
• Boost invariant?Boost invariant?
• Averaged over transverse area. Effect of Averaged over transverse area. Effect of thickness? How to estimate area?thickness? How to estimate area?
Gyulassy, Matsui(’84) Ruuskanen(’84)
Basic Checks (II): Chemical Basic Checks (II): Chemical Eq.Eq.
Two fitting parameters: TTwo fitting parameters: Tchch, , BB
directdirect Resonance decayResonance decay
Amazing fit!Amazing fit!
T=177MeV, T=177MeV, BB = 29 MeV = 29 MeV
Close to TClose to Tcc from lattice from lattice
CAVEATS (II)CAVEATS (II)• Even eEven e++ee-- or pp data can be fitted or pp data can be fitted
well!well!See, e.g., Becattini&Heinz(’97)See, e.g., Becattini&Heinz(’97)
• What is the meaning of fitting What is the meaning of fitting parameters? parameters? See, e.g., See, e.g.,
Rischke(’02),Koch(’03)Rischke(’02),Koch(’03) • Why so close to TWhy so close to Tcc??
No chemical eq. in hadron phase!?No chemical eq. in hadron phase!? Essentially dynamical problem!Essentially dynamical problem!
Expansion rate Expansion rate Scattering rate Scattering rate (Process dependent)(Process dependent)
see, e.g., U.Heinz, nucl-th/0407067see, e.g., U.Heinz, nucl-th/0407067
Statistical Model Fitting to Statistical Model Fitting to ee&ppee&pp
Becattini&Heinz(’97)Becattini&Heinz(’97)
Phase space dominance? Phase space dominance? ““T” prop to E/N?T” prop to E/N? See, e.g., Rischke(’02),Koch(’03)See, e.g., Rischke(’02),Koch(’03)
Basic Checks (III): Radial Basic Checks (III): Radial FlowFlow
Spectrum for heavier particlesSpectrum for heavier particlesis a good place to see radial flow.is a good place to see radial flow.
Blast wave model Blast wave model (thermal+boost)(thermal+boost)
Driving force of flow:Driving force of flow:Inside: high pressureInside: high pressure
Outside: vacuum (Outside: vacuum (pp=0) =0) pressure gradientpressure gradient
Sollfrank et al.(’93)Sollfrank et al.(’93)
Spectrum change is seen in Spectrum change is seen in AA!AA!
O.B
ara
nn
ikova,
talk
at
QM
05
Power law in pp & Power law in pp & dAudAu
Convex to Power Convex to Power law law
in Au+Auin Au+Au•““Consistent” Consistent” with thermal + with thermal + boost pictureboost picture•Pressure can be Pressure can be built up in AAbuilt up in AA
CAVEATS (III)CAVEATS (III)• Finite radial flow even in pp collisions? Finite radial flow even in pp collisions?
– (T,v(T,vTT)~(140MeV,0.2))~(140MeV,0.2)– Is blast wave reliable quantitatively?Is blast wave reliable quantitatively?
• Not necessary to be thermalized completely Not necessary to be thermalized completely – Results from hadronic cascade models.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 Chi square minimum located a different point for and 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 1010-23-23 (10 yocto) sec. in H.I.C. (10 yocto) sec. in H.I.C.• Flow profile? Freezeout hypersurface? Sudden Flow profile? Freezeout hypersurface? Sudden
freezeout?freezeout?
Basic Checks Basic Checks Necessary Necessary Conditions to Study QGP at Conditions to Study QGP at RHICRHIC• Energy density can be well above Energy density can be well above cc..
– tau? thermalized?tau? thermalized?
• ““Temperature” can be extracted. Temperature” can be extracted. (particle ratio)(particle ratio)– ee++ee-- and pp? Why freezeout happens so and pp? Why freezeout happens so
close to Tclose to Tcc
• Pressure can be built up. (pPressure can be built up. (pTT spectra) spectra)– Completely thermalized?Completely thermalized?
Importance of Systematic Study Importance of Systematic Study based on Dynamical Frameworkbased on Dynamical Framework
Dynamics of Heavy Ion Dynamics of Heavy Ion CollisionsCollisions
Time scale10fm/c~10-23sec
Temperature scale 100MeV~1012K
Freezeout
“Re-confinement”
Expansion, cooling
Thermalization
First contact (two bunches of gluons)
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.
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
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,…
resp
on
se =
(outp
ut)
/(in
pu
t)
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
Chemically Frozen Hadron Chemically Frozen Hadron Phase Phase
Chemical parameters particle ratioThermal parameters pt spectra
•Statistical modelTch>Tth
•(conventional) hydroTch=Tth
• No reproductionof ratio and spectrasimultaneously
Nobody knows this factNobody knows this fact……P.Huovinen, QM2002 proceedings
Extension of Phase DiagramExtension of Phase Diagram
iIntroduction of chemical potentialfor each hadron!
•Single Tf in hydro•Hydro works?•Both ratio andspectra?
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?
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!
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)!!!
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; ; nucl-th/0607018nucl-th/0607018
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
(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-)
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%
vv22(N(Npartpart) and v) and v22(eta)(eta)
Significant Hadronic Viscous EffectsSignificant Hadronic Viscous Effects at Small Multiplicityat Small Multiplicity!
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)
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
Taken from Csernai-Kapusta-Taken from Csernai-Kapusta-McLerran paperMcLerran paper
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
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!
Experimental FactsExperimental Facts
Explosive increase!Hadron and nucleusas a bunch of gluons
What happens eventually?Unitarity? Froissart bound?
Interplay between Emission Interplay between Emission and Recombinationand RecombinationSmall 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 HadronPhase Diagram” of Hadron
0
non
-pe
rtu
rba
tive
regi
on
dilute parton
CGC
geometrical s
calin
g
Q2: Size of a probe(resolution)x: Momentum fraction
DGLAP
BFKL
Linear region(s)•dilute parton•geometrical scalingNon-linear region•CGC
Color Glass Condensate Color Glass Condensate (CGC)(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”saturation”
Gribov, Levin Ryskin (’83)Gribov, Levin Ryskin (’83)Mueller, Qiu (’86)Mueller, Qiu (’86)Blaizot, Mueller (’87)Blaizot, Mueller (’87)
A Saturation ModelA Saturation ModelZ~1/mx
BFKL eq.:linearNon-linear evolution isimportant in high density.
Gluon Production from a Gluon Production from a Saturation ModelSaturation Model
Qs2
kT20
1/Qs ““saturation scale”saturation scale”
Mueller diagramggg
A la Karzeev and Levin
Results from Kharzeev & Results from Kharzeev & LevinLevin
Parton-hadron duality (gluon dist. Parton-hadron duality (gluon dist. pion dist.) pion dist.)
Unintegrated gluon dist.Unintegrated gluon dist.
dilutedilute
densedense
A Closer Look Reveals Details A Closer Look Reveals Details of Hadronic Matterof Hadronic Matter S
tole
n fro
m M
.Ble
icher (T
he B
erke
ley S
chool)
How Reliable How Reliable Quantitatively?Quantitatively?
Radial flow in pp collisions?Radial flow in pp collisions?
central
peripheral
SmallSmallrescatteringrescattering
SystemSystemexpandsexpandslike thislike thistrajectory?trajectory?
Excitation Function of vExcitation Function of v22
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.
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
Phi meson as a direct Phi meson as a direct messenger of QGP messenger of QGP hadronizationhadronization
Violation of mass orderingin low pT region!
Tiny splitting
Just after hadronization Final v2
Phi spectraPhi spectra
What happens above pT=1.5GeV/c?
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
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!
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
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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?
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))