what can we learn from hydrodynamic analysis of elliptic flow? tetsufumi hirano dept. of physics,...
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What can we learn What can we learn from hydrodynamic from hydrodynamic analysis of elliptic analysis of elliptic
flow?flow?Tetsufumi HiranoTetsufumi Hirano
Dept. of Physics, Columbia Dept. of Physics, Columbia Univ.Univ.
T.H. and M.Gyulassy, nucl-th/0506049T.H. and M.Gyulassy, nucl-th/0506049T.H., Y.Nara T.H., Y.Nara et alet al., work in progress.., work in progress.
Quark Matter 2005, August 4-9, Budapest, HungaryQuark Matter 2005, August 4-9, Budapest, Hungary
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OutlineOutline
1.1. Perfect fluidity of sQGP core and Perfect fluidity of sQGP core and highly dissipative hadronic coronahighly dissipative hadronic corona
2.2. CGC + full 3D hydro + cascadeCGC + full 3D hydro + cascade
3.3. Hydrodynamic analysis suggests Hydrodynamic analysis suggests even a signal ofeven a signal of
DECONFINEMENT?!DECONFINEMENT?!
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Bases of the DiscoveryBases of the Discovery
Integrated elliptic flow
NA49(’03)
PHENIX white paper
Differential elliptic flow
Our claims:Our claims:1.1. Ideal hydrodynamics Ideal hydrodynamics
accidentally accidentally reproduces these reproduces these
data!data!2.2. Nevertheless, Nevertheless,
“perfect fluidity of the “perfect fluidity of the sQGP” statement and sQGP” statement and early thermalization early thermalization
still hold. still hold.
WHY!!!???WHY!!!???
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Classification of Hydro Classification of Hydro ModelsModels
Tc
QG
P p
has
eH
ad
r on
ph a
s e
Partial
Chemical
Equilibrium
EOS
Model PCE:Hirano & Tsuda;
Teaney;Kolb & Rapp…
Model HC:Teaney, Lauret
& Shuryak;Bass & Dumitru…
Tch
Tth
Hadronic
Cascade
Chemical
Equilibrium
EOS
Tth
Model CE:Kolb, Sollfrank,
Huovinen & Heinz;Hirano;…
Perfect Fluid of QGP
T
~1 fm/c
~3 fm/c
~10-15 fm/c
ideal hydrodynamics
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PH
EN
IX w
hite
pa
per, N
PA
757
,184
(200
5)
Are hydro results consistent?If not, what does it mean?
elliptic flow
pT spectra
p
PartialCEPartialCE
Chem.Eq.Chem.Eq.
HadronicCascadeHadronicCascade
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Differential Elliptic Flow Differential Elliptic Flow DevelopsDevelops
in the Hadron Phase?in the Hadron Phase?
T.H
. and K.T
suda (’02)
Ko
lb a
nd
Hei
nz(
’04)
0.4 0.6 0.80.20 0.4 0.6 0.80.20 1.0
140MeV
100MeV
transverse momentum (GeV/c)
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Mean pT is the Key
Response to decreasing Tth (or increasing )v2
PCE
CE
v2/<pT><pT>
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Cancel between vCancel between v22 and and <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
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1.Why mean pT behaves so differently?2. Why CE result ~ HC result?
PartialCEPartialCE
Chem.Eq.Chem.Eq.
HadronicCascadeHadronicCascade
PH
EN
IX w
hite
pa
per,
NP
A75
7,1
84
(20
05
)
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Intuitive PictureIntuitive Picture
ChemicalFreezeoutChemicalFreezeout
Chemical EquilibriumChemical
Equilibrium
Mean ET decreasesdue to pdV work
For a more rigorous discussion, see T.H. and M.Gyulassy, nucl-th/0506049
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!!!
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Summary of Hydro Summary of Hydro ResultsResults
Models for
Hadron
Phasev2(pT,m)
pT
spectra
Yield
or ratio
Viscous
effectCaveat
Chemical
Equilibrium Yes Yes* No No
* P (Pbar) yields
<< exp. data
Partial
Chemical
EquilibriumNo Yes* Yes No
*Only low pT for pions
Hadronic Cascade Yes Yes Yes Yes*
*Kinetic approach•Boundary
(QGPhadron)
“No-Go theorem”Ruled out!
WINNER for hydro race at RHIC ! Hybrid model (Ideal QGP fluid + dissipative hadron gas)
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CGC + Full 3D Hydro + CGC + Full 3D Hydro + CascadeCascade
0z
t
ColorGlassCondensate
sQGP core(Full 3DHydro)
HadronicCorona(Cascade)
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CGC + Full 3D Hydro CGC + Full 3D Hydro + Hadronic Cascade+ Hadronic Cascade
PHOBOS data:“Triangle shape”prop. to dN/dTth=100MeV:“Trapezoidal shape”Typical hydro resultTth=169MeV:Triangle shape!Just after hadronization
CGC+hydro+cascade:Good agreement!
Perfect fluid sQGP core +dissipative hadronic corona picture
works as well in forward region!
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What Have We Learned?What Have We Learned?T
.H. a
nd
M.G
yula
ssy
(’05
)
!•Absolute value of viscosity •Its ratio to entropy density
What makes this sudden behavior?
: shear viscosity, s : entropy density
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ConclusionConclusionCritical data harvested at RHICCritical data harvested at RHIC1.1.Particle ratio (Particle yield)Particle ratio (Particle yield)2.2.ppT T spectraspectra3.3.vv22, v, v22(p(pTT), and v), and v22(())
Nearly perfect fluidity of the sQGP coreNearly perfect fluidity of the sQGP coreANDAND
Highly dissipative hadronic coronaHighly dissipative hadronic corona DECONFINEMENT!?DECONFINEMENT!?
Hydrodynamic analysesHydrodynamic analyses
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BONUS SLIDES!BONUS SLIDES!
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Tth<Tch
Chemical parameters particle ratioThermal parameters pt spectra
•Statistical modelTch>Tth
•(conventional) hydroTch=Tth
• No reproductionof ratio and spectrasimultaneously
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Many people don’t know this…
P.Huovinen, QM2002 proceedings
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Extension of Parameter Space
i Introduction of chemical potentialfor each hadron!
•Single Tf in hydro•Hydro works?•Both ratio andspectra?
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Chemical Potential & Chemical Potential & EoSEoS
EOS
Example of chem. potential
Partial chemical equilibrium (PCE)
Expansion dynamics is changed(or not)?
T.H
. an
d K
.Tsu
da(
’02)
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Does Dynamics change?
Model PCE
Model CE
Contour(T=const.)
T() at origin
T.H
. an
d K
.Tsu
da(
’02)
<vr>(Tth)
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pT Spectra
•How to fix Tth in conventional hydro
• Response to pT slope• Spectrum harder with decreasing Tth
• Up to how large pT?
•Tth independence of slope in chemically frozen hydro
• No way to fix Tth
• Suggests necessity of (semi)hard components
Charged hadrons in AuAu 130AGeV
Chemical
Equilibrium
Partial
Chemical
EquilibriumT.H
. an
d K
.Tsu
da (
’02)
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Why <pT> behaves differently?Simplest case: Pion gasLongitudinal expansion
pdV work!
dET/dy should decrease with decreasing Tth. <ET>dN/dy should so.
CFO: dS/dy = const. dN/dy = const. <pT> MUST decreases
CE: dS/dy = const.dN/dy decreases (mass effect)<pT> can increase as long as <ET>dN/dy decreases.
Result from the 1st law of thermodynamics &
Bjorken flow
dET/d
y
proper time
ideal hydro
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QGPQGP
Fuzzy imageif focus is not adjusted yet.
QGPQGP
QGP Wanna see this?
Fine-tune the “hadronic” focus!
focus:
hadron coronaThe importance of the dissipative
hadronic corona to understand“perfect fluid” sQGP core!
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The End of 50-Year-OldThe End of 50-Year-Old Ideal, Chem. Eq. Hadronic Ideal, Chem. Eq. Hadronic
FluidFluidAfter the famous Landau’s paper (1953), ideal and chemical equilibrium hadronic hydrodynamics has been exploited for along time. However, the model may notbe used when chemical freezeout happens earlier than thermal freezeoutsince it accidentally reproduces pT spectra and v2(pT)at the cost of particle yields.
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A Long Long Time Ago…A Long Long Time Ago…
…we obtain the value R (Reynolds number)=1~10…Thus we may infer that the assumption of theperfect fluid is not so good as supposed by Landau.
Digression
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1. Ideal hydrodynamics reproduce v2(pT) remarkably well, but not HBT radii.
TRUEFALSE
2. v2(pT) is not sensitive to the late hadronic stage. TRUE
FALSE
TRUE: Ideal Hydrodynamics reproduces neither v2(pT) nor HBT radii at RHIC.
TRUE: v2(pT) depends on thermal equilibrium, chemicalequilibrium, and viscous effects in the hadron phase.
Check Sheet for Prevailing Check Sheet for Prevailing OpinionOpinion
X
X
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FAQFAQ1. We cannot say “Hydro works very well at RHIC”anymore?
Yes/No. Only a hydro+cascade model does a good job.Nevertheless, HBT puzzle!QGP as a perfect fluid. Hadron as a viscous fluid.
2. Why ideal hydro can be used for chemically frozenhydro?
We can show from AND .One has to distinguish “chemical freeze out” from “chemical non-equilibrium”.
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Finite Mean Free Path & Finite Mean Free Path & ViscosityViscosity
See, e.g. Danielewicz&Gyulassy(1985)
For ultra-relativistic particles, the shear viscosity is
Ideal hydro: 0 shear viscosity 0
Transport cross section
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Toward a Unified Model in Toward a Unified Model in H.I.C.H.I.C.
T.H. and Y.Nara (’02-)T.H. and Y.Nara (’02-)P
rope
r tim
e
Transverse momentum
CGCCGC(a la KLN)(a la KLN)
Color QuantumColor QuantumFluidFluid(Q(QSS
22<k<kTT22<Q<QSS
44//22))((xx-evolution eq.)-evolution eq.)
Shattering CGCShattering CGC(k(kTT factorization) factorization)
HydrodynamicsHydrodynamics(full 3D hydro)(full 3D hydro)
Parton energy lossParton energy loss(a la Gyulassy-Levai-Vitev)(a la Gyulassy-Levai-Vitev)
HadronicHadroniccascadecascade(JAM)(JAM)
Low pLow pTT High pHigh pTT
RecombinationRecombination
Collinear factorizedCollinear factorizedParton distributionParton distribution(CTEQ)(CTEQ)
LOpQCDLOpQCD(PYTHIA)(PYTHIA)
Nuc
lear
wav
efu
nctio
nP
arto
n di
strib
utio
n
Par
ton
prod
uctio
n(d
issi
pativ
epr
oces
s?)
QG
PH
adro
nga
s
FragmentationFragmentation
(MV model(MV modelon 2D lattice)on 2D lattice)
(classical Yang-Mills(classical Yang-Millson 2D lattice)on 2D lattice)
Jet quenchingJet quenching
Intermediate pIntermediate pTT
important in forward region?Not
cov
ered
in thi
s ta
lk
Not
cov
ered
in thi
s ta
lk
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Importance of Importance of Thermalization Stage at Thermalization Stage at
RHICRHIC
•CGC + hydro + cascade agreement only up to 15~20% centrality(impact parameter ~5fm)•Centrality dependenceof thermalization time
Semi-central to peripheral collisions:Not interpreted only by hadronic dissipationImportant to understand pre-thermalization stage
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Initial EccentricityInitial Eccentricity
CGC initial conditiongives ~25% largerinitial eccentricitythan participant orbinary collision scaling.
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Viscosity and EntropyViscosity and Entropy
•1+1D Bjorken flow(Ideal)
(Viscous)
•Reynolds number
: shear viscosity (MeV/fm2)s : entropy density (1/fm3)
where
/s is a good dimensionless measureto see viscous effects.
R>>1 Perfect fluid
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Large radial flow reduces Large radial flow reduces vv22 for protonsfor protons
•Radial flow pushes protons to high pT regions•Low pT protons are likely to come from fluid elements with small radial flow
Even for positive elliptic flow of matter, v2 for heavy particles can be negative in low pT regions!
High pTprotons
Low pTprotons
xy
pT
Blast wave peak depends on
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vv22((ppTT) Stalls in Hadron ) Stalls in Hadron Phase?Phase?
D.T
eaney(’02)
Pb+Pb, SPS 17 GeV, b=6 fm
Hadronic rescattering via RQMDdoes not change v2(pT) for !
Solid lines are guide to eyes
Mechanism for stalling v2(pT)•Hydro (chem. eq.): Cancellation betweenv2 and <pT>Effect of EoS
•Hydro+RQMD: Effective viscosity
Effect of finite