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Hydrodynamic Models of Heavy- I on Collisions. Tetsufumi Hirano RIKEN BNL Research Center. Parallel Talks Based on Hydro. Jan. 13 H. Niemi , Photon production from non-equilibrium QGP in heavy-ion collisions M. Csanad , Indication for quark deconfinement and - PowerPoint PPT Presentation
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Hydrodynamic Hydrodynamic Models of Heavy-Models of Heavy-
IIon Collisionson CollisionsTetsufumi HiranoTetsufumi Hirano
RIKEN BNL Research RIKEN BNL Research CenterCenter
Tetsufumi Hirano (RBRC)Tetsufumi Hirano (RBRC) 22
Parallel Talks Based on Parallel Talks Based on HydroHydroJan. 13Jan. 13
•H. NiemiH. Niemi, , Photon production from non-equilibriumPhoton production from non-equilibrium QGP in heavy-ion collisionsQGP in heavy-ion collisions•M. CsanadM. Csanad, Indication for quark deconfinement and, Indication for quark deconfinement and evidence for a Hubble flow in Au+Au collisions at RHICevidence for a Hubble flow in Au+Au collisions at RHIC
Jan. 15Jan. 15•Y. NaraY. Nara, , CGC, hydrodynamics and the partonCGC, hydrodynamics and the parton energy lossenergy loss•E. ShuryakE. Shuryak, , Why does the QGP behaves liWhy does the QGP behaves likkee a perfect fluid?a perfect fluid?•U. HeinzU. Heinz, , Rapidity dependence of momentumRapidity dependence of momentum anisotropiesanisotropies in nuclear collisionsin nuclear collisions•D. TeaneyD. Teaney, , Viscosity and thermalizationViscosity and thermalization
Tetsufumi Hirano (RBRC)Tetsufumi Hirano (RBRC) 33
OutlineOutline1.1. Why hydrodynamics?Why hydrodynamics?2.2. How hydrodynamics works at RHICHow hydrodynamics works at RHIC3.3. Hybrid models based on Hybrid models based on
hydrodynamicshydrodynamics– Information of the insideInformation of the inside (jet quenching , EM probe)(jet quenching , EM probe)– Improvement of initial stageImprovement of initial stage
4.4. Improvement of ideal hydro Improvement of ideal hydro (viscosity)(viscosity)
5.5. SummarySummary
Tetsufumi Hirano (RBRC)Tetsufumi Hirano (RBRC) 44
1. Why Hydrodynamics?1. Why Hydrodynamics?Static•EoS from Lattice QCD•Finite T, field theory•Critical phenomena•Chiral property of hadron
Dynamic Phenomena in HIC•Expansion, Flow•Space-time evolution of thermodynamic variables
Once we accept localthermalization ansatz,life becomes very easy.
Caveat: Thermalization in HIC is a tough problem like building
the Golden Gate Bridge!
Energy-momentum:
Conserved number:
Tetsufumi Hirano (RBRC)Tetsufumi Hirano (RBRC) 55
1. Why Hydrodynamics 1. Why Hydrodynamics (contd.)(contd.)
Transverse Longitudinal
e (GeV/fm
3)
e (GeV/fm
3)
A full 3D hydrodynamic simulation with a CGC initial conditionTalk by Y.Nara
Space-time evolution of energy density in sqrt(sNN)=200 GeV Au+Au collision at b=7.2fm
spac
e-ti
me
rapi
dityHydrodynamics provides
us a very intuitive and simple description of
relativistic heavy ion collisions.
Tetsufumi Hirano (RBRC)Tetsufumi Hirano (RBRC) 66
OutlineOutline1.1. Why hydrodynamics?Why hydrodynamics?2.2. How hydrodynamics works at RHICHow hydrodynamics works at RHIC3.3. Hybrid models based on Hybrid models based on
hydrodynamicshydrodynamics– Information of the insideInformation of the inside (jet quenching , EM probe)(jet quenching , EM probe)– Improvement of initial stageImprovement of initial stage
4.4. Improvement of ideal hydro Improvement of ideal hydro (viscosity)(viscosity)
5.5. SummarySummary
Tetsufumi Hirano (RBRC)Tetsufumi Hirano (RBRC) 77:P.Kolb(’03), talk by A.Poskanzer
2. How Hydrodynamics 2. How Hydrodynamics Works at RHICWorks at RHIC
Elliptic flow (J.-Y.Ollitrault (’92))Elliptic flow (J.-Y.Ollitrault (’92))How does the system respond to initial spatial anisotropy?How does the system respond to initial spatial anisotropy?
A.Poskanzer & S.Voloshin (’98)
Dense or dilute?Dense or dilute?If dense, thermalization?If dense, thermalization?
If thermalized, EoS?If thermalized, EoS?
Tetsufumi Hirano (RBRC)Tetsufumi Hirano (RBRC) 88
Elliptic Flow of Charged Elliptic Flow of Charged ParticlesParticles
T.H.(’01)
P.Huovinen(’03)Roughly speaking,ideal hydro gives a good description
For improvement of models, talk by U.Heinz
P.Kolb et al.(’01)
Tetsufumi Hirano (RBRC)Tetsufumi Hirano (RBRC) 99
More on Elliptic FlowMore on Elliptic Flow
See recent excellent reviews, P.Huovinen (QM2002) , nucl-th/0305064; P.Kolb and U.Heinz, nucl-th/0305084; E.Shuryak, hep-ph/0312227, today’s talk.
Hydro: P.Kolb et al.(’99)(Note: Hydro+RQMD
gives a better description.D.Teaney et al.(’01))
STAR, PRC66(’02)034904
Hydro: P.Huovinen et al.(’01)
PHENIX, PRL91(’03)182301.
Tetsufumi Hirano (RBRC)Tetsufumi Hirano (RBRC) 1010
What’s next?What’s next?
Ideal hydro seems to give Ideal hydro seems to give aa
good description at RHICgood description at RHIC
1.1. Making the most use of hydroMaking the most use of hydromodels to study the RHIC physicsmodels to study the RHIC physics
2.2. Checking how robust theChecking how robust thecurrent results are whencurrent results are when
hydro models are improvedhydro models are improved
Tetsufumi Hirano (RBRC)Tetsufumi Hirano (RBRC) 1111
OutlineOutline1.1. Why hydrodynamics?Why hydrodynamics?2.2. How hydrodynamics works at RHICHow hydrodynamics works at RHIC3.3. Hybrid models based on hydrodynamicsHybrid models based on hydrodynamics
– Information inside fluidsInformation inside fluids (jet quenching , EM probe)(jet quenching , EM probe)– Improvement of initial stageImprovement of initial stage
4.4. Improvement of ideal hydro (viscosity)Improvement of ideal hydro (viscosity)5.5. SummarySummary
Tetsufumi Hirano (RBRC)Tetsufumi Hirano (RBRC) 1212
3.1 Information inside 3.1 Information inside fluidsfluids
Jet quenching isJet quenching is a manifestationa manifestation
of interaction betweenof interaction betweenmattermatter and partons and partons
(Talks by G.Moore and I.Vitev)(Talks by G.Moore and I.Vitev)
For quantitative analysis,For quantitative analysis,the information aboutthe information about
the space-time evolutionthe space-time evolutionof matterof matter
is indispensable!is indispensable!
Tetsufumi Hirano (RBRC)Tetsufumi Hirano (RBRC) 1313
3.1.1 Hydro as a Tool to 3.1.1 Hydro as a Tool to Analyze Analyze Jet QuenchingJet Quenching
Color: parton densityPlot: mini-jets
Au+Au 200AGeV, b=8 fmtransverse plane@midrapidityFragmentation switched off
hydro+jet modelJet quenching analysis takingJet quenching analysis takingaccount of (2+1)D hydro resultsaccount of (2+1)D hydro results (M.Gyulassy et al.(’02))(M.Gyulassy et al.(’02))
Hydro+Jet modelHydro+Jet model (T.H. & Y.Nara (’02))(T.H. & Y.Nara (’02))
Parton density Parton density ((xx) taken) taken from full 3D hydro simulationsfrom full 3D hydro simulations
x
yGLV 1GLV 1stst order formula (M.Gyulassy et al.(’00)) order formula (M.Gyulassy et al.(’00))
Movie and data ofMovie and data of ((xx) ) are available atare available athttp://quark.phy.bnl.gov/~hirano/http://quark.phy.bnl.gov/~hirano/
Tetsufumi Hirano (RBRC)Tetsufumi Hirano (RBRC) 1414
Interplay between Soft Interplay between Soft and Hardand Hard
NSOFT~NHARD
ppTT(1
/(1
/ ppTT)()
( dNdN
// dpdpTT))
HydrodynamicHydrodynamicafterburnerafterburner
JetJetquenchingquenching
Interesting regionIntermediate pT
(2<pT<3.5 GeV/c)Pion hard, Proton soft
It’s the veryheavy ion physics!
T.H & Y.Nara(’03)
Crossing pCrossing pTT moves movestoward high ptoward high pTT
softhard
Au+Au at b=2 fm
Tetsufumi Hirano (RBRC)Tetsufumi Hirano (RBRC) 1515
Consequense from hadron Consequense from hadron species dependent pspecies dependent pT,crossT,cross
Hydro+Jet
Talk by R.FriesTalk by R.Fries
Recombination+Fragmentation
RAA Particle ratio
“Scaling v2”Interplay between soft and hard?
Recombination mechanism?
Tetsufumi Hirano (RBRC)Tetsufumi Hirano (RBRC) 1616
Thermal photon is a penetrating probe of QGP (E.Shuryak(’78))
3.1.2 Hydro as a Tool to 3.1.2 Hydro as a Tool to Analyze Analyze Electromagnetic Electromagnetic RadiationRadiation
T, u
• Production rateProduction rate (Number per unit space-time volume)(Number per unit space-time volume)
• Invariant spectrum of photonsInvariant spectrum of photons
H.A.Weldon (’83), L.McLerran & T.Toimela (’84)C.Gale & J.Kapusta (’91)Talk by G.Moore
D.K.Srivastava & B.Sinha(’94), J.Sollfrank et al.(’97),J.Alam et al.(’01) and a lot of work
Importance of temperature profile
Tetsufumi Hirano (RBRC)Tetsufumi Hirano (RBRC) 1717
Chemical Non-Chemical Non-EquilibriumEquilibriumQGP phaseQGP phase ““Gluon Plasma (GP)” Gluon Plasma (GP)”
QGPQGPHadron Hadron phasephase
Chemical freezeoutChemical freezeout
Talk by H.Niemi
Hydro + rate eq.Hydro + rate eq.Smaller d.o.f. Smaller d.o.f. Larger Larger
initial initial TT
T.H. & K.Tsuda(’02)
Hydro( )Hydro( )Overpopulation of Overpopulation of resonance resonance Rapid Rapid
cooling cooling
T.S.Biro et al.(’93), D.K.Srivastava et al.(’97),A.K.Chaudhuri(’00), D.M.Elliott & D.Rischke(’00)
N.Arbex et al.(’01), T.H. & K.Tsuda(’02),D.Teaney(’02), P.Kolb & R.Rapp(’03)
Talk by H.Niemi
QGP phaseQGP phase Hadron phaseHadron phase
100200300400500600700800
Tem
pera
ture
(MeV
)
0
Tetsufumi Hirano (RBRC)Tetsufumi Hirano (RBRC) 1818
Novel Temperature Novel Temperature EvolutionEvolution
Caveat: one has to take account offugacity in calculating EMspectra.
•QGP phase: <1•Hadron phase: >1
Compensation betweenT and ? Talk by H.Niemiproper time
Tc
tem
pera
ture
chemical non-eq.chemical eq.
Tetsufumi Hirano (RBRC)Tetsufumi Hirano (RBRC) 1919
3.2 Improvement of Initial 3.2 Improvement of Initial ConditionCondition -Toward an unified model -Toward an unified model in HIC-in HIC-GroupGroup HydroHydro Initial conditionInitial condition
M.Gyulassy et M.Gyulassy et al.al.
SHASTA (2+1D, SHASTA (2+1D, Bjorken)Bjorken)
HIJING, event-by-eventHIJING, event-by-event
C.Nonaka et C.Nonaka et al.al.
Lagrangian hydro (full Lagrangian hydro (full 3D)3D)
URASiMA, event averageURASiMA, event average
B.Schlei et al.B.Schlei et al. HYLANDER (2+1D)HYLANDER (2+1D) VNI, event averageVNI, event averageC.E.Aguiar et C.E.Aguiar et al.al.
SPheRIO (full 3D)SPheRIO (full 3D) NeXus, event-by-eventNeXus, event-by-event
L.P.Csernai et L.P.Csernai et al.al.
Particle-in-cell (full Particle-in-cell (full 3D)3D)
String ropes, flux tubes, String ropes, flux tubes, classical YMclassical YM
K.Eskola et al.K.Eskola et al. SHASTA (2+1D, SHASTA (2+1D, Bjorken)Bjorken)
pQCD + final state pQCD + final state saturationsaturation
T.H. & Y.NaraT.H. & Y.Nara coordinate (full coordinate (full 3D)3D)
CGC, CGC, ((kkTT22,,xx) a la Kharzeev ) a la Kharzeev
& Levin& Levin…… …… ……
Tetsufumi Hirano (RBRC)Tetsufumi Hirano (RBRC) 2020
3.2.1 SPheRIO*3.2.1 SPheRIO*Main features:Main features:• ““Particle” method (a kind of Lagrangian hydro)Particle” method (a kind of Lagrangian hydro)• Numerical cost cheaper than conventional finite Numerical cost cheaper than conventional finite
grids method (Even in 3+1 D, any geometry)grids method (Even in 3+1 D, any geometry)• Event-by-event physicsEvent-by-event physics ( (NeXusNeXus + +
SPheRIO=NeXSPheRIO) SPheRIO=NeXSPheRIO) (NeXus: parton based Gribov-Regge theory)(NeXus: parton based Gribov-Regge theory)
*Smoothed Particle hydrodynamical evolution of Relativistic heavy IOn collisions (Sao Paulo & Rio de Janeiro)
C.E.Aguiar, R.Andrade, F.Grassi, Y.Hama,T.Kodama, T.Osada, O.Socolowski Jr….Poster by F.Grassi
Energy Energy densitydensityof single of single
eventeventSpectrafrom
Energy Energy densitydensityof single of single
eventevent Spectrafrom
Conventional approachSPheRIO
Similar approach based on HIJING: M.Gyulassy et al.(’97)
Tetsufumi Hirano (RBRC)Tetsufumi Hirano (RBRC) 2121
Initial Conditions in Initial Conditions in NeXSPheRIONeXSPheRIO
Single event (b=0fm)Single event (b=0fm) Average over 30 events (b=0fm)Average over 30 events (b=0fm)
Energy density in the transverse plane (z=0)Energy density in the transverse plane (z=0)
Bumpy!
Tetsufumi Hirano (RBRC)Tetsufumi Hirano (RBRC) 2222
Results from Results from NeXSPheRIONeXSPheRIOPb+Pb 17.3A GeV
Multiplicity is reduced by ~10%!
:(event average)
Effect of initial energy densityfluctuation (simple EoS case):
Negative!
pT slope is not affected largely. v2(pT) and its fluctuation?
Now the hydro simulation becomes
close to experimental situations
like event-generators!
Tetsufumi Hirano (RBRC)Tetsufumi Hirano (RBRC) 2323
3.2.2 CGC+Hydro+Jet 3.2.2 CGC+Hydro+Jet ModelModel T.H. & Y.Nara
Talk by Y.Nara
Dense MediumDense Medium
These three physics closely related with each other!
Talk by J.Jalilian-Marian
Talk by I.Vitev
Tetsufumi Hirano (RBRC)Tetsufumi Hirano (RBRC) 2424
CGC+Hydro+Jet Model CGC+Hydro+Jet Model (contd.)(contd.)
Full 3Dhydro evolution
pQCDpQCDpartonpartondilutedilute
timetimemom
entu
m s
cale
mom
entu
m s
cale
ggg
22
CGCCGCsmall xsmall xdensedense
collinearfactorization
kT factorization
Partonenergy loss
Initial condition of
energy density from
CGCAu+Au
200AGeVb=7.2fm, =0.6fm
transversetransverse longitudinallongitudinal
Tetsufumi Hirano (RBRC)Tetsufumi Hirano (RBRC) 2525
Results from Results from CGC+hydro+jetCGC+hydro+jet
Au+Au sqrt(sNN) = 200 GeV
For details, talk by Y.Nara
CGC initial conditionworks very well!
(Energy, rapidity, centralitydependences)
Tetsufumi Hirano (RBRC)Tetsufumi Hirano (RBRC) 2626
OutlineOutline1.1. Why hydrodynamics?Why hydrodynamics?2.2. How hydrodynamics works at RHICHow hydrodynamics works at RHIC3.3. Hybrid models based on Hybrid models based on
hydrodynamicshydrodynamics– Information of the insideInformation of the inside (jet quenching , EM probe)(jet quenching , EM probe)– Improvement of initial stageImprovement of initial stage
4.4. Improvement of ideal hydro (viscosity)Improvement of ideal hydro (viscosity)5.5. SummarySummary
Tetsufumi Hirano (RBRC)Tetsufumi Hirano (RBRC) 2727
4. Viscosity4. ViscosityChange not only the equations of motionbut the local thermal distribution function A.Dumitru(’02), D.Teaney(’03)
• Blast wave model + dist. fn. with viscous correction
Talks by E.Shuryak and D.Teaney
1st order correction to dist. fn.:
:Sound attenuation length
:Tensor part of thermodynamic forceReynolds number in Bjorken flow
Nearly ideal hydro !? D.Teaney(’03)
Tetsufumi Hirano (RBRC)Tetsufumi Hirano (RBRC) 2828
Break Down of Naive Break Down of Naive Navier-Stokes Eq. and a Navier-Stokes Eq. and a Relaxation MethodRelaxation Method•Non-relativistic case (Based on discussion by Cattaneo (1948))
0: Fourier’s law
: “relaxation time”
Parabolic equation (heat equation)ACAUSAL!!
Finite Hyperbolic equation (telegraph equation)
Balance eq.:
Constitutive eq.:
Talk by D.TeaneySee also, A.Muronga (’02)
Tetsufumi Hirano (RBRC)Tetsufumi Hirano (RBRC) 2929
5. Summary5. Summary
• Open our mind Open our mind !! Hydrodynamics Hydrodynamics can be used even can be used even for “high pfor “high pTT physics in HIC”.physics in HIC”.– Jet tomographyJet tomography– EM probeEM probe– (J/(J/ suppression) suppression)– ……
• Keep in mind Keep in mind !! How robust is the How robust is the
current agreement current agreement of hydro?:of hydro?:– Chemical non-eq.?Chemical non-eq.?– Initial fluctuation?Initial fluctuation?– Viscosity?Viscosity?– Thermalization?Thermalization?– EoS?EoS?– (Freeze-out?)(Freeze-out?)
Hydrodynamics is one of the valuable tools at RHIC energies
Tetsufumi Hirano (RBRC)Tetsufumi Hirano (RBRC) 3030
Thank you!Thank you!Special thanks goes to:
H.Niemi, D.Teaney,
Y.Hama, T.Kodama(SPheRIO collaboration),
Y.Nara,and
L.McLerranSpace-time evolution of energy density in
sqrt(sNN)=200 GeV Au+Au collision at b=7.2fm
Tetsufumi Hirano (RBRC)Tetsufumi Hirano (RBRC) 3131
Spare SlidesSpare Slides
Tetsufumi Hirano (RBRC)Tetsufumi Hirano (RBRC) 3232
No Boost Invariant Region No Boost Invariant Region at RHIC?at RHIC?
Basic assumption1.Finite Bjorken rod (-0<s<0)2.Massless pions3.Thermalization and Boltzmann approximation
20
Spac
e-tim
e rap
idity
Not free streaming,but thermal fluctuation!
Tetsufumi Hirano (RBRC)Tetsufumi Hirano (RBRC) 3333
Thermalization?Thermalization?Hydro people often usedHydro people often used
00 =0.2-1.0 fm/c =0.2-1.0 fm/cat RHIC energies to get large vat RHIC energies to get large v22..
pQCD +Boltzmann eq. analyses :pQCD +Boltzmann eq. analyses :•Elastic (ggElastic (gggg) collisions:gg) collisions:eqeq>6-10 fm/c>6-10 fm/c•Inelastic (ggInelastic (ggggg) collisions:ggg) collisions:eqeq=2-3fm/c=2-3fm/c
A.H.Mueller, R.Baier et al., J.Serreau et al., A.Dumitru et al.,J.Bjoraker et al. …
Thermalization controlled byThermalization controlled bynon-perturbative physics?non-perturbative physics?
Tetsufumi Hirano (RBRC)Tetsufumi Hirano (RBRC) 3434
Protons with pProtons with pTT=4 GeV/c in =4 GeV/c in hydro?hydro?
Proton: Proton: ppTT=4 GeV/=4 GeV/cc in lab. frame in lab. frame
ppTT~2.4GeV/~2.4GeV/cc in local rest frame with in local rest frame with vvTT=0.5=0.5cc
No!No!
Lorentz tr.Lorentz tr.Suppose momentum parallel to flowSuppose momentum parallel to flow
Tetsufumi Hirano (RBRC)Tetsufumi Hirano (RBRC) 3535
RecombinatioRecombinationn + +
FragmentatioFragmentation?n?
•Work in intermediate and high pT•Parameterized flow•How do we obtain such a large flow(vT~0.55c) at T=Tc?•What happens for high pT v2 if a realistic density profile is used instead of hard sphere?
•Work in low and high pT•Flow is dynamically obtained.•Radial flow in hadron phase is also important. At T=Tc, <vT>~0.25c T=100 MeV, <vT>~0.55c
Talk by R.FriesTalk by R.FriesT.H. & Y.NaraT.H. & Y.Nara
Hydro + Jet ?Hydro + Jet ?
Tetsufumi Hirano (RBRC)Tetsufumi Hirano (RBRC) 3636
Hydro + Rate Eq. in QGP Hydro + Rate Eq. in QGP phasephase
Including ggqqbar and ggggg
Collision term:
T.S.Biro et al.,Phys.Rev.C48(’93)1275.
Assuming “multiplicative” fugacity, EoS is unchanged.
Tetsufumi Hirano (RBRC)Tetsufumi Hirano (RBRC) 3737
Hydro+Jet ModelHydro+Jet Model
N
N
3
4
Fragmentation:IndependentFragmentationModel
PYTHIA3D Hydro PYTHIA
hadrons
hadronsPDF:Collinear: CTEQ5LOkT: Gaussian
Parton energy loss
pQCD LO:
*Initial and final state radiation are included.
Tetsufumi Hirano (RBRC)Tetsufumi Hirano (RBRC) 3838
Initial energy density Initial energy density fluctuationfluctuation
Suppose massless free EoS,Multiplicity is proportional to the entropy.
The 1st order term vanishes.
In the conventional approach,one uses average
initial energy density
Multiplicity WITH fluctuation < Multiplicity WITHOUT fluctuation
Tetsufumi Hirano (RBRC)Tetsufumi Hirano (RBRC) 3939
dN/ddN/d from a Saturation from a Saturation ModelModel
Qs2
kT20
gggggg
D. Kharzeev and E. Levin, Phys.Lett.B523,79(2001)
Parton-hadron dualityParton-hadron duality
s
Tetsufumi Hirano (RBRC)Tetsufumi Hirano (RBRC) 4040
Initial Condition from CGCInitial Condition from CGC
““CGC +CGC + Hydro + Jet model” Hydro + Jet model”
Saturation scale at a transverse position: Saturation scale at a transverse position:
Momentum rapidity Momentum rapidity yy space time rapidity space time rapidity ss
Input for hydrodynamicsInput for hydrodynamics
wherewhere
Unintegrated gluon distribution can be writtenUnintegrated gluon distribution can be written
Tetsufumi Hirano (RBRC)Tetsufumi Hirano (RBRC) 4141
vv22(() from CGC+Hydro) from CGC+Hydro
Tetsufumi Hirano (RBRC)Tetsufumi Hirano (RBRC) 4242
22ndnd order formula… order formula…
14 equations…
1st order 2nd orderHow obtain additional equations?
In order to ensure the second law of thermodynamics , one can choose
Balance eqs.
Constitutive eqs.