Hydrodynamic Analysis of Heavy Ion Collisions at RHIC
Tetsufumi HiranoTetsufumi HiranoDepartment of PhysicsDepartment of Physics
The University of TokyoThe University of Tokyo
Strangeness in Quark MatterStrangeness in Quark MatterTsinghua University, Beijing, ChinaTsinghua University, Beijing, China
October 6-10, 2008October 6-10, 2008
Strangeness in Quark MatterStrangeness in Quark MatterTsinghua University, Beijing, ChinaTsinghua University, Beijing, China
October 6-10, 2008October 6-10, 2008
“Hydrodynamics and Flow”,T. Hirano, N. van der Kolk, A. Bilandzic, arXiv:0808.2684
Dynamical Modeling with Hydrodynamics
Initial condition(thermalization)
Hydrodynamicevolution of QGP
•Jet quenching/Di-jet•Heavy quark diffusion•J/psi suppression•Electromagnetic radiation•…
Informationinside QGP
Kinetic evolution
RecombinationCoalescence
Hadronic spectra(Collective flow)
Information onsurface of QGP
QGP fluid + hadronic cascadein full 3D space
0collision axis
tim
e
Au Au
QGP fluid
Initial condition (=0.6fm):1. Glauber model2. CGC modelQGP fluid:3D ideal hydrodynamics (Tc = 170 MeV) Massless free u,d,s+ggas + bag const. Hadron phase:1. Tth=100MeV2. Hadronic cascade (JAM)(Tsw = 169 MeV)
hadron gas
Hybrid approaches:(1D) Bass, Dumitru (2D) Teaney, Lauret, Shuryak, (3D) Nonaka, Bass, Hirano et al.
Two Hydro Initial Conditions Which Clear the “First Hurdle”
1.Glauber model Npart:Ncoll = 85%:15%2. CGC model Matching I.C. via e(x,y,s)
Centrality dependence Rapidity dependence
Kharzeev, Levin, and NardiImplemented in hydro by TH and Nara
pT Spectra for PID hadrons
A hybrid model works well up to pT~1.5GeV/c.Other components (reco/frag) would appear above.
QGP fluid+hadron gas with Glauber I.C.
Centrality Dependence of v2
• v2 data are comparable with hydro results.• Hadronic cascade cannot reproduce data.• Note that, in v2 data, there exists eccentricity fluctuation which is not considered in model calculations.
hadronic cascade result(Courtesy of M.Isse)
TH et al. (’06)
QGP+hadron fluids with Glauber I.C.
Pseudorapidity Dependence of v2
=0 >0<0
•v2 data are comparable with hydro results again around =0•Not a QGP gas sQGP•Nevertheless, large discrepancy in forward/backward rapidity
TH(’02); TH and K.Tsuda(’02); TH et al. (’06).
QGP onlyQGP+hadron
QGP+hadron fluids with Glauber I.C.
Importance of Hadronic “Corona”
•Boltzmann Eq. for hadrons instead of hydrodynamics•Including effective viscosity through finite mean free path
QGP only QGP+hadron fluidsQGP fluid+hadron gas
T.Hirano et al.,Phys.Lett.B636(2006)299.
QGP fluid+hadron gas with Glauber I.C.
Differential v2 & Centrality Dependence
Mass dependence is o.k.Note: First result was obtained by Teaney et al.
20-30%
•Centrality dependence is ok•Large reduction from pure hydro in small multiplicity events
QGP fluid+hadron gas with Glauber I.C.
Mass Ordering for v2(pT)
Mass dependence is o.k. from hydro+cascade.
20-30%
Proton
Pion
Mass ordering comes fromhadronic rescattering effect. Interplay btw. radial and elliptic flows.
QGP fluid+hadron gas with Glauber I.C.
What happens to strangeness sector?
Distribution of Freeze-Out Time
b=2.0fm
(no decay)
Early kinetic freezeout for multistrange hadrons: van Hecke, Sorge, Xu(’98)Phi can serve a direct information at the hadronization.
phi/p Ratio as a function of pT
•pp collisions•Pure hydro in AA collisions
•Hydro + cascade in AA collisions
Clear signal for early decouplingof phi mesons
Violation of Mass Ordering for -mesons
in pT < 1 GeV/c
Just after hadronization Final results
T = Tsw = 169 MeV
b=7.2fm b=7.2fm
Caveat: Published PHENIX data obtained in pT>~1GeV/c for mesons
Violation of mass ordering for phi mesons!Clear signal of early decoupling!
QGP fluid+hadron gas with Glauber I.C.
Eccentricity Fluctuation
Interaction points of participants varyevent by event. Apparent reaction plane also varies. The effect is significant for smaller system such as Cu+Cu collisions
Adopted from D.Hofman(PHOBOS),talk at QM2006
A sample eventfrom Monte CarloGlauber model
i
0
Initial Condition with an Effect of Eccentricity Fluctuation
Rotate each i
to true
Throw a diceto choose b:bmin<b<bmax
averageover events
averageover events
E.g.)bmin= 0.0fmbmax= 3.3fmin Au+Au collisionsat 0-5% centrality
Effect of Eccentricity Fluctuation on v2
v2(w.rot) ~ 2 v2(w.o.rot) at Npart~350 in AuAuv2(w.rot) ~ 4 v2(w.o.rot) at Npart~110 in CuCu
Still a lack of flow? CGC initial conditions?
Significant effects of fluctuation!
Summary So Far
• A hybrid approach (QGP fluid + hadronic cascade) initialized by Glauber model works reasonably well at RHIC.
• Starting point to study finite temperature QCD medium in H.I.C.
• More detailed comparison with data is mandatory. (EoS, CGC initial conditions, viscosity, eccentricity fluctuation, …)
Application of Hydro Results
Jet quenchingJ/psi suppression
Heavy quark diffusionMeson
RecombinationCoalescence
Thermalradiation
(photon/dilepton)
Information along a path
Information on surface
Information inside medium
Baryon
J/psic
c bar
J/psi Suppression
Color Screening
cc
M.Asakawa and T.Hatsuda, PRL. 92, 012001 (2004)A. Jakovac et al. PRD 75, 014506 (2007)G.Aarts et al. arXiv:0705.2198 [hep-lat]. (Full QCD)See also T.Umeda,PRD75,094502(2007)
Quarkonium suppression in QGPColor Debye Screening
T.Matsui & H. Satz PLB178 416 (1986)
Suppression depends on temperature (density) and radius of QQbar system.
TJ/psi : 1.6Tc~2.0Tc T, T’ : ~ 1.1Tc
May serve as the thermometer in the QGP.
Talk by T.Gunji, in Parallel 6, 11:15-(Tues.)
Results from Hydro+J/psi Model• Best fit @ (TJ/, T, fFD) = (2.00Tc, 1.34Tc, 10%)
Bar: uncorrelated sys.Bracket: correlated sys.
• Onset of J/ suppression at Npart ~ 160. ( Highest T at Npart~160 reaches to 2.0Tc.)• Gradual decrease of SJ/
tot above Npart~160 reflects transverse area with T>TJ/ increases.• TJ/ can be determined in a narrow region.
Contour map
1 2
T. Gunji et al. Phys. Rev. C 76:051901 (R), 2007;J.Phys.G: Nucl.Part.Phys. 35, 104137 (2008).
Heavy Quark DiffusionRelativistic Langevin Eq. in local rest frame
: Drag coefficient: Gaussian white noize
Phenomenological parametrization of
LOpQCD(PYTHIA) Langevin sim. in QGP (Indep.) fragmentation Semi leptonic Decay
T: temperature from hydro sim.M: Mass of c or b quark
Y.Akamatsu, T.Hatsuda,T.Hirano,arXiv:0809.1499.
Results from Langevin Simulations on 3D QGP Hydro
~1-3 from RAA
Heavy quarks are not completely thermalized
Y.Akamatsu, T.Hatsuda,T.Hirano,arXiv:0809.1499.
Application of Hydro ResultsJet quenching
J/psi suppressionHeavy quark diffusion
Meson
RecombinationCoalescence
Thermalradiation
(photon/dilepton)
Information along a path
Information on surface
Information inside medium
Baryon
J/psic
c bar
Direct and Thermal Photon Emission
Photons from:Thermal+pQCD L.O.+fragmentation+jet conversion
Dynamics is importantin estimation of energyloss as well as thermalphoton radiation.
F.-M.Liu, T.Hirano, K.Werner, Y.Zhu, arXiv:0807.4771[hep-ph].
Talk by F.M.Liu, in Parallel IV, 16:00-(Thur)
Summary
• Current status of dynamical modeling in relativistic heavy ion collisions.
• Glauber I.C. + QGP fluid + hadron gas– J/psi suppression– Heavy quark diffusion– Direct photon emission
• Towards establishment of
“Observational QGP physics”
References and CollaboratorsHydro+Cascade:
•T.Hirano, U.W.Heinz, D.Khaezeev, R.Lacey, Y.Nara Phys.Lett.B636, 299 (2006); J.Phys.G34, S879 (2007); Phys. Rev. C77, 044909 (2008).
Eccentricity fluctuation effects on v2:•T.Hirano, Y.Nara, work in progress.
J/psi suppression:•T.Gunji, H.Hamagaki, T.Hatsuda, T.Hirano, Phys.Rev.C76, 051901 (2007).
Heavy quark diffusion:•Y.Akamatsu, T.Hatsuda, T.Hirano, arXiv:0809.1499 [hep-ph]
Photon production:•F.-M.Liu, T.Hirano, K.Werner, Y.Zhu, arXiv:0807.4771[hep-ph].
Eccentricity from CGC Initial Condition
x
y
Hirano et al.(’06). Kuhlman et al.(’06),Drescher et al.(’06). See also,Lappi, Venugopalan (’06)Drescher, Nara (’07)
v2 Depends on Initialization
Glauber:Early thermalizationDiscovery of Perfect Fluid QGPCGC:No perfect fluid?Additional viscosity
required in QGP?
Important to understand initial conditions much better for making a conclusion
TH et al.(’06)
Adil, Gyulassy, Hirano(’06)
QGP fluid+hadron gas with CGC I.C.
Soft EoS or Viscosity?
v2 is sensitive tosound velocity.Soft EoS in theQGP phase leadsto reasonablereproduction of v2
Again, importanceof understandinginitial conditions.Imprement ofLattice EoS?
QGP fluid+hadron gas with CGC I.C.
Current Status of Dynamical Modeling in H.I.C. in Our Study
Pro
per
tim
ePro
per
tim
e
Transverse momentumTransverse momentum
CGCCGC Geometric ScalingGeometric Scaling
Shattering CGCShattering CGC
HydrodynamicsHydrodynamics•viscosityviscosity•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)LOpQCDBefo
re
Befo
re
colli
sions
colli
sions
Part
on
Part
on
pro
duct
ion
pro
duct
ion
Pre
-Pre
-equili
bri
um
equili
bri
um
““ Perf
ect
” Perf
ect
” fluid
fluid
QG
P o
r G
PQ
GP o
r G
P
Dis
sipa
tive
Dis
sipa
tive
hadr
onha
dron
gas
gas
FragmentationFragmentation
InteractionInteraction
Intermediate pIntermediate pTT
GlasmaGlasmafluctuationfluctuationInstability?Instability?Equilibration?Equilibration?
T.Hirano and Y.Nara(’02-)
Inputs for Hydrodynamic Simulations for Perfect Fluids
Final stage:Free streaming particlesNeed decoupling prescription
Intermediate stage:Hydrodynamics can be validas far as local thermalization isachieved. Need EOS P(e,n)
Initial stage:Particle production, pre-thermalization?Instead, initial conditionsfor hydro simulations
0z
t
Why they shift oppositely?protonspions
pT
v 2(p
T)
v 2
<pT>
must decrease with proper timev2 for protons can be negativeeven in positive elliptic flow
TH and M.Gyulassy, NPA769,71(06) P.Huovinen et al.,PLB503,58(01)
Source ImagingPrimed quantitiesin Pair Co-MovingSystem (PCMS)(P = 0)
Source Imaging:Inverse problem from C to D with a kernel K
No more Gaussian parameterization!
Source Imaging:Inverse problem from C to D with a kernel K
No more Gaussian parameterization!
Koonin-Pratt eq. (Koonin(’77),Pratt(’84)):
Source function and normalized emission rate
(Brown&Danielewicz (’97-))
Distribution of the Last Interaction Point from Hydro + Cascade
Blink: Ideal Hydro, no resonance decaysKolb and Heinz (2003)
x-t x-y
px ~ 0.5 GeV/c for pions•Long tail ( decay? elastic scattering?)•Positive x-t correlation
QGP fluid+hadron gas with Glauber I.C.
1D (Angle-averaged) Source Function from Hydro + Cascade
0.48 < KT <0.6 GeV/c0.2 < KT <0.36 GeV/c
•Broader than PHENIX data•Almost no KT dependence ?PHENIX data•Significant effects of hadronic rescatterings
KT=PT/2
PHENIX, PRL98,132301(2007); arXiv:0712.4372[nucl-ex]
QGP fluid+hadron gas with Glauber I.C.
Long Tail Attributable to Decay ?
No!Switch off omega decay by hand in hadronic cascade Long tail is still seen. Soft elastic scattering of pions?
b=5.8fmPlot: PHENIXHist.: Hydro+cascade w/o decay
3D Source Function from Hydro + Cascade
side out long
•Source function in PCMS•1fm-slice in each direction •0.2<KT<0.4 GeV/c, || < 0.35, +-+, --- pairs•Black: With rescattering, Red: Without rescattering •No longer Gaussian shape (Lines: Gaussian)•Significantly broadened by hadronic rescatterings
Differential v2 in Forward
Adopted from S.J.Sanders (BRAHMS) talk @ QM2006
Our hybrid modelAMPT
QGP fluid+hadron gas with Glauber I.C.
Centrality Dependence of Differential v2
QGP fluid+hadron gas with Glauber I.C.
Thanks to M.Shimomura (Tsukuba)
Pions, AuAu 200 GeV
PHENIXPHENIX
Hybrid Model at Work at sqrt(sNN)=62.4 GeV
QGP fluid+hadron gas with Glauber I.C.
Thanks to M.Shimomura (Tsukuba)
Pions, AuAu 62.4 GeV
PHENIXPHENIX
Differential v2 in Au+Au and Cu+Cu Collisions
Same Npart, different eccentricity
Au+Au Cu+Cu
Same eccentricity, different Npart
Au+Au Cu+Cu
QGP fluid+hadron gas with Glauber I.C.
QGP shines at pT~3 GeV/c
Thermal emission isdominant at low pT.Emission from QGP isdominant at ~3GeV/c