1. Hydrodynamic Analysis of Heavy Ion Collisions at RHIC
Strangeness in Quark Matter
Tsinghua University, Beijing, China
October 6-10, 2008
Hydrodynamic Analysis of Heavy Ion Collisions at RHIC
Tetsufumi Hirano
Department of Physics
The University of Tokyo
“Hydrodynamics and Flow”,
T. Hirano, N. van der Kolk, A. Bilandzic, arXiv:

2. Dynamical Modeling with Hydrodynamics
Initial condition
(thermalization)
Recombination
Coalescence
Information on
surface of QGP
Hydrodynamic
evolution of QGP
Information
inside QGP
Kinetic evolution
Jet quenching/Di-jet
Heavy quark diffusion
J/psi suppression
Electromagnetic radiation …
Hadronic spectra
(Collective flow)

3. QGP fluid + hadronic cascade in full 3D space
Initial condition (t=0.6fm):
Glauber model
CGC model
QGP fluid:
3D ideal hydrodynamics
(Tc = 170 MeV)
Massless free u,d,s+g
gas + bag const.
Hadron phase:
Tth=100MeV
Hadronic cascade (JAM)
(Tsw = 169 MeV)
hadron gas
time
QGP fluid
collision axis Au Au
Hybrid approaches:
(1D) Bass, Dumitru (2D) Teaney, Lauret, Shuryak, (3D) Nonaka, Bass, Hirano et al.

4. Two Hydro Initial Conditions Which Clear the “First Hurdle”
Centrality dependence
Rapidity dependence
1.Glauber model
Npart:Ncoll = 85%:15%
2. CGC model
Matching I.C. via e(x,y,hs)
Kharzeev, Levin, and Nardi
Implemented in hydro
by TH and Nara

5. pT Spectra for PID hadrons
QGP fluid+hadron gas with Glauber I.C.
pT Spectra for PID hadrons
A hybrid model works well up to pT~1.5GeV/c.
Other components (reco/frag) would appear above.

6. Centrality Dependence of v2
QGP+hadron fluids with Glauber I.C.
TH et al. (’06)
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)

7. Pseudorapidity Dependence of v2
QGP+hadron fluids with Glauber I.C.
Pseudorapidity Dependence of v2
v2 data are comparable with hydro results again around h=0
Not a QGP gas  sQGP
Nevertheless, large discrepancy in forward/backward rapidity
QGP+hadron
QGP only
h<0
h=0
h>0
TH(’02); TH and K.Tsuda(’02); TH et al. (’06).

8. Importance of Hadronic “Corona”
QGP fluid+hadron gas with Glauber I.C.
Importance of Hadronic “Corona”
QGP fluid+hadron gas
Boltzmann Eq. for hadrons instead of hydrodynamics
Including effective viscosity through finite mean free path
QGP+hadron fluids
QGP only
T.Hirano et al.,Phys.Lett.B636(2006)299.

9. Differential v2 & Centrality Dependence
QGP fluid+hadron gas with Glauber I.C.
Differential v2 & Centrality Dependence
20-30%
Centrality dependence is ok
Large reduction from pure hydro in small multiplicity events
Mass dependence is o.k.
Note: First result was
obtained by Teaney et al.

10. Mass Ordering for v2(pT)
QGP fluid+hadron gas with Glauber I.C.
Mass Ordering for v2(pT)
Pion
20-30%
Proton
Mass ordering comes from
hadronic rescattering effect. Interplay btw. radial and elliptic flows.
Mass dependence is o.k. from hydro+cascade.

11. What happens to strangeness sector?

12. Distribution of Freeze-Out Time
(no decay)
b=2.0fm
Early kinetic freezeout for multistrange hadrons: van Hecke, Sorge, Xu(’98)
Phi can serve a direct information at the hadronization.

13. phi/p Ratio as a function of pT
pp collisions
Pure hydro in AA
collisions
Hydro + cascade
in AA collisions
Clear signal for
early decoupling
of phi mesons

14. Violation of Mass Ordering for f-mesons
QGP fluid+hadron gas with Glauber I.C.
Violation of Mass Ordering for f-mesons
Just after hadronization
Final results
b=7.2fm
b=7.2fm
T = Tsw = 169 MeV
in pT < 1 GeV/c
Violation of mass ordering for phi mesons!
Clear signal of early decoupling!
Caveat: Published PHENIX data obtained in pT>~1GeV/c for f mesons

15. Eccentricity Fluctuation
Adopted from D.Hofman(PHOBOS),
talk at QM2006 Yi
A sample event
from Monte Carlo
Glauber model Y0
Interaction points of participants vary
event by event.
 Apparent reaction plane also varies.
 The effect is significant for smaller system such as Cu+Cu collisions

16. Initial Condition with an Effect of Eccentricity Fluctuation
Throw a dice
to choose b:
bmin<b<bmax
average
over events
Rotate each Yi
to Ytrue
E.g.)
bmin= 0.0fm
bmax= 3.3fm
in Au+Au collisions
at 0-5% centrality
average
over events

17. Effect of Eccentricity Fluctuation on v2
v2(w.rot) ~ 2 v2(w.o.rot) at Npart~350 in AuAu
v2(w.rot) ~ 4 v2(w.o.rot) at Npart~110 in CuCu
Significant effects of fluctuation!
Still a lack of flow?  CGC initial conditions?

18. 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, …)

19. Application of Hydro Results
Thermal
radiation
(photon/dilepton)
Jet quenching
J/psi suppression
Heavy quark diffusion
Recombination
Coalescence
Meson
J/psi c
Baryon
c bar
Information
along a path
Information
on surface
Information
inside medium

20. J/psi Suppression Tc, Ty’ : ~ 1.1Tc Quarkonium suppression in QGP
Talk by T.Gunji, in Parallel 6, 11:15-(Tues.)
J/psi Suppression
Quarkonium suppression in QGP
Color Debye Screening
T.Matsui & H. Satz PLB (1986)
Suppression depends on temperature (density) and radius of QQbar system.
TJ/psi : 1.6Tc~2.0Tc
Tc, Ty’ : ~ 1.1Tc
May serve as the thermometer in the QGP.
M.Asakawa and T.Hatsuda, PRL. 92, (2004)
A. Jakovac et al. PRD 75, (2007)
G.Aarts et al. arXiv: [hep-lat]. (Full QCD)
See also T.Umeda,PRD75,094502(2007)

21. Results from Hydro+J/psi Model
T. Gunji et al. Phys. Rev. C 76: (R), 2007;
J.Phys.G: Nucl.Part.Phys. 35, (2008).
Results from Hydro+J/psi Model
Best (TJ/y, Tc, fFD) = (2.00Tc, 1.34Tc, 10%) 1s 2s
Bar: uncorrelated sys.
Bracket: correlated sys.
Contour map
Onset of J/y suppression at Npart ~ 160.
( Highest T at Npart~160 reaches to 2.0Tc.)
Gradual decrease of SJ/ytot above Npart~160 reflects transverse area with T>TJ/y increases.
TJ/y can be determined in a narrow region.

22. Heavy Quark Diffusion Relativistic Langevin Eq. in local rest frame
Y.Akamatsu, T.Hatsuda,T.Hirano,arXiv:
Heavy Quark Diffusion
Relativistic Langevin Eq. in local rest frame
G: Drag coefficient
x: Gaussian white noize
Phenomenological parametrization of G
T: temperature from hydro sim.
M: Mass of c or b quark
LOpQCD(PYTHIA)  Langevin sim. in QGP 
(Indep.) fragmentation  Semi leptonic Decay

23. Results from Langevin Simulations on 3D QGP Hydro
Y.Akamatsu, T.Hatsuda,T.Hirano,arXiv:
Results from Langevin Simulations on 3D QGP Hydro
g~1-3 from RAA
Heavy quarks are not
completely thermalized

24. Application of Hydro Results
Jet quenching
J/psi suppression
Heavy quark diffusion
Thermal
radiation
(photon/dilepton)
Recombination
Coalescence
Meson
J/psi c
Baryon
c bar
Information
along a path
Information
on surface
Information
inside medium

25. Direct and Thermal Photon Emission
Talk by F.M.Liu, in Parallel IV, 16:00-(Thur)
Direct and Thermal Photon Emission
Photons from:
Thermal
+pQCD L.O.
+fragmentation
+jet conversion
Dynamics is important
in estimation of energy
loss as well as thermal
photon radiation.
F.-M.Liu, T.Hirano, K.Werner, Y.Zhu, arXiv: [hep-ph].

26. “Observational QGP physics”
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”

27. References and Collaborators
Hydro+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, (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, (2007).
Heavy quark diffusion:
Y.Akamatsu, T.Hatsuda, T.Hirano, arXiv: [hep-ph]
Photon production:
F.-M.Liu, T.Hirano, K.Werner, Y.Zhu, arXiv:
[hep-ph].

28. Eccentricity from CGC Initial Conditionx
Hirano et al.(’06). Kuhlman et al.(’06),
Drescher et al.(’06). See also,
Lappi, Venugopalan (’06)
Drescher, Nara (’07)

29. v2 Depends on Initialization
QGP fluid+hadron gas with CGC I.C.
v2 Depends on Initialization
Glauber:
Early thermalization
Discovery of Perfect Fluid QGP
CGC:
No perfect fluid?
Additional viscosity
required in QGP?
TH et al.(’06)
Important to understand initial conditions much better for making a conclusion
Adil, Gyulassy, Hirano(’06)

30. QGP fluid+hadron gas with CGC I.C.
Soft EoS or Viscosity?
v2 is sensitive to
sound velocity.
Soft EoS in the
QGP phase leads
to reasonable
reproduction of v2 
Again, importance
of understanding
initial conditions.
Imprement of
Lattice EoS?

31. Current Status of Dynamical Modeling in H.I.C. in Our Study
T.Hirano and Y.Nara(’02-)
Current Status of Dynamical Modeling in H.I.C. in Our Study
Before collisions
CGC
Geometric Scaling
“DGLAP region”
Transverse momentum
Shattering CGC
(N)LOpQCD
production
equilibrium
Parton
Pre-
Glasma
fluctuation
Instability?
Equilibration?
Interaction
Parton energy loss
Inelastic
Elastic
QGP or GP
“Perfect” fluid
Hydrodynamics
viscosity
non chem. eq.
Recombination
Coalescence
Dissipative
hadron
gas
Hadronic
cascade
Fragmentation
Proper time
Low pT
Intermediate pT
High pT

32. Inputs for Hydrodynamic Simulations for Perfect Fluids
Final stage:
Free streaming particles
Need decoupling prescription t
Intermediate stage:
Hydrodynamics can be valid
as far as local thermalization is
achieved. Need EOS P(e,n) z
Initial stage:
Particle production,
pre-thermalization?
Instead, initial conditions
for hydro simulations

33. Why they shift oppositely?
pions
protons
v2(pT) v2
<pT> pT
v2 for protons can be negative
even in positive elliptic flow
must decrease with proper time
TH and M.Gyulassy, NPA769,71(06)
P.Huovinen et al.,PLB503,58(01)

34. No more Gaussian parameterization!
Source Imaging
Primed quantities
in Pair Co-Moving
System (PCMS)
(P = 0)
Koonin-Pratt eq. (Koonin(’77),Pratt(’84)):
Source function and normalized emission rate
Source Imaging:
Inverse problem from C to D with a kernel K
No more Gaussian parameterization!
(Brown&Danielewicz (’97-))

35. Distribution of the Last Interaction Point from Hydro + Cascade
QGP fluid+hadron gas with Glauber I.C.
Distribution of the Last Interaction Point from Hydro + Cascade
x-y
x-t
px ~ 0.5 GeV/c for pions
Long tail (w decay? elastic scattering?)
Positive x-t correlation
Blink: Ideal Hydro, no resonance decays
Kolb and Heinz (2003)

36. 1D (Angle-averaged) Source Function from Hydro + Cascade
QGP fluid+hadron gas with Glauber I.C.
1D (Angle-averaged) Source Function from Hydro + Cascade
KT=PT/2
0.2 < KT <0.36 GeV/c
0.48 < KT <0.6 GeV/c
Broader than PHENIX data
Almost no KT dependence ?PHENIX data
Significant effects of hadronic rescatterings
PHENIX, PRL98,132301(2007); arXiv: [nucl-ex]

37. Long Tail Attributable to w Decay ?
b=5.8fm
No!
Switch off omega decay by hand in hadronic cascade
 Long tail is still seen.
 Soft elastic scattering of pions?
Plot: PHENIX
Hist.: Hydro+cascade
w/o w decay

38. 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, |h| < 0.35, p+-p+, p--p- pairs
Black: With rescattering, Red: Without rescattering
No longer Gaussian shape (Lines: Gaussian)
Significantly broadened by hadronic rescatterings

39. Differential v2 in Forward
QGP fluid+hadron gas with Glauber I.C.
Differential v2 in Forward
Our hybrid model
AMPT
Adopted from S.J.Sanders
(BRAHMS) QM2006

40. Centrality Dependence of Differential v2
QGP fluid+hadron gas with Glauber I.C.
Centrality Dependence of Differential v2
PHENIX
PHENIX
Pions, AuAu 200 GeV
Thanks to M.Shimomura (Tsukuba)

41. Hybrid Model at Work at sqrt(sNN)=62.4 GeV
QGP fluid+hadron gas with Glauber I.C.
Hybrid Model at Work at sqrt(sNN)=62.4 GeV
PHENIX
PHENIX
Pions, AuAu 62.4 GeV
Thanks to M.Shimomura (Tsukuba)

42. Differential v2 in Au+Au and Cu+Cu Collisions
QGP fluid+hadron gas with Glauber I.C.
Differential v2 in Au+Au and Cu+Cu Collisions
Au+Au
Cu+Cu
Same Npart, different eccentricity
Au+Au
Cu+Cu
Same eccentricity, different Npart

43. QGP shines at pT~3 GeV/c Thermal emission is dominant at low pT.
Emission from QGP is
dominant at ~3GeV/c