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### Hydrodynamic Analysis of Heavy Ion Collisions at RHIC

Tsinghua University, Beijing, China

October 6-10, 2008

Tetsufumi Hirano

Department of Physics

The University of Tokyo

“Hydrodynamics and Flow”,

T. Hirano, N. van der Kolk, A. Bilandzic, arXiv:0808.2684

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)

QGP fluid + hadronic cascadein 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

0

Au

Au

Hybrid approaches:

(1D) Bass, Dumitru (2D) Teaney, Lauret, Shuryak, (3D) Nonaka, Bass, Hirano et al.

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

QGP fluid+hadron gas with Glauber I.C.

pT Spectra for PID hadronsA hybrid model works well up to pT~1.5GeV/c.

Other components (reco/frag) would appear above.

QGP+hadron fluids with Glauber I.C.

Centrality Dependence of v2TH et al. (’06)

- 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)

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).

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.

QGP fluid+hadron gas with Glauber I.C.

Differential v2 & Centrality Dependence20-30%

- 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.

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.

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.

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

QGP fluid+hadron gas with Glauber I.C.

Violation of Mass Ordering for f-mesonsJust 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

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

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

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?

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

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

Talk by T.Gunji, in Parallel 6, 11:15-(Tues.)

J/psi Suppression- Quarkonium suppression in QGP
- Color 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
- Tc, Ty’ : ~ 1.1Tc
- May serve as the thermometer in the QGP.

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)

Best fit @ (TJ/y, Tc, fFD) = (2.00Tc, 1.34Tc, 10%)

T. Gunji et al. Phys. Rev. C 76:051901 (R), 2007;

J.Phys.G: Nucl.Part.Phys. 35, 104137 (2008).

Results from Hydro+J/psi Model1s

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/ytotabove Npart~160 reflects transverse area with T>TJ/y increases.
- TJ/ycan be determined in a narrow region.

Y.Akamatsu, T.Hatsuda,T.Hirano,arXiv:0809.1499.

Heavy Quark DiffusionRelativistic 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

Y.Akamatsu, T.Hatsuda,T.Hirano,arXiv:0809.1499.

Results from Langevin Simulations on 3D QGP Hydrog~1-3 from RAA

Heavy quarks are not

completely thermalized

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

Talk by F.M.Liu, in Parallel IV, 16:00-(Thur)

Direct and Thermal Photon EmissionPhotons 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:0807.4771[hep-ph].

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 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, 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

y

x

Hirano et al.(’06). Kuhlman et al.(’06),

Drescher et al.(’06). See also,

Lappi, Venugopalan (’06)

Drescher, Nara (’07)

QGP fluid+hadron gas with CGC I.C.

v2 Depends on InitializationGlauber:

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)

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?

Current Status of Dynamical Modeling in H.I.C. in Our Study

CGC

Geometric Scaling

Before collisions

“DGLAP region”

Transverse momentum

Shattering CGC

(N)LOpQCD

Parton

production

Pre-

equilibrium

Glasma

fluctuation

Instability?

Equilibration?

- Parton energy loss
- Inelastic
- Elastic

Interaction

- Hydrodynamics
- viscosity
- non chem. eq.

“Perfect” fluid

QGP or GP

Recombination

Coalescence

Dissipative

hadron

gas

Hadronic

cascade

Fragmentation

Proper time

Low pT

Intermediate pT

High pT

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

0

Initial stage:

Particle production,

pre-thermalization?

Instead, initial conditions

for hydro simulations

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)

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-))

QGP fluid+hadron gas with Glauber I.C.

Distribution of the Last Interaction Point from Hydro + Cascadex-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)

QGP fluid+hadron gas with Glauber I.C.

1D (Angle-averaged) Source Function from Hydro + CascadeKT=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:0712.4372[nucl-ex]

Long Tail Attributable to w Decay ?

No!

Switch off omega decay by hand in hadronic cascade

Long tail is still seen.

Soft elastic scattering of pions?

b=5.8fm

Plot: PHENIX

Hist.: Hydro+cascade

w/o w 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, |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

QGP fluid+hadron gas with Glauber I.C.

Differential v2 in ForwardOur hybrid model

AMPT

Adopted from S.J.Sanders

(BRAHMS) talk @ QM2006

QGP fluid+hadron gas with Glauber I.C.

Centrality Dependence of Differential v2PHENIX

PHENIX

Pions, AuAu 200 GeV

Thanks to M.Shimomura (Tsukuba)

QGP fluid+hadron gas with Glauber I.C.

Hybrid Model at Work at sqrt(sNN)=62.4 GeVPHENIX

PHENIX

Pions, AuAu 62.4 GeV

Thanks to M.Shimomura (Tsukuba)

QGP fluid+hadron gas with Glauber I.C.

Differential v2 in Au+Au and Cu+Cu CollisionsAu+Au

Cu+Cu

Same Npart, different eccentricity

Au+Au

Cu+Cu

Same eccentricity, different Npart

QGP shines at pT~3 GeV/c

Thermal emission is

dominant at low pT.

Emission from QGP is

dominant at ~3GeV/c

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