Hydrodynamic Modeling ofHeavy Ion Collisions

Tetsufumi HiranoTetsufumi Hirano

平野哲文平野哲文Department of PhysicsDepartment of Physics

The University of TokyoThe University of Tokyo

ATHIC2008ATHIC2008Tsukuba University, Tsukuba, JapanTsukuba University, Tsukuba, Japan

October 13-15, 2008October 13-15, 2008

ATHIC2008ATHIC2008Tsukuba University, Tsukuba, JapanTsukuba University, Tsukuba, Japan

October 13-15, 2008October 13-15, 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 model)QGP 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.

Inputs to Hydro: Multiplicity

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.

T.Hirano et al., Phys.Rev.C77, 044909 (2008).

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, 299 (2006)

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

T.Hirano et al., Phys.Lett.B636, 299 (2006);Phys.Rev.C77, 044909 (2008).

Centrality Dependence of Differential v2

Pions, AuAu 200 GeV

PHENIXPHENIX

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

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

Talk by M. Shimomura

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.

T.Hirano et al., Phys.Rev.C77, 044909 (2008).

Phi-mesons as a Probe at Hadronization

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.

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!

T.Hirano et al., Phys.Rev.C77, 044909 (2008).

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

CGC initial conditions?

Significant effects of fluctuation!

Talk by Y. Nara

T. Hirano and Y. Nara, work in progress

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

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]

T. Hirano and U. Heinz, work in progress

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, source imaging,…)

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.

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.)• 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).

Talk by T. Gunji

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 RAAHeavy quarks are notcompletely thermalized

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

Talk by Y. Akamatsu

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

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).

Elliptic flow scaling:•M.Shimomura, S.Esumi, T.Hirano, Y.Nara, work in progress.

Eccentricity fluctuation effects on v2:•T.Hirano, Y.Nara, work in progress.

Source function:•T.Hirano and U.Heinz, 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].

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)