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