Dynamical Modeling ofHeavy Ion Collisions

Tetsufumi HiranoTetsufumi Hirano

Department of PhysicsDepartment of Physics

The University of TokyoThe University of Tokyo

Seminar @ YITP12/10/2008

OUTLINE

• Introduction• Basic Checks of observables

– Energy density– Chemical and kinetic equilibrium

• Dynamics of Heavy Ion Collisions– Hydrodynamic modeling– Elliptic flow

• Towards precision physics of QGP– Jet quenching (Transport coefficient) – J/psi suppression

• Summary and Outlook

Two Faces of QCD

Confinement Asymptotic free

q-qbar potentialRunning coupling of QCD

Physics depends on (energy) scale.

Recipe for QGP

Compress and/or Heat-up!•Density (chemical potential) scale•Temperature scale

Quark Gluon Plasma

Hadronization

Nucleosynthesis

History of the Universe ~ History of Matter

QGP study

Understandingearly universe

Little Bang!

Relativistic Heavy Ion Collider(2000-)

RHIC as a time machine!

100 GeV per nucleonAu(197×100)+Au(197×100)

Collision energy

Multiple production(N~5000)

Heat

sideview

frontview

STAR

STAR

Dynamics of Heavy Ion Collisions

Dynamics of Heavy Ion Collisions

Time scale10fm/c~10-23sec<<10-4(early universe)

Temperature scale 100MeV~1012K

Freezeout

“Re-confinement”

Expansion, cooling

Thermalization

First contact (two bunches of gluons)

# of binary collisions

x

y

Thickness function:

Woods-Saxon nuclear density:Gold nucleus:0=0.17 fm-3

R=1.12A1/3-0.86A-1/3

d=0.54 fm

in = 42mb @200GeV

# of participants

1 －（ survival probability ）

Ncoll & Npart

Centrality

PHENIX: Correlation btw. BBC and ZDC signals

Npart and Ncoll as a function of impact parameter

Elliptic Flow

What is Elliptic Flow?

How does the system respond to spatial anisotropy?

Ollitrault (’92)Ollitrault (’92)

Hydro behavior

Spatial Anisotropy

Momentum Anisotropy

INPUT

OUTPUT

Interaction amongproduced particles

dN

/d

No secondary interaction

0 2

dN

/d

0 2

2v2

x

y

v2 from a Boltzmann simulation

b = 7.5fm

generated through secondary collisions saturated in the early stage sensitive to cross section (~1/m.f.p.~1/viscosity)

v2 is

Zhang et al.(’99) ideal hydro limit

t(fm/c)

v2 : Ideal hydro

: strongly interactingsystem

Why Hydrodynamics?

StaticStatic•EoS from Lattice QCDEoS from Lattice QCD•Finite Finite TT, , field theory field theory•Critical phenomenaCritical phenomena•Chiral property of hadronChiral property of hadron

Dynamic Phenomena in HICDynamic Phenomena in HIC•Expansion, FlowExpansion, Flow•Space-time evolution ofSpace-time evolution of thermodynamic variablesthermodynamic variables

Once one accepts localOnce one accepts localthermalization ansatz,thermalization ansatz,life becomes very easy.life becomes very easy.

Energy-momentum:Energy-momentum:

Conserved number:Conserved number:

Why Hydrodynamics? (contd.)• We would like to understand the QCD matter

under equilibrium.• Lattice QCD is not able to describe dynamics

of heavy ion collisions.• Analyze heavy ion reaction based on a

model with an assumption of local equilibrium, and see what happens and whether it is consistent with data.

• If consistent, it would be a starting point of the physics of QCD matter.

Freezeout

“Re-confinement”

Expansion, cooling

Thermalization

First contact (two bunches of gluons)

Dynamics of Heavy Ion Collisions

Inputs in hydrodynamic simulations:•Initial condition•Equation of state•Decoupling prescription

Recent Hydro Results

from Our Group

QGP fluid + hadronic cascade

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=100MeV

2. 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.

Centrality Dependence of v2

Discovery of “Large” v2 at RHIC• 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.

Result from a hadronic cascade (JAM)(Courtesy of M.Isse)

TH et al. (’06).

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 rapiditySee next slides

TH(’02); TH and K.Tsuda(’02); TH et al. (’06).

QGP onlyQGP+hadron

Hadron Gas Instead of Hadron Fluid

QGP coreQGP core

A QGP fluid surrounded by hadronic gas

QGP: Liquid (hydro picture)Hadron: Gas (particle picture)

“Reynolds number”

Matter proper part: (shear viscosity)(entropy density)

bigin Hadron

smallin QGP

T.Hirano and M.Gyulassy,Nucl.Phys.A769 (2006)71.

Importance of Hadronic “Corona”

•Boltzmann Eq. for hadrons instead of hydrodynamics•Including viscosity through finite mean free path•Suggesting rapid increase of entropy density•Deconfinement makes hydro work at RHIC!? Signal of QGP!?

QGP only QGP+hadron fluids

QGP fluid+hadron gas

T.Hirano et al.,Phys.Lett.B636(2006)299.

QGP Liquid + Hadron Gas Picture Works Well

Mass dependence is o.k.Note: First result was obtainedby 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(2006)299; 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

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 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 (Glauber)

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

Significant effects of fluctuation!

CuCuAuAu

Effect of Eccentricity Fluctuation on v2 (CGC)

CuCuAuAu

CGC + QGP with (small) viscosity + hadronic gas!?

Toward precisionphysics of QGP

Lesson from Observational Cosmology

ObservationCOBE, WMAP,…

Taken fromhttp://lambda.gsfc.nasa.gov/

“Best” cosmological parametersC.L.Bennett et al.,Ap.J.Suppl(’03)

CMB tools:CMBFAST, CAMB,

…

CMB tools:CMBFAST, CAMB,

…

Analysis codes play a major role in precision physics.

Hydrodynamic model in H.I.C.

Tomography

* 平野哲文、浜垣秀樹、「ジェットで探るクォークグルーオンプラズマ」、日本物理学会誌 2004 年 12 月号

CT (computed tomography) scan

“Tomography”1. Known probes: Spectra reliably calculable via pQCD2. Good detector: RHIC experiments!3. Interaction btw. probes and unknowns: Recent development in this field

Jet Tomography

g g

g

Tool 1. Jet quenching

High “density” matter

Tool 2. Jet acoplanarity

180 deg. correlation?

Bjorken(’82)Gyulassy,PlümerWang (’90)

Bjorken(’82)Appel (’86)Blaizot & McLerran (’86)

Difference btw. pp and AA

f

f

D

D

a

b

c

d

f’

f’

a

b

Dc

Dd

A×

A×

pp collisions AA collisions

f: Parton distributionD: Fragmentation function

QGP?

JetNucleon

Nucleon

pT

RAA 1

binary collision scaling

Au+Au 0-10% central•b=2.8 fm

•Ncoll = 978•Npart = 333

•Npart/Ncoll = 0.341

participant scaling0.341

Nuclear Modification Factor

(null result)

“Transport Coefficient”

R.Baier, hep-ph/0209038

for pQCD

For static medium,

Baier et al.

Stopping power One of the important quantity to characterize

the QGP

RAA for 0 and IAA for charged

How do we understand this large K?

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.)• Gradual decrease of SJ/

tot above Npart~160 reflects transverse area with T>TJ/ increases.• TJ/can be determined in a narrow region.

8

Contour map

1 2

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

Summary and Outlook

• Elliptic flow– QGP fluid + hadron gas picture works well.– Starting Point of finite temperature QCD in

H.I.C.

• Tomography utilizing hydro model– Statistical analysis of jet quenching parameter

(stopping power of high energy partons)

– J/psi suppression above T~2Tc. (Melting temperature of charmonium)

• Toward establishment of the

“observational QGP physics”.