Parton Thermalization and Energy Loss in ultrarelativistic Heavy-Ion Collisions within a Parton Cascade

Zhe Xu

Johann Wolfgang Goethe-Universität Frankfurt

Institut für Theoretische Physik

QM2006, Shang Hai

in collaboration with A. El, O.Fochler and C.Greiner

Motivation

• fast thermalization

),(),(),( pxIpxIpxfp ggggggggg

• on-shell parton cascade Z. Xu and C. Greiner, PRC 71, 064901 (2005)

• with only pQCD gg<->gg : no thermalization except with large (AMPT,MPC) • including pQCD gg<->ggg: thermalization, hydro. behaviour and Jet-Quenching

cmt d 2sin

gg gg

gg ggg

B.Müller‘s question in Quark Matter 2005

ggggtgggggt 2.1

What is the correct quantity describing kinetic equilibration?

• NOT the mean free path or collision rate n• maybe nt with the transport cross section

One has to do detailed studies.

momentum isotropization and kinetic equilibration

Initial condition: Minijets p0=1.4 GeV

0

2

2

02

2

2

2

2

2

exp)()(tt

E

pt

E

p

E

pt

E

peq

ZZeq

ZZ

(t) gives the timescale of kinetic equilibration.

Transport Rates

Definition: ,/ 22 EPQ Z

),,(

),,(|)(

3

3

3

3

)2(

)2(0

txpf

QtxpfQtQ

pd

pd

x

t

fpdtfpd tQ

nQ

ntQ 3

3

3

3

)2()2()(

11)(

322322 IIIfE

P

t

f

Boltzmann equation

322322)( CCCCtQ drift

,1 .

32.

23.

22. trtrtrtr

drift RRRR )(

.

tQQ

CR

eq

jtrj

)(

)(

tQQ

tQ

eq

5.

22

.32

.23 tr

trtr

R

RR

The drift term is large.

.

.32

.23

.22

trdrift

tr

tr

tr

R

R

R

R

special case )()(),,( EpEptxpf ZZ

.23

.23

.22

.22 2

3

2

3,

2

3 trrel

trtrrel

tr vnRvnR

for isotropic distribution of collision angle

32.

3223.

2322.

22 3

2,

2

3, RRRRRR trtrtr

LPM

DDggggg

mqkk

qg

mq

sgM

222

22

222

242

)(

12

)(2

9

J.F.Gunion, G.F.Bertsch, Phys. Rev. D 25, 746(1982)Bremsstrahlung processes

LPM suppression: the formation time

)cosh( yk gLPM

gk y

cosh1

2/

/123 )log(~1

~s

gg

sk

dk

Bethe-Heitler regime

)/(1 Ag )log()log(~ As g

)log(.~23 Aconst

Initial condition with Color Glass Condensate

: [-0.05:0.05] and xt < 1.5 fm)()(~),( 22Tsz pQppxf

→ Particle number decreases rapidly in the very first moment→ No net soft gluon production at early times!

Evolution of Particle Number in bottom-up scenario Andrej El

Jet-Quenching in a central Au Au collision at RHIC

3~4 too much

Oliver Fochler

elliptic flow in noncentral Au+Au collisions at RHIC:

central

peripheral

Summary

• PQCD Bremsstrahlung gg↔ggg are essential for the thermalization.

• The transport rates are quantities determining the contribution of

different processes to kinetic equilibration.

• no bottom –up

• large v2, but small RAA

.32

.23

.22

.1 trtrtrtrdrift RRRR

.23

.23

.22

.22 2

3

2

3,

2

3 trrel

trtrrel

tr vnRvnR

Minijets p0=1.4 GeV

(t)

thermalization and hydrodynamical behavior

NO thermalization and free streaming

Question: Why are gg<->ggg interactions essential for thermalization?

Simulation 1 Simulation 2

Stochastic algorithm P.Danielewicz, G.F.Bertsch, Nucl. Phys. A 533, 712(1991)A.Lang et al., J. Comp. Phys. 106, 391(1993)

for particles in 3x with momentum p1,p2,p3 ...

collision probability:

23321

3232

32323

32222

)(823

32

22

x

t

EEE

IPfor

x

tvPfor

x

tvPfor

rel

rel

)()2(2)2(2)2(2

1'2'1321

)4(42

'2'1123'2

3'2

3

'13

'13

32 pppppME

pdE

pdI

cell configuration in space

3x

Initial conditions: minijets production with pt > p0

dcba

cdab

TbTa

T

jet

td

dpxfxpxfxK

dydydp

d

,;,

2

22

2

11

21

2 ˆ),(),(

ppjetAA

AAjet bTN )0(2 binary approximation

830gN for a central Au+Au collision at RHICat 200 AGeV using p0=2 GeV

Initial conditions with smaller p0

Kinetic and chemical equilibration

in the central region:: [-0.5:0.5] and xt < 1.5 fm

1~2 fm/c for the kinetic equilibration ~ 4 fm/c for the chemical equilibration

Kinetic and chemical equilibration

transverse energy at y=0 in Au+Au central collision

Kinetic and chemical equilibration