Space time evolution of QCD matter

• Parton cascade with stochastic algorithm

• Transport rates and momentum isotropization

• Thermalization of gluons due to

• Results: bottom-up scenario, jet-quenching,

elliptic flow, viscosity,… viscous hydro, …

I. Bouras, A. El, O. Fochler, F. Reining, Z. Xu, CG

Johann Wolfgang Goethe-Universität Frankfurt

Institut für Theoretische Physik

Focus week, HIC at the LHC, CERN , may 2007

Relativistic Quantum Transport for URHIC

• microscopic transport calculations of partonic degrees of freedom

RHIC, LHC

),(),(),( pxCpxCpxfp ggggggggg

new development

Z. Xu and C. Greiner, PRC 71, 064901 (2005)

Boltzmann Approach of MultiParton Scatterings (BAMPS)

LPM

DDggggg

mqkk

qg

mq

sgM

222

22

222

242

)(

12

)(2

9

3x

23321

3232

32323

32222

)(823

32

22

x

t

EEE

IPfor

x

tvPfor

x

tvPfor

rel

rel

collision probability

particle in cell method

LPM

DDggggg

Dgggg

mqkk

qg

mq

sgM

mq

sgM

222

22

222

242

222

242

)(

12

)(2

9

,)(2

9

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

parton scatterings in leading order pQCD

),3(16 1)2(

23

3

qfgppd

sD fnfm

screening mass:

LPM suppression: the formation time

)cosh( yk g

gk y

cosh1

)/ln()233(12

QCDf sns

MeVTfmgs 400~5.0~3.0~ fugacity ~ 0.5

Example

Important scales for kinetic transport & simulations

Simulations solve Boltzmann equation:→ test particles and other schemes

Semiclassical kinetic theory:

(Quantum mechanics: )

Initial production of partons

dt

dpxfxpxfxK

dydydp

d cdab

tbtadcbat

jet

),(),( 2

222

11,;,21

2

minijets

string matter

CGC

central

elliptic flow in noncentral Au+Au collisions at RHIC:

)(exp)()( 0

2

2

02

2

2

2

2

2

t

tt

E

pt

E

p

E

pt

E

peq

ZZeq

ZZ

fast isotropization and thermalisation

hydrodynamical evolution of momentum spectrum,… micr. determination of transport parameter …

Z. Xu and C. Greiner, hep-ph/0703233 Z. Xu and C. Greiner,

NPA 774, 787 (2006)

3+1dim. full cascade: comparison with RHIC data

5.

22

.32

.23 tr

trtr

R

RR

The drift term is large.

.

.32

.23

.22

trdrift

tr

tr

tr

R

R

R

R

ggggg interactions are essential for kinetic equilibration!

Z. Xu and C. Greiner, arXiv:hep-ph/0703233

trz

z

Rfvpd

fvEpdn

1

)(

)(

5

12

313

2313

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

Initial condition with Color Glass Condensate

: [-0.05:0.05] and xt < 1.5 fm

bottom-up scenario of thermalization

R.Baier, A.H.Mueller, D.Schiff and D.T.Son, PLB502(2001)51

• Qs-1 << t << -3/2 Qs

-1 Hard gluons with momenta about Qs are freedand phase space occupation becomes of order 1.

• -3/2 Qs-1 << t << -5/2 Qs

-1 (h+h h+h+s)Hard gluons still outnumber soft ones, but soft gluons give most of theDebye screening.

• -5/2 Qs-1 << t << -13/5 Qs

-1 (h+h h+h+s; s+s s+s; h+s sh+sh+s)Soft gluons strongly outnumber hard gluons.Hard gluons loose their entire energy to the thermal bath.

• After -13/5 Qs-1 the system is thermalized: T ~ t-1/3, T0 ~ 2/5 Qs

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

evolution of particle number in bottom-up scenario in 1+1 dim. geometry

Not the full Bottom-Up story...

LHC …

RHIC

Evolution of temperature and spectrum … Andrej El

extracting the viscosity

preliminary

Bjorken geometry:

Jet-Quenching in a central Au Au collision at RHIC

Oliver Fochler

RAA higher?

RAA ~ 0.04–0.05

old:

new:preliminary

quarks not yet included …

Summary

• A new parton cascade including inelastic multiparton scatterings gg↔ggg

• Explains thermalization and hydrodynamical expansion at RHIC

• PQCD inspired gg↔ggg are important for the thermalization.

• PQCD gg↔ggg generate the elliptic flow in noncentral collisions.

• Not full bottom-up thermalization scenario with CGC

• 3~4 too much jet-quenching

Outlook

• viscosity

• including quarks, heavy quark production

• Test for initial conditions (boundaries)

possible Chromo/Weibel instabilities

B.Schenke, A. Dumitru, Y. Nara, M. Strickland

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

rapidity distributionResults

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

thermalization and hydrodynamical behavior

NO thermalization and free streaming

including ggggg without ggggg

cmt d 2sin

transport cross section:

Why fast thermalization?

gg gg

gg ggg

2

gggg

gggggBUT! This is not the whole story...

… transport rates !

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.

,/ 22 EPQ Z

),,(

),,(

3

3

3

3

)2(

)2(

txpf

QtxpfQ

pd

pd

t

fpdtfpd tQ

nQ

ntQ 3

3

3

3

)2()2()(

11)(

322322 IIIfE

P

t

f

322322)( CCCCtQ drift

,1 .

32.

23.

22. trtrtrtr

drift RRRR

)(

)(

tQQ

tQ

eq

special case )()(),( EpEppxf 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

cmt d 2sin

momentum isotropization and kinetic equilibration

Initial condition: Minijets p0=1.4 GeV

Important scales for kinetic transport & simulations

Simulations solve Boltzmann equation:→ test particles and other schemes

Semiclassical kinetic theory:

(Quantum mechanics: )

E

dmfp

... kinetic transport still valid

Thermalization times: comparison with bottom-up prediction

• 1/Qs behavior seems to be correct.

• instead -13/5 behavior but -x with x < 13/5

Jet-Quenching Box calculation: T=400MeV

Oliver Fochler

dominant process is 2->3

LPM

DDggggg

mqkk

qg

mq

sgM

222

22

222

242

)(

12

)(2

9

Bremsstrahlung processes

LPM suppression: the formation time

)cosh( yk gLPM

gk y

cosh1

Bethe-Heitler regime

varying the cut-off for kT: )cosh( yAk gLPM