qcd matter thermalization at rhic and lhc

QCD Matter Thermalization at RHIC and LHC

Zhe Xu

with L.Cheng, A. El, K. Gallmeister and C. Greiner

SQM 2008, Beijing, China, Oct. 9

Zhe Xu, Beijing, SQM 2008

From transport calculations using BAMPS

• Fast Thermalization from pQCD: 2-3 important

equilibration time: eq=1 fm/c

• Elliptic flow v2: high in 2-3

Viscosity: small ~ 0.08-0.16

Motivation and Summary

P.Huovinen et al., PLB 503, 58 (2001)

Assumption: full thermalization at 0.6 fm/c


Outline

• Transport model

• Why 2-3 important

• Initial condition dependence of thermalization at RHIC and LHC

• Summary


),(),(),( pxCpxCpxfv ggggggggg

BAMPS: Boltzmann Approach of MultiParton Scatterings

A transport algorithm solving the Boltzmann-Equations for on-shell partons with pQCD interactions

new development ggg gg(Z)MPC, VNI/BMS, AMPT, PACIAE

Elastic scatterings are ineffective in thermalization !

Inelastic interactions are needed !

Transport Model


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

3x

)''()2(||'2)2(

''2)2(

'!2

12)2(2

1

)''()2(||'''2)2(

''2)2(

'!2

12)2(2

1 ),(

2121)4(42

'2'112212

32

3

13

13

23

23

1

2121)4(42

12'2'1212

32

3

13

13

23

23

1122

ppppMffE

pdE

pdE

pdE

ppppMffE

pdE

pdE

pdE

pxC

collision rate per unit phase space for incomingparticles p1 and p2 with 3p1 and 3p2:

22212

32

3

1133

)2(1

22

22)2(2

13

sffE

pEpxt

Ncoll

j

jj px

Nf 33

)2(1

3

xtv

NNN

relcoll

32221

22

collision probability (Monte Carlo)

Space has to be dividedinto small cells !


ZX and C. Greiner, PRC 71, 064901 (2005)

Interaction Probability

23321

3232

32323

32222

)(823for

32for

22for

xt

EEEIP

xtvP

xtvP

rel

rel

)''()2('2)2(

''2)2(

'21

21321)4(42

'2'11232

32

3

13

13

32 pppppME

pdE

pdI


)cosh()(

12)(2

9

,)(2

9

222

22

222

242

222

242

ykmqkk

qgmqsgM

mqsgM

gLPMDD

ggggg

Dgggg

J.F.Gunion, G.F.Bertsch, PRD 25, 746(1982)T.S.Biro at el., PRC 48, 1275 (1993)S.M.Wong, NPA 607, 442 (1996)

screened partonic interactions in leading order pQCD

),3(16 1)2(

23

3

qfgppd

sD fnfm

screening mass:

LPM suppression: the formation time g1 cosh

ykg: mean free path


gg gg: small-angle scatterings

gg ggg: large-angle bremsstrahlung

distribution of collision angles

at RHIC energies


Transport Rates

trggggg

trggggg

trgggg

trdrift

eq

RRRR 1

ZX and C. Greiner, PRC 76, 024911 (2007)

ggggggggggggggiEpn

fCpdEpfC

Eppd

Rz

iz

iz

tri

,,

,)

31(

][)2(

][)2(

with

2

2

3

3

2

2

2

2

3

3

• Transport rate is the correct quantity describing kinetic equilibration.• Transport collision rates have an indirect relationship to the collision-angle distribution.


trggggg

trggggg

trgggg

trggggg

RR

RR

32

53

Transport Rates for a static gluon gas

222222 )(ln~~: sss

tr RRgggg

01.0for)(ln~~: 222323 sss

tr RRggggg

01.0for)(ln~~ 232323 ssss

tr RR

Large Effect of 2-3 !

ZX and C.Greiner, PRL 100, 172301, 2008


time scale of thermalization in heavy ion collisions

eqeq

ZZeq

ZZ ttEpt

Ep

Ept

Ep

0

2

2

02

2

2

2

2

2

exp)()(

eq = time scale of kinetic equilibration.

fm/c 1eq

theoretical result from parton cascadecalculations

at collision center: xT<1.5 fm, | < 0.2 of a central Au+Au at s1/2=200 GeVInitial conditions: minijets pT>1.4 GeV; coupling s=0.3


Elliptic Flow and Shear Viscosity in 2-3 at RHIC 2-3 Parton cascade BAMPS ZX, Greiner, Stöcker, PRL 101, 082302, 2008

viscous hydro.Romatschke, PRL 99, 172301,2007

322323

31

31

1)(

51

2

2

2

2

RRR

En tr

Ep

Ep

z

z

/s at RHIC > 0.08


ZX, C.Greiner, H. Stöcker, PRL 101:082302,2008

Perturbation QCD describes well

• fast thermalization, • low /s,• large v2 at RHIC.


Initial Condition – Wounded Nucleons

binaryN PP from Gluons and Quarks A Afrom Gluons and Quarks

P+P using PYTHIA 6.4

semi-hard partonic collisionswith initial and final radiationsstring breaking

GeV200A of %80E

RHIC at Au Aucentral for 1000N

partons

binary

by L.Cheng


Initial Condition – Color Glass Condensate

max

))(,(),(1

4 22

21

22

2

22

p

BAsc

cg kpxpxkdppd

NN

dyrddN

,1min)(

1~),,( KLN

01.053.1

)(GeV2),(

),max()(1~),,( KLN

),(

2

22

,2

,2

22

22

2

kx

s

ss

BApart

BAs

s

s

ss

kQ

Qrkx

xrn

rxQ

kQQ

Qrkx

GeV200A of %80Egluons

Kharzeev, Levin, Nardi, NPA 730, 448 (2004); 747, 609 (2005)Hirano and Nara, NPA 743, 305 (2004)Adil, Drescher, Dumitru, Hayashigaki, Nara, PRC 74, 044905 (2006)


Wounded nucleons vs Color Glass Condensate

Initial Conditions: I. Only gluons from WNII. Gluons and quarks from WN. Quarks as gluons.III. Color Glass condensate

Formation time: 0.15 fm/c

by L.Cheng and A. El


Decrease of the transverse energy

3-fmGeV 6.0

15.0/3.0

c

s

s

QGP from wn has a larger /s than 0.15.QGP from cgc has a smaller /s than 0.15.

(RHIC)GeV 33620

using BAMPS


Kinetic equilibration

fm/c 1.5

exp)()( 02

2

02

2

2

2

2

2

eq

eqeq

ZZeq

ZZ ttEpt

Ep

Ept

Ep

no difference betweenwn and cgc !

0.25 || fm, 5.1x :region central the within


Chemical equilibration due to gg gggnn

nn

eqeq

3/T withT16 where,fugacity 32

wn: gluons system stays in chemical equilibrium.cgc: chemical equilibrium is achieved at the same timesacle, 1.5 fm/c, as the kinetic equilibration.


Initial conditions at LHC

by L.Cheng and A. El

Initial Conditions: I. Gluons and quarks from WN, Quarks as gluonsII. Color Glass condensate

Formation time: 0.15 fm/c

Gluons dominante the initial conditions.


Prediction of final dET/dy at LHC

2150 GeV

1620 GeV

-3fmGeV 6.0 ,2.0 withBAMPS cs


Thermal equilibration at LHC

no difference between wn and cgctime scale of kinetic equilibration: 0.8 ~ 1.6 fm/c

initial difference between wn and cgctime scale of chemical equilibration: 1.5 fm/c


Inelastic pQCD interactions (23 + 32) explain:

• Fast Thermalization• Large Collective Flow• Small shear Viscosity of QCD matter at RHIC

Wounded nucleons vs. CGC• wn: smaller dET/dy smaller /s

cgc: larger dET/dy larger /s

• same kinetic equil., different chemical equil.

Summary


more details on elliptic flow at RHIC …

moderate dependence on critical energy density

/s at RHIC: 0.08-0.2


… looking on transverse momentum distributions

gluons are not simply pions …

need hadronization (and models) to understand

the particle spectra


Life time of QGPnT 3/

Tc=175 MeV


Comparisons with 1+1 Bjorken


pt-spectra


3-2 + 2-3: thermalization! Hydrodynamic behavior! 2-2: NO thermalization

simulation pQCD 2-2 + 2-3 + 3-2simulation pQCD, only 2-2

at collision center: xT<1.5 fm, z < 0.4 t fm of a central Au+Au at s1/2=200 GeVInitial conditions: minijets pT>1.4 GeV; coupling s=0.3

pT spectra


mb 0.57

mb 0.82

MeV 400T,3.0 for s

ggggg

gggg

Cross section does not determine !

relvnR11~

ZX and C.Greiner, arXiv: 0710.5719 [nucl-th]

ggggggggg

What determinesthe equilibration time scale ?


2tr sin section cross transportddd

trgggg

trggggg BUT, this is not the full story !


)3(22uuTTT

zz

zzyyxx

From Navier-Stokes approximation

Cfv From Boltzmann-Eq.

Cpdvuun

Cvpdfvvpd

zzz

zz

3

32

23

32

3

3

)2()41()3(

152

)2()2(

322323

31

31

1)(

51

2

2

2

2

RRR

En tr

Ep

Ep

z

z

relation between and Rtr


)(71)( ggggs

gggggs

Ratio of shear viscosity to entropy density in 2-3

AdS/CFTRHIC


total transverse energy per rapidity at midrapidity


Initial conditions

dcba

cdab

TbTa

T

jet

tddpxfxpxfxK

dydydpd

,;,

2

22

2

11

21

2 ˆ),(),(

ppjetAA

AAjet bTN )0(2

Glauber-type: Woods-Saxon profile, binary nucleon-nucleon collision

700/ dydN gfor a central Au+Au collision at RHICat 200 AGeV using p0=1.4 GeV

minijets production with pt > p0


5.22

.32

.23

tr

trtr

RRR

The drift term is large.

.

.32

.23

.22

trdrift

tr

tr

tr

R

R

R

R

ggggg interactions are essential for kinetic equilibration!


trireli

tri vnAR

due to the fact that a 2->3 process brings one more particletoward isotropy than a gg->gg process.

ggggggggg AA

qcd matter thermalization at rhic and lhc

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