QCD Plasma Equilibration and Collective Flow Effects

QCD Plasma Equilibration and Collective Flow Effects

Zhe Xu

with C. Greiner and H. Stöcker

Quark Matter 2008, Jaipur, India, Feb. 6

Zhe Xu, Jaipur, Quark Matter 2008

Y

X• Fast Thermalization from

QCD: 3-2 important!

• Equilibr. time short in 2-3!

• Elliptic flow v2 high in 2-3!

• Viscosity small ~ 0.08!

Three body effects in parton cascades!

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

from R. Bellwied


Thermalization driven by plasma instabilitiesRefs.:

Mrowczynski;

Arnold, Lenaghan, Moore, Yaffe;

Rebhan, Romatschke, Strickland,

Bödeker, Rummukainen;

Dumitru, Nara;

Berges, Scheffler, Sexty

Dumitru, Nara, Strickland, PRD 75, 025016 (2007)

Dumitru, Nara, Schenke, Strickland, arXiv:0710.1223

talk by B. Schenkeparallel session VIII


QCD thermalization usingparton cascade

VNI/BMS: K.Geiger and B.Müller, NPB 369, 600 (1992)

S.A.Bass, B.Müller and D.K.Srivastava, PLB 551, 277(2003)

ZPC: B. Zhang, Comput. Phys.Commun. 109, 193 (1998)

MPC: D.Molnar and M.Gyulassy, PRC 62, 054907 (2000)

AMPT: B. Zhang, C.M. Ko, B.A. Li, and Z.W. Lin, PRC 61, 067901 (2000)

BAMPS: Z. Xu and C. Greiner, PRC 71, 064901 (2005); 76, 024911 (2007)


),(),(),( pxCpxCpxfp 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

Elastic scatterings are ineffective in thermalization !

Inelastic interactions are needed !

Xiong, Shuryak, PRC 49, 2203 (1994)Dumitru, Gyulassy, PLB 494, 215 (2000)Serreau, Schiff, JHEP 0111, 039 (2001)Baier, Mueller, Schiff, Son, PLB 502, 51 (2001)


)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


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


A,El, ZX and C.Greiner, arXiv: 0712.3734 [hep-ph]

talk by A. Elparallel session VI

ggg gg !This 3-2 is missing in the Bottom-Up scenario(Baier et al.).

Initial conditions: Color Glass Condensate Qs=3 GeV; coupling s=0.3

pT spectra


time scale of thermalization

0

2

2

02

2

2

2

2

2

exp)()( ttEpt

Ep

Ept

Ep

eqZZ

eqZZ

= time scale of kinetic equilibration.

fm/c 1Theoretical Result !


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 !


Transport Rates

trggggg

trggggg

trgggg

trdrift RRRR

1

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

ggggggggggggggi

vn

CpdvCvpd

Rz

iziztri

,,

,)

31(

)2()2( with2

3

322

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

2222 )(ln~: sstrRgggg

01.0for)(ln~: 2223 ssstrRggggg

01.0for)(ln~ 2323 ssstrR

Large Effect of 2-3 !


Shear Viscosity

D.Teaney, PRC 68, 034913 (2003)

P.Arnold, G.D.Moore, L.G.Yaffe, JHEP 0011, 001 (2001); 0305, 051 (2003)

T.Hirano, M.Gyulassy, NPA 769, 71 (2006)

M.Asakawa, S.A.Bass, B.Müller, Prog.Theor.Phys. 116, 725 (2007)

A.Muronga, PRC 76, 014910 (2007)

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


)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


transverse flow velocity of local cell in thetransverse plane of central rapidity bin

Au+Au b=8.6 fmusing BAMPS =c

22yx vv

Collective Effects


Elliptic Flow and Shear Viscosity in 2-3 at RHIC 2-3 Parton cascade BAMPS ZX, Greiner, Stöcker, arXiv: 0711.0961 [nucl-th]

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


Rapidity Dependence of v2: Importance of 2-3! BAMPS ZX,G,S

see also:

L.W.Chen, et al., PLB 605, 95 (2005)

C.Nonaka, et al., JPG 31, 429 (2005)

T.Hirano, et al., PLB 636, 299 (2006)

J.Bleibel, et al., PRC 76, 024912 (2007); PLB 659, 520 (2008)

Hama, et al., arXiv: 0711.4544 [hep-ph]

A.K.Chaudhuri, arXiv: 0801.3180

Session XVI, Collectivity-theoryHirano, Molnar, Bhalerao, Song,Muronga, Csorgo


Inelastic pQCD interactions (23 + 32) explain:

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

Initial conditions, hadronization and afterburning determine

how imperfect the QGP at RHIC & LHC can be.

further investigations in progress:H. Petersen, G. Burau, J. Steinheimer, M. Bleicher (University of Frankfurt)see Poster P68

Summary


total transverse energy per rapidity at midrapidity


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 ...

interaction probability:

23321

3232

32323

32222

)(823

32

22

xt

EEEIPfor

xtvPfor

xtvPfor

rel

rel

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

1'2'1321

)4(42'2'1123

'23

'23

'13

'13

32 pppppME

pdE

pdI

cell configuration in space

3x

)())((),( )3()3(i

ii pptxxpxf


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 Plasma Equilibration and Collective Flow Effects

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