Microscopic Understanding of ultrarel. HIC – parton cascade and dissipative phenomena

C. Greiner,

Johann Wolfgang Goethe-Universität Frankfurt

Institut für Theoretische Physik

in collaboration with: I.Bouras, L. Chen, A. El, O. Fochler, J. Uphoff, Zhe Xu

- fast thermalization within a pQCD cascade- viscosity calculation by Navier-Stokes and

Israel-Stewart- elliptic flow …- dissipative shocks

list of contents

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,radiative „corrections“

(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

qg

mq

sgM

mq

sgM

gLPM

DDggggg

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(

223

3

qfgppd

sDD fnftxmm

screening mass:

LPM suppression: the formation time g1 cosh

ykg: mean free path

radiative part

elastic part

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 production of partons

dt

dpxfxpxfxK

dydydp

d cdab

tbtadcbat

jet

),(),( 2

222

11,;,21

2

minijets

string matter

color glass condensate

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

gg gg: small-angle scatterings

gg ggg: large-angle bremsstrahlung

distribution of collision angles

at RHIC energies

time scale of thermalization

0

2

2

02

2

2

2

2

2

exp)()(tt

E

pt

E

p

E

pt

E

peq

ZZeq

ZZ

= time scale of kinetic equilibration.

fm/c 1Theoretical Result !

Transport Rates

trggggg

trggggg

trgggg

trdrift RRRR

1

Z. Xu and CG, PRC 76, 024911 (2007)

ggggggggggggggi

vn

Cpd

vCvpd

R

z

iziztri

,,

,)

31

(

)2()2( with

2

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

R

R

3

2

53

Transport Rates

2222 )(ln~: sstrRgggg

01.0for)(ln~: 2223 ssstrRggggg

01.0for)(ln~ 2323 ssstrR

Large Effect of 2-3 !

ggggggggg

mb 0.57

mb 0.82

MeV 400T,3.0 for s

ggggg

gggg

Shear Viscosity

)3(2

2

uu

TTT

zz

zzyyxx

From Navier-Stokes approximation

Cfv From Boltzmann-Eq.

Cpd

vuun

Cvpd

fvvpd

zzz

zz

3

32

23

32

3

3

)2()41()3(

15

2

)2()2(

322323

31

31

1)(

5

1

2

2

2

2

RRR

En

tr

E

p

E

p

z

z

relation between and Rtr Z. Xu and CG,

Phys.Rev.Lett.100:172301,2008.

)(7

1)( gggg

sggggg

s

Ratio of shear viscosity to entropy density in 2<->3

AdS/CFTRHIC

Shear viscosity from kinetic theory – part II

px,fC=px,fp

Boltzmann Equation

ppxC+eqf=px,f 01

),( px

PπCC=s 0ln

12

1 T

+JT

=s

Kinetic:

Hydro:

PCT

=02

1

+

px,,px,fCdw=C

px,,px,fCppdw=P

eq

eq

with eqTT=

px,fpx,fpEpd

=s ln3

6

2

0 128 T=C

for (0+1) dimgluon gas

A. El, A. Muronga, Z. Xu and CG, arXiv: …

n=

ddn

e+

e+

e=

dd

+e

=dde

278

34

92

34

21

Shear viscosity from Israel-Stewart theory

Shear viscosity from Israel-Stewart theory vs BAMPS

0.18

Validity of Israel-Stewart in (0+1)Dim

2212

02

212

01

TpzpC=

TpzpC+eqf=px,f ,

pdfφn

=>φ<=σ eqeqφ322 1

Israel-Stewart BAMPS

tr

tr

Validity of Israel-Stewart in (0+1)Dim

1

//

TTeq

TT

dppdNdppdN

(from BAMPS)

1

zeq

zeq

dpf

dpλT,π,φf

22

022

0 2

1

2

11 TzTzeq ppπC=φ,ppπC+f=px,f

Elliptic Flow and Shear Viscosity in 2-3 at RHIC 2-3 Parton cascade BAMPS Z. Xu, CG, H. Stöcker, PRL 101:082302,2008

viscous hydro.Romatschke, PRL 99, 172301,2007

322323

31

31

1)(

5

1

2

2

2

2

RRR

En

tr

E

p

E

p

z

z

/s at RHIC > 0.08

Z. Xu

Rapidity Dependence of v2: Importance of 2-3! BAMPS

evolution of transverse energy

more details on elliptic flow at RHIC …

moderate dependence on critical energy density

/s at RHIC: 0.08-0.2

Z. Xu and CG, arXiv:0811.2940

… looking on transverse momentum distributions

gluons are not simply pions …

light quarks have to be included

need hadronization (and models) to understand the particle spectra

Barbara Betz, Dirk Rischke, Horst Stöcker, Giorgio Torrieri

Mach Cones in Ideal Hydrodynamics

Box Simulation

Bjorken Expansion

Parton cascade meets ideal shocks: Riemann problem

λ = 0.1 fm

λ = 0.01 fm

λ = 0.001 fm

Tleft = 400 MeVTright = 200 MeVt = 1.0 fm/c

I. Bouras

Time evolution of viscous shocksTleft = 400 MeVTright = 320 MeV

η/s = 1/(4 π)

t=0.5 fm/c t=1.5 fm/c

t=3 fm/c t=5 fm/c

Viscous shocks

η/s ~ 0.01 - 1.0

Tleft = 400 MeV - Tright = 320 MeV ,t = 3.0 fm/c

Comparison to Israel-Stewart

Comparison to full pQCD transport

η/s = 0.02 η/s = 0.1

η/s ~ 0.1 - 0.13

Tleft = 400 MeVTright = 320 MeV

t = 3 fm/c

t = 1.6 fm/c

Inelastic/radiative pQCD interactions (23 + 32) in BAMPS explain:

fast thermalization

large collective flow

small shear viscosity of QCD matter at RHIC

realistic jet-quenching of gluons

Summary

Future/ongoing analysis and developments:

light and heavy quarks

jet-quenching (Mach Cones, ridge)

hadronisation and afterburning (UrQMD) needed to determine

how imperfect the QGP at RHIC and LHC can be

… and dependence on initial conditions

backup

Semiclassical kinetic theory:

Validity of kinetic transport - relation to shear viscosity

Quantum mechanis: quasiparticle limit:

RAA ~ 0.06

cf. S. Wicks et al.Nucl.Phys.A784, 426

nuclear modification factorcentral (b=0 fm) Au-Au at 200 AGeV

O. Fochler et al

Quenching of jetsfirst realistic 3d results with BAMPS

arXiv:0806.1169

LPM-effect transport model: incoherent treatment of ggggg processes parent gluon must not scatter during formation time of emitted gluon

discard all possible interference effects (Bethe-Heitler regime)

kt

CM frame

p1 p2

lab frame

kt

= 1 / kt

total boost

O. Fochler

inclusion of light quarks is

mandatory !

… lower color factor

comparison to other

approaches

… LPM bremsstrahlung

jet fragmentation scheme

… possible improvements of microscopic treatment