Collective Flow Effects and Energy Loss in ultrarelativistic

Heavy Ion Collisions

Zhe Xu

USTC, Hefei, July 11, 2008

with A. El, O. Fochler, C. Greiner and H. Stöcker

Zhe Xu

• Fast Thermalization from

pQCD: 2-3 important

Equilibr. time: 1 fm/c

• Elliptic flow v2: high in 2-3

Viscosity: small ~ 0.08

• Hard probe: RAA ~ 0.1

collisional 2-2 vs. radiational 2-3

energy loss

Motivation and Summary

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

Zhe Xu

Outline

• Transport model

• Results from simulations

• Analytical calculations

Zhe Xu

),(),(),( 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

Zhe Xu

Old collision algorithm

BUT, difficult to 3 2 !

/ particles incoming two of distance closest The

collision criterion:

(ZPC, MPC, VNI/BMS, AMPT, PACIAE)

Zhe Xu

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

1

2)2(2

1

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

'

'2)2(

'

!2

1

2)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

pd

E

pd

E

pd

E

ppppMffE

pd

E

pd

E

pd

EpxC

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

1

3

sffE

p

Epxt

Ncoll

j

jj px

Nf

33

)2(1

3

x

tv

NN

Nrel

coll322

21

22

collision probability (Monte Carlo)

Space has to be dividedinto small cells !

Zhe Xu

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

Interaction Probability

23321

3232

32323

32222

)(823for

32for

22for

x

t

EEE

IP

x

tvP

x

tvP

rel

rel

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

'

'2)2(

'

2

121321

)4(42

'2'11232

32

3

13

13

32 pppppME

pd

E

pdI

Zhe Xu

)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(

23

3

qfgppd

sD fnfm

screening mass:

LPM suppression: the formation time g1 cosh

ykg: mean free path

Gluons freeze out at local energy density = 1 GeV/fm3.

Zhe Xu

Results from the parton cascade BAMPS

thermalization

transverse energyelliptic flow

shear viscosityjet quenching

Zhe Xu

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

Zhe Xu

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 !

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

Zhe Xu

total transverse energy per rapidity at midrapidity y=0

Zhe Xu

Rapidity dependence of total transverse energy

ZX, Greiner, Stöcker, arXiv: 0711.0961 [nucl-th]

Zhe Xu

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

ln4

1)(

5

1

322323

31

31

2

2

2

2

nns

RRR

En

tr

E

p

E

p

z

z

/s at RHIC > 0.08

Zhe Xu

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

Zhe Xu

first realistic 3d results on jet-quenching with BAMPS

3.0s

dE/dx, static medium (T = 400 MeV)

RAA ~ 0.1

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

central (b=0 fm) Au-Au at 200 AGeV

O. Fochler

2-32-2

Zhe Xu

Inelastic pQCD interactions (23+32) explain:

• Fast Thermalization

• Large Collective Flow

• Small shear Viscosity of QCD matter at RHIC

• Part of energy loss (for very high energy parton

collisional energy loss due to 2-2 dominates.)

Zhe Xu

Analytical Calculations for a Gluon Gas

Zhe Xu

)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(

23

3

qfgppd

sD fnfm

screening mass:

LPM suppression: the formation time g1 cosh

ykg: mean free path

Zhe Xu

mb 0.57

mb 0.82

MeV 400T,3.0 for s

ggggg

gggg

Cross section does not determine !

relvnR

11

ggggggggg

Collision Rate

Zhe Xu

gg gg: small-angle scatterings

gg ggg: large-angle bremsstrahlung

distribution of collision angles

at RHIC energies

Zhe Xu

2tr sin section cross transportd

dd

trgggg

trggggg

BUT, this is not the full story !

Zhe Xu

Transport Rates

trggggg

trggggg

trgggg

trdrift RRRR

1

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

ggggggggggggggi

Ep

n

fCpd

Ep

fCEppd

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.

0 ,2

12

E

pedf zE

Gassume

Zhe Xu

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 gg->ggg !

Zhe Xu

)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

Shear Viscosity

Zhe Xu

)(7

1)( gggg

sggggg

s

Ratio of shear viscosity to entropy density in 2-3

AdS/CFTRHIC

ZX and C.Greiner, PRL 100, 172301, 2008; arXiv: 0710.5719 [nucl-th].

0.13/s

3.0 for s

Zhe Xu

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

ln4

1)(

5

1

322323

31

31

2

2

2

2

nns

RRR

En

tr

E

p

E

p

z

z

/s at RHIC > 0.08

Zhe Xu

Inelastic pQCD interactions (23 + 32) explain:

• Fast Thermalization

• Large Collective Flow

• Small shear Viscosity of QCD matter at RHIC

• Part of energy loss (for very high energy parton

collisional energy loss due to 2-2 dominates.)

Initial conditions, hadronization and afterburning

determine

how imperfect the QGP at RHIC & LHC can be.

Conclusion

Zhe Xu

Initial conditions in heavy ion collisions

dcba

cdab

TbTaT

jet

td

dpxfxpxfxK

dydydp

d

,;,

222

211

212 ˆ

),(),(

ppjetAA

AAjet bTN )0(2

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

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

minijets production with pt > p0

Zhe Xu

Zhe Xu

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!

Zhe Xu

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

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

Zhe Xu

trireli

tri vnAR

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

ggggggggg AA