Thermalization of the quark gluon matter in ultrarelativistic heavy ion collisions

Thermalization of the quark gluon matter in ultrarelativistic heavy ion collisions

Zhe Xu

Weihai, August 14, 2009

Institut für Theoretische PhysikGoethe-Universität Frankfurt, Germany

Zhe Xu, Weihai 2009 2/44

Outline

• Motivation

• Transport model

• Why 2-3 important

• Initial condition dependence

• Summary


Motivation

sonfermion/bo : ,)1(

1),(

/

TEeq epxf

thermal equilibrium

non-equilibrium

),(~),( pxfpxf eq

),(~),( pxfpxf eq

in kinetic equilibrium, but not in chemical equilibrium

not in kinetic equilibrium


deviation from thermal equilibrium

1. momentum spectra

2. mometum isotropy, average of angles

3. momentum energy tensor

TTdppdN /

2

2

eq

2

2

2

23

2

2

or ; 3

1 ),,(

1

T

zzzz

p

p

E

ppxf

E

ppd

NE

p

frame moving-co in ),,,( diag

),,(3

PPPeT

TTpxfppE

pdT

eq

eq


High energy heavy ion collisions


Momentum space anisotropy:Time dependence

M. Strickland


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

nearly perfect fluid

Assumption: full thermalization at 0.6 fm/c


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


),(),(),( 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

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 !


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


A simple case

2->2 with isotropic differential cross section

p1 p2

p1‘

p2‘

const.cos

22

d

d

225

6

T

shear viscosity

Huovinen and Molnar, PRC 79, 014906 (2009)

Zhe Xu, Weihai 2009 13/44A. El, ZX and C. Greiner, arXiv: 0907.4500 [hep-ph]

225

6

T

),2/,2/,0( diag

eqTT

deviation from equilibrium, relaxation towards equilibrium

2/

PP

PP

T

L

one-dimensional expansion with Bjorken boost invariance

ln4 nns


Relativistiv shock waves

I. Bouras et al. PRL 103, 032301 (2009)

P0 > P4


)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)

screened partonic interactions in leading order pQCD

Incoherent treatment: the formation time g1 cosh

ykg: mean free path

LPM suppression:


frame CM in axis collision the and between angle :

frame CM to frame comoving the fromvelocity boost :

where,1

costanh1 with

)cosh()(

12

)(2

9

2

222

22

222

242

yL

yLkmqkk

qg

mq

sgM gLPM

DDggggg

Jet-quenching

O. Fochler, ZX and C. Greiner,PRL 102, 202301 (2009)


T.S.Biro at el., PRC 48, 1275 (1993) chemical equilibration of quarks and gluons by solving the rate equations

S.M.Wong, NPA 607, 442 (1996) kinetic equilibration within the relaxation time approach

J.Chen, H.Dong, K.Ohnishi, Q.Wang, arXiv:0907.2486 [nucl-th] shear viscosity using the variation method

rel

eq fffC

~][


mb 0.57

mb 0.82

MeV 400T,3.0 for s

ggggg

gggg

-23 T ~ ,T~ , nvnR rel

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

ggggggggg

collision rates


What leads to fast thermalization?

• large cross section (collision rate)

• large collision angle -> large momentum deflection -> fast momentum isotropization


,)(2

9222

242

Dgggg mq

sgM

p1 p2

p1‘

p2‘

qT

small angle scatterings


J.F.Gunion, G.F.Bertsch, PRD 25, 746(1982)

yyyE

pz small for tanhcos 3

Central plateau in cos3 , thus not small angluar scatterings


gg gg: small-angle scatterings

gg ggg: large-angle bremsstrahlung

distribution of collision angles

at RHIC energies

central plateau


2tr sin section cross transportd

dd

trgggg

trggggg

BUT, this is not the full story !


Transport Rates

trggggg

trggggg

trgggg

trdrift

z

z

eq

RRRRtEp

Epdtd

)(/3/1

/122

22


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.


53

tr

gggg

trggggg

R

R

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 gg->ggg

ZX and C.Greiner, PRL 100,172301, (2008))1(

2

TE

pff zeq assume:


)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

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


)(7

1)( gggg

sggggg

s

Ratio of shear viscosity to entropy density in 2-3

AdS/CFTRHIC


A. El, A. Muronga, ZX and C. Greiner, PRC 79, 044914 (2009)

]1)[,(),( with),(

method sGrad' using 2

00

3

0

ppcpxfpxfpxfCppp

pdP

PTc

eq

)1(

2

TE

pff zeq comparing


Calculating f(x,p) in heavy ion collisionsusing 3+1 dimensional parton cascade

BAMPS


Initial conditions

dcba

cdab

TbTa

T

jet

td

dpxfxpxfxK

dydydp

d

,;,

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


total transverse energy per rapidity at midrapidity

b=0 fms=0.3


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, || < 0.2

pT spectra


time scale of thermalization in heavy ion collisions

eqeq

ZZeq

ZZ tt

E

pt

E

p

E

pt

E

p

0

2

2

02

2

2

2

2

2

exp)()(

eq = time scale of kinetic equilibration.

fm/c 1eq

theoretical result from parton cascadecalculations


Transport Rates

trggggg

trggggg

trgggg

trdrift

z

z

eq

RRRRtEp

Epdtd

)(/3/1

/122

22


ggggggggggggggi

Ep

n

fCpd

Ep

fCEppd

Rz

iz

iz

tri

,,

,

)31

(

][)2(

][)2(

with

2

2

3

3

2

2

2

2

3

3


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!


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)(

5

1

2

2

2

2

RRR

En

tr

E

p

E

p

z

z

/s at RHIC > 0.08


Initial condition dependenceof thermalization 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 radiations

GeV200A of %80E

RHIC at Au Aucentral for 1000N

partons

binary

new work by L.Cheng


Initial Condition – Color Glass Condensate

max

))(,(),(1

4 22

21

22

2

22

p

BAsc

cg kpxkxkdp

pd

N

N

dyrd

dN

,1min)(

1~),,( KLN

01.0

53.1

)(GeV2),(

),max()(

1~),,( KLN

),(

2

22

,2

,2

22

22

2

kx

s

ss

BApart

BAs

s

s

ss

k

Q

Qrkx

x

rnrxQ

kQ

Q

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 needs a larger /s than 0.15.QGP from cgc needs 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 tt

E

pt

E

p

E

pt

E

p

no difference betweenwn and cgc !

0.25 || fm, 5.1x

:region central the within


Chemical equilibration due to gg ggg

nnn

neq

eq

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.


Inelastic pQCD interactions (23 + 32) explain:

• Fast Thermalization,

• Large Collective Flow,

• Small shear Viscosity of QCD matter at RHIC,

because the bremsstrahlung favors large-angle radiation.

Summary


chemical equilibration in a box

gluons and light quarks

eqnn /fugacity

qqqq ,qqqq

gqgq ,

,

qqgg

ggggggggg

gluons and charm quarks

ccgg

by J. Uphoff (diploma thesis)


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

new work planned with G. Burau et al.


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

Perturbation QCD describes well

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



trireli

tri vnAR

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

ggggggggg AA


pt-spectra


Life time of QGP

nT 3/

Tc=175 MeV

Documents

Thermalization of the quark gluon matter in ultrarelativistic heavy ion collisions