QCD Plasma Equilibration, Collective Flow Effects and Jet-Quenching –Phenomena of Common Origin

C. Greiner,

24th winter workshop on nuclear dynamics, South Padre Island, 2008

Johann Wolfgang Goethe-Universität Frankfurt

Institut für Theoretische Physik

in collaboration with

A. El, O. Fochler, B. Schenke, H. Stöcker, Zhe Xu

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!

RAA,gluon ~ 0.1 !

Three body effects in parton cascades!

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

from R. Bellwied

Initial production of partons

dt

dpxfxpxfxK

dydydp

d cdab

tbtadcbat

jet

),(),( 2

222

11,;,21

2

minijets

string matter

color glass condensate

Momentum space anisotropy:Time dependence

Michael Strickland

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

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

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, Z. Xu and CG, arXiv: 0712.3734 [hep-ph]

ggg gg !This 3-2 is missing in the Bottom-Up scenario(Baier, Dohkshitzer, Mueller, Son (2001)).

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

pT spectra

Bottom up is not working as advocated: no tremendous soft gluon production,soft modes do not thermalize before the hard modes

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 !

mb 0.57

mb 0.82

MeV 400T,3.0 for s

ggggg

gggg

Cross section does not determine !

relvnR

11~

Z. Xu and CG, arXiv: 0710.5719 [nucl-th]

ggggggggg

What determinesthe equilibration time scale ?

2tr sin section cross transport

d

dd

trgggg

trggggg BUT, this is not the full story !

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 !

Shear Viscosity Z. Xu and CG, arXiv: 0710.5719 [nucl-th]

)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

)(7

1)( gggg

sggggg

s

Ratio of shear viscosity to entropy density in 2-3

AdS/CFTRHIC

Z. Xu, A. El

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 Z. Xu, CG, H. Stöcker, arXiv: 0711.0961 [nucl-th]

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

Dissipative HydrodynamicsShear, bulk viscosity and heat conductivity of dense QCD matter could be prime

candidates for the next Particle Data Group, if they can be extracted from data.

Need a causal hydrodynamical theory.What are the criteria of applicability?

Causal stable hydrodynamics can be derrived from the Boltzmann Equation:

-Renormalization Group Method by Kunihiro/Tsumura-->stable 1st Order linearized BE with f=f

0+εf

1+ε²f

2 yields (2nd Order – work in progress)

can be solved by introducing projector P on Ker{A}, where A-linearized collision operator

-Grad‘s 14-momentum method-->2nd Order causal hydrodynamics.

Calculate momenta of the BE. Transport coefficients and relaxation times for dissipative quantities can be calculated as functions of collision terms in BE.

Compare dissipative relaxation times to the mean free pass from cascade simulation.

Andrej E

l

nuclear modification factor

relative to pp (binary collision scaling)

experiments show approx. factor 5 of suppression in hadron yields

Hard probes of the medium

high energy particles are promising probes of the medium created in AA-collisions

QM 2008, T. Awes

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

first realistic 3d results on jet-quenching with BAMPS

LPM cut-off increases

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

2/, static medium (T = 400 MeV)

RAA ~ 0.1

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

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

O. Fochler

Jet propagation within YM fields

Poynting vectors

Dynamical simulation of jet propagation in the plasma

Björn Schenke

preliminary

Stronger longitudinal broadeningcaused by domains of strong chromo-fields with

Explaining the “ridge”

Additional near-side long range correlation in

(“ridge like” corrl.) observed.

Dan Magestro, Hard Probes 2004, STAR, nucl-ex/0509030, Phys. Rev. C73 (2006) 064907 and P. Jacobs, nucl-ex/0503022

Au+Au 0-10%

STAR

preliminary

J. Pu

tschke, QM

2006

Dumitru, Nara, Schenke, Stricklande-Print: arXiv:0710.1223 [hep-ph]

Inelastic/radiative pQCD interactions (23 + 32) 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

dissipative hydrodynamics

Au+Au – Setup central (b=0 fm) Au-Au collision at 200 AGeV sampling of initial gluon plasma:

initial momentum distribution (mini-jets) according to

Glück-Reya-Vogt parameterization for structure functions; K = 2 lower cut-off: p0 = 1.4 GeV (reproduces dET/dy)

particle production via standard nuclear geometry(Wood-Saxon density profile, Glauber-Model)

each parton is given a formation time 35 testparticles simulate evolution of fireball up to ~5 fm/c when energy density in a cell drops below = 1 GeV

free streaming (in the respective cell)

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

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

Simulations solve Boltzmann equation:→ test particles and other schemes

Semiclassical kinetic theory:

(Quantum mechanics: )

Important scales for kinetic transport & simulations

E

dmfp

... kinetic transport still valid

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!

0

2

2

02

2

2

2

2

2

exp)()(tt

E

pt

E

p

E

pt

E

peq

ZZeq

ZZ

(t) gives the timescale of kinetic equilibration.

,/ 22 EPQ Z

),,(

),,(

3

3

3

3

)2(

)2(

txpf

QtxpfQ

pd

pd

t

fpdtfpd tQ

nQ

ntQ 3

3

3

3

)2()2()(

11)(

322322 IIIfE

P

t

f

322322)( CCCCtQ drift

,1 .

32.

23.

22. trtrtrtr

drift RRRR

)(

)(

tQQ

tQ

eq

bottom-up scenario of thermalization

R.Baier, A.H.Mueller, D.Schiff and D.T.Son, PLB502(2001)51

• Qs-1 << t << -3/2 Qs

-1 Hard gluons with momenta about Qs are freedand phase space occupation becomes of order 1.

• -3/2 Qs-1 << t << -5/2 Qs

-1 •(h+h h+h+s)Hard gluons still outnumber soft ones, but soft gluons give most of theDebye screening.

• -5/2 Qs-1 << t << -13/5 Qs

-1

(h+h h+h+s; s+s s+s; h+s sh+sh+s)Soft gluons strongly outnumber hard gluons.Hard gluons loose their entire energy to the thermal bath.

• After -13/5 Qs-1 the system is thermalized: T ~ t-1/3, T0 ~ 2/5 Qs

Au-Au – Reconstruction partons with high-pt too rare simulate large number of initial conditions select events according to highest pt-(test)particle simulate only selected events and weight results

full: 200000 events; reconstruction: 40 events per pt-bin, ~1000 total