Collective Flow and Energy Loss with parton transport in collaboration with: I.Bouras, A. El, O. Fochler, F. Reining, J. Uphoff, C. Wesp, Zhe Xu - viscosity

Collective Flow and Energy Loss

with parton transport

in collaboration with:

I.Bouras, A. El, O. Fochler, F. Reining, J. Uphoff, C. Wesp, Zhe Xu

- viscosity and its extraction from elliptic flow- jet quenching … same phenomena?- dissipative shocks and Mach Cones- charm quarks

C. Greiner

WISH 2010, Catania, september 2010

),(),(),( 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)

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

)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

yk

g: mean free path

radiative part

elastic part

suppressed!

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

Simulation: parton cascade

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

Shear Viscosity

)3(2

2

uu

TTT

zz

zzyyxx

Navier-Stokes approximation

322323

31

31

1)(

5

1

2

2

2

2

RRR

En

tr

E

p

E

p

z

z

relation: <-> Rtr

Z. Xu and CG,

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

RHIC

AdS/CFT

yux

xy

...extracting viscosity

>νμ<μνeq

μνμν uη=TT=π 2

Finally we find

Starting from a classical ansatz

0.1180.3 ==αs

ηs

x

vη=

A

F zz

With the Navier-stokes approximaion

We find a velocity profile

F. Reining

rt,ππrddtTVk

=η xyxy

B

0,0

10

1 3 1.040.3 22 ==α

s

ηs

0.130.3 33 ==αs

ηs

VTπ

=π xy

52 4

0,0

GeVfm

τT

π=

s

η

0.19720

1

τtπ=rt,ππ xyxyxy /exp0,00,0 2

...extracting viscosity C. Wesp

Green-Kubo relation:

equilibrium fluctuations:

Motion Is Hydrodynamic

x

yz

• When does thermalization occur? – Strong evidence that final state bulk behavior

reflects the initial state geometry

• Because the initial azimuthal asymmetry persists in the final state dn/d ~ 1 + 2 v2(pT) cos (2) + ...

2v2

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: 0.08-0.2

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

evolution of transverse energy

… looking on transverse momentum distributions

gluons are not simply pions …

need hadronization (and models) to understand the particle spectra

… and adding quarks as further degrees of freedom

quarks are helping in the right direction …

Z. Xu and C. Greiner, arxiv:1001.2912

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

Energy Loss in gg ggg Processes

Reasonable partonic cross sections over the whole energy range. Definition of the energy loss E matters

E = Ein – max( Eiout )

E =

Cross sections ( T = 400 MeV) Energy loss in single gg ggg

Gluon Radiation and Energy Loss

Heavy tail in E distribution leads to large mean <E>

Radiaton spectrum (E = 50 GeV) E distribution (E = 400 GeV)

Some BAMPS Events (CM frame)

E = 0.67 GeV E = 206.43 GeV

E = 26.01 GeV E = 117.01 GeV

RAA ~ 0.052

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

nuclear modification factorcentral (b=0 fm) Au-Au at 200 AGeVO. Fochler et al

Quenching of jetsfirst realistic 3d results with BAMPS

PRL102:202301:2009

inclusion of light quarks is

mandatory !

… lower color factor

jet fragmentation scheme

O. Fochler, Z. Xu and C. Greiner, arxiv:1003.4380

Non-Central RAA

and High-pT Elliptic Flow

Gluonic RAA for b = 0 and b = 7 fm

Differential v2 for b = 7 fm

Experimental v2 from PHENIX, arXiv: 0903.4886

B. Betz, M. Gyulassy, D. Rischke, H. Stöcker, G. Torrieri

Mach Cones in Ideal Hydrodynamics

Box Simulation

QCD “sonic boom”

T L=400 MeVT R=200 MeV

t=3.2 fm/c

−c s

c s v shock

sshock c>v

a shock wave travels with a speed higher than speed of sound

a rarefaction wave travels to the left with the speed of sound

The Relativistic Riemann Problem

Riemann problem at finite viscosity

Cfp

Development of a shock plateau

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

/s less than 0.1-0.2

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

time evolution of viscous shocks

Tleft = 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

27

Medium

jet

T = 400 M eV

E jet=200 GeV

Box scenario, no expansion of the medium, massless Boltzmann gasinteractions: 2 2 with isotropic distribution of the collision angle

Mach Cones in BAMPS

Setup

Jet has constant mean free path and onlymomentum in z-direction!

fmGeV=dxdE / 1411/

Zhe Xu, Jaipur, Quark Matter 2008

Mach Cones in BAMPS:Different Viscosities

E jet=200 GeVη / s=0.005

The results agree qualitatively with hydrodynamic and transport calculations→ B. Betz, PRC 79:034902, 2009 Strong collective behaviour is observed A diffusion wake is also visible, momentum flows in direction of the jet

o

jet

s

v

c=θ 54.7arccos



E jet=200 GeVη / s=0.025



E jet=200 GeVη / s=0.08



E jet=200 GeVη / s=0.32

The shock front (Mach front) gets broader and vanish with more dissipation The viscosity smears the profile out, but does it affect the Mach angle?


Stoped Jet in BAMPS:

0.025/

GeV 20

=sη

=E jet



0.08/

GeV 20

=sη

=E jet



0.2/

GeV 20

=sη

=E jet



0.5/

GeV 20

=sη

=E jet

Initial charm in hard parton scatterings

Two approaches:

1. LO pQCD: mini-jets

2. PYTHIAMonte Carlo Event Generatorfor nucleon-nucleon collisions

both very sensitive on•parton distribution functions•factorization scale •renormalization scale•charm mass

Charm production in the QGP at RHIC

RHIC

BAMPS

ccggccgg K

Maximum charm production of 3.4 pairs

J. Uphoff et al., arXiv:1003.4200 [hep-ph]

Charm production in the QGP at LHC

LHC

BAMPS

Elliptic flow v2 for charm at RHIC

J. Uphoff et al., arXiv:1004.4091 [hep-ph]only elastic charm processes

gQgQgQgQ K

Heavy quark elliptic flow v2 at RHIC

PHENIX, arXiv:1005.1627A. Peshier,

arXiv:0801.0595 [hep-ph]

P.B. Gossiaux, J. Aichelin,Phys.Rev.C78 (2008)

Jan Uphoff

Heavy quark RAA at RHIC

PHENIX, arXiv:1005.1627

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

… and dependence on initial conditions

dissipative hydrodynamics

Semiclassical kinetic theory?

Weak or strong ….Validity of kinetic transport - relation to shear viscosity

Quantum mechanics: quasiparticles?

Energy Loss in a Static Medium Elastic energy loss ~T2 ln(E / T) Large differential energy loss due to

ggggg Roughly dE / dx ~ E Rapid evolution of energy spectrum

E-spectrum (T = 400 MeV, E0 = 50 GeV)

Documents

Collective Flow and Energy Loss with parton transport in collaboration with: I.Bouras, A. El, O. Fochler, F. Reining, J. Uphoff, C. Wesp, Zhe Xu - viscosity