The importance of multiparticle collisions in heavy ion reactions

C. GreinerThe Physics of High Baryon Density

IPHC Strasbourg, Sept. 2006

Johann Wolfgang Goethe-Universität Frankfurt

Institut für Theoretische Physik

• Motivation: chemical equilibration of anti-baryons

• Equilibration by potential Hagedorn states

• Thermalization at RHIC by

• Outlook

Exploring the phases of nuclear matter

Strangeness production at SpS energies

J. Geiss

Production of Antihyperons:QGP signature…?

P. Koch, B. Müller, J. Rafelski

Production of Anti-Baryons

R.Rapp and E. Shuryak, Phys.Rev.Lett.86 (2001) 2980

C.Greiner and S.Leupold, J.Phys. G27 (2001) L95

Multimesonic channels

C.Greiner, AIP Conf. Proc. 644:337 (2003)

production at RHIC

I. Shovkovy, J. Kapusta

Thermal rates within chiral SU(3) description

Chemical population ofbaryons / anti-baryons:

P. Huovinen, J. Kapusta

Insufficient by a factor of 3 to 4

Chemical Freeze-out and of QCD

Hadronic resonance gas

vs. lattice:

(P. Braun-Munzinger, J. Stachel, C. Wetterich, Phys.Lett.B596:61-69 (2004))

Chemical equilibration of baryon / anti-baryons:

Multimesonic channels:

Possible solution by Hagedorn statesC. Greiner, P. Koch, F. Liu,

I. Shovkovy, H. Stöcker J.Phys.G31 (2005)

K. Redlich et al, K. Bugaev et al

Hagedorn gas close to

• Hagedorn spectrum:

• Hagedorn like excitations in transport models:

RQMD

HSD

Estimate for baryon/antibaryon production

Microcanonical decay of HS(Fuming Liu)

Master Equations for the decay HS→nπ+BaB

J. Noronha-Hostler

dNR (i )

dt= ¡ ¡ tot

i NR (i ) +X

n

¡ toti ;¼<i ;n(T)(N¼)nB i ! n¼

+ ¡ toti ;B ¹B <<n>¼B ¹B

i ;<n> (T)(N¼)<n>N 2B ¹B

dN¼

dt=

X

i

X

n

¡ toti ;¼nB i ! n¼

¡NR (i ) ¡ <(T)(N¼)n¢

+X

i

¡ toti ;B ¹B < n >

³NR (i ) ¡ <<n>¼B ¹B

i ;<n> (T)(N¼)<n>N 2B ¹B

´

dNB ¹B

dt= ¡

X

i

¡ toti ;B ¹B

¡N 2

B ¹B N <n>¼ <i ;<n>(T) ¡ NR (i )

¢

(1)

dNR (i )

dt= ¡ ¡ tot

i NR (i ) +X

n

¡ toti ;¼<i ;n(T)(N¼)nB i ! n¼

+ ¡ toti ;B ¹B <<n>¼B ¹B

i ;<n> (T)(N¼)<n>N 2B ¹B

dN¼

dt=

X

i

X

n

¡ toti ;¼nB i ! n¼

¡NR (i ) ¡ <(T)(N¼)n¢

+X

i

¡ toti ;B ¹B < n >

³NR (i ) ¡ <<n>¼B ¹B

i ;<n> (T)(N¼)<n>N 2B ¹B

´

dNB ¹B

dt= ¡

X

i

¡ toti ;B ¹B

¡N 2

B ¹B N <n>¼ <i ;<n>(T) ¡ NR (i )

¢

(1)

12 1

2

12 a

b

f (x;y) =

(x + 1 if y = 0xy if y 6= 0

dNR(i)/dt=-iNR(i)+ni, < i,n(T) (N)nBi! n+i,BaB<i,<n>BaB (T)(N )<n> N2BaB

dN /dt=i ni,nBi! n(NR(i)-< (T) (N )n)+i i,BaB<n>(NR(i)-<i,<n>BaB(T)(N )<n>N2BaB)

dNBaB/dt=-ii,BaB(NBaB2 N

<n> < i,<n>(T)-NR(i))

Considering the decay HS→nπ

HS→nπ+BaB

Nπ (t=0)=EquilibriumNRes(t=0)=0

Nπ (t=0) =EquilibriumNRes(t=0)=Equilibrium

HS→nπ+BaB when the Hagedorn Resonances start at twice equilibrium values and the rest starts at zero.

HS→nπ+BaB when the Hagedorn Resonances start at twice equilibrium values and the rest starts at equilibrium.

The strange sector of baryons/antibaryons

Importance of baryonic HS CBM?

The order and shape of QGP phase transitionnucl-th/0605052, I. Zakout, CG and J. Schaffner-Bielich

)4(~),( ][)2( Bvmemcvm BHTm

density of states:

4

1

)( B

Thermalization at RHIC

elliptic flow --- `early signature´ of QGP

...)2cos2cos21( 211

22 vv

dydp

dN

dyddp

dN

T

h

T

h

evidence for an early buildup of pressure anda fast thermalization of the quark-gluon system

• How can one describe the fast thermalization by the partonic collisions? • How can one understand the hydrodynamical behavior by the partonic collisions?

),(),(),( pxCpxCpxfp ggggggggg

transport simulation: on-shell parton cascade

solving the Boltzmann-equations for quarks and gluons

new development(Z)MPC, VNI/BMS

Z. Xu and C. Greiner, PRC 71, 064901 (2005)

Initial production of partons

dt

dpxfxpxfxK

dydydp

d cdab

tbtadcbat

jet

),(),( 2

222

11,;,21

2

minijets

string matter

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

LPM

DDggggg

Dgggg

mqkk

qg

mq

sgM

mq

sgM

222

22

222

242

222

242

)(

12

)(2

9

,)(2

9

parton scatterings in leading order pQCD

the central region:: [-0.5:0.5] and xt < 1.5 fm

thermalization and hydrodynamical behavior

NO thermalization and free streaming

including ggggg without ggggg

transverse energy at y=0 in Au+Au central collision

elliptic flow in noncentral Au+Au collisions at RHIC:

central

peripheral

Comparison with RHIC data

Conclusions and Outlook• Potential Hagedorn states as additional dof can explain

and also strange baryon production close to ; (re-)population and decay are governed by detailed balance

• Three main assumptions:(1):

(2):

(3): microcanonical statistical decay

• Multiparticle interactions also important for very high energies ( )

• Future: Embedding into UrQMD

CERES

Nonequilibrium dilepton productionSpectral function of the ρ-meson:

free ρ in-medium

→ quantum “off-shell”-transport description

(B. Schenke)

Non-equilibrium dilepton production rate:

Evolving spectral function and dilepton rate

Contributions to the rate at time τ at constant energy ω

B. Schenke, C. Greiner, Phys.Rev.C73:034909 (2006)

Dilepton yields from fireball (B. Schenke)

0.0 0.2 0.4 0.6 0.8 1.0

0.5

1.0

1.5

2.0

2.5

3.0

dN

/dM

[10

-3 G

eV

-1]

M [GeV]

Dynamic Markov

Dropping mass scenario integrated over momenta:

Dropping mass (linearly in time) and resonance coupling scenarios for k=0:

B. Schenke, C. Greiner, Phys.Rev.C73:034909 (2006)

B. Schenke, C. Greiner, arXiv:hep-ph/0608032 (2006)