the importance of multiparticle collisions in heavy ion reactions c. greiner the physics of high...

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)