Johann Wolfgang Goethe-Universität Frankfurt
Institut für Theoretische Physik
The importance of multiparticle
collisions in heavy ion reactions
C. Greiner
The Physics of High Baryon Density
IPHC Strasbourg, Sept. 2006
• 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
Multimesonic channels
R.Rapp and E. Shuryak,
Phys.Rev.Lett.86 (2001) 2980
C.Greiner and S.Leupold, J.Phys. G27 (2001) L95
C.Greiner, AIP Conf. Proc. 644:337 (2003)
production at RHIC
Thermal rates within
chiral SU(3) description
Chemical population of
baryons / anti-baryons:
I. Shovkovy, J. Kapusta
P. Huovinen, J. Kapusta
Insufficient by a factor of 3 to 4
Chemical Freeze-out and
of QCD
(P. Braun-Munzinger, J. Stachel, C. Wetterich, Phys.Lett.B596:61-69 (2004))
Hadronic resonance gas
vs. lattice:
Chemical equilibration
of baryon / anti-baryons:
Multimesonic channels:
Possible solution by Hagedorn states
C. Greiner, P. Koch, F. Liu,
I. Shovkovy, H. Stöcker
J.Phys.G31 (2005)
Hagedorn gas close to
• Hagedorn spectrum:
K. Redlich et al, K. Bugaev et al
• 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
dNR(i)/dt=-GiNR(i)+nGi,p < i,n(T) (Np)nBi! np+Gi,BaB<i,<n>BaB (T)(Np )<n> N2BaB
dNp /dt=i nGi,pnBi! np(NR(i)-< (T) (Np )n)+i Gi,BaB<n>(NR(i)-<i,<n>BaB(T)(Np )<n>N2BaB)
dNBaB/dt=-iGi,BaB(NBaB2 Np<n> < i,<n>(T)-NR(i))
J. Noronha-Hostler
Considering the decay HS→nπ
HS→nπ+BaB
Nπ (t=0)=Equilibrium
NRes(t=0)=0
Nπ (t=0) =Equilibrium
NRes(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 transition
nucl-th/0605052, I. Zakout, CG and J. Schaffner-Bielich


 1
4
density of states:
 (m, v) ~ c m
(  2 )
e
m
TH [ B ]
 (m  4Bv )
 (B )
Thermalization at RHIC
elliptic flow --- `early signature´ of QGP
dNh
dpT2 dyd
 dpdN2 dyh p1 (1  2v cos   2v
1
2
cos 2  ...)
T
evidence for an early buildup of pressure and
a 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?
transport simulation: on-shell parton cascade
Z. Xu and C. Greiner, PRC 71, 064901 (2005)
solving the Boltzmann-equations for quarks and gluons
p    f ( x, p)  Cgg  gg ( x, p)  Cgg  ggg ( x, p)
(Z)MPC, VNI/BMS
new development
Initial production of partons
minijets
d jet
abcd
d

2
2

K
x
f
(
x
,
p
)
x
f
(
x
,
p

1 a 1 t
2 b 2
t )
2
dt
a ,b;c ,d
dpt dy1dy2
string matter
P.Danielewicz, G.F.Bertsch, Nucl. Phys. A 533, 712(1991
A.Lang et al., J. Comp. Phys. 106, 391(1993)
Stochastic algorithm
cell configuration in space
for particles in D3x with momentum p1,p2,p3 ...
D3x
collision probability:
parton scatterings in leading order pQCD
M gg  gg
M gg  ggg
2
2
9g 4
s2

,
2
2 2
2 ( q   mD )
 9g 4

s2
12 g 2 q2

  2
 
2
2 2  2
2
2
(
q

m
)
k
(
k

D

     q  )  mD

I 32


  LPM


Dt
for 2  2 P22  vrel 22 3
Dx
Dt
for 2  3 P23  vrel 23 3
Dx
I 32
Dt
for 3  2 P32 
8E1 E2 E3 (D3 x) 2
1
d 3 p1'
d 3 p2 '
2
4 ( 4)
 
M
( p1  p2  p3  p1'  p2
1231' 2 ' ( 2p ) 
3
3
2 (2p ) 2 E1' (2p ) 2 E2 '
the central region:
h: [-0.5:0.5] and xt < 1.5 fm
including gg<>ggg
thermalization and
hydrodynamical behavior
without gg<>ggg
NO thermalization and
free streaming
transverse energy at y=0 in Au+Au central collision
elliptic flow in noncentral Au+Au collisions at RHIC:
peripheral
central
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
Nonequilibrium dilepton production
Spectral function
(B. Schenke)
of the ρ-meson:
free ρ
in-medium
CERES
→ quantum “off-shell”-transport description
Non-equilibrium dilepton production rate:
Contributions to the rate at time τ at constant energy ω
Evolving spectral function
B. Schenke, C. Greiner, Phys.Rev.C73:034909 (2006)
and dilepton rate
Dilepton yields from fireball
(B. Schenke)
Dropping mass (linearly in time) and resonance coupling scenarios for k=0:
3.0
Dynamic
Markov
2.5
2.0
-3
dN/dM [10 GeV
-1
]
Dropping mass scenario integrated over momenta:
B. Schenke, C. Greiner, Phys.Rev.C73:034909 (2006)
B. Schenke, C. Greiner, arXiv:hep-ph/0608032 (2006)
1.5
1.0
0.5
0.0
0.2
0.4
0.6
M [GeV]
0.8
1.0