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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)