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 Production of Antihyperons: QGP signature…? J. Geiss 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. G 27 (2001) L95
C.Greiner, AIP Conf. Proc. 644:337 (2003)
production at RHIC Thermal rates within Chemical population of chiral SU(3) description 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. B 596:61-69 (2004)) Hadronic resonance gas Chemical equilibration of baryon / anti-baryons: vs. lattice: Multimesonic channels:
Possible solution by Hagedorn states C. Greiner, P. Koch, F. Liu, I. Shovkovy, H. Stöcker J.Phys.G 31 (2005)
Hagedorn gas close to • Hagedorn spectrum: • Hagedorn like excitations K. Redlich et al, K. Bugaev et al in transport models: RQMD HSD
Estimate for baryon/antibaryon production
Microcanonical decay of HS (Fuming Liu)
Master Equations for the decay HS →nπ +BaB dN R(i) /dt=- Γ i N R(i) + ∑ n Γ i, π < i,n (T) (N π ) n B i ! n π + Γ i,BaB < i,<n>BaB (T)(N π ) <n> N 2 BaB dN π /dt= ∑ i ∑ n Γ i, π nB i ! n π (N R(i) - < (T) (N π ) n )+ ∑ i Γ i,BaB <n>(N R(i) - < i,<n>BaB (T)(N π ) <n> N 2 BaB ) dN BaB /dt=- ∑ i Γ i,BaB (N BaB 2 N π <n> < i,<n> (T)-N R(i) ) J. Noronha-Hostler
Considering the decay HS →nπ
HS →nπ +BaB N π (t=0)=Equilibrium N Res (t=0)=0 N π (t=0) =Equilibrium N Res (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 density of states: = α + } 1 γ m ρ − α + δ − ( 2 ) 4 ( m , v ) ~ c m e T [ B ] ( m 4 Bv ) H α µ ( ) B
Thermalization at RHIC elliptic flow --- `early signature´ of QGP = dN dN 1 h h + φ + φ + ( 1 2 v cos 2 v cos 2 ...) π 1 2 φ 2 2 dp dyd dp dy T 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 µ ∂ µ = + p f ( x , p ) C ( x , p ) C ( x , p ) ↔ ↔ gg gg gg ggg new development (Z)MPC, VNI/BMS
Initial production of partons minijets σ → σ ab cd d d = jet 2 2 ∑ K x f ( x , p ) x f ( x , p ) 1 a 1 t 2 b 2 t 2 dt dp dy dy a , b ; c , d 1 2 t string matter
P.Danielewicz, G.F.Bertsch, Nucl. Phys. A 533, 712(1991 Stochastic algorithm A.Lang et al., J. Comp. Phys. 106, 391(1993) cell configuration in space ∆ 3 x for particles in ∆ 3 x with momentum p 1 , p 2 , p 3 ... collision probability: ∆ t ↔ = σ parton scatterings in leading order pQCD for 2 2 P v ∆ 22 rel 22 3 x 4 2 9 g s 2 = ∆ M , → t + gg gg 2 2 2 2 ( q m ) → = σ ⊥ D for 2 3 P v ∆ 23 rel 23 3 4 2 2 2 x 9 g s 12 g q 2 = Θ ( ⊥ ) M → + − + gg ggg LPM 2 2 2 2 2 2 ∆ 2 ( ) q m ( ) k k q m ⊥ ⊥ ⊥ ⊥ I t D D → = 32 for 3 2 P ∆ 32 3 2 8 E E E ( x ) 1 2 3 = ∫ 3 3 1 d p d p π δ + + − − 2 4 ( 4 ) 1 ' 2 ' I M ( 2 ) ( p p p p p → π π 32 123 1 ' 2 ' 1 2 3 1 ' 2 3 3 2 ( 2 ) 2 E ( 2 ) 2 E 1 ' 2 '
the central region: η : [-0.5:0.5] and x t < 1.5 fm including gg <−> ggg without gg <−> ggg thermalization and NO thermalization and hydrodynamical behavior 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 (B. Schenke) Spectral function 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 and dilepton rate B. Schenke, C. Greiner, Phys.Rev.C 73 :034909 (2006)
Dilepton yields from fireball (B. Schenke) Dropping mass (linearly in time) and resonance coupling scenarios for k=0: 3.0 Dropping mass scenario integrated over momenta: Dynamic 2.5 -1 ] Markov -3 GeV 2.0 dN/dM [ 10 1.5 1.0 0.5 B. Schenke, C. Greiner, Phys.Rev.C 73 :034909 (2006) 0.0 0.2 0.4 0.6 0.8 1.0 M [GeV] B. Schenke, C. Greiner, arXiv:hep-ph/0608032 (2006)
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