1. Microscopic Understanding of ultrarel. HIC – parton cascade and dissipative phenomena C. Greiner, Johann Wolfgang Goethe-Universität Frankfurt Institut für Theoretische Physik in collaboration with: I.Bouras, L. Chen, A. El, O. Fochler, J. Uphoff, Zhe Xu - fast thermalization within a pQCD cascade - viscosity calculation by Navier-Stokes and Israel-Stewart - elliptic flow … - dissipative shocks list of contents

2. QCD thermalization using parton cascade VNI/BMS: K.Geiger and B.Müller, NPB 369, 600 (1992) S.A.Bass, B.Müller and D.K.Srivastava, PLB 551, 277(2003) ZPC: B. Zhang, Comput. Phys.Commun. 109, 193 (1998) MPC: D.Molnar and M.Gyulassy, PRC 62, 054907 (2000) AMPT: B. Zhang, C.M. Ko, B.A. Li, and Z.W. Lin, PRC 61, 067901 (2000) BAMPS: Z. Xu and C. Greiner, PRC 71, 064901 (2005); 76, 024911 (2007)

3. BAMPS: B oltzmann A pproach of M ulti P arton S catterings A transport algorithm solving the Boltzmann-Equations for on-shell partons with pQCD interactions new development ggg gg, radiative „corrections“ (Z)MPC, VNI/BMS, AMPT Elastic scatterings are ineffective in thermalization ! Inelastic interactions are needed ! Xiong, Shuryak, PRC 49, 2203 (1994) Dumitru, Gyulassy, PLB 494, 215 (2000) Serreau, Schiff, JHEP 0111, 039 (2001) Baier, Mueller, Schiff, Son, PLB 502, 51 (2001)

4. J.F.Gunion, G.F.Bertsch, PRD 25, 746(1982) T.S.Biro at el., PRC 48, 1275 (1993) S.M.Wong, NPA 607, 442 (1996) screened partonic interactions in leading order pQCD screening mass: LPM suppression : the formation time  g : mean free path radiative part elastic part

5. 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  3 x with momentum p 1,p 2,p 3... collision probability: cell configuration in space 3x3x

6. Initial production of partons minijets string matter color glass condensate

7. 3-2 + 2-3: thermalization! Hydrodynamic behavior! 2-2: NO thermalization simulation pQCD 2-2 + 2-3 + 3-2 simulation pQCD, only 2-2 at collision center: x T <1.5 fm,  z < 0.4 t fm of a central Au+Au at s 1/2 =200 GeV Initial conditions: minijets p T >1.4 GeV; coupling  s =0.3 p T spectra

8. gg  gg: small-angle scatterings gg  ggg: large-angle bremsstrahlung distribution of collision angles at RHIC energies

9. time scale of thermalization  = time scale of kinetic equilibration. Theoretical Result !

10. Transport Rates Z. Xu and CG, PRC 76, 024911 (2007) Transport rate is the correct quantity describing kinetic equilibration. Transport collision rates have an indirect relationship to the collision-angle distribution.

11. Transport Rates Large Effect of 2-3 !

12. Shear Viscosity  From Navier-Stokes approximation From Boltzmann-Eq. relation between  and R tr Z. Xu and CG, Phys.Rev.Lett.100:172301,2008.

13. Ratio of shear viscosity to entropy density in 2 3 AdS/CFT RHIC

14. Shear viscosity from kinetic theory – part II Boltzmann Equation Kinetic: Hydro: + with for (0+1) dim gluon gas A. El, A. Muronga, Z. Xu and CG, arXiv: …

15. Shear viscosity from Israel-Stewart theory

16. vs BAMPS 0.18

17. Validity of Israel-Stewart in (0+1)Dim Israel-StewartBAMPS

18. Validity of Israel-Stewart in (0+1)Dim (from BAMPS)‏

19. Elliptic Flow and Shear Viscosity in 2-3 at RHIC 2-3 Parton cascade BAMPS Z. Xu, CG, H. Stöcker, PRL 101:082302,2008 viscous hydro. Romatschke, PRL 99, 172301,2007  /s at RHIC > 0.08 Z. Xu

20. Rapidity Dependence of v 2 : Importance of 2-3! BAMPS evolution of transverse energy

21. more details on elliptic flow at RHIC … moderate dependence on critical energy density  /s at RHIC: 0.08-0.2 Z. Xu and CG, arXiv:0811.2940

22. … looking on transverse momentum distributions gluons are not simply pions … light quarks have to be included need hadronization (and models) to understand the particle spectra

23. Barbara Betz, Dirk Rischke, Horst Stöcker, Giorgio Torrieri Mach Cones in Ideal Hydrodynamics Box Simulation Bjorken Expansion

24. Parton cascade meets ideal shocks: Riemann problem λ = 0.1 fm λ = 0.01 fm λ = 0.001 fm Tleft = 400 MeV Tright = 200 MeV t = 1.0 fm/c I. Bouras

25. Time evolution of viscous shocks Tleft = 400 MeV Tright = 320 MeV η/s = 1/(4 π) t=0.5 fm/c t=1.5 fm/c t=3 fm/c t=5 fm/c

26. Viscous shocks η/s ~ 0.01 - 1.0 Tleft = 400 MeV - Tright = 320 MeV,t = 3.0 fm/c

27. Comparison to Israel-Stewart Comparison to full pQCD transport η/s = 0.02 η/s = 0.1 η/s ~ 0.1 - 0.13 Tleft = 400 MeV Tright = 320 MeV t = 3 fm/c t = 1.6 fm/c

28. Inelastic/radiative pQCD interactions (23 + 32) in BAMPS explain: fast thermalization large collective flow small shear viscosity of QCD matter at RHIC realistic jet-quenching of gluons Summary Future/ongoing analysis and developments: light and heavy quarks jet-quenching (Mach Cones, ridge) hadronisation and afterburning (UrQMD) needed to determine how imperfect the QGP at RHIC and LHC can be … and dependence on initial conditions

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30. Semiclassical kinetic theory: Validity of kinetic transport - relation to shear viscosity Quantum mechanis: quasiparticle limit:

31. R AA ~ 0.06 cf. S. Wicks et al. Nucl.Phys.A784, 426 nuclear modification factor central (b=0 fm) Au-Au at 200 AGeV O. Fochler et al Quenching of jets first realistic 3d results with BAMPS arXiv:0806.1169

32. LPM-effect transport model: incoherent treatment of gg  ggg processes  parent gluon must not scatter during formation time of emitted gluon discard all possible interference effects (Bethe-Heitler regime) ktkt CM frame p1p1 p2p2 lab frame ktkt  = 1 / k t total boost O. Fochler

33. inclusion of light quarks is mandatory ! … lower color factor comparison to other approaches … LPM bremsstrahlung jet fragmentation scheme … possible improvements of microscopic treatment