1. Microscopic Understanding of ultrarel. HIC – How dissipative is the RHIC matter ? C. Greiner, 30th Course of Intl. School of Nuclear Physics, Erice-Sicily, september 2008 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 and its extraction from elliptic flow - jet quenching … same phenomena? - new: 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. Dissipative Hydrodynamics Shear, bulk viscosity and heat conductivity of dense QCD matter could be prime candidates for the next Particle Data Group, if they can be extracted from data. Need a causal hydrodynamical theory. What are the criteria of applicability? Causal stable hydrodynamics can be derrived from the Boltzmann Equation: -Renormalization Group Method by Kunihiro/Tsumura-->stable 1 st Order linearized BE with f=f 0 +εf 1 +ε²f 2 yields (2nd Order – work in progress) can be solved by introducing projector P on Ker{A}, where A-linearized collision operator -Grad‘s 14-momentum method-->2 nd Order causal hydrodynamics. Calculate momenta of the BE. Transport coefficients and relaxation times for dissipative quantities can be calculated as functions of collision terms in BE. Compare dissipative relaxation times to the mean free pass from cascade simulation. Andrej El

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

16. transverse flow velocity of local cell in the transverse plane of central rapidity bin Au+Au b=8.6 fm using BAMPS =c Collective Effects

18. 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

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

20. more details on elliptic flow at RHIC … moderate dependence on critical energy density  /s at RHIC: 0.08-0.2

21. … looking on transverse momentum distributions gluons are not simply pions … need hadronization (and models) to understand the particle spectra

22. 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

23. 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

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

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

26. 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

27. 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

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

29. 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

30. Inelastic/radiative pQCD interactions (23 + 32) 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 dissipative hydrodynamics Thanks to the organizers for the invitation !