1. QCD Plasma Equilibration, Collective Flow Effects and Jet-Quenching – Phenomena of Common Origin C. Greiner, 24th winter workshop on nuclear dynamics, South Padre Island, 2008 Johann Wolfgang Goethe-Universität Frankfurt Institut für Theoretische Physik in collaboration with A. El, O. Fochler, B. Schenke, H. Stöcker, Zhe Xu

2. Y X Fast Thermalization from QCD: 3-2 important! Equilibr. time short in 2-3! Elliptic flow v 2 high in 2-3! Viscosity small ~ 0.08! R AA,gluon ~ 0.1 ! Three body effects in parton cascades! P.Huovinen et al., PLB 503, 58 (2001) from R. Bellwied

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

4. Momentum space anisotropy: Time dependence Michael Strickland

5. Thermalization driven by plasma instabilities Refs.: Mrowczynski; Arnold, Lenaghan, Moore, Yaffe; Rebhan, Romatschke, Strickland, Bödeker, Rummukainen; Dumitru, Nara; Berges, Scheffler, Sexty Dumitru, Nara, Strickland, PRD 75, 025016 (2007) Dumitru, Nara, Schenke, Strickland, arXiv:0710.1223

6. 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)

7. 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)

8. 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

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

10. 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

11. A.El, Z. Xu and CG, arXiv: 0712.3734 [hep-ph] ggg gg ! This 3-2 is missing in the Bottom-Up scenario (Baier, Dohkshitzer, Mueller, Son (2001)). Initial conditions: Color Glass Condensate Q s =3 GeV; coupling  s =0.3 p T spectra Bottom up is not working as advocated: no tremendous soft gluon production, soft modes do not thermalize before the hard modes

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

13. Cross section does not determine  ! Z. Xu and CG, arXiv: 0710.5719 [nucl-th] What determines the equilibration time scale  ?

14. BUT, this is not the full story !

15. 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.

16. Transport Rates Large Effect of 2-3 !

17. Shear Viscosity  Z. Xu and CG, arXiv: 0710.5719 [nucl-th] From Navier-Stokes approximation From Boltzmann-Eq. relation between  and R tr

18. Ratio of shear viscosity to entropy density in 2-3 AdS/CFT RHIC Z. Xu, A. El

19. 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

21. Elliptic Flow and Shear Viscosity in 2-3 at RHIC 2-3 Parton cascade BAMPS Z. Xu, CG, H. Stöcker, arXiv: 0711.0961 [nucl-th] viscous hydro. Romatschke, PRL 99, 172301,2007  /s at RHIC > 0.08 Z. Xu

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

23. 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

24. nuclear modification factor relative to pp (binary collision scaling) experiments show approx. factor 5 of suppression in hadron yields Hard probes of the medium high energy particles are promising probes of the medium created in AA-collisions QM 2008, T. Awes

25. 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

26. first realistic 3d results on jet-quenching with BAMPS LPM cut-off increases dE/dx, static medium (T = 400 MeV) <q T 2 / , static medium (T = 400 MeV) R AA ~ 0.1 cf. S. Wicks et al. Nucl.Phys.A784, 426 nuclear modification factor central (b=0 fm) Au-Au at 200 AGeV O. Fochler

27. Jet propagation within YM fields Poynting vectors Dynamical simulation of jet propagation in the plasma Björn Schenke preliminary

28. Stronger longitudinal broadening caused by domains of strong chromo-fields with Explaining the “ridge” Additional near-side long range correlation in  (“ridge like” corrl.) observed. Dan Magestro, Hard Probes 2004, STAR, nucl-ex/0509030, Phys. Rev. C73 (2006) 064907 and P. Jacobs, nucl-ex/0503022 Au+Au 0- 10% STAR preliminary J. Putschke, QM2006 Dumitru, Nara, Schenke, Strickland e-Print: arXiv:0710.1223 [hep-ph]

29. 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 dissipative hydrodynamics

30. Au+Au – Setup central (b=0 fm) Au-Au collision at 200 AGeV sampling of initial gluon plasma:  initial momentum distribution (mini-jets) according to  Glück-Reya-Vogt parameterization for structure functions; K = 2  lower cut-off: p 0 = 1.4 GeV (reproduces dE T /dy)  particle production via standard nuclear geometry (Wood-Saxon density profile, Glauber-Model)  each parton is given a formation time  35 testparticles  simulate evolution of fireball up to ~5 fm/c  when energy density in a cell drops below  = 1 GeV  free streaming (in the respective cell)

31. Initial conditions Glauber-type: Woods-Saxon profile, binary nucleon-nucleon collision for a central Au+Au collision at RHIC at 200 AGeV using p 0 =1.4 GeV minijets production with p t > p 0

32. 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

33. Simulations solve Boltzmann equation: → test particles and other schemes Semiclassical kinetic theory: ( Quantum mechanics: ) Important scales for kinetic transport & simulations

35. ... kinetic transport still valid

36. The drift term is large. gg  ggg interactions are essential for kinetic equilibration!

37.  (t) gives the timescale of kinetic equilibration.

38. bottom-up scenario of thermalization R.Baier, A.H.Mueller, D.Schiff and D.T.Son, PLB502(2001)51 Q s -1 << t <<  -3/2 Q s -1 Hard gluons with momenta about Q s are freed and phase space occupation becomes of order 1.  -3/2 Q s -1 << t <<  -5/2 Q s -1 (h+h  h+h+s) Hard gluons still outnumber soft ones, but soft gluons give most of the Debye screening.  -5/2 Q s -1 << t <<  -13/5 Q s -1 (h+h  h+h+s; s+s  s+s; h+s  sh+sh+s) Soft gluons strongly outnumber hard gluons. Hard gluons loose their entire energy to the thermal bath. After  -13/5 Q s -1 the system is thermalized: T ~ t -1/3, T 0 ~  2/5 Q s

39. Au-Au – Reconstruction partons with high-pt too rare  simulate large number of initial conditions  select events according to highest pt-(test)particle  simulate only selected events and weight results full: 200000 events; reconstruction: 40 events per pt-bin, ~1000 total