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C. Greiner , 30th Course of Intl. School of Nuclear Physics , Erice-Sicily, september 2008

Johann Wolfgang Goethe-Universität Frankfurt Institut für Theoretische Physik. 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.

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C. Greiner , 30th Course of Intl. School of Nuclear Physics , Erice-Sicily, september 2008

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  1. Johann Wolfgang Goethe-Universität Frankfurt Institut für Theoretische Physik 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 in collaboration with: I.Bouras, L. Chen, A. El, O. Fochler, J. Uphoff, Zhe Xu list of contents • fast thermalization within a pQCD cascade • viscosity and its extraction from elliptic flow • jet quenching … same phenomena? • new: dissipative shocks

  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: BoltzmannApproachofMultiPartonScatterings 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. screened partonic interactions in leading order pQCD elastic part radiative part 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) screening mass: LPMsuppression: the formation time Lg: mean free path

  5. P.Danielewicz, G.F.Bertsch, Nucl. Phys. A 533, 712(1991) A.Lang et al., J. Comp. Phys. 106, 391(1993) Stochastic algorithm cell configuration in space D3x for particles in D3x with momentum p1,p2,p3 ... collision probability:

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

  7. pT spectra at collision center: xT<1.5 fm, Dz < 0.4 t fm of a central Au+Au at s1/2=200 GeV Initial conditions: minijets pT>1.4 GeV; coupling as=0.3 simulation pQCD 2-2 + 2-3 + 3-2 simulation pQCD, only 2-2 3-2 + 2-3: thermalization! Hydrodynamic behavior! 2-2: NOthermalization

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

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

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

  11. Transport Rates Large Effect of 2-3 !

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

  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 1st Order linearized BE with f=f0+εf1+ε²f2 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-->2nd 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. Validity of kinetic transport - relation to shear viscosity Semiclassical kinetic theory: Quantum mechanis: quasiparticle limit:

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

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

  18. Rapidity Dependence of v2: Importance of 2-3! BAMPS evolution of transverse energy

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

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

  21. Quenching of jets first realistic 3d results with BAMPS RAA ~ 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 arXiv:0806.1169

  22. transport model: incoherent treatment ofggggg processes • parent gluon must not scatter during formation time of emitted gluon • discard all possible interference effects (Bethe-Heitler regime) p1 p2 kt kt lab frame CM frame t = 1 / kt • total boost LPM-effect O. Fochler

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

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

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

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

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

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

  29. Summary 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 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 !

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