Johann Wolfgang Goethe-Universität Frankfurt Institut für Theoretische Physik

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

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)

BAMPS: Boltzmann Approach of Multi. Parton Scatterings A transport algorithm solving the Boltzmann-Equations for on-shell partons with p. QCD interactions (Z)MPC, VNI/BMS, AMPT new development ggg radiative „corrections“ 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) gg,

screened partonic interactions in leading order p. QCD 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: LPM suppression: the formation time Lg: mean free path

Stochastic algorithm P. Danielewicz, G. F. Bertsch, Nucl. Phys. A 533, 712(1991) A. Lang et al. , J. Comp. Phys. 106, 391(1993) cell configuration in space for particles in D 3 x with momentum p 1, p 2, p 3. . . collision probability: D 3 x

Initial production of partons minijets color glass condensate string matter

p. T spectra at collision center: x. T<1. 5 fm, Dz < 0. 4 t fm of a central Au+Au at s 1/2=200 Ge. V Initial conditions: minijets p. T>1. 4 Ge. V; coupling as=0. 3 simulation p. QCD, only 2 -2: NO thermalization simulation p. QCD 2 -2 + 2 -3 + 3 -2 + 2 -3: thermalization! Hydrodynamic behavior!

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

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

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)

Transport Rates Large Effect of 2 -3 !

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

Ratio of shear viscosity to entropy density in 2<->3 RHIC Ad. S/CFT

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

Shear viscosity from Israel-Stewart theory

Shear viscosity from Israel-Stewart theory vs BAMPS 0. 18

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

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

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 h/s at RHIC > 0. 08 Z. Xu

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

more details on elliptic flow at RHIC … moderate dependence on critical energy density h/s at RHIC: 0. 08 -0. 2 Z. Xu and CG, ar. Xiv: 0811. 2940

… 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

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

Parton cascade meets ideal shocks: Riemann problem Tleft = 400 Me. V Tright = 200 Me. V t = 1. 0 fm/c λ = 0. 1 fm λ = 0. 001 fm I. Bouras

Tleft = 400 Me. V Tright = 320 Me. V Time evolution of viscous shocks t=0. 5 fm/c t=1. 5 fm/c η/s = 1/(4 π) t=3 fm/c t=5 fm/c

Viscous shocks Tleft = 400 Me. V - Tright = 320 Me. V , t = 3. 0 fm/c η/s ~ 0. 01 - 1. 0

Comparison to Israel-Stewart t = 1. 6 fm/c η/s = 0. 02 η/s = 0. 1 Comparison to full p. QCD transport Tleft = 400 Me. V Tright = 320 Me. V t = 3 fm/c η/s ~ 0. 1 - 0. 13

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

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

Quenching of jets first realistic 3 d results with BAMPS RAA ~ 0. 06 cf. S. Wicks et al. Nucl. Phys. A 784, 426 O. Fochler et al ar. Xiv: 0806. 1169 nuclear modification factor central (b=0 fm) Au-Au at 200 AGe. V

LPM-effect n è transport model: incoherent treatment of gg ggg processes parent gluon must not scatter during formation time of emitted gluon n discard all possible interference effects (Bethe-Heitler regime) p 1 lab frame n kt p 2 CM frame kt t = 1 / kt total boost O. Fochler

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