Space time evolution of QCD matter Parton cascade with stochastic algorithm Transport rates and momentum isotropization Thermalization of gluons due to Results: bottom-up scenario, jet-quenching, elliptic flow, viscosity,… viscous hydro, … I. Bouras, A. El, O. Fochler, F. Reining, Z. Xu, CG Johann Wolfgang Goethe-Universität Frankfurt Institut für Theoretische Physik Focus week, HIC at the LHC, CERN, may 2007

Relativistic Quantum Transport for URHIC microscopic transport calculations of partonic degrees of freedom RHIC, LHC new development Z. Xu and C. Greiner, PRC 71, (2005) Boltzmann Approach of MultiParton Scatterings (BAMPS) 3x3x collision probability particle in cell method

J.F.Gunion, G.F.Bertsch, Phys. Rev. D 25, 746(1982) parton scatterings in leading order pQCD screening mass: LPM suppression: the formation time

fugacity ~ 0.5 Example

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

Initial production of partons minijets string matter CGC

central elliptic flow in noncentral Au+Au collisions at RHIC: fast isotropization and thermalisation hydrodynamical evolution of momentum spectrum, … micr. determination of transport parameter … Z. Xu and C. Greiner, hep-ph/ Z. Xu and C. Greiner, NPA 774, 787 (2006)

3+1dim. full cascade: comparison with RHIC data

The drift term is large. gg  ggg interactions are essential for kinetic equilibration! Z. Xu and C. Greiner, arXiv:hep-ph/

transverse energy at y=0 in Au+Au central collision

Initial condition with Color Glass Condensate  : [-0.05:0.05] and x t < 1.5 fm

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

→ Particle number decreases in the very first moment → No net soft gluon production at early times! evolution of particle number in bottom-up scenario in 1+1 dim. geometry Not the full Bottom-Up story... LHC … RHIC

Evolution of temperature and spectrum … Andrej El

extracting the viscosity preliminary Bjorken geometry:

Jet-Quenching in a central Au Au collision at RHIC Oliver Fochler R AA higher ? R AA ~ 0.04–0.05 old : new : preliminary quarks not yet included …

Summary A new parton cascade including inelastic multiparton scatterings gg↔ggg Explains thermalization and hydrodynamical expansion at RHIC PQCD inspired gg↔ggg are important for the thermalization. PQCD gg↔ggg generate the elliptic flow in noncentral collisions. Not full bottom-up thermalization scenario with CGC 3~4 too much jet-quenching Outlook viscosity including quarks, heavy quark production Test for initial conditions (boundaries)

possible Chromo/Weibel instabilities B.Schenke, A. Dumitru, Y. Nara, M. Strickland

Initial conditions: minijets production with p t > p 0 binary approximation  for a central Au+Au collision at RHIC at 200 AGeV using p 0 =2 GeV

rapidity distribution Results

the central region:  : [-0.5:0.5] and x t < 1.5 fm thermalization and hydrodynamical behavior NO thermalization and free streaming including gg  ggg without gg  ggg

transport cross section: Why fast thermalization? gg  gg gg  ggg BUT! This is not the whole story... … transport rates !

 (t) gives the timescale of kinetic equilibration.

special case for isotropic distribution of collision angle

momentum isotropization and kinetic equilibration Initial condition: Minijets p 0 =1.4 GeV

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

... kinetic transport still valid

Thermalization times: comparison with bottom-up prediction 1/Q s behavior seems to be correct. instead  -13/5 behavior but  -x with x < 13/5

Jet-Quenching Box calculation: T=400MeV Oliver Fochler dominant process is 2->3

Bremsstrahlung processes LPM suppression: the formation time Bethe-Heitler regime varying the cut-off for k T :