Thermalization of the quark gluon matter in ultrarelativistic heavy ion collisions Zhe Xu Weihai, August 14, 2009 Institut für Theoretische Physik Goethe-Universität.

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Thermalization of the quark gluon matter in ultrarelativistic heavy ion collisions Zhe Xu Weihai, August 14, 2009 Institut für Theoretische Physik Goethe-Universität Frankfurt, Germany

Zhe Xu, Weihai 20092/44 Outline Motivation Transport model Why 2-3 important Initial condition dependence Summary

Zhe Xu, Weihai 20093/44 Motivation thermal equilibrium non-equilibrium in kinetic equilibrium, but not in chemical equilibrium not in kinetic equilibrium

Zhe Xu, Weihai 20094/44 deviation from thermal equilibrium 1. momentum spectra 2. mometum isotropy, average of angles 3. momentum energy tensor

Zhe Xu, Weihai 20095/44 High energy heavy ion collisions

Zhe Xu, Weihai 20096/44 Momentum space anisotropy: Time dependence M. Strickland

Zhe Xu, Weihai 20097/44 P.Huovinen et al., PLB 503, 58 (2001) nearly perfect fluid Assumption: full thermalization at 0.6 fm/c

Zhe Xu, Weihai 20098/44 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, (2007) Dumitru, Nara, Schenke, Strickland, arXiv:

Zhe Xu, Weihai 20099/44 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 (Z)MPC, VNI/BMS, AMPT, PACIAE Elastic scatterings are ineffective in thermalization ! Inelastic interactions are needed ! Transport Model

Zhe Xu, Weihai /44 Stochastic algorithm P.Danielewicz, G.F.Bertsch, Nucl. Phys. A 533, 712(1991) A.Lang et al., J. Comp. Phys. 106, 391(1993) 3x3x collision rate per unit phase space for incoming particles p 1 and p 2 with  3 p 1 and  3 p 2 : collision probability (Monte Carlo) Space has to be divided into small cells !

Zhe Xu, Weihai /44 ZX and C. Greiner, PRC 71, (2005) Interaction Probability

Zhe Xu, Weihai /44 A simple case 2->2 with isotropic differential cross section p1 p2 p1‘ p2‘  shear viscosity Huovinen and Molnar, PRC 79, (2009)

Zhe Xu, Weihai /44 A. El, ZX and C. Greiner, arXiv: [hep-ph] deviation from equilibrium, relaxation towards equilibrium one-dimensional expansion with Bjorken boost invariance

Zhe Xu, Weihai /44 Relativistiv shock waves I. Bouras et al. PRL 103, (2009) P0 > P4

Zhe Xu, Weihai /44 J.F.Gunion, G.F.Bertsch, PRD 25, 746(1982) screened partonic interactions in leading order pQCD Incoherent treatment: the formation time  g : mean free path LPM suppression :

Zhe Xu, Weihai /44 Jet-quenching O. Fochler, ZX and C. Greiner, PRL 102, (2009)

Zhe Xu, Weihai /44 T.S.Biro at el., PRC 48, 1275 (1993) chemical equilibration of quarks and gluons by solving the rate equations S.M.Wong, NPA 607, 442 (1996) kinetic equilibration within the relaxation time approach J.Chen, H.Dong, K.Ohnishi, Q.Wang, arXiv: [nucl-th] shear viscosity using the variation method

Zhe Xu, Weihai /44 ZX and C.Greiner, PRL 100, (2008) collision rates

Zhe Xu, Weihai /44 What leads to fast thermalization? large cross section (collision rate) large collision angle -> large momentum deflection -> fast momentum isotropization

Zhe Xu, Weihai /44 p1 p2 p1‘ p2‘  qTqT small angle scatterings

Zhe Xu, Weihai /44 J.F.Gunion, G.F.Bertsch, PRD 25, 746(1982) Central plateau in cos  3, thus not small angluar scatterings

Zhe Xu, Weihai /44 gg  gg: small-angle scatterings gg  ggg: large-angle bremsstrahlung distribution of collision angles at RHIC energies central plateau

Zhe Xu, Weihai /44 BUT, this is not the full story !

Zhe Xu, Weihai /44 Transport Rates ZX and C. Greiner, PRC 76, (2007) Transport rate is the correct quantity describing kinetic equilibration. Transport collision rates have an indirect relationship to the collision-angle distribution.

Zhe Xu, Weihai /44 Transport Rates for a static gluon gas Large Effect of gg->ggg ZX and C.Greiner, PRL 100, , (2008) assume:

Zhe Xu, Weihai /44 From Navier-Stokes approximation From Boltzmann-Eq. relation between  and R tr ZX and C.Greiner, PRL 100, , (2008)

Zhe Xu, Weihai /44 Ratio of shear viscosity to entropy density in 2-3 AdS/CFT RHIC

Zhe Xu, Weihai /44 A. El, A. Muronga, ZX and C. Greiner, PRC 79, (2009) comparing

Zhe Xu, Weihai /44 Calculating f(x,p) in heavy ion collisions using 3+1 dimensional parton cascade BAMPS

Zhe Xu, Weihai /44 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

Zhe Xu, Weihai /44 total transverse energy per rapidity at midrapidity b=0 fm  s =0.3

Zhe Xu, Weihai / : thermalization! Hydrodynamic behavior! 2-2: NO thermalization simulation pQCD simulation pQCD, only 2-2 at collision center: x T <1.5 fm, |  | < 0.2 p T spectra

Zhe Xu, Weihai /44 time scale of thermalization in heavy ion collisions  eq = time scale of kinetic equilibration. theoretical result from parton cascade calculations

Zhe Xu, Weihai /44 Transport Rates ZX and C. Greiner, PRC 76, (2007)

Zhe Xu, Weihai /44 The drift term is large. gg  ggg interactions are essential for kinetic equilibration!

Zhe Xu, Weihai /44 Elliptic Flow and Shear Viscosity in 2-3 at RHIC 2-3 Parton cascade BAMPS ZX, Greiner, Stöcker, PRL 101, , 2008 viscous hydro. Romatschke, PRL 99, ,2007  /s at RHIC > 0.08

Zhe Xu, Weihai /44 Initial condition dependence of thermalization at RHIC

Zhe Xu, Weihai /44 Initial Condition – Wounded Nucleons P+P using PYTHIA 6.4 semi-hard partonic collisions with initial and final radiations new work by L.Cheng

Zhe Xu, Weihai /44 Initial Condition – Color Glass Condensate Kharzeev, Levin, Nardi, NPA 730, 448 (2004); 747, 609 (2005) Hirano and Nara, NPA 743, 305 (2004) Adil, Drescher, Dumitru, Hayashigaki, Nara, PRC 74, (2006)

Zhe Xu, Weihai /44 Wounded nucleons vs Color Glass Condensate Initial Conditions: I.Only gluons from WN II.Gluons and quarks from WN. Quarks as gluons. III.Color Glass condensate Formation time: 0.15 fm/c by L.Cheng and A. El

Zhe Xu, Weihai /44 Decrease of the transverse energy QGP from wn needs a larger  /s than QGP from cgc needs a smaller  /s than using BAMPS

Zhe Xu, Weihai /44 Kinetic equilibration no difference between wn and cgc !

Zhe Xu, Weihai /44 Chemical equilibration due to gg  ggg wn: gluons system stays in chemical equilibrium. cgc: chemical equilibrium is achieved at the same timesacle, 1.5 fm/c, as the kinetic equilibration.

Zhe Xu, Weihai /44 Inelastic pQCD interactions ( ) explain: Fast Thermalization, Large Collective Flow, Small shear Viscosity of QCD matter at RHIC, because the bremsstrahlung favors large-angle radiation. Summary

Zhe Xu, Weihai /44 chemical equilibration in a box gluons and light quarks gluons and charm quarks by J. Uphoff (diploma thesis)

Zhe Xu, Weihai /44 more details on elliptic flow at RHIC … moderate dependence on critical energy density  /s at RHIC:

Zhe Xu, Weihai /44 … looking on transverse momentum distributions gluons are not simply pions … need hadronization (and models) to understand the particle spectra new work planned with G. Burau et al.

Zhe Xu, Weihai /44 ZX, C.Greiner, H. Stöcker, PRL 101:082302,2008 Perturbation QCD describes well fast thermalization, low  /s, large v2 at RHIC.

Zhe Xu, Weihai /44

Zhe Xu, Weihai /44 due to the fact that a 2->3 process brings one more particle toward isotropy than a gg->gg process.

Zhe Xu, Weihai /44 pt-spectra

Zhe Xu, Weihai /44 Life time of QGP T c =175 MeV