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Thermalization of the quark gluon matter in ultrarelativistic heavy ion collisions

Thermalization of the quark gluon matter in ultrarelativistic heavy ion collisions. Zhe Xu. Institut für Theoretische Physik Goethe-Universität Frankfurt, Germany. Weihai, August 14, 2009. Outline. Motivation Transport model Why 2-3 important Initial condition dependence

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Thermalization of the quark gluon matter in ultrarelativistic heavy ion collisions

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

  2. Outline • Motivation • Transport model • Why 2-3 important • Initial condition dependence • Summary Zhe Xu, Weihai 2009

  3. Motivation thermal equilibrium non-equilibrium in kinetic equilibrium, but not in chemical equilibrium not in kinetic equilibrium Zhe Xu, Weihai 2009

  4. deviation from thermal equilibrium • momentum spectra • mometum isotropy, average of angles • momentum energy tensor Zhe Xu, Weihai 2009

  5. High energy heavy ion collisions Zhe Xu, Weihai 2009

  6. Momentum space anisotropy:Time dependence M. Strickland Zhe Xu, Weihai 2009

  7. nearly perfect fluid P.Huovinen et al., PLB 503, 58 (2001) Assumption: full thermalization at 0.6 fm/c Zhe Xu, Weihai 2009

  8. Thermalization driven byplasma 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 Zhe Xu, Weihai 2009

  9. Transport Model BAMPS: BoltzmannApproachofMultiPartonScatterings 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 ! Zhe Xu, Weihai 2009

  10. Stochastic algorithm P.Danielewicz, G.F.Bertsch, Nucl. Phys. A 533, 712(1991) A.Lang et al., J. Comp. Phys. 106, 391(1993) Space has to be divided into small cells ! D3x collision rate per unit phase space for incoming particles p1 and p2 with D3p1 and D3p2: collision probability (Monte Carlo) Zhe Xu, Weihai 2009

  11. Interaction Probability ZX and C. Greiner,PRC 71, 064901 (2005) Zhe Xu, Weihai 2009

  12. A simple case 2->2 with isotropic differential cross section p1‘ q p1 p2 shear viscosity p2‘ Huovinen and Molnar, PRC 79, 014906 (2009) Zhe Xu, Weihai 2009

  13. deviation from equilibrium, relaxation towards equilibrium one-dimensional expansion with Bjorken boost invariance A. El, ZX and C. Greiner, arXiv: 0907.4500 [hep-ph] Zhe Xu, Weihai 2009

  14. P0 > P4 Relativistiv shock waves I. Bouras et al. PRL 103, 032301 (2009) Zhe Xu, Weihai 2009

  15. screened partonic interactions in leading order pQCD J.F.Gunion, G.F.Bertsch, PRD 25, 746(1982) LPMsuppression: Incoherent treatment: the formation time Lg: mean free path Zhe Xu, Weihai 2009

  16. Jet-quenching O. Fochler, ZX and C. Greiner, PRL 102, 202301 (2009) Zhe Xu, Weihai 2009

  17. 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:0907.2486 [nucl-th] shear viscosity using the variation method Zhe Xu, Weihai 2009

  18. collision rates ZX and C.Greiner, PRL 100, 172301 (2008) Zhe Xu, Weihai 2009

  19. What leads to fast thermalization? • large cross section (collision rate) • large collision angle -> large momentum deflection • -> fast momentum isotropization Zhe Xu, Weihai 2009

  20. small angle scatterings p1‘ qT q p1 p2 p2‘ Zhe Xu, Weihai 2009

  21. J.F.Gunion, G.F.Bertsch, PRD 25, 746(1982) Central plateau in cosq3 , thus not small angluar scatterings Zhe Xu, Weihai 2009

  22. distribution of collision angles at RHIC energies gg gg: small-angle scatterings gg ggg: large-angle bremsstrahlung central plateau Zhe Xu, Weihai 2009

  23. BUT, this isnotthefull story ! Zhe Xu, Weihai 2009

  24. Transport Rates ZX and C. Greiner, 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. Zhe Xu, Weihai 2009

  25. Transport Rates for a static gluon gas ZX and C.Greiner, PRL 100, 172301, (2008) assume: Large Effect of gg->ggg Zhe Xu, Weihai 2009

  26. relation between h and Rtr From Navier-Stokes approximation From Boltzmann-Eq. ZX and C.Greiner, PRL 100, 172301, (2008) Zhe Xu, Weihai 2009

  27. Ratio of shear viscosity to entropy density in 2-3 AdS/CFT RHIC Zhe Xu, Weihai 2009

  28. A. El, A. Muronga, ZX and C. Greiner, PRC 79, 044914 (2009) comparing Zhe Xu, Weihai 2009

  29. Calculating f(x,p) in heavy ion collisions using 3+1 dimensional parton cascade BAMPS Zhe Xu, Weihai 2009

  30. Initial conditions Glauber-type: Woods-Saxon profile, binary nucleon-nucleon collision minijets production with pt > p0 for a central Au+Au collision at RHIC at 200 AGeV using p0=1.4 GeV Zhe Xu, Weihai 2009

  31. total transverse energy per rapidity at midrapidity b=0 fm as=0.3 Zhe Xu, Weihai 2009

  32. pT spectra at collision center: xT<1.5 fm, |Dh| < 0.2 simulation pQCD 2-2 + 2-3 + 3-2 simulation pQCD, only 2-2 3-2 + 2-3: thermalization! Hydrodynamic behavior! 2-2: NOthermalization Zhe Xu, Weihai 2009

  33. time scale of thermalization in heavy ion collisions theoretical result from parton cascade calculations teq = time scale of kinetic equilibration. Zhe Xu, Weihai 2009

  34. Transport Rates ZX and C. Greiner, PRC 76, 024911 (2007) Zhe Xu, Weihai 2009

  35. The drift term is large. gg<->ggg interactions are essential for kinetic equilibration! Zhe Xu, Weihai 2009

  36. Elliptic Flow and Shear Viscosity in 2-3 at RHIC 2-3Parton cascade BAMPS ZX, Greiner, Stöcker, PRL 101, 082302, 2008 viscous hydro. Romatschke, PRL 99, 172301,2007 h/s at RHIC > 0.08 Zhe Xu, Weihai 2009

  37. Initial condition dependence of thermalization at RHIC Zhe Xu, Weihai 2009

  38. 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 2009

  39. 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, 044905 (2006) Zhe Xu, Weihai 2009

  40. Wounded nucleons vs Color Glass Condensate by L.Cheng and A. El Initial Conditions: • Only gluons from WN • Gluons and quarks from WN. Quarks as gluons. • Color Glass condensate Formation time: 0.15 fm/c Zhe Xu, Weihai 2009

  41. Decrease of the transverse energy using BAMPS QGP from wn needs a larger h/s than 0.15. QGP from cgc needs a smallerh/s than 0.15. Zhe Xu, Weihai 2009

  42. Kinetic equilibration no difference between wn and cgc ! Zhe Xu, Weihai 2009

  43. 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 2009

  44. Summary Inelastic pQCD interactions (23 + 32) explain: • Fast Thermalization, • Large Collective Flow, • Small shear Viscosity of QCD matter at RHIC, because the bremsstrahlung favors large-angle radiation. Zhe Xu, Weihai 2009

  45. chemical equilibration in a box gluons and light quarks gluons and charm quarks by J. Uphoff (diploma thesis) Zhe Xu, Weihai 2009

  46. more details on elliptic flow at RHIC … moderate dependence on critical energy density h/s at RHIC: 0.08-0.2 Zhe Xu, Weihai 2009

  47. … 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 2009

  48. ZX, C.Greiner, H. Stöcker, PRL 101:082302,2008 • Perturbation QCD describes well • fast thermalization, • low h/s, • large v2 at RHIC. Zhe Xu, Weihai 2009

  49. Zhe Xu, Weihai 2009

  50. due to the fact that a 2->3 process brings one more particle toward isotropy than a gg->gg process. Zhe Xu, Weihai 2009

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