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Applications of Parton Cascade Models in Heavy-Ion Collisions

SchoolNP , Wuhan, Nov 5 , 201 1. Applications of Parton Cascade Models in Heavy-Ion Collisions. Zhe Xu ( 徐喆 ) xuzhe@mail.tsinghua.edu.cn. Tsinghua University, China Frankfurt Institute for Advanced Studies (FIAS), Germany. Outline. Motivation Parton Cascade Models

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Applications of Parton Cascade Models in Heavy-Ion Collisions

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  1. SchoolNP, Wuhan, Nov 5, 2011 Applications of Parton Cascade Models in Heavy-Ion Collisions Zhe Xu(徐喆) xuzhe@mail.tsinghua.edu.cn Tsinghua University, China Frankfurt Institute for Advanced Studies (FIAS), Germany

  2. Outline • Motivation • Parton Cascade Models • Thermalization, Viscosity, Flow, Energy Loss, ... • Outlook Zhe Xu

  3. Ultrarelativistic Heavy-Ion Collisions Zhe Xu

  4. Quark-Gluon Plasma QCD (Quantum Chromo-Dynamik), theory of strong interactions Gluon-Gluon interaction Zhe Xu

  5. QGP was created at 10-6s after the big bang. Zhe Xu

  6. PHOBOS BRAHMS STAR PHENIX Relativistic Heavy Ion Collider (RHIC), BNL, USA circumference 3.8 km first collision in 2000 experiments: STAR, PHENIX, PHOBOS, BRAHMS max. collider energy: 500 GeV for proton-proton 200 GeV per ion pair for Au-Au Zhe Xu

  7. The Large Hadron Collider (LHC), CERN, Europe circumference 27 km first collision on March 30, 2010 experiments: ALICE, ATLAS, CMS, LHCb max. collider energy: 14 TeV for proton-proton 5.75 TeV per ion pair for Pb-Pb Zhe Xu

  8. RHIC experiments Zhe Xu

  9. Zhe Xu

  10. Parton Cascade Models based on a semi-classical, relativistic kinetic equation in the framework of pQCD solved by Monte Carlo simulations Zhe Xu

  11. classical non-relativistictransport(with external force) Zhe Xu

  12. Collisions of hard spheres in mechanics R R: radius Collisions of particles in quantum mechanics s: cross section semi-classical parton cascade: Partons are classical point particles and propagate along classical trajectories, but interact by means of individual scatterings. Zhe Xu

  13. perturbative QCD (pQCD) interactions elastic scattering bremsstrahlung Zhe Xu

  14. to deal with the singularity differential cross sections at the leading order of as Mandelstam variables sampling momenta of outgoing particles by Monte Carlo Zhe Xu

  15. Action of relativistic particles at a distance Collision scheme 1 (geometrical method): When two particles collide, the collision occurs at the closest distance. • The closest distance is frame dependent. It is usually calculated in • the CM frame of individual particle pairs to keep Lorentz covariance • of the transport approach. • Collision times: in CM and in the system frame • Ordering time: not unique, for example Zhe Xu B. Zhang and Y. Pang, PRC56 1997

  16. Operation of the cascade Standard procedure for two-body parton scatterings 1. calculate cta, ctb, otab for each particle pair number of pairs = Na*Nb operations 2. find out the next collision 3. determine the momenta of outgoing particles by Monte Carlo 4. update the positions and momenta of the colliding particles 5. back to 1. and find out next collision ..., The system propagates from one collision to the next. 6. Cascade ends when no more collisions take place. Zhe Xu

  17. Problem: causality violation Causality violation arises in high energy nulceus(nucleon)-nucleus collisions when the parton mean free paths approach the interparton distance. G. Kortemeyer, et al., PRC 52, 1995 1. superluminous macroscopic information transport (shock waves) A series of subsequent causality violating interactions can lead to shock waves with a velocity Zhe Xu

  18. 2: noncausal collisions Particle a is involved in two collisions: ai and aj Collision aj is a noncausal collision, because at time ctaj the collision ai is not complete yet. huge reduction of causal collision rate in dense medium test particle method solves this numerical artifact. ZX, C. Greiner, PRC71 2005 Zhe Xu

  19. ZPC, MPC on-shell parton cascade withpQCD 2->2 closest distance method B. Zhang Y. Pang M. Gyulassy D. Molnar 1997,2000 Zhe Xu

  20. AMPT ZPC is included in AMPT (A Multiphase Transport Model) Z. Lin B. Zhang C.M. Ko B.A. Li S. Pal 2005 PACIAE A parton and hadron cascade model B. Sa, D. Zhou, et.al, 1999,2011 Zhe Xu

  21. VNI K. Geiger B. Müller 1992 initial parton structure function (SF) (Semi) Hard scatterings (HS) 2->2 Soft interactions (SS) 2->2 Space-like branchings (SB) 1->2 Time-like branchings (TB) 1->2 Parton fusions (FU) 2->1 (intermediate state in ab->e*->cd) LPM effect and soft gluon interference Recombinations and fragmentations (H) off-shell partons propagating as on-shell ones Zhe Xu

  22. VNI / BMS S.A. Bass B. Müller D.K. Srivastava 2003 initial parton structure function (SF) (Semi) Hard scatterings (HS) 2->2 Soft interactions (SS) 2->2 Space-like branchings (SB) 1->2 Time-like branchings (TB) 1->2 Parton fusions (FU) 2->1 (intermediate state in ab->e*->cd) LPM effect and soft gluon interference Recombinations and fragmentations (H) Partons are on-shell except the first scattering X X X Zhe Xu

  23. with radiations G.R. Shin B. Müller 2003 on-shell parton cascade with pQCD 2->2 and gg->ggg closest distance method test particle method minimum momentum transfer LPM no 3->2, no detailed balance Zhe Xu

  24. BAMPS: Boltzmann Approach of MultiParton Scatterings A transport algorithm solving the Boltzmann-Equations for on-shell partons with pQCD interactions ZX and C. Greiner,PRC 71, 064901 (2005) new development ggg gg VNI/BMS, ZPC, MPC, PACIAE 2<->3 are essential forfast thermalization and the buidup of elliptic flow due to large open angle. ZX, Greiner, Stöcker, PRL 101, 2008 Zhe Xu

  25. Collision Terms Zhe Xu

  26. collision rate per unit phase space for incoming particles p1 and p2 with D3p1 and D3p2: collision probability (Monte Carlo) Zhe Xu

  27. Collision scheme 2: stochastic method ZX and C. Greiner,PRC 71, 064901 (2005) Zhe Xu

  28. Zhe Xu

  29. Advantages: simulating m<->n no noncausal collisions Zhe Xu

  30. other parton cascade models using the stochastic method 1. by G. Ferini, M. Colonna, M. Di Toroa, V. Greco, PLB 670, 2009 only 2->2 2. by B. Zhang, W.A. Wortman, PLB 693, 2010 2->2 and 2<->3 Zhe Xu

  31. screened pQCD based partonic interactions J.F.Gunion, G.F.Bertsch, PRD 25, 746(1982) LPMsuppression: treatment for incoherent interactions: the formation time Lg: mean free path Zhe Xu

  32. Zhe Xu

  33. Initial Conditions Parton Cascade Results Zhe Xu

  34. Initial conditions of partons 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

  35. Initial conditions of partons • Minijets (low pT cut-off at 1.4 GeV) • PYTHIAscaling to heavy-ion collisions with Glauber model (considering shadowing) • Color glass condensate H.J. Drescher & Y. Nara, Phys. Rev. C75 (2007) • Minijets +thermal soft partons • HIJING with string melting • hard partons ~ Nbin: number of binary collision • soft partons ~ A: number of nucleons Zhe Xu

  36. Zhe Xu

  37. Thermalization central Au+Au at 200 GeV VNI K. Geiger PRD 1992 first hard scattering 2->2 1->2 2->1 thermal equilibrium Global Equilibration: spectrum extracted at the midrapidity region of a volume of 180 fm3 Local Equilibration? Zhe Xu

  38. Thermalization VNI / BMS Bass et al. PLB 2003 NO local equilibrium 2->2 1->2 spectrum extracted at the midrapidity region with RT < 2 fm Zhe Xu

  39. Thermalization 2<->3 processes may be important. Parton Chemical Equilibration T.S. Biro et al., Phys. Rev. C 48, 1275(1993) Gluon Multiplication L. Xiong, E.V. Shuryak, Phys. Rev. C 49, 2203(1994) Thermal and Chemical Equilibration S.M.H. Wong, Nucl.Phys.A 607, 442(1996) Bottom-Up Thermalization R. Baier, A.H. Mueller, D. Schiff, D.T. Son, Phys. Lett. B502, 51(2001) Kinetic Equilibration J. Serreau and D. Schiff, JHEP 0111, 039(2001) Transport Opacity D. Molnar, M. Gyulassy, Nucl. Phys. A 697, 495(2002) Zhe Xu

  40. Thermalization radiation Shin and Müller JPG 2003 thermalized at 1.6 fm/c 2->2 2->3 No 3->2 in a small sphere with radius R=1.1 fm at the collision center minijets initial condition with p0=1 GeV Zhe Xu

  41. Thermalization the central region: h: [-0.5:0.5] and xt < 1.5 fm BAMPS ZX, Greiner PRC 2005 initial 0.2 fm/c 0.5 fm/c 1.0 fm/c 2.0 fm/c 3.0 fm/c 4.0 fm/c 2->2 NO thermalization almost free streaming Zhe Xu

  42. Thermalization the central region: h: [-0.5:0.5] and xt < 1.5 fm BAMPS ZX, Greiner PRC 2005 initial 0.2 fm/c 0.5 fm/c 1.0 fm/c 2.0 fm/c 3.0 fm/c 4.0 fm/c 2->2 2->3 3->2 Thermalization is achieved. Zhe Xu

  43. Thermalization central collision theoretical result from BAMPS BAMPS ZX, Greiner PRC 2005 2->2 2->3 3->2 teq = time scale of kinetic equilibration. Zhe Xu

  44. cross sections in the central region: h: [-0.5:0.5] and xt < 1.5 fm transport cross section: gg -> gg gg -> ggg The inelastic collisions are the dominant processes to drive the system to kinetic equilibrium. Zhe Xu

  45. Distribution of collision angle gg gg: small-angle scatterings gg ggg: large-angle bremsstrahlung Zhe Xu

  46. 2 -> 2 pQCD cross section Zhe Xu

  47. 2 -> 2isotropic cross section Zhe Xu

  48. Shear Viscosity large momentum transfer -> small shear viscosity -> perfect fluid Gyulassy, Molnar Greco, et al. A. El, A. Muronga, ZX and C. Greiner, PRC 79, 044914 (2009) Zhe Xu

  49. Shear Viscosity various methods to extract h/s in BAMPS C. Wesp, F. Reining, et al. arXiv: 1106.4306 Zhe Xu

  50. How viscous (h/s) is the QGP ? M.Luzum and P. Romatschke, PRC 78, 034915 (2008) Consensus talk of B. Schenke at QM 2011 R.Lacey Zhe Xu

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