A Multi-Phase Transport Model for High Energy Heavy Ion Collisions

1. A Multi-Phase Transport Model for High Energy Heavy Ion Collisions Zi-wei Lin The Ohio State University in collaboration with C.M. Ko (TAMU), Bao-An Li (ASU), Subrata Pal (MSU) and Bin Zhang (ASU) NSSTC Marshall Space Flight Center August 7, 2003

2. Outline 1 Why do we need a transport model? Structure of a multi-phase transport (AMPT) model Selected results at high energies from AMPT Summary

3. Major Experiments High Energy Heavy Ion Machines s (AGeV) Main Beam CERN-SPS (past) 8-17 Pb+Pb BNL-RHIC (now) ~20-200 Au+Au CERN-LHC (future) up to 5500 Pb+Pb

4. RHIC (Relativistic Heavy Ion Collider) at Brookhaven National Laboratory Au+Au collisions up to 200AGeV

5. How high is the initial energy density? ~ 2.56 20 GeV/fm3 SPSRHIC200 LHC >>critical energy density for QCD phase transition nuclear radius proper formation time, take 1fm/c High energy density/temperature ~ universe 1ms after the Big Bang Study properties of high density partonic and hadronic matter

6. A general modelfor high energy heavy ion collisions some options: soft+hard model, saturation models, ... parton cascade, hydrodynamics, ... string fragmentation, coalescence, statistical hadronization, ... hadron cascade (ART, RQMD, ...) needs: • Initial condition for particle and energy production • Parton stage with EoS • hadronization/phase transition • hadronic interactions A Multi-Phase Transport (AMPT) model includes the above green ingredients

7. Advantages of a transport model • Can address dynamics at non-equilibrium • Chemical and kinetic freezeouts are generated self-consistently • Allows numerical studies beyond limits of analytical methods • Can learn about details of the evolution of many-body systems

8. Zhang et al, PRC61, PRC65; Lin et al, PRC64, NPA698, PRC65, PRL89. Structure of AMPT model A+B HIJING (Heavy Ion Jet Interaction Generator) minijet partons(hard) +strings(soft) Wang&Gyulassy, PRD43,44,45 Generate parton space-time ZPC (Zhang's Parton Cascade) Zhang, CompPhysComm82 Parton freezeout Lund fragmentation to hadrons ART (A Relativistic Transport model for hadrons) Li&Ko, PRC52 Strong-decay all resonances for final particle spectra

9. Main Ingredients HIJING version 1.383 ZPC 2-2 parton processes: gg-gg, gg-qqbar, gq-gq, ... Hadronization Lund string fragmentation/quark coalescence ART hadron interactions including:

10. Parton Cascade To study dynamics of strong interactions in a QCD matter. The equation of motion may be written as For 2-2 interacitons: ZPC (Zhang's Parton Cascade) solves these Boltzmann equations by the cascade method: 2 particles scatter if their distance <

11. Parton cross sections From leading-order QCD: Use a medium-generated screening mass to regulate the divergence:

12. Causality violation and a solution • Causality problem: Classical cascade breaks down when Mean-Free-Path < Interaction length • A solution: particle subdivision unchanged Zhang,Gyulassy&Pang, PRC58

13. Lund String Fragmentation • Assume: • production positions at a constant proper time, • left-right symmetry (ordering of Vn just represent different Lorentz frames) Lund symmetric splitting function Andersson et al, PhysRep 97; ZPC20 percentage of light-cone momentum of the produced parton

14. The Schwinger Mechanism: • particle production from an external field via tunneling Potential energy= • Production probability the string tension • Strangeness suppression: ~0.3

15. The Schwinger Mechanism Lund String Model Mean Momentum square:

16. Hadron Cascade Based on ART Li&Ko, PRC52 Kbar interactions added Song,Li&Ko, NPA646 NNbar annhilation, K0 productions Zhang et al, PRC61 BBbar-mesons, explicit K*, Lin et al, PRC64, NPA698  interactions Lin&Ko,PRC65 Lin,Ko&Pal, PRL89 Multi-strange () interactions Pal,Ko&Lin, nucl/0106073  interactions Pal,Ko&Lin, NPA707

17. Meson-Meson channels SU(2): with strangeness:

18. Example:  meson cross sections Pal,Ko&Lin, NPA707

19. Meson-Baryon channels

20. Example: K- baryon cross sections Pal,Ko&Lin, nucl/0106073

21. Baryon-Baryon channels Baryon-AntiBaryon channels Pion multiplicity distribution from ppbar annihilation: Ko&Yuan, PLB192

22. Example:

23. 130AGeV Central AuAu Event from AMPT

24. SPS: Pb+Pb collisions at 17AGeV a&b in the Lund splitting function: In default HIJING, a=0.5, b=0.9/GeV2 need changes: a=2.2, b=0.5/GeV2 ~same Lin et al, PRC64, NPA698

25. m spectra at SPS Lin et al, NPA698 Final-state rescatterings in AMPT model increase mslope of heavy particles

26. Results at RHIC Energies (b=0-3fm Au+Au) Lin et al, PRC64, NPA698

27. Particle yields and ratio: energy dependence Lin et al, PRC64 Rapid increase for pbar/p, baryon-antibaryon symmetric ~ early universe

28. AMPT versus RHIC data: Pseudo-rapidity distribution at 130AGeV BRAHMS, PLB523

29. AMPT versus RHIC data: Ratios of 200AGeV/130AGeV: BRAHMS, PRL88 AMPT QCD saturation model

30. More Studies with AMPT Azimuthal momentum asymmetryLin&Ko,PRC65 Multi-strange baryon () enhancement Pal,Ko&Lin, nucl/0106073 • meson puzzle Pal,Ko&Lin, NPA707 J/ production/suppression Zhang et al, PRC62, PRC65  - interferometry/HBT Lin,Ko&Pal, PRL89

31. Summary A Multi-Phase Transport (AMPT) model is constructed for high energy heavy ion collisions including both partonic and hadronic interactions Hadronic/partonic interactions are important for particle multiplicities and momentum spectra AMPT model provides a valuable tool to study heavy ion collisions Slides of this talk available at http://nt3.phys.columbia.edu/people/zlin/PUBLICATIONS