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Recent Developments of A Multi-Phase Transport Model

Zi -Wei Lin Department of Physics East Carolina University AMPT Collaborators: Che Ming Ko (Texas A&M University) Bao -A n Li (Texas A&M University-Commerce) Subrata Pal ( Tata Institute of Fundamental Research , India) Bin Zhang (Arkansas State University).

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Recent Developments of A Multi-Phase Transport Model

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  1. Zi-Wei Lin Department of Physics East Carolina University AMPT Collaborators: Che Ming Ko(Texas A&M University) Bao-An Li (Texas A&M University-Commerce) Subrata Pal (Tata Institute of Fundamental Research, India) Bin Zhang (Arkansas State University) Recent Developments of A Multi-Phase Transport Model Acknowledgements to HelmholtzInternational Center for FAIR, Workshop organizers

  2. Outline Structure of A Multi-Phase Transport (AMPT) model Present status of AMPT Recent developments Possible future directions Summary All the best, Kryzrof

  3. What do we need for simulations of high energy heavy ion collisions? Options: Soft+hard model, CGC, pQCD, ... Parton cascade (ZPC, MPC, BAMPS), (ideal, viscous) hydrodynamics, dE/dx, ... String fragmentation, quark coalescence/parton recombination, statistical hadronization, Cooper-Frye, independent fragmentation, rate equations, ... Hadron cascade (ART, RQMD, UrQMD, ...), thermal model (w/ freezeout temperatures), … We need: Initial particle/energy production Partonic interactions, thermalization & evolution Hadronization /QCD phase transition Hadronic interactions The AMPT model currently includes the green components. In particular, it can be used to study fluctuation, quark coalescence, multi-particle correlation, …

  4. Structure of AMPT v1.xx (default version) HIJING (parton dist. functions, nuclear shadowing): minijet partons, excitedstrings, spectators A+B ZPC(parton cascade) Partons freeze out Hadronization (Lund string fragmentation) Extended ART Hadrons freeze out (at a global cut-off time); strong-decay all remaining resonances Final particle spectra

  5. A central Au+Au event at 200AGeV from the default AMPT model after the primary AA collisions Only formed particles are shown 60fm box Beam axis 1st frame: spectator nucleons. Dynamics is time-delayed at large rapidities

  6. A central Au+Au event at 200AGeV from the default AMPT model View on thebeam axis E.g. at middle right: rho (green) decayed at 7.0 fm/c at lower right: K*bar is produced at 16.6 fm/c & vanishes at 20.8fm/c.

  7. Why string melting version of AMPT? Estimate the initial energy density in AA collisions: ~ 2.56 20 GeV/fm3 SPSRHIC LHC >>critical energy density for QCD phase transition: εc~ O(1) GeV/fm3 Nuclear radius Proper formation time, taken as 1 fm/c At high-enough energies, hadronic matter such as strings cannot exist early on, they should be represented by a high density partonic matter:  the string melting version of AMPTLin&Ko, PRC65

  8. Structure of AMPT v2.xx (String Melting version) HIJING (parton dist. functions, nuclear shadowing): minijet partons, excitedstrings, spectators A+B "Melt" to q & qbar via intermediate hadrons ZPC(parton cascade) Partons freeze out Hadronization (Quark Coalescence) Extended ART Hadrons freeze out (at a global cut-off time); strong-decay all remaining resonances Final particle spectra

  9. A central Au+Au event at 200AGeV from the String Melting AMPT σp=3mb 60fm box Beam axis E.g. middle region (near mid-rapidity): coalescence of q (red) and qbar (cyan)

  10. A central Au+Au event at 200AGeV from the String Melting AMPT View on thebeam axis

  11. Compare the same eventdefault AMPT vsString Melting AMPT At t=5 fm/c: With string melting: many more partons, parton stage dominates; hadron stage starts much later

  12. Present status of AMPT First public release of AMPT codes: ~ April 2004. Detailed physics descriptions in the long paper: Lin, Ko, Li, Zhang & Pal, PRC 72, 064901 (2005). "Official" versions v1.11/v2.11(2004) and v1.21/v2.21 (2008) are available at https://karman.physics.purdue.edu/OSCAR More versions, including recent & test versions, are available at http://personal.ecu.edu/linz/ampt/ v1.25t3/v2.25t3 (8/2009) v1.25t7/v2.25t7 (9/2011) v1.25t7d/v2.25t7d (4/2012) v1.26t1/v2.26t1 (9/2012) The webpage looks like this or this (offline)

  13. The heavy ion community is also using AMPT as a valuable tool What really happens in an event Simplified Picture Example: Triangular Flow discovered using AMPT: Alver & Roland, PRC81 From Alver’s talk:

  14. A b=10fm Au+Au event at 200AGeV from String Melting AMPT View on thebeam axis Initial overlap region has an irregular geometry

  15. Summary of modifications in AMPT (1) 9/2012 test version v1.26t1/v2.26t1: To avoid crash (segmentation fault due to s<0) at high energy such as LHC at large NT: use double precision in art1f.f when calculating sqrt(s), use double precision in linana.f to calculate β avoid NaN. use a more general formula in amptsub.f to calculate rapidity (valid for hadrons at large rapidities that have |PZ|≥E due to finite precision) 4/2012 testversion v1.25t7d/v2.25t7d: Added an option to enable π0electromagnetic decay after hadron cascade 2/2012 testversion v1.25t7b/v2.25t7b: Added an option to enable random orientation of reaction plane

  16. Summary of modifications in AMPT (2) 5/2011 testversion v1.25t4/v2.25t5: Include finite widths of resonances (K* ηρωΦΔ) when produced from quark coalescence in the string melting version, added for the purpose of resonance reconstruction using invariant mass. 7/2009 test version v1.25t2/v2.25t2: Added an option to enable users to modify nuclear shadowing smoothly between no-shadowing and the default HIJING shadowing 6/2009 test version v1.25t1/v2.25t1: Added an option of event selection so that each event will have at least 1 mini-jet parton above a set Pt value in the initial condition; added an option to embed a back-to-back high-Pt q/qbar pair in each event; write out Npart information (spatial coordinates and status of each incoming nucleon); added option to write complete parton information before &after parton cascade and the full parton collision history for the string melting version

  17. Summary of modifications in AMPT (3) 3/2009 testversion v1.23/v2.23: Included a subroutine to enable users to insert user-defined hadrons before the start of the hadron cascade 10/2008 test version v1.22/v2.22:Included deuteron(d) interactions in hadron cascade via d+M↔ B+B (M or B represents a meson or a baryon), also included elastic collisions of d+Mand d+B; similar anti-deuteron interactions are also included 10/2008 v1.21/v2.21: Added option to turn off φ meson decays at the end of hadron cascade i.e., at NT=NTMAX ……

  18. Example: extension of AMPT to deformed Uranium (1) 2011: Added deformed Uranium U238 as projectile/target. This test version (v1.25t8/v2.25t8) is not online. Considered a few special geometries and MB UU RihanHaque, Lin & Mohanty, PRC 85 Spatial anisotropy

  19. Example: extension of AMPT to deformed Uranium (2) v2 closely resembles ε2

  20. Ongoing work: fix charge conservation in AMPT (1) After fixing this problem, AMPT will be better suited for studies of charge fluctuation and balance functions. Why is charge conservation violated in AMPT? Problems come from hadron cascade of AMPT

  21. Ongoing work: fix charge conservation in AMPT (2) History of hadron cascade in AMPT Based on the ART modelLi&Ko, PRC52 Kbar interactions added Song,Li&Ko, NPA646 NNbar <> mesonsZhang et al, PRC61 BBbar <> mesons, explicit K*Lin et al, PRC64, NPA698 • interactions Lin&Ko,PRC65 • interactions Pal,Ko&Lin, NPA707 Multi-strange interactions (  ) Pal,Ko&Lin, NPA730 • Deuteron interactions Oh,Lin&Ko, PRC80, NPA834

  22. Ongoing work: fix charge conservation in AMPT (3) Hadronization Why is charge conservation violated in AMPT? First reason: The hadron cascade has K+ and K- as explicit particles, but not K0 and K0-bar. K- K0-bar K0 K+ K- K+ • To let all kaons interact: • before hadron cascade, • we change K0 to K+(also: K0-bar to K-) • after hadron cascade, • we change half of final K+ into K0. Hadron cascade K+ K- K- K0-bar K0 K+

  23. Ongoing work: fix charge conservation in AMPT (4) Why is charge conservation violated in AMPT? • Second reason: • Many reactions in the hadron cascade • are not implemented for each possible isospin configuration: • isospin-averaged cross section is used, • final state particles have randomly-generated isospin. For example: each final-state pion could have +, 0, – charge in AMPT: so we can have or allowedshould be forbidden

  24. Ongoing work: fix charge conservation in AMPT (5) We need to: add K0& K0-bar as explicit particles, allow similar interaction types as for K+& K-. Several steps: 1) Forbid final states that violate charge conservation: this is enough to conserve charge. 2) Update/determine cross sections of allowed final states including the branching ratios 3) Check detailed balance among related cross sections Hadronization K0 K+ K0-bar K- Hadron cascade (w/ full isospin) K0 K+ K0-bar K- Requires checking essentially all hadron reactions in AMPT

  25. Ongoing work: fix charge conservation in AMPT (6) Meson-Meson channels SU(2): With strangeness:

  26. Ongoing work: fix charge conservation in AMPT (7) Meson-Baryon & Baryon-Baryon channels

  27. Possible future directions 1 2 • Improve parton recombination • by using local density as criteria • Coalescence in phase-space • Gluons in parton recombination • (energy-momentum conservation) • Couple AMPT with • viscous hydrodynamics • Fragmentation of high-Pt partons

  28. Possible future direction 1: Coalescence Improve the quark coalescence model for hadronization Currently, a parton can coalesce after kinetic freeze-out (i.e. after it will not have further interactions) Average parton density at coalescence depends on parton scattering cross sectionσp; & typical value is too low (<< εc~ 1 GeV/fm3) We need to start coalescence around energy density ~εc independent of σp Quark coalescence will work better due to the much higher density at the time of coalescence Zhang,Chen&Ko, JPG35

  29. Possible future direction 2: hybrid model HIJING (parton dist. functions, nuclear shadowing): minijet partons, excitedstrings, spectators A+B "Melt" to q & qbar via intermediate hadrons AMPT v2.xx (String Melting) ZPC(parton cascade) Partons freeze out Hadronization (Quark Coalescence) Extended ART Final particle spectra

  30. Possible future direction 2: hybrid model HIJING (parton dist. functions, nuclear shadowing): minijet partons, excitedstrings, spectators A+B Direct link to QCD: (EoS, viscosity) Self-contained initial condition, including fluctuations Other initial condition allowed, e.g. CGC Can compare with current AMPT: hydro vs parton cascade "Melt" to q & qbar via intermediate hadrons Partons  Distribution Hydrodynamics (viscous, 3+1d,event-by-event) Distribution  hadrons Extended ART Final particle spectra

  31. Summary AMPT has been a self-contained phenomenological model (from initial condition to final observables event-by-event): includes fluctuations and non-equilibrium dynamics; can be a test-bed of different conceptual ideas; should incorporate essential stages of heavy ion collisions. The approach needs furtherdevelopments (more direct link to QCD variables & properties): improving the parton recombination model for hadronization or couple with 3+1d viscous hydrodynamics. Comments, suggestions, collaborations are greatly welcome.

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