1. XXXI Max Born Symposium and HIC for FAIR Workshop, Wrocław June 15, 20131/31 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-An Li (Texas A&M University-Commerce) Subrata Pal (Tata Institute of Fundamental Research, India) Bin Zhang (Arkansas State University) Acknowledgements to Helmholtz International Center for FAIR, Workshop organizers

2. XXXI Max Born Symposium and HIC for FAIR Workshop, Wrocław June 15, 20132/31 Outline Structure of A Multi-Phase Transport (AMPT) model Present status of AMPT Recent developments Possible future directions Summary All the best, Kryzrof

3. XXXI Max Born Symposium and HIC for FAIR Workshop, Wrocław June 15, 20133/31 What do we need for simulations of high energy heavy ion collisions? We need: Initial particle/energy production Partonic interactions, thermalization & evolution Hadronization /QCD phase transition Hadronic interactions 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), … The AMPT model currently includes the green components. In particular, it can be used to study fluctuation, quark coalescence, multi-particle correlation, …

4. XXXI Max Born Symposium and HIC for FAIR Workshop, Wrocław June 15, 20134/31 Extended ART A+B Final particle spectra Hadrons freeze out (at a global cut-off time); strong-decay all remaining resonances Hadronization (Lund string fragmentation) Structure of AMPT v1.xx (default version) Partons freeze out HIJING (parton dist. functions, nuclear shadowing): minijet partons, excited strings, spectators ZPC (parton cascade)

5. XXXI Max Born Symposium and HIC for FAIR Workshop, Wrocław June 15, 20135/31 1 st frame: spectator nucleons. Dynamics is time-delayed at large rapidities A central Au+Au event at 200AGeV from the default AMPT model Beam axis after the primary AA collisions Only formed particles are shown 60fm box

6. XXXI Max Born Symposium and HIC for FAIR Workshop, Wrocław June 15, 20136/31 View on the beam axis A central Au+Au event at 200AGeV from the default AMPT model 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. XXXI Max Born Symposium and HIC for FAIR Workshop, Wrocław June 15, 20137/31 ~ 2.56 20 GeV/fm 3 SPS RHIC LHC >>critical energy density for QCD phase transition: ε c ~ O(1) GeV/fm 3 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 Estimate the initial energy density in AA collisions: Nuclear radius Why string melting version of AMPT?

8. XXXI Max Born Symposium and HIC for FAIR Workshop, Wrocław June 15, 20138/31 A+B Final particle spectra Hadronization (Quark Coalescence) Structure of AMPT v2.xx (String Melting version) HIJING (parton dist. functions, nuclear shadowing): minijet partons, excited strings, spectators Partons freeze out ZPC (parton cascade) "Melt" to q & qbar via intermediate hadrons Hadrons freeze out (at a global cut-off time); strong-decay all remaining resonances Extended ART

9. XXXI Max Born Symposium and HIC for FAIR Workshop, Wrocław June 15, 20139/31 A central Au+Au event at 200AGeV from the String Melting AMPT Beam axis σ p =3mb 60fm box E.g. middle region (near mid-rapidity): coalescence of q (red) and qbar (cyan)

10. XXXI Max Born Symposium and HIC for FAIR Workshop, Wrocław June 15, 201310/31 A central Au+Au event at 200AGeV from the String Melting AMPT View on the beam axis

11. XXXI Max Born Symposium and HIC for FAIR Workshop, Wrocław June 15, 201311/31 Compare the same event default AMPT vs String Melting AMPT At t=5 fm/c: With string melting: many more partons, parton stage dominates; hadron stage starts much later

12. XXXI Max Born Symposium and HIC for FAIR Workshop, Wrocław June 15, 201312/31 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 this or this (offline)this

13. XXXI Max Born Symposium and HIC for FAIR Workshop, Wrocław June 15, 201313/31 Example: Triangular Flow discovered using AMPT: Alver & Roland, PRC81 From Alver’s talk: Simplified Picture What really happens in an event The heavy ion community is also using AMPT as a valuable tool

14. XXXI Max Born Symposium and HIC for FAIR Workshop, Wrocław June 15, 201314/31 A b=10fm Au+Au event at 200AGeV from String Melting AMPT View on the beam axis Initial overlap region has an irregular geometry

15. XXXI Max Born Symposium and HIC for FAIR Workshop, Wrocław June 15, 201315/31 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 |P Z |≥E due to finite precision) 4/2012 test version v1.25t7d/v2.25t7d: Added an option to enable π 0 electromagnetic decay after hadron cascade 2/2012 test version v1.25t7b/v2.25t7b: Added an option to enable random orientation of reaction plane Summary of modifications in AMPT (1)

16. XXXI Max Born Symposium and HIC for FAIR Workshop, Wrocław June 15, 201316/31 5/2011 test version v1.25t4/v2.25t5: Include finite widths of resonances (K* η ρ ω Φ Δ) 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 N part 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 Summary of modifications in AMPT (2)

17. XXXI Max Born Symposium and HIC for FAIR Workshop, Wrocław June 15, 201317/31 3/2009 test version 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+M and 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 …… Summary of modifications in AMPT (3)

18. XXXI Max Born Symposium and HIC for FAIR Workshop, Wrocław June 15, 201318/31 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 Rihan Haque, Lin & Mohanty, PRC 85 Spatial anisotropy

19. XXXI Max Born Symposium and HIC for FAIR Workshop, Wrocław June 15, 201319/31 v 2 closely resembles ε 2 Example: extension of AMPT to deformed Uranium (2)

20. XXXI Max Born Symposium and HIC for FAIR Workshop, Wrocław June 15, 201320/31 Problems come from hadron cascade of AMPT Ongoing work: fix charge conservation in AMPT (1) Why is charge conservation violated in AMPT? After fixing this problem, AMPT will be better suited for studies of charge fluctuation and balance functions.

21. XXXI Max Born Symposium and HIC for FAIR Workshop, Wrocław June 15, 201321/31 Based on the ART modelLi&Ko, PRC52 Kbar interactions addedSong,Li&Ko, NPA646 NNbar <> mesonsZhang et al, PRC61 BBbar <> mesons, explicit K*Lin et al, PRC64, NPA698  interactionsLin&Ko,PRC65  interactionsPal,Ko&Lin, NPA707 Multi-strange interactions (    ) Pal,Ko&Lin, NPA730 Deuteron interactionsOh,Lin&Ko, PRC80, NPA834 Ongoing work: fix charge conservation in AMPT (2) History of hadron cascade in AMPT

22. XXXI Max Born Symposium and HIC for FAIR Workshop, Wrocław June 15, 201322/31 First reason: The hadron cascade has K + and K - as explicit particles, but not K 0 and K 0 -bar. Why is charge conservation violated in AMPT? K0K+K0K+ K+K+ K+K+ Hadron cascade Hadronization K0K+K0K+ Ongoing work: fix charge conservation in AMPT (3) K - K 0 -bar K-K- K-K- To let all kaons interact: before hadron cascade, we change K 0 to K + (also: K 0 -bar to K - ) after hadron cascade, we change half of final K + into K 0.

23. XXXI Max Born Symposium and HIC for FAIR Workshop, Wrocław June 15, 201323/31 each final-state pion could have +, 0, – charge in AMPT: so we can haveor 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: allowed should be forbidden Ongoing work: fix charge conservation in AMPT (4) Why is charge conservation violated in AMPT?

24. XXXI Max Born Symposium and HIC for FAIR Workshop, Wrocław June 15, 201324/31 We need to: add K 0 & K 0 -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 K 0 K + K 0 -bar K - Hadron cascade (w/ full isospin) Hadronization K 0 K + K 0 -bar K - Requires checking essentially all hadron reactions in AMPT Ongoing work: fix charge conservation in AMPT (5)

25. XXXI Max Born Symposium and HIC for FAIR Workshop, Wrocław June 15, 201325/31 Meson-Meson channels SU(2): With strangeness: Ongoing work: fix charge conservation in AMPT (6)

26. XXXI Max Born Symposium and HIC for FAIR Workshop, Wrocław June 15, 201326/31 Meson-Baryon & Baryon-Baryon channels Ongoing work: fix charge conservation in AMPT (7)

27. XXXI Max Born Symposium and HIC for FAIR Workshop, Wrocław June 15, 201327/31 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 Possible future directions 12

28. XXXI Max Born Symposium and HIC for FAIR Workshop, Wrocław June 15, 201328/31 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 section σ p ; & typical value is too low (<< ε c ~ 1 GeV/fm 3 ) Zhang,Chen&Ko, JPG35 We need to start coalescence around energy density ~ε c independent of σ p  Quark coalescence will work better due to the much higher density at the time of coalescence Improve the quark coalescence model for hadronization Possible future direction 1: Coalescence

29. XXXI Max Born Symposium and HIC for FAIR Workshop, Wrocław June 15, 201329/31 A+B Final particle spectra Hadronization (Quark Coalescence) AMPT v2.xx (String Melting) HIJING (parton dist. functions, nuclear shadowing): minijet partons, excited strings, spectators Partons freeze out ZPC (parton cascade) "Melt" to q & qbar via intermediate hadrons Extended ART Possible future direction 2: hybrid model

30. XXXI Max Born Symposium and HIC for FAIR Workshop, Wrocław June 15, 201330/31 A+B Final particle spectra HIJING (parton dist. functions, nuclear shadowing): minijet partons, excited strings, spectators Hydrodynamics (viscous, 3+1d, event-by-event ) 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 Extended ART Possible future direction 2: hybrid model Distribution  hadrons Partons  Distribution

31. XXXI Max Born Symposium and HIC for FAIR Workshop, Wrocław June 15, 201331/31 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 further developments (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. Summary