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Recent Developments of A Multi-Phase Transport ModelZi-Wei LinDepartment of PhysicsEast 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 toHelmholtz International Center for FAIR,Workshop organizersXXXI Max Born Symposium and HIC for FAIR Workshop, Wrocaw June 15, 2013#/31OutlineStructure of A Multi-Phase Transport (AMPT) model

Present status of AMPT

Recent developments

Possible future directions

SummaryAll the best, KryzrofXXXI Max Born Symposium and HIC for FAIR Workshop, Wrocaw June 15, 2013#/31What 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 interactionsOptions: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 studyfluctuation, quark coalescence, multi-particle correlation, XXXI Max Born Symposium and HIC for FAIR Workshop, Wrocaw June 15, 2013#/31Extended ARTA+BFinal particle spectraHadrons freeze out (at a global cut-off time);strong-decay all remaining resonancesHadronization (Lund string fragmentation)Structure of AMPT v1.xx (default version)Partons freeze outHIJING (parton dist. functions, nuclear shadowing): minijet partons, excited strings, spectatorsZPC (parton cascade)XXXI Max Born Symposium and HIC for FAIR Workshop, Wrocaw June 15, 2013#/311st frame: spectator nucleons.

Dynamics istime-delayedat large rapiditiesA central Au+Au event at 200AGeV from the default AMPT model

Beam axisafter the primary AA collisions

Only formed particles are shown

60fm boxXXXI Max Born Symposium and HIC for FAIR Workshop, Wrocaw June 15, 2013#/31Color: gluon (2 red), q (2 red), qbar (5 cyan); pi (15 gray), k (11 light blue), kbar (14 dark gray), K*/K*bar (6 magenta), rho (3 deep green), omega/phi/eta/allOthers (1 white), p/n (7 yellow), pbar/nbar (12 violet), Delta/N*/Lambda/Sigma & bar (12 violet).View on the beam axis

A central Au+Au event at 200AGeV from the default AMPT modelE.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.XXXI Max Born Symposium and HIC for FAIR Workshop, Wrocaw June 15, 2013#/31~ 2.56 20 GeV/fm3SPS RHIC LHC>>critical energy densityfor QCD phase transition:c ~ O(1) GeV/fm3Proper formation time, taken as 1 fm/cAt 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, PRC65Estimate the initial energy density in AA collisions:Nuclear radius

Why string melting version of AMPT?XXXI Max Born Symposium and HIC for FAIR Workshop, Wrocaw June 15, 2013#/31A+BFinal particle spectraHadronization (Quark Coalescence)Structure of AMPT v2.xx (String Melting version)HIJING (parton dist. functions, nuclear shadowing): minijet partons, excited strings, spectatorsPartons freeze outZPC (parton cascade)"Melt" to q & qbar via intermediate hadronsHadrons freeze out (at a global cut-off time);strong-decay all remaining resonancesExtended ARTXXXI Max Born Symposium and HIC for FAIR Workshop, Wrocaw June 15, 2013#/31A central Au+Au event at 200AGeV from the String Melting AMPTBeam axisp=3mb

60fm boxE.g. middle region(near mid-rapidity):coalescence of q (red) andqbar (cyan)

XXXI Max Born Symposium and HIC for FAIR Workshop, Wrocaw June 15, 2013#/31Color: gluon (2 red), q (2 red), qbar (5 cyan); pi (15 gray), k (11 light blue), kbar (14 dark gray), K*/K*bar (6 magenta), rho (3 deep green), omega/phi/eta/allOthers (1 white), p/n (7 yellow), pbar/nbar (12 violet), Delta/N*/Lambda/Sigma & bar (12 violet).% Look at bottom middle: an anti-strange meson (turns out to be K*bar) is created ~3.8 fm/c, then decayed to a Kbar and a pion at ~10.6 fm/c.You can see rho decays on middle to left, a white object decays to pions at top middle.A central Au+Au event at 200AGeV from the String Melting AMPT

View on the beam axisXXXI Max Born Symposium and HIC for FAIR Workshop, Wrocaw June 15, 2013#/31Look at bottom middle: an anti-strange meson (turns out to be K*bar) is created ~3.8 fm/c, then decayed to a Kbar and a pion at ~10.6 fm/c.Note: K* width=51 MeV, K*bar is deep green while Kbar is light green here.You can see rho decays on middle to left, a white object decays to pions at top middle.Compare the same event

default AMPT vs String Melting AMPTAt t=5 fm/c:With string melting: many more partons, parton stage dominates; hadron stage starts much later

XXXI Max Born Symposium and HIC for FAIR Workshop, Wrocaw June 15, 2013#/31Present status of AMPTFirst 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 athttps://karman.physics.purdue.edu/OSCAR

More versions, including recent & test versions, are available athttp://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 thisor this (offline)XXXI Max Born Symposium and HIC for FAIR Workshop, Wrocaw June 15, 2013#/31Example: Triangular Flow discovered using AMPT:Alver & Roland,PRC81From Alvers talk:

Simplified PictureWhat really happens in an eventThe heavy ion community is also using AMPT as a valuable tool XXXI Max Born Symposium and HIC for FAIR Workshop, Wrocaw June 15, 2013#/31A b=10fm Au+Au event at 200AGeV from String Melting AMPTView on the beam axis

Initial overlap region has an irregular geometryXXXI Max Born Symposium and HIC for FAIR Workshop, Wrocaw June 15, 2013#/31Look at bottom middle: an anti-strange meson (turns out to be K*bar) is created ~3.8 fm/c, then decayed to a Kbar and a pion at ~10.6 fm/c.Note: K* width=51 MeV, K*bar is deep green while Kbar is light green here.You can see rho decays on middle to left, a white object decays to pions at top middle.9/2012 test version v1.26t1/v2.26t1:To avoid crash (segmentation fault due to s 3 configurations; possible since other odd configurations may increase e3.

Problems come fromhadron cascade of AMPTOngoing work: fix charge conservation in AMPT (1)Why is charge conservation violated in AMPT? After fixing this problem,AMPT will be better suitedfor studies of charge fluctuation and balance functions. XXXI Max Born Symposium and HIC for FAIR Workshop, Wrocaw June 15, 2013#/31Charge correlations using the balance function in PbPb collisions at sqrt(sNN) = 2.76 TeV, ALICE 1301.3756v1 (nucl-ex)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,PRC65interactionsPal,Ko&Lin, NPA707

Multi-strange interactions ( ) Pal,Ko&Lin, NPA730

Deuteron interactionsOh,Lin&Ko, PRC80, NPA834Ongoing work: fix charge conservation in AMPT (2)History of hadron cascade in AMPTXXXI Max Born Symposium and HIC for FAIR Workshop, Wrocaw June 15, 2013#/31First reason:The hadron cascade has K+ and K- as explicit particles, but not K0 and K0-bar.Why is charge conservation violated in AMPT? K0K+K+K+Hadron cascadeHadronizationK0K+Ongoing work: fix charge conservation in AMPT (3)K- K0-barK-K- K0-barK-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.XXXI Max Born Symposium and HIC for FAIR Workshop, Wrocaw June 15, 2013#/31each final-state pion could have +, 0, charge in AMPT:so we can haveorSecond 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 forbiddenOngoing work: fix charge conservation in AMPT (4)Why is charge conservation violated in AMPT? XXXI Max Born Symposium and HIC for FAIR Workshop, Wrocaw June 15, 2013#/31We 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 statesincluding the branching ratios

3) Check detailed balance among related cross sectionsK0 K+ K0-bar K-Hadron cascade(w/ full isospin)HadronizationK0 K+ K0-bar K-Requires checking essentially all hadron reactions in AMPTOngoing work: fix charge conservation in AMPT (5)XXXI Max Born Symposium and HIC for FAIR Workshop, Wrocaw June 15, 2013#/31Meson-Meson channels

SU(2):With strangeness:Ongoing work: fix charge conservation in AMPT (6)XXXI Max Born Symposium and HIC for FAIR Workshop, Wrocaw June 15, 2013#/31Meson-Baryon & Baryon-Baryon channels

Ongoing work: fix charge conservation in AMPT (7)XXXI Max Born Symposium and HIC for FAIR Workshop, Wrocaw June 15, 2013#/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 hydrodynamicsFragmentation of high-Pt partonsPossible future directions12XXXI Max Born Symposium and HIC for FAIR Workshop, Wrocaw June 15, 2013#/31Consistent initial state using local density (default vs string melting). Inelastic (23, ) parton interactions (can be used for both directions).

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 p; & typical value is too low (