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Zi -Wei Lin Department of Physics East Carolina University Greenville, NC

Zi -Wei Lin Department of Physics East Carolina University Greenville, NC. Update of Initial Conditions in A Multiple Phase Transport (AMPT) Model. Work still in progress. Outline. Present status of the AMPT model Need to update the initial conditions

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Zi -Wei Lin Department of Physics East Carolina University Greenville, NC

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  1. Zi-Wei Lin Department of Physics East Carolina University Greenville, NC Update of Initial Conditions in A Multiple Phase Transport (AMPT) Model Work still in progress

  2. Outline Present status of the AMPT model Need to update the initial conditions Optimize parameters/functions by fitting dNch/dη data Outlook Summary

  3. What do we needfor simulations of high energy heavy ion collisions? Options: Soft+hard model, CGC, pQCD, ... Parton cascade (ZPC, MPC, BAMPS), hydrodynamics, dE/dx, ... String fragmentation, quark coalescence, independent fragmentation, statistical hadronization,... Hadron cascade (ART, RQMD, UrQMD, ...), freezeout temperature, … We need: Initial particle/energy production Parton interactions/ equation-of-state Hadronization /QCD phase transition Hadron interactions The AMPT model includes the components in green. In particular, it can be used to study coalescence of partons into hadrons, thermalization and flow, dynamical chemical freeze-out and kinetic freeze-out

  4. Structure of AMPT v1.xx (default model) HIJING (PDFs, nuclear shadowing): minijet partons, excitedstrings, spectators A+B Lesspartonic interaction Dominated by hadronic interactions (at very high densities) ZPC(Zhang's Parton Cascade) Partons freeze out Hadronization (Lund String fragmentation) ART (A Relativistic Transport model for hadrons) Hadrons freeze out (at a global cut-off time); strong-decay all remaining resonances Final particle spectra

  5. Structure of AMPT v2.xx (String Melting model) HIJING (PDFs, nuclear shadowing): minijet partons, excitedstrings, spectators A+B Melt to q & qbar via intermediate hadrons Partonic interactions dominate. Better describes flow& HBT, but does not describe well single particle spectra ZPC(Zhang's Parton Cascade) Partons freeze out Hadronization (Quark Coalescence) ART (A Relativistic Transport model for hadrons) Hadrons freeze out (at a global cut-off time); strong-decay all remaining resonances Final particle spectra

  6. AMPT Source Codes First public release of AMPT codes: ~ April 2004. Detailed physics descriptions in Lin, Ko, Li, Zhang & Pal, PRC 72, 064901 (2005). Versions v1.21/v2.21 (2008) and v1.11/v2.11(2004) are available at https://karman.physics.purdue.edu/OSCAR-old/ http://personal.ecu.edu/linz/ampt/ also contains more recent test versions, including v1.25t3/v2.25t3 (8/2009) v1.25t7/v2.25t7 (9/2011) v1.25t7b/v2.25t7b (2/2012)

  7. http://personal.ecu.edu/linz/ampt/looks like this

  8. Update Initial Conditions of AMPT HIJING (PDFs, nuclear shadowing): minijet partons, excitedstrings, spectators A+B Final particle spectra

  9. Similar updates have been done recently: In HIJING2.0: Deng, Wang and Xu, PRC 83 (2011) & PLB 701 (2011): used GRV (Gluck-Reya-Vogt) parton distribution functions,  parameterized functions p0(√sNN) & σsoft(√sNN); new parameters for quark and gluon nuclear shadowing functions are used to reproduce dNch/dηin AA collisions. In AMPT: Pal & Bleicher, PLB 709 (2012) used HIJING2.0 as initial conditions, smaller value for the gluon shadowing parameter sg is needed to reproduce dNch/dη in AA collisions at LHC, since rescatterings considerably reduce hadron yields at mid-rapidity

  10. Rescatterings considerably reduce hadron yields at mid-rapidity In AMPT: Lund model's a & b values used for pp/HIJING can describe SPS dN/dy when final state interactions are turned off. but this agreement is gone when final state interactions are included. We have to use different a & b values to describe dN/dy of AA collisions. Lin, Ko, Li, Zhang & Pal, PRC 72 (2005); first shown in PRC 64 (2001).

  11. 1) Need to Use up-to-date parton distribution functions It is essential to use up-to-date PDF for LHC & for heavy flavors (since ~all come from gluons) Duke-Owens Set 1 (1984) used in HIJING1.0 & AMPT significantly under-estimates the gluon density at small-x LHC RHIC For this study, we have incorporated into AMPT the CTEQ6MPDF

  12. 2) Need to use up-to-date nuclear shadowing functions RA(x) Central Pb+Pb collisions at √sNN=5.5 TeV from default AMPT v1.11: shadowing has a large effect PDF in a nucleus ≠ PDF in a nucleon *A Deng, Wang and Xu, PLB 701 (2011) For this study, we have incorporated into AMPT the EPS09nuclearshadowing

  13. Optimize parameters by fitting dNch/dηdata with the default AMPT model (+CTEQ6M & EPS09) In AMPT/HIJING1.0: p0=2.0 GeV/c, σsoft≈57 mb. The nucleon-nucleon cross section in the eikonal approximation: • We follow the following strategy • similar to Deng, Wang and Xu, PRC 83 (2011): • At each collision energy √sNN: • choose different p0 values • for each p0, determine the σsoft value that reproduces the experimental σpptotal • run AMPT for each(p0, σsoft) set, • then compare with dNch/dηdata to find the best (p0, σsoft) value. Go through all relevant collision energies: p0(√sNN) & σsoft(√sNN)

  14. Example of the (p0, σsoft) sets √sNN=200 GeV from PDG √sNN=7 TeV

  15. AMPT results for different (p0, σsoft) sets vspp inelastic data At √sNN=19.6 GeV: p0=1.0, 1.2, 1.4, 1.6, 1.8 GeV/c. … At √sNN=200 GeV: p0=2.0, 2.2, 2.4, 2.6 GeV/c. … At √sNN=7 TeV: p0=3.0, 3.5, 4.0, 4.5, 5.0, 5.5, 6.0 GeV/c. Higher p0 gives lower dNch/dη (except for the lowest energy √sNN=19.6 GeV)

  16. Fit p0 to inelastic pp data at different energies dNch/dη(|η|<0.5) INEL =2.22 ±0.05 p0=2.35 +0.08-0.09 GeV/c using AMPT results with interpolation √sNN=200 GeV √sNN=2360 GeV dNch/dη(|η|<0.5) INEL =3.77 +0.25-0.12 p0=3.77 +0.18-0.33 GeV/c

  17. p0 values fitted to inelastic pp data p0(√sNN) increases with collision energy, related to more partons at small-x in the new PDF

  18. Fit p0 to central AA data at different energies after incorporating EPS09 shadowing functions in AMPT

  19. AMPT results for different (p0, σsoft) sets vs central AA data AuAu at √sNN=19.6 GeV: p0=1.2, 1.4, 1.6, 1.8 GeV/c. … AuAuat √sNN=200 GeV: p0=2.0, 2.2, 2.3, 2.4, 2.6 GeV/c. PbPb at √sNN=2760 GeV: p0=3.5, 4.0, 4.5 GeV/c. Higher p0 gives lower dNch/dη/(Npart/2)

  20. Fitted p0 values combined p0(√sNN) fitted to pp data and to AA data are not consistent  This test of the PDF+shadowing update cannot systematically describe dNch/dη of pp & AA collisions throughout this energy range

  21. Outlook Search for consistent p0(√sNN) from fits to ppdata and to AA data Possibilities include: 1) a & b parameters in Lund string fragmentation: a=0.3 & b=0.8/GeV2 are used in this study, this is one set of the2009 fitvaluesin PYTHIA 8.1; we can explore the a-b parameter space: e.g. PYTHIA have used a=0.76, b=0.58/GeV2(2007 fit values), and used a=0.30, b=0.58/GeV2 before. 2) Alternative nuclear shadowing.

  22. Summary • Work is under way to incorporate into AMPT • up-to-date parton distribution functions and nuclear shadowing functions • CTEQ6M and EPS09 have been tested within AMPT, • but the functions p0(√sNN)& σsoft(√sNN) • from fits to ppdNch/dηdata and fits to central AA data are not consistent • We will investigate • Lund a,b parameters and alternative nuclear shadowing functions • to obtain consistent p0(√sNN) & σsoft(√sNN) from fits to pp and AA data; • that would allow systematic descriptions • of dNch/dη in pp & AA collisions throughout a wide energy range. • May require more significant developments: • dynamical quark coalescence in phase space • (instead of space/nearest neighbors), • inelastic parton interactions

  23. Thank you!

  24. Backup Slides

  25. Files in the Source Code include amptsub.f art1f.f hijing1.383_ampt.f hipyset1.35.f linana.f main.f zpc.f input.ampt Fortran routines Input parameter values Update of initial conditions introduces new input data files: cteq6m.tbl EPS09LOR_197 EPS09LOR_208 CTEQ6M PDF table EPS09 shadowing function table for Au and Pb nucleus

  26. Main Ingredients HIJINGsoft strings + hard minijets ZPC2↔2 parton cascade: gg↔gg, gg↔qqbar, gq↔gq, ... Hadronization Lund string fragmentation or quark coalescence ARThadron cascade including:

  27. Earlier modifications in the AMPT source code 2005 v1.12/v2.12: Freezeout time of spectator projectile and target nucleons should be ~0 but not correctly updated in 'ampt.dat'; now corrected 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 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. 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

  28. Recent modifications in the AMPT source code 6/2009 test version v1.25t1/v2.25t1: Added an option of event selection so that each event will have at least 1 minijetparton 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 informationbefore and after the parton cascade and the full parton collision historyfor the string melting version 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 5/2011 testversion v1.25t4/v2.25t5: Included the finite widths of resonances (K* ηρωΦΔ) when they are produced from quark coalescence in the string melting version 2/2012 testversion v1.25t7b/v2.25t7b: Added option to enable random orientation of reaction plane

  29. Files in the Source Code include amptsub.f art1f.f hijing1.383_ampt.f hipyset1.35.f linana.f main.f zpc.f README Makefile exec input.ampt ana/ Fortran routines Instructions (including summary of changes) Script to run AMPT Input parameter settings Directory for output data and diagnostics files update of initial conditions will introduce new input data files:

  30. Parameters in input.ampt:New options in red 200. ! EFRM (sqrt(S_NN) in GeV)CMS ! FRAMEA ! PROJA ! TARG197 ! IAP (projectile A number)79 ! IZP (projectile Z number)197 ! IAT (target A number)79 ! IZT (target Z number)2 ! NEVNT (total number of events)0. ! BMIN (mininum impact parameter in fm) 13. ! BMAX (maximum impact parameter in fm, also see below)1 ! ISOFT (D=1): select Default AMPT or String Melting(see below)150 ! NTMAX: number of timesteps (D=150), see below0.2 ! DT: timestep in fm (hadron cascade time= DT*NTMAX) (D=0.2)2.2 ! PARJ(41): parameter a in Lund symmetric splitting function0.5 ! PARJ(42): parameter b in Lund symmetric splitting function1 ! (D=1,yes;0,no) flag for popcorn mechanism(netbaryon stopping)1.0 ! PARJ(5) to control BMBbar vs BBbar in popcorn (D=1.0)1 ! shadowing flag (Default=1,yes; 0,no)0 ! quenching flag (D=0,no; 1,yes)1.0 ! quenching parameter -dE/dx (GeV/fm) in case quenching flag=12.0 ! p0 cutoff in HIJING for minijet productions (D=2.0)3.2264d0 ! parton screening mass in fm^(-1) (D=3.2264d0), see below0 ! IZPC: (D=0 forward-angle parton scatterings; 100,isotropic)0.47140452d0 ! alpha in parton cascade1d6 ! dpcoal in GeV1d6 ! drcoal in fm0 ! ihjsed: take HIJING seed from below (D=0)or at runtime(11)53153523 ! random seed for HIJING8 ! random seed for parton cascade0 ! flag for Ks0 weak decays (D=0,no; 1,yes)1 ! flag for phi decays at end of hadron cascade (D=1,yes; 0,no)0 ! optional OSCAR output (D=0,no; 1,yes; 2,initial parton info) Initial Conditions/ HIJING (e.g. turn on quenching to mimic inelastic energy loss) Hadron Cascade (e.g. NTMAX=2 turns off hadron cascade but still has full parton cascade & hadronization) Parton Cascade Hadronization Output options

  31. Output files ampt.dat Npart2 Event# Particle# b(fm) Npart1 Test# 1 1 4218 8.0000 84 84 2 82 1 83 2112 0.000 0.000 99.996 0.940 6.00 -4.86 0.23 0.00 2112 0.000 0.000 99.996 0.940 6.78 3.61 0.21 0.00 2212 0.000 0.000 99.996 0.940 5.53 1.48 0.26 0.00 2212 0.000 0.000 -99.996 0.940 -9.31 -2.75 -0.16 0.00 111 0.071 -0.334 -0.376 0.135 1.81 -0.96 -1.18 7.00 mass Particle ID (PYTHIA) Final momentum Final position & time (at kinetic freeze-out) zpc.dat Final momentum, position & time of all partons (at kinetic freeze-out)

  32. EPS09 (JHEP 2009) determines the nuclear modification to the free proton PDF from the CTEQ6.1M set in the MS scheme The CTEQ6.1M set provides a global fit that is almost equivalent in every respect to the published CTEQ6M

  33. Needs to Further Develop AMPT • Need to use up-to-date Parton Distribution Functions in nuclei: • essential for heavy flavors & LHC • Parton coalescence to hadrons: Currently, a parton can only coalesce after it does not have further interactions (i.e., after kinetic freezeout); • Average parton density at coalescence, and effective equation of state of AMPT depends on σp; • Need to improve Parton coalescence for better EoS; • hadronization condition (~HBT) • & parton cross section (~v2)will be decoupled • Inelastic partonic interactions • Including color fields in parton phase.

  34. RRPL2u (19) model predictions of sigma_total for pp collisions (ecm==sqrt_s>=5GeV): sigma_total= 35.45 - 33.34/((ecm^2)^0.5453) + 42.53/((ecm^2)^0.4581) + 0.3079*(-3.364 + Log[ecm^2])^2

  35. Fitting ALICE INEL>0 pp data At √sNN=900 GeV: p0=2.0, 2.5, 3.0, 3.5, 4.0, 4.5, 5.0 GeV/c At √sNN=2360 GeV: p0=2.5, 3.0, 3.5, 4.0, 4.5, 5.0, 5.5 GeV/c At √sNN=7 TeV: p0=3.0, 3.5, 4.0, 4.5, 5.0, 5.5, 6.0 GeV/c

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