Zi-Wei Lin (ECU) 28th WWND, Puerto Rico April 10, Update of Initial Conditions in A Multiple Phase Transport (AMPT) Model Zi-Wei Lin Department of Physics East Carolina University Greenville, NC Work still in progress

Zi-Wei Lin (ECU) 28th WWND, Puerto Rico April 10, Outline Present status of the AMPT model Need to update the initial conditions Optimize parameters/functions by fitting dN ch /dη data Outlook Summary

Zi-Wei Lin (ECU) 28th WWND, Puerto Rico April 10, What do we need for simulations of high energy heavy ion collisions? We need: Initial particle/energy production Parton interactions/ equation-of-state Hadronization /QCD phase transition Hadron interactions 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, … 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

Zi-Wei Lin (ECU) 28th WWND, Puerto Rico April 10, ZPC (Zhang's Parton Cascade) ART (A Relativistic Transport model for hadrons) 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 model) Partons freeze out HIJING (PDFs, nuclear shadowing): minijet partons, excited strings, spectators Less partonic interaction Dominated by hadronic interactions (at very high densities)

Zi-Wei Lin (ECU) 28th WWND, Puerto Rico April 10, A+B Final particle spectra Hadronization (Quark Coalescence) Structure of AMPT v2.xx (String Melting model) HIJING (PDFs, nuclear shadowing): minijet partons, excited strings, spectators ART (A Relativistic Transport model for hadrons) Partons freeze out ZPC (Zhang's Parton Cascade) Partonic interactions dominate. Better describes flow & HBT, but does not describe well single particle spectra Melt to q & qbar via intermediate hadrons Hadrons freeze out (at a global cut-off time); strong-decay all remaining resonances

Zi-Wei Lin (ECU) 28th WWND, Puerto Rico April 10, AMPT Source Codes First public release of AMPT codes: ~ April Detailed physics descriptions in Lin, Ko, Li, Zhang & Pal, PRC 72, (2005). Versions v1.21/v2.21 (2008) and v1.11/v2.11 (2004) are available at 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)

Zi-Wei Lin (ECU) 28th WWND, Puerto Rico April 10, looks like thisthis

Zi-Wei Lin (ECU) 28th WWND, Puerto Rico April 10, A+B Update Initial Conditions of AMPT HIJING (PDFs, nuclear shadowing): minijet partons, excited strings, spectators Final particle spectra

Zi-Wei Lin (ECU) 28th WWND, Puerto Rico April 10, 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 p 0 (√s NN ) & σ soft (√s NN ); new parameters for quark and gluon nuclear shadowing functions are used to reproduce dN ch /dη in AA collisions. In AMPT: Pal & Bleicher, PLB 709 (2012) used HIJING2.0 as initial conditions,  smaller value for the gluon shadowing parameter s g is needed to reproduce dN ch /dη in AA collisions at LHC, since rescatterings considerably reduce hadron yields at mid-rapidity

Zi-Wei Lin (ECU) 28th WWND, Puerto Rico April 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).

Zi-Wei Lin (ECU) 28th WWND, Puerto Rico April 10, ) Need to Use up-to-date parton distribution functions Duke-Owens Set 1 (1984) used in HIJING1.0 & AMPT significantly under-estimates the gluon density at small-x It is essential to use up-to-date PDF for LHC & for heavy flavors (since ~all come from gluons) LHC RHIC For this study, we have incorporated into AMPT the CTEQ6M PDF

Zi-Wei Lin (ECU) 28th WWND, Puerto Rico April 10, ) Need to use up-to-date nuclear shadowing functions R A (x) PDF in a nucleus ≠ PDF in a nucleon *A Central Pb+Pb collisions at √s NN =5.5 TeV from default AMPT v1.11: shadowing has a large effect Deng, Wang and Xu, PLB 701 (2011) For this study, we have incorporated into AMPT the EPS09 nuclear shadowing

Zi-Wei Lin (ECU) 28th WWND, Puerto Rico April 10, We follow the following strategy similar to Deng, Wang and Xu, PRC 83 (2011): At each collision energy √s NN : choose different p 0 values for each p 0, determine the σ soft value that reproduces the experimental σ pp total run AMPT for each (p 0, σ soft ) set, then compare with dN ch /dη data to find the best (p 0, σ soft ) value. Optimize parameters by fitting dN ch /dη data with the default AMPT model (+CTEQ6M & EPS09) The nucleon-nucleon cross section in the eikonal approximation: In AMPT/HIJING1.0: p 0 =2.0 GeV/c, σ soft ≈57 mb. Go through all relevant collision energies:  p 0 (√s NN ) & σ soft (√s NN )

Zi-Wei Lin (ECU) 28th WWND, Puerto Rico April 10, Example of the (p 0, σ soft ) sets √s NN =200 GeV √s NN =7 TeV from PDG

Zi-Wei Lin (ECU) 28th WWND, Puerto Rico April 10, At √s NN =19.6 GeV: p 0 =1.0, 1.2, 1.4, 1.6, 1.8 GeV/c. … At √s NN =200 GeV: p 0 =2.0, 2.2, 2.4, 2.6 GeV/c. … At √s NN =7 TeV: p 0 =3.0, 3.5, 4.0, 4.5, 5.0, 5.5, 6.0 GeV/c. Higher p 0 gives lower dN ch /dη (except for the lowest energy √s NN =19.6 GeV) AMPT results for different (p 0, σ soft ) sets vs pp inelastic data

Zi-Wei Lin (ECU) 28th WWND, Puerto Rico April 10, Fit p 0 to inelastic pp data at different energies √s NN =200 GeV dN ch /dη (|η|<0.5) INEL =2.22 ±0.05  p 0 = GeV/c using AMPT results with interpolation √s NN =2360 GeV dN ch /dη (|η|<0.5) INEL =  p 0 = GeV/c

Zi-Wei Lin (ECU) 28th WWND, Puerto Rico April 10, p 0 values fitted to inelastic pp data p 0 (√s NN ) increases with collision energy, related to more partons at small-x in the new PDF

Zi-Wei Lin (ECU) 28th WWND, Puerto Rico April 10, Fit p 0 to central AA data at different energies after incorporating EPS09 shadowing functions in AMPT

Zi-Wei Lin (ECU) 28th WWND, Puerto Rico April 10, AuAu at √s NN =19.6 GeV: p 0 =1.2, 1.4, 1.6, 1.8 GeV/c. … AuAu at √s NN =200 GeV: p 0 =2.0, 2.2, 2.3, 2.4, 2.6 GeV/c. PbPb at √s NN =2760 GeV: p 0 =3.5, 4.0, 4.5 GeV/c. Higher p 0 gives lower dN ch /dη/(N part /2) AMPT results for different (p 0, σ soft ) sets vs central AA data

Zi-Wei Lin (ECU) 28th WWND, Puerto Rico April 10, p 0 (√s NN ) fitted to pp data and to AA data are not consistent  This test of the PDF+shadowing update cannot systematically describe dN ch /dη of pp & AA collisions throughout this energy range Fitted p 0 values combined

Zi-Wei Lin (ECU) 28th WWND, Puerto Rico April 10, Search for consistent p 0 (√s NN ) from fits to pp data and to AA data Possibilities include: 1) a & b parameters in Lund string fragmentation: a=0.3 & b=0.8/GeV 2 are used in this study, this is one set of the 2009 fit values in PYTHIA 8.1; we can explore the a-b parameter space: e.g. PYTHIA have used a=0.76, b=0.58/GeV 2 (2007 fit values), and used a=0.30, b=0.58/GeV 2 before. 2) Alternative nuclear shadowing. Outlook

Zi-Wei Lin (ECU) 28th WWND, Puerto Rico April 10, 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 p 0 (√s NN ) & σ soft (√s NN ) from fits to pp dN ch /dη data and fits to central AA data are not consistent We will investigate Lund a,b parameters and alternative nuclear shadowing functions to obtain consistent p 0 (√s NN ) & σ soft (√s NN ) from fits to pp and AA data; that would allow systematic descriptions of dN ch /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 Summary

Zi-Wei Lin (ECU) 28th WWND, Puerto Rico April 10, Thank you!

Zi-Wei Lin (ECU) 28th WWND, Puerto Rico April 10, Backup Slides

Zi-Wei Lin (ECU) 28th WWND, Puerto Rico April 10, amptsub.f art1f.f hijing1.383_ampt.f hipyset1.35.f linana.f main.f zpc.f input.ampt Files in the Source Code include Fortran routines EPS09 shadowing function table for Au and Pb nucleus Input parameter values Update of initial conditions introduces new input data files: cteq6m.tbl EPS09LOR_197 EPS09LOR_208 CTEQ6M PDF table

Zi-Wei Lin (ECU) 28th WWND, Puerto Rico April 10, HIJINGsoft strings + hard minijets ZPC2↔2 parton cascade: gg↔gg, gg↔qqbar, gq↔gq,... HadronizationLund string fragmentation or quark coalescence ARThadron cascade including: Main Ingredients

Zi-Wei Lin (ECU) 28th WWND, Puerto Rico April 10, 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 test version v1.23/v2.23: Included a subroutine to enable users to insert user-defined hadrons before the start of the hadron cascade Earlier modifications in the AMPT source code

Zi-Wei Lin (ECU) 28th WWND, Puerto Rico April 10, /2009 test version v1.25t1/v2.25t1: Added an option of event selection so that each event will have at least 1 minijet 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 and after the parton cascade and the full parton collision history for 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 test version v1.25t4/v2.25t5: Included the finite widths of resonances (K* η ρ ω Φ Δ) when they are produced from quark coalescence in the string melting version 2/2012 test version v1.25t7b/v2.25t7b: Added option to enable random orientation of reaction plane Recent modifications in the AMPT source code

Zi-Wei Lin (ECU) 28th WWND, Puerto Rico April 10, amptsub.f art1f.f hijing1.383_ampt.f hipyset1.35.f linana.f main.f zpc.f README Makefile exec input.ampt ana/ Files in the Source Code include 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:

Zi-Wei Lin (ECU) 28th WWND, Puerto Rico April 10, Parameters in input.ampt: New options in red 200. ! EFRM (sqrt(S_NN) in GeV) CMS ! FRAME A ! PROJ A ! TARG 197 ! 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 below 0.2! DT: timestep in fm (hadron cascade time= DT*NTMAX) (D=0.2) 2.2! PARJ(41): parameter a in Lund symmetric splitting function 0.5 ! PARJ(42): parameter b in Lund symmetric splitting function 1! (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=1 2.0! p0 cutoff in HIJING for minijet productions (D=2.0) d0! parton screening mass in fm^(-1) (D=3.2264d0), see below 0! IZPC: (D=0 forward-angle parton scatterings; 100,isotropic) d0! alpha in parton cascade 1d6! dpcoal in GeV 1d6! drcoal in fm 0! ihjsed: take HIJING seed from below (D=0)or at runtime(11) ! random seed for HIJING 8! random seed for parton cascade 0! 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

Zi-Wei Lin (ECU) 28th WWND, Puerto Rico April 10, Output files ampt.dat Event# Test# Particle# b(fm)Npart1 Npart2 Particle ID (PYTHIA) Final momentum mass Final position & time (at kinetic freeze-out) zpc.dat Final momentum, position & time of all partons (at kinetic freeze-out)

Zi-Wei Lin (ECU) 28th WWND, Puerto Rico April 10, 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

Zi-Wei Lin (ECU) 28th WWND, Puerto Rico April 10,  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 σ p ; Need to improve Parton coalescence for better EoS; hadronization condition (~HBT) & parton cross section (~v2) will be decoupled Needs to Further Develop AMPT  Need to use up-to-date Parton Distribution Functions in nuclei: essential for heavy flavors & LHC  Inelastic partonic interactions  Including color fields in parton phase.

Zi-Wei Lin (ECU) 28th WWND, Puerto Rico April 10, RRPL2u (19) model predictions of sigma_total for pp collisions (ecm==sqrt_s>=5GeV): sigma_total= /((ecm^2)^0.5453) /((ecm^2)^0.4581) *( Log[ecm^2])^2

Zi-Wei Lin (ECU) 28th WWND, Puerto Rico April 10, At √s NN =900 GeV: p 0 =2.0, 2.5, 3.0, 3.5, 4.0, 4.5, 5.0 GeV/c At √s NN =2360 GeV: p 0 =2.5, 3.0, 3.5, 4.0, 4.5, 5.0, 5.5 GeV/c At √s NN =7 TeV: p 0 =3.0, 3.5, 4.0, 4.5, 5.0, 5.5, 6.0 GeV/c Fitting ALICE INEL>0 pp data

Zi-Wei Lin (ECU) 28th WWND, Puerto Rico April 10,