A Multi-Phase Transport Modelfor High Energy Heavy Ion Collisions

NSSTC Marshall Space Flight Center August 7, 2003

Zi-wei LinThe Ohio State University

in collaboration with C.M. Ko (TAMU), Bao-An Li (ASU),

Subrata Pal (MSU) and Bin Zhang (ASU)

Outline

Why do we need a transport model?

Structure of a multi-phase transport (AMPT) model

Selected results at high energies from AMPT

Summary

1

Major Experiments

High Energy Heavy IonMachines s (AGeV) Main Beam

CERN-SPS (past) 8-17 Pb+PbBNL-RHIC (now) ~20-200 Au+AuCERN-LHC (future) up to 5500 Pb+Pb

RHIC (Relativistic Heavy Ion Collider) at Brookhaven National Laboratory

Au+Au collisions up to 200AGeV

~ 2.5 6 20 GeV/fm3SPS RHIC200 LHC

>>critical energy densityfor QCD phase transitionproper formation

time, take 1fm/c

High energy density/temperature ~ universe 1ms after the Big Bang

Study properties of high density partonic and hadronic matter

How high is the initial energy density?

nuclear radius

A general modelfor high energy heavy ion collisions

needs:

●Initial condition for particle and energy production

●Parton stage with EoS

●hadronization/phase transition

●hadronic interactions

some options:

soft+hard model, saturation models, ...

parton cascade, hydrodynamics, ...

string fragmentation, coalescence, statistical hadronization, ...

hadron cascade (ART, RQMD, ...)

A Multi-Phase Transport (AMPT) model includes the above green ingredients

Advantages of a transport model

Can address dynamics at non-equilibrium Chemical and kinetic freezeouts are generated self-consistently

Allows numerical studies beyond limits of analytical methods

Can learn about details of the evolution of many-body systems

HIJING (Heavy Ion Jet Interaction Generator) minijet partons(hard)

+strings(soft)

ZPC (Zhang's Parton Cascade)

Lund fragmentation to hadrons

ART (A Relativistic Transport model for hadrons)

A+B

Strong-decay all resonances for final particle spectra

Structure of AMPT model Zhang et al, PRC61, PRC65;

Lin et al, PRC64, NPA698,

PRC65, PRL89.

Wang&Gyulassy, PRD43,44,45

Zhang, CompPhysComm82

Li&Ko, PRC52

Parton freezeout

Generate parton space-time

Main Ingredients

HIJING version 1.383

ZPC 2-2 parton processes: gg-gg, gg-qqbar, gq-gq, ...

Hadronization Lund string fragmentation/quark coalescence

ART hadron interactions including:

Parton Cascade

To study dynamics of strong interactions in a QCD matter.

The equation of motion may be written as

For 2-2 interacitons:ZPC (Zhang's Parton Cascade) solves theseBoltzmann equations by the cascade method:

2 particles scatter if their distance <

Parton cross sections

From leading-order QCD:

Use a medium-generated screening mass to regulate the divergence:

Causality violation and a solution

●Causality problem:Classical cascade breaks down when Mean-Free-Path < Interaction length

•A solution: particle subdivision

unchanged

Zhang,Gyulassy&Pang, PRC58

Lund String Fragmentation

Assume:production positions at a constant proper time,left-right symmetry (ordering of Vn just represent different Lorentz frames)

Lund symmetric splitting function

Andersson et al,

PhysRep 97; ZPC20

percentage of light-cone momentum of the produced parton

The Schwinger Mechanism: •particle production from an external field via tunneling

Potential energy=

•Production probability

•Strangeness suppression:~0.3

the string tension

The Schwinger Mechanism Lund String Model

Mean Momentum square:

Hadron Cascade

Based on ART Li&Ko, PRC52

Kbar interactions added Song,Li&Ko, NPA646

NNbar annhilation, K0 productions Zhang et al, PRC61

BBbar-mesons, explicit K*, Lin et al, PRC64, NPA698

interactions Lin&Ko,PRC65Lin,Ko&Pal, PRL89

Multi-strange () interactions Pal,Ko&Lin, nucl/0106073

interactions Pal,Ko&Lin, NPA707

Meson-Meson channels

SU(2):

with strangeness:

Example: meson cross sections Pal,Ko&Lin, NPA707

Meson-Baryon channels

Example: K- baryon cross sections Pal,Ko&Lin, nucl/0106073

Pion multiplicity distribution from ppbar annihilation:

Ko&Yuan, PLB192

Baryon-AntiBaryon channels

Baryon-Baryon channels

Example:

130AGeV Central AuAu Event from AMPT

In default HIJING, a=0.5, b=0.9/GeV2

need changes:a=2.2, b=0.5/GeV2

a&b in the Lund splitting function:

~same

Lin et al, PRC64, NPA698

SPS: Pb+Pb collisions at 17AGeV

m spectra at SPS

Final-state rescatteringsin AMPT modelincrease mslopeof heavy particles

Lin et al, NPA698

Results at RHIC Energies (b=0-3fm Au+Au)

Lin et al, PRC64,

NPA698

Particle yields and ratio: energy dependence

Rapid increase for pbar/p,

baryon-antibaryon symmetric ~ early universe

Lin et al, PRC64

BRAHMS, PLB523

AMPT versus RHIC data:Pseudo-rapidity distribution at 130AGeV

AMPT versus RHIC data:Ratios of 200AGeV/130AGeV:

BRAHMS, PRL88

AMPT

QCD saturation model

More Studies with AMPT

Azimuthal momentum asymmetry Lin&Ko,PRC65

Multi-strange baryon () enhancement Pal,Ko&Lin, nucl/0106073

meson puzzle Pal,Ko&Lin, NPA707

J/ production/suppression Zhang et al, PRC62, PRC65

- interferometry/HBT Lin,Ko&Pal, PRL89

A Multi-Phase Transport (AMPT) model

is constructed for high energy heavy ion collisions

including both partonic and hadronic interactions

Hadronic/partonic interactions are important

for particle multiplicities and momentum spectra

AMPT model provides a valuable tool to study heavy ion collisions

Summary

Slides of this talk available at http://nt3.phys.columbia.edu/people/zlin/PUBLICATIONS