Partonic Cascade and Hadronic Evolution Dynamics in AMPT

CCAST Summer School August 24-27 2002 Beijing 林子威

Partonic Cascade and Hadronic Evolution Dynamics

in AMPT

林子威 (Zi-wei Lin)Texas A&M University

in collaboration with C.M. Ko, Bao-An Li, Subrata Pal, and Bin Zhang

AMPT: A Multi-Phase TransportBased on following references:nucl-th/9904075; PRC61, 067901(00); PRC62, 054905(00);PRC64, 011902(01); NPA698, 375c(02); nucl-th/0106073; PRC65, 034904 (02); PRC65, 054909(02); NPA707, 525(02);nucl-th/0204054(PRL in press)


Our GoalRelativistic Heavy Ion Collisions:

machines sqrt(s) (AGeV) main HI beamCERN-SPS (past) 8-17 PbPbBNL-RHIC (now) ~20-200 AuAuCERN-LHC (future) up to 5500 PbPb

study properties of partonic and hadronic matter,especially non-equilibrium and dynamical properties,

systematic studies including pp and pA.


Media coverage on RHIC (QM’01)


Theorists were thinking (QM01)…


Lots of new data (QM02)


Theorists are still thinking (QM02)…


Theorists are also talking to experimentalists…


OutlineWhy do we need a transport model?

What need to be included in such a model?Current Structure of AMPTInitial conditionParton cascade

Hadronization / phase transitionHadron cascade

Tests at SPS energyResults at RHIC energiesdN/dy, mt spectra, centrality dependence

J/psi, elliptic flow, high Pt

HBTOutstanding Problems Summary

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Section I


Why transport model?

Formation of partonic matter:

~ 2.5 6 20 GeV/fm3SPS RHIC200 LHC

>>QCD critical energy densitytake 1fm

The parton or hadron matter may not be in local thermal equilibrium:need to solve field equations or Boltzmann equations, instead of hydrodynamics

transport modelQuantum transport:Boedecker at QM02Freezeout in transport: BleicherParton cascade model: Bass


A general model for RHIC

needs:

Initial condition for particle and energy production

Parton stage with EoS

hadronization/phase transition

hadronic interactions

some options:

soft+hard model, color glass condensate, final-state saturation, ...

parton cascade, hydro, field equations

coalescence, string fragmentation, statistical hadronization, ...

hadron cascade (ART, RQMD, ...)

AMPT is a multi-phase transport, including the above ingredients in green


HIJING energy in strings(soft)+minijet partons(hard)

ZPC (Zhang's Parton Cascade)

Lund fragmentation to hadrons

ART (A Relativistic Transport model for hadrons)

A+A

Strong-decay all resonancesfor final particle spectra

Structure of Default AMPT Zhang et al, PRC61;Lin et al, PRC64, NPA698.

Wang&Gyulassy, PRD43,44,45

Zhang, CompPhysComm82

Li&Ko, PRC52

Jet quechingreplaced by parton cascade

Parton freezeout

Generate parton space-time


Main Ingredients of AMPT

HIJING default version 1.36

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

ART hadron interactions including

included interactions:meson-meson: pi pi - rho, pi pi - K Kbar, ...meson-baryon: pi Lamba-Kbar N, ...baryon-baryon: N N - N Delta, ...baryon-antibaryon: rho rho - N Nbar, ...


Key Parameters of AMPT

A+A Parton Distribution Function (PDF), nuclear shadowing (gA(x,Q2), qA(x,Q2))

HIJING lower Pt cutoff for minijet (p0)

ZPC initial parton space-time distribution (tau0_p, z0, ...)screening mass for parton cross section (mu: sigma_p)

ART hadron formation time (tau0_h)cross sections of hadron interactions (sigma, ...)take care of detailed balance


Initial condition from HIJINGHIJING: a 2-component (soft+hard) model + nuclear geometry

LUND string pQCD minijets Woods-Saxon

Eikonal formulism for cross sections:

Overlap function

Probability for minijet production:

Take dipole form factor and assume


HIJING fit to pp/ppbar dataDetermine 2 parameters: (lower Pt cutoff for minijets)

Wang, PRD43

P0: independent of colliding energy


Gluon PDF in HIJING

Used in HIJING: too few small-x partons

For minijets at RHIC:XBj ~2/100 ~0.02sizeable effects


Nuclear shadowing in HIJING

Wang&Gyulassy, PRD44

Assumed the same for g & q;no Q2 dependence


Other shadowing parametrizations

Eskola et al, hep-ph/0110348

Different for g & q;strong Q2 dependence

PDF & shadowing: Qiu at QM02


Recent update of PDF and shadowing in HIJING: Li&Wang, PLB527

GRV used for structure function;new shadowing parametrizationdifferent for g & q:

now depends on colliding energy:~1.7 GeV at SPS~3.5 GeV at LHC.


Initial condition from final-state saturation model

Geometrical saturation: when produced midrapidity partons occupies the whole transverse plane

RA

Simple estimate:

Saturation momentum scale

Eskola et al, NPB570Tuominen at QM02


Final-state saturation modelEskola et al, NPB570

Put in PDF and shadowing:


Initial condition from initial-state saturation model

McLerran & Venugopalan, PRD49QCD: Mueller at QM02; Initial-State Saturation:Iancu, Kharzeev, Kovchegov, Krasnitz at QM02

Considers valence quarks in fast A as frozen and random color charges,produce classical Yang-Mills field for gluons:

Compared to saturation model F:

Differ by alpha_s and constant,but similar A & s dependence


Parton Cascadeto study strong interactions of QCD matter.

Final-state parton interactions can be described byparton Wigner operators:

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 <

Zhang, Comp.Phys.Comm.109;Zhang,Gyulassy&Pang, PRC58


Parton cross sectionsFrom leading-order QCD:

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

In ZPC, make total cross section s-independent:


Screening mass muNear equilibrium:

Gluon spectrum: dN/dy/d2KT

For exponential KT spectra with boost-invariance:

Estimate:

Screening mass will be taken as ~ several/fm


Parton processes and subdivisionZPC only includes 2-2 processes:

Right now, only and other elastic processes

To be added later:

Hard to implement:

Particle subdivision to cure causality problem:Classical cascade breaks down when Mean-Free-Path < Interaction length

Subdivide:

is not changed

Zhang,Gyulassy&Pang, PRC58








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Section II


Hadronization

A pp collision in the string picture:

P1 P2 after momentum transfer P2' P1'Invariant mass Mp Mp >Mp

particle production

P1': quark+diquark with large invariant mass,a color singlet system confined by a linear potential

string tension: ~1GeV/fm


Schwinger Mechanism: particle production from an external field via tunneling

Potential energy=

Production probability

Strangeness suppression:0.3 as default value


Lund FragmentationAssume: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 produced parton


Schwinger vs Lund Model

Mean Momentum square:

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


Default hadronization of AMPT

string1'+minijet1string2'+minijet2

HIJING produces string3independent minijets.....proj & targ spectators

ZPC

string1'+minijet1'=string1string2'+minijet2'=string2string3independent minijets'.....proj & targ spectators

apply Lund string fragmentation

these have no actions in parton stageminijet1 -minijet1' recombine with the original string1'

Zhang et al, PRC61;Lin et al, PRC64, NPA698


Modified AMPT model: string meltingLin&Ko, PRC65;Lin,Ko&Pal, nucl-th/0204054(PRL in press)

Initial energy in default AMPT:soft (strings) & hard (minijets)

In high density overlap areabut not in parton cascade


Initial energy density from minijet partons >> 1 GeV/fm^3critical energy density for QCD phase transition

strings will not exist, need to be converted into partons (or color field)

this is why most transport models underpredict v2 at RHIC,since 2/3 of energy in strings (outside of parton cascade),

lack of early pressure

Zhang et al, PRC62

QCD phase diagram: Kanaya, Fodor at QM02


String Melting converts strings at high density to partons at RHIC energies:

Initial conditions:excited strings (Lund-)fragment to hadrons, then

according to valence quark structure

Proj & targ spectators remain nucleons


Parton colescence after string meltingNearest partons form a hadron:

find closest qbar form a meson mfind closest q2 & q3 form a baryon B

Determine Flavor, examples:ubar d: form pi- if invariant mass is closer to Mpi

form rho- to Mrhoubar u: lowest masses form pi0, #=(pi+&pi-) average;

then randomly form rho0, #=(rho+&rho-) average;then form omega & eta with equal probability

Most hadrons in PYTHIA are included:


HIJINGenergy in strings and minijet partons

ZPC (Zhang's Parton Cascade)

Till Parton freezeout

ART (A Relativistic Transport model for hadrons)

A+A

Structure of AMPT model with String Melting

Fragment excited strings into partons

Nearest partonscoalesce into hadrons

Strong-decay all resonances for final particle spectra


Coalescence in ALCORBiro et al, PLB347;Biro, hep-ph/0005067; Zimanyi et al,Heavy Ion Phys4,15;PLB472, hep-ph/0103156

ALgebraic COalescence Rehadronization model

Near hadronization, gluon may decouple (decayed or absorbed), thus consider only constituent q+qbar:

2Nf normalization factors, determined from 2Nf equations for quark # conservation:

coalescence factor


coalescence factors:

For mesons bound in a Coulomb-like potential:

Bohr radius for

momentum of q in CMS

Debye screening length

spin-degeneracy

Assume baryons created in 2-steps:

baryon supression factor


Hadron CascadeBased on ART Li&Ko, PRC52

Kbar channels added Song,Li&Ko, NPA646

NNbar annhilation, K0 productions Zhang et al, PRC61

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

eta channels Lin&Ko,PRC65Lin,Ko&Pal, nucl-th/0204054(PRL in press)

multistrange channels Pal,Ko&Lin, nucl/0106073

phi interactions Pal,Ko&Lin, NPA707

Include


Meson-Meson channels

SU(2):

with strangeness:


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


Meson-Baryon channels

Note: detail balance, charge conjugation, crossing symmetry


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


Baryon-Baryon channels

Examples: pp inelastic cross sections

Li&Ko, PRC52


Pion multiplicity distribution from ppbar annihilation:

Ko&Yuan, PLB192

Assumed:

Baryon-AntiBaryon channels


Example:








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,Section III


Time evolution of a RHIC event at 130G

10 20 25 30 fm/c

2 4 6 8

Tt= 0.4 0.6 0.8 1.0

Animation at http://nt3.phys.columbia.edu/people/zlin/ZLIN/publication.html


130AGeV Central AuAu Event from AMPT


Rapidity shift due tomodification to LUND fragmentation:

MSTJ(11)=3 instead of 1 to allow diquark split according to popcorn scheme.

Zhang et al, nucl-th/9904075

Tests at SPS EnergiesNetBaryon Stopping


Defaults HIJING:

Popcorn scheme:

for a q-qbar string:

BBbar

BMBbar


Schematic Representation for Baryon Number Transport Dynamics

Di-quark and quark Fragmentation Leading baryon + meson

Three quark Fragmentation Leading baryon + meson + meson

Gluon Junction Fragmentation Leading meson + meson + meson and a Baryon

From H. Huang

Popcorn scheme in AMPT:diquark allowed to split

normal

BBbar

BMBbar


Rapidity shift due topopcorn scheme.

pbar yield decreases from HIJING due to moreannihilation than production(annihilation alone gives too low)

P and Pbar rapidity spectra at SPS

Lin et al, PRC64


After hadron scattering

Net baryon: same Net p: large increase

isospin equilibration


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

changed toa=2.2, b=0.5/GeV2

a&b in the Lund splitting function:

~same

Lin et al, PRC64


m spectra at SPS

Final-state rescatteringsincrease mslopeof heavy particles

Lin et al, NPA698


Results at RHIC Energies

Lin et al, PRC64


Yield and ratio: energy dependence

Rapid increase for pbar/p.(p+pbar is not small)

Lin et al, PRC64


Quenching and Shadowing on dN/dy at 130A GeV (def.)

No shadowing is inconsistent with data.

Lin et al, NPA698


Hadronic scattering effects on dN/dy at 130A GeV (def.)


BRAHMS, PLB523Pseudo-rapidity distribution at 130AGeV


Ratios of 200G/130G: BRAHMS, PRL88

AMPT

Saturation (Kharzeev&Levin)


Rapidity spectra at RHIC P/Pbar Ratio


p ~ at PT~2 GeV mainly due to hadronic scatterings


p ~ at PT~2 GeV

130G b=0-3 fm


Centrality dependence of Nch , Et and <Et> near =0

Npart


centrality dependence from other models

PHOBOS, PRC65

Kharzeev&Nardi, PLB507Kharzeev&Levin, PLB523


centrality dependence from other models








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J/psi production at RHIC from AMPT

t

parton density from AMPT Radius (J/psi dissolved insidedue to color screening)

color Debye-screening

Zhang et al, PRC62

Color deconfinement: Satz at QM02


parton phase: production and annihilation

Zhang et al, PRC65


hadron phase: production and annihilation


J/psi yield dependence on charm mass


Other models for J/psi yields at RHIC

Andronic at QM02, also see Kostyuk at QM02

1) Statistical model:relative chemical equilibriumbetween open charm and J/psi:

Overiew of statistical model: Bialas, Rafelski & Koch at QM02Thermal model: Cleymans, Becattini, Tounsi at QM02


2) Statistical model+ Multiphase Suppression:

Grandchamp at QM02

detailed balance?

Prel data on open charm& J/psi at RHIC available now to constrain models


J/psi cross section with mesons

3 Kharzeev-Satz

2b Lin-Ko

1a Martins et al.

1b Wong et al.

2a Haglin

Gossiaux, Lin & Wong, discussion on comovers at QM02

1) Quark-exchange models ~= 2) Meson-exchange models >> 3) pQCD model

affects interpretation of SPS data &production in hadron phase at RHIC


Definitions:

X

YAzimuthal asymmetry

in momentum:

in space: According to positionsat previous scatterings

Elliptic FlowFlow summary: Voloshin at QM02


Ackermann et al, PRL86

Snellings, NPA698

STAR data vs Hydro model

Are we near hydro limit at RHIC? How and when does hydro break down?

Hydro flow: Huovinen at QM02viscosity correction of hydro: Teaney at QM022d hydro on v2: Heinz at QM02


Inside the parton cascade ZPC:

At present:partonic 2-2 elastic processes: abab Cross section:

controled by 3.2/fm3 mb

Zhang, CompPhysComm82


Dependence on parton (130 GeV Au+Au, b=8 fm):

3 mb 6 mb

Lin&Ko, PRC65


Centrality dependence of v2 at 130A GeV:


PT dependence of v2 at 130A GeV: eta (-1.3, 1.3), minimum bias (b=0-13fm)


v2 at large PT: eta (-1.3, 0.3), minimum bias

However, needsx50 statistics to reach 4 GeV


v2 for different particles: compare with data


200A GeV: centrality dependence of v2

Small increase(<1%) with energy


200A GeV: PT dependence of v2 eta (-1.3, 0.3), minimum bias

Lin&Ko, PRC65


Pion PT spectra


With string melting:

large suppression at high pT, similar to jet quenching?

mT slope sensitive to parton cross section

MT spectra vs

Jet quenching: Baier, Salgado, Sarcevic, Vitev,Wang, Wang at QM02








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HBT method Hanbury-Brown Twiss effect

measured star size from photon interferometrysince identical particles interfere

Observed experimentally in particle physicsfirst by Goldhaber et al, PR120

For nuclear collisions, theorists predicts its sensitivity toExpansion velocitySource sizephase transition to QGPSoftest point in EOS

Measured extensively in heavy ion collisionsreasonably described by models (hydro,transport)

RHIC

Hanbury Brown&Twiss,Nature(London)178

Pratt,PRL53Bertsch et al,PRC37Pratt et al,PRC42Rischke&Gyulassy,NPA608......


From http://www.pa.msu.edu/~bauer

Some Definitions

in the Pratt-Bertsch out-side-long system Pratt, PRD33; Pratt et al,PRC42 Bertsch et al,PRC37

qi(1-3)=Qout, Qside, Qlong => Rout, Rside, Rlong

=> Rinv

K

2


Pion HBT data at RHIC 130AGeV

STAR, PRL87

4-parameter Gaussian fit to C(q) w/o Coulomb effects:

2


Pion HBT data vs Hydro Model (130AGeV)

Rout/Rside<1

Small radii

Small duration time dt(extracted)

from S. Johnson at RWW02

Hydro parameterization with high opacity Tomasik&Heinz,nucl-th/9805016

HBT summary, Pratt at QM02Failure of hydro: SoffDynamic freezeout: Tomasiknon-central HBT: Kolb3d hydro: Hirano


Some Definitions:

in the Pratt-Bertsch out-side-long system

qi(1-3)=Qout, Qside, Qlong => Rout, Rside, Rlong

=> Rinv

Pratt, PRD33; Pratt et al, PRC42;Bertsch et al, PRC37


Radii fromEmission function S and correlation function C

If source is Gaussian in space-time, then:

And R0ij= Rij

1) Curvature at q=0: 2) Often use 4-parameter fitfor C(q) w/o Coulomb effects:

Pratt,PRL84

Pratt,PRL84Wiedemann,PRC57

Dx,y=<x*y>-<x><y>

. ___ 2


1) From emission function (10mb) for midrapidity charged pions, central 130AGeV:


- correlation function (w/o Coulomb effects):data corrected for Coulomb effects


2) From Gaussian fits to 3-d correlation functionC(Q) in LCMS frame (pz1+pz2=0) obtained from CRAB Pratt, NPA566


Compare: source radii and fitted radii

Lin,Ko&Pal,nucl-th/0204054(PRL in press)


Ratio from source

> ratio from fit (~=1)


Correlations in emission source: out-side out-t

for midrapidity pions, 125<pt<225 MeV/c

<Xout (t)>

Positive and large, reduces Rout

Values: (17fm)**2 = 185 -2*168 + 431

SourceSpatial-size x-t correlation Duration time

Lin,Ko&Pal,nucl-th/0204054(PRL in press)


Compare to - data (not corrected for Coulomb):

Self-consistent: theory `knows’ the distance for Coulomb corrections


mT dependence of fitted radii (10mb):


MT-scaling for fitted R

Kaon source radii~fitted radii

10 mb results


Outstanding Problems

The Bottom Linewe do not (yet) have one consistent model for all observables

on phenomenology:Good Bad or even Ugly

Default AMPT: dN/dy, mt, Baryon stopping v2, HBT

AMPT w. string melting: dN/dy(meson), v2, HBT dN/dy(Baryon)mt of pions mt of heavier hadrons

on theoretical foundation:coherent/multi-particle interaction at high densitiesAA->QGP: creation of partonic matter (now modeled by string melting)parton->hadron phase transition (now modeled by coalescence)...


Example: dN/dy with String Melting,problem for baryons (3-quark coalescence)


A transport model is constructed for SPS,RHIC and above,

a tool to study most aspects of high-energy heavy ion collisions:

2-component model (soft+hard) for initial energy production

parton cascade with 2-2 interactions

parton-to-hadron phase transition (Lund model or coalescence)

hadron cascade with extensive interactions

Summary


default AMPT model

(conservative model with only minijets in parton cascade):

well describes dN/dy and centrality dependence, mt spectra, and baryon stopping

but fails in elliptic flow and HBT

AMPT model extended with string melting

(model with all produced energy, excited strings+minijets, in parton cascade):

many more partons: more early interactions

elliptic flow sensitive to parton cross section

HBT sensitive to parton dynamics (cross section, or phase transition density)

but fails in dN/dy of baryons and mt of heavy hadrons

Summary


1) String melting to describe initial condition of partons

Model breaking of color-singlet strings in strong color field,

and gluon production

2) Parton elastic collisions ab ab

Include parton inelastic processes (ggqqbar, gqgq, ...)

3) Naïve parton cascade even with large cross section

parton subdivision to avoid causality violation (interaction at a

distance)

Current treatment vs future improvement

Further improvement of AMPT


4) Partonic matter with current quark mass

changing quark mass with temperature, or include color field (better EoS)

5) Coalescence when partons reach kinetic freezeout in parton cascade

phase transition density ~1/p

Coalescence when local energy density < a critical value

6) Coalescence of quarks with current mass

Coalescence of quarks with constituent mass

& treat the problem of Goldstone-boson mass

or a more general hadronization (thermal emission, ...)

Current treatment vs future improvement


Last words but not least

Dilepton, photons, fluctuations, lattice QCD &color superconductivity are not covered in this talk. Please refer to Quark Matter '02 at http://alice-france.in2p3.fr/qm2002/

Some figures from AMPT shown here may have come from earlier calculations, thus subject to changes

Coming soon:AMPT source code will be available online,for all users, with a detailed writeup

Partonic Cascade and Hadronic Evolution Dynamics in AMPT

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