Post on 11-Jan-2016
description
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)
CCAST Summer School August 24-27 2002 Beijing 林子威
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.
CCAST Summer School August 24-27 2002 Beijing 林子威
Media coverage on RHIC (QM’01)
CCAST Summer School August 24-27 2002 Beijing 林子威
Theorists were thinking (QM01)…
CCAST Summer School August 24-27 2002 Beijing 林子威
Lots of new data (QM02)
CCAST Summer School August 24-27 2002 Beijing 林子威
Theorists are still thinking (QM02)…
CCAST Summer School August 24-27 2002 Beijing 林子威
Theorists are also talking to experimentalists…
CCAST Summer School August 24-27 2002 Beijing 林子威
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
1I
II
III
IV
V
Section
Section I
CCAST Summer School August 24-27 2002 Beijing 林子威
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
CCAST Summer School August 24-27 2002 Beijing 林子威
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
CCAST Summer School August 24-27 2002 Beijing 林子威
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
CCAST Summer School August 24-27 2002 Beijing 林子威
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, ...
CCAST Summer School August 24-27 2002 Beijing 林子威
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
CCAST Summer School August 24-27 2002 Beijing 林子威
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
CCAST Summer School August 24-27 2002 Beijing 林子威
HIJING fit to pp/ppbar dataDetermine 2 parameters: (lower Pt cutoff for minijets)
Wang, PRD43
P0: independent of colliding energy
CCAST Summer School August 24-27 2002 Beijing 林子威
Gluon PDF in HIJING
Used in HIJING: too few small-x partons
For minijets at RHIC:XBj ~2/100 ~0.02sizeable effects
CCAST Summer School August 24-27 2002 Beijing 林子威
Nuclear shadowing in HIJING
Wang&Gyulassy, PRD44
Assumed the same for g & q;no Q2 dependence
CCAST Summer School August 24-27 2002 Beijing 林子威
Other shadowing parametrizations
Eskola et al, hep-ph/0110348
Different for g & q;strong Q2 dependence
PDF & shadowing: Qiu at QM02
CCAST Summer School August 24-27 2002 Beijing 林子威
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.
CCAST Summer School August 24-27 2002 Beijing 林子威
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
CCAST Summer School August 24-27 2002 Beijing 林子威
Final-state saturation modelEskola et al, NPB570
Put in PDF and shadowing:
CCAST Summer School August 24-27 2002 Beijing 林子威
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
CCAST Summer School August 24-27 2002 Beijing 林子威
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
CCAST Summer School August 24-27 2002 Beijing 林子威
Parton cross sectionsFrom leading-order QCD:
Use a medium-generated screening mass to regulate the divergence:
In ZPC, make total cross section s-independent:
CCAST Summer School August 24-27 2002 Beijing 林子威
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
CCAST Summer School August 24-27 2002 Beijing 林子威
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
CCAST Summer School August 24-27 2002 Beijing 林子威
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
1I
II
III
IV
V
Section
Section II
CCAST Summer School August 24-27 2002 Beijing 林子威
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
CCAST Summer School August 24-27 2002 Beijing 林子威
Schwinger Mechanism: particle production from an external field via tunneling
Potential energy=
Production probability
Strangeness suppression:0.3 as default value
CCAST Summer School August 24-27 2002 Beijing 林子威
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
CCAST Summer School August 24-27 2002 Beijing 林子威
Schwinger vs Lund Model
Mean Momentum square:
In default HIJING, a=0.5, b=0.9/GeV2
CCAST Summer School August 24-27 2002 Beijing 林子威
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
CCAST Summer School August 24-27 2002 Beijing 林子威
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
CCAST Summer School August 24-27 2002 Beijing 林子威
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
CCAST Summer School August 24-27 2002 Beijing 林子威
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
CCAST Summer School August 24-27 2002 Beijing 林子威
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:
CCAST Summer School August 24-27 2002 Beijing 林子威
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
CCAST Summer School August 24-27 2002 Beijing 林子威
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
CCAST Summer School August 24-27 2002 Beijing 林子威
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
CCAST Summer School August 24-27 2002 Beijing 林子威
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
CCAST Summer School August 24-27 2002 Beijing 林子威
Meson-Meson channels
SU(2):
with strangeness:
CCAST Summer School August 24-27 2002 Beijing 林子威
Example: phi meson cross sections Pal,Ko&Lin, NPA707
CCAST Summer School August 24-27 2002 Beijing 林子威
Meson-Baryon channels
Note: detail balance, charge conjugation, crossing symmetry
CCAST Summer School August 24-27 2002 Beijing 林子威
Example: K-baryon cross sections Pal,Ko&Lin, nucl/0106073
CCAST Summer School August 24-27 2002 Beijing 林子威
Baryon-Baryon channels
Examples: pp inelastic cross sections
Li&Ko, PRC52
CCAST Summer School August 24-27 2002 Beijing 林子威
Pion multiplicity distribution from ppbar annihilation:
Ko&Yuan, PLB192
Assumed:
Baryon-AntiBaryon channels
CCAST Summer School August 24-27 2002 Beijing 林子威
Example:
CCAST Summer School August 24-27 2002 Beijing 林子威
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
1I
II
III
IV
V
Section
,Section III
CCAST Summer School August 24-27 2002 Beijing 林子威
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
CCAST Summer School August 24-27 2002 Beijing 林子威
130AGeV Central AuAu Event from AMPT
CCAST Summer School August 24-27 2002 Beijing 林子威
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
CCAST Summer School August 24-27 2002 Beijing 林子威
Defaults HIJING:
Popcorn scheme:
for a q-qbar string:
BBbar
BMBbar
CCAST Summer School August 24-27 2002 Beijing 林子威
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
CCAST Summer School August 24-27 2002 Beijing 林子威
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
CCAST Summer School August 24-27 2002 Beijing 林子威
After hadron scattering
Net baryon: same Net p: large increase
isospin equilibration
CCAST Summer School August 24-27 2002 Beijing 林子威
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
CCAST Summer School August 24-27 2002 Beijing 林子威
m spectra at SPS
Final-state rescatteringsincrease mslopeof heavy particles
Lin et al, NPA698
CCAST Summer School August 24-27 2002 Beijing 林子威
Results at RHIC Energies
Lin et al, PRC64
CCAST Summer School August 24-27 2002 Beijing 林子威
Yield and ratio: energy dependence
Rapid increase for pbar/p.(p+pbar is not small)
Lin et al, PRC64
CCAST Summer School August 24-27 2002 Beijing 林子威
Quenching and Shadowing on dN/dy at 130A GeV (def.)
No shadowing is inconsistent with data.
Lin et al, NPA698
CCAST Summer School August 24-27 2002 Beijing 林子威
Hadronic scattering effects on dN/dy at 130A GeV (def.)
CCAST Summer School August 24-27 2002 Beijing 林子威
BRAHMS, PLB523Pseudo-rapidity distribution at 130AGeV
CCAST Summer School August 24-27 2002 Beijing 林子威
Ratios of 200G/130G: BRAHMS, PRL88
AMPT
Saturation (Kharzeev&Levin)
CCAST Summer School August 24-27 2002 Beijing 林子威
Rapidity spectra at RHIC P/Pbar Ratio
CCAST Summer School August 24-27 2002 Beijing 林子威
p ~ at PT~2 GeV mainly due to hadronic scatterings
CCAST Summer School August 24-27 2002 Beijing 林子威
p ~ at PT~2 GeV
130G b=0-3 fm
CCAST Summer School August 24-27 2002 Beijing 林子威
Centrality dependence of Nch , Et and <Et> near =0
Npart
CCAST Summer School August 24-27 2002 Beijing 林子威
centrality dependence from other models
PHOBOS, PRC65
Kharzeev&Nardi, PLB507Kharzeev&Levin, PLB523
CCAST Summer School August 24-27 2002 Beijing 林子威
centrality dependence from other models
CCAST Summer School August 24-27 2002 Beijing 林子威
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
1I
II
III
IV
V
Section
,Section IV
CCAST Summer School August 24-27 2002 Beijing 林子威
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
CCAST Summer School August 24-27 2002 Beijing 林子威
parton phase: production and annihilation
Zhang et al, PRC65
CCAST Summer School August 24-27 2002 Beijing 林子威
hadron phase: production and annihilation
CCAST Summer School August 24-27 2002 Beijing 林子威
J/psi yield dependence on charm mass
CCAST Summer School August 24-27 2002 Beijing 林子威
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
CCAST Summer School August 24-27 2002 Beijing 林子威
2) Statistical model+ Multiphase Suppression:
Grandchamp at QM02
detailed balance?
Prel data on open charm& J/psi at RHIC available now to constrain models
CCAST Summer School August 24-27 2002 Beijing 林子威
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
CCAST Summer School August 24-27 2002 Beijing 林子威
Definitions:
X
YAzimuthal asymmetry
in momentum:
in space: According to positionsat previous scatterings
Elliptic FlowFlow summary: Voloshin at QM02
CCAST Summer School August 24-27 2002 Beijing 林子威
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
CCAST Summer School August 24-27 2002 Beijing 林子威
Inside the parton cascade ZPC:
At present:partonic 2-2 elastic processes: abab Cross section:
controled by 3.2/fm3 mb
Zhang, CompPhysComm82
CCAST Summer School August 24-27 2002 Beijing 林子威
Dependence on parton (130 GeV Au+Au, b=8 fm):
3 mb 6 mb
Lin&Ko, PRC65
CCAST Summer School August 24-27 2002 Beijing 林子威
Centrality dependence of v2 at 130A GeV:
CCAST Summer School August 24-27 2002 Beijing 林子威
PT dependence of v2 at 130A GeV: eta (-1.3, 1.3), minimum bias (b=0-13fm)
CCAST Summer School August 24-27 2002 Beijing 林子威
v2 at large PT: eta (-1.3, 0.3), minimum bias
However, needsx50 statistics to reach 4 GeV
CCAST Summer School August 24-27 2002 Beijing 林子威
v2 for different particles: compare with data
CCAST Summer School August 24-27 2002 Beijing 林子威
200A GeV: centrality dependence of v2
Small increase(<1%) with energy
CCAST Summer School August 24-27 2002 Beijing 林子威
200A GeV: PT dependence of v2 eta (-1.3, 0.3), minimum bias
Lin&Ko, PRC65
CCAST Summer School August 24-27 2002 Beijing 林子威
Pion PT spectra
CCAST Summer School August 24-27 2002 Beijing 林子威
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
CCAST Summer School August 24-27 2002 Beijing 林子威
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
1I
II
III
IV
V
Section
,Section V
CCAST Summer School August 24-27 2002 Beijing 林子威
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......
CCAST Summer School August 24-27 2002 Beijing 林子威
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
CCAST Summer School August 24-27 2002 Beijing 林子威
Pion HBT data at RHIC 130AGeV
STAR, PRL87
4-parameter Gaussian fit to C(q) w/o Coulomb effects:
2
CCAST Summer School August 24-27 2002 Beijing 林子威
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
CCAST Summer School August 24-27 2002 Beijing 林子威
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
CCAST Summer School August 24-27 2002 Beijing 林子威
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
CCAST Summer School August 24-27 2002 Beijing 林子威
1) From emission function (10mb) for midrapidity charged pions, central 130AGeV:
CCAST Summer School August 24-27 2002 Beijing 林子威
- correlation function (w/o Coulomb effects):data corrected for Coulomb effects
CCAST Summer School August 24-27 2002 Beijing 林子威
2) From Gaussian fits to 3-d correlation functionC(Q) in LCMS frame (pz1+pz2=0) obtained from CRAB Pratt, NPA566
CCAST Summer School August 24-27 2002 Beijing 林子威
Compare: source radii and fitted radii
Lin,Ko&Pal,nucl-th/0204054(PRL in press)
CCAST Summer School August 24-27 2002 Beijing 林子威
Ratio from source
> ratio from fit (~=1)
CCAST Summer School August 24-27 2002 Beijing 林子威
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)
CCAST Summer School August 24-27 2002 Beijing 林子威
Compare to - data (not corrected for Coulomb):
Self-consistent: theory `knows’ the distance for Coulomb corrections
CCAST Summer School August 24-27 2002 Beijing 林子威
mT dependence of fitted radii (10mb):
CCAST Summer School August 24-27 2002 Beijing 林子威
MT-scaling for fitted R
Kaon source radii~fitted radii
10 mb results
CCAST Summer School August 24-27 2002 Beijing 林子威
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)...
CCAST Summer School August 24-27 2002 Beijing 林子威
Example: dN/dy with String Melting,problem for baryons (3-quark coalescence)
CCAST Summer School August 24-27 2002 Beijing 林子威
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
CCAST Summer School August 24-27 2002 Beijing 林子威
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
CCAST Summer School August 24-27 2002 Beijing 林子威
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
CCAST Summer School August 24-27 2002 Beijing 林子威
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
CCAST Summer School August 24-27 2002 Beijing 林子威
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