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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 Transport Based 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)
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CCAST Summer School August 24-27 2002 Beijing 林子威 Our Goal Relativistic Heavy Ion Collisions: machinessqrt(s) (AGeV)main HI beam CERN-SPS (past) 8-17PbPb BNL-RHIC (now) ~20-200AuAu CERN-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.
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CCAST Summer School August 24-27 2002 Beijing 林子威 Media coverage on RHIC (QM’01)
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CCAST Summer School August 24-27 2002 Beijing 林子威 Theorists were thinking (QM01)…
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CCAST Summer School August 24-27 2002 Beijing 林子威 Lots of new data (QM02)
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CCAST Summer School August 24-27 2002 Beijing 林子威 Theorists are still thinking (QM02)…
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CCAST Summer School August 24-27 2002 Beijing 林子威 Theorists are also talking to experimentalists…
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CCAST Summer School August 24-27 2002 Beijing 林子威 Outline Why do we need a transport model? What need to be included in such a model? Current Structure of AMPT Initial condition Parton cascade Hadronization / phase transition Hadron cascade Tests at SPS energy Results at RHIC energies dN/dy, mt spectra, centrality dependence J/psi, elliptic flow, high Pt HBT Outstanding Problems Summary 1 I II III IV V Section Section I
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CCAST Summer School August 24-27 2002 Beijing 林子威 Why transport model? Formation of partonic matter: ~ 2.5620 GeV/fm3 SPS RHIC200 LHC >>QCD critical energy density take 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 model Quantum transport:Boedecker at QM02 Freezeout in transport: Bleicher Parton cascade model: Bass
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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
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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 queching replaced by parton cascade Parton freezeout Generate parton space-time
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CCAST Summer School August 24-27 2002 Beijing 林子威 Main Ingredients of AMPT HIJINGdefault version 1.36 ZPC2-2 parton processes: gg-gg, (gg-qqbar, gq-gq,...) ARThadron 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,...
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CCAST Summer School August 24-27 2002 Beijing 林子威 Key Parameters of AMPT A+AParton Distribution Function (PDF), nuclear shadowing (gA(x,Q2), qA(x,Q2)) HIJINGlower Pt cutoff for minijet (p0) ZPCinitial parton space-time distribution (tau0_p, z0,...) screening mass for parton cross section (mu: sigma_p) ARThadron formation time (tau0_h) cross sections of hadron interactions (sigma,...) take care of detailed balance
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CCAST Summer School August 24-27 2002 Beijing 林子威 Initial condition from HIJING HIJING: a 2-component (soft+hard) model + nuclear geometry LUND stringpQCD minijetsWoods-Saxon Eikonal formulism for cross sections: Overlap function Probability for minijet production: Take dipole form factor and assume
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CCAST Summer School August 24-27 2002 Beijing 林子威 HIJING fit to pp/ppbar data Determine 2 parameters: (lower Pt cutoff for minijets) Wang, PRD43 P 0 : independent of colliding energy
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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: X Bj ~2/100 ~0.02 sizeable effects
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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
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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
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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 parametrization different for g & q: now depends on colliding energy: ~1.7 GeV at SPS ~3.5 GeV at LHC.
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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 RARA Simple estimate: Saturation momentum scale Eskola et al, NPB570 Tuominen at QM02
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CCAST Summer School August 24-27 2002 Beijing 林子威 Final-state saturation model Eskola et al, NPB570 Put in PDF and shadowing:
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CCAST Summer School August 24-27 2002 Beijing 林子威 Initial condition from initial-state saturation model McLerran & Venugopalan, PRD49 QCD: 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
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CCAST Summer School August 24-27 2002 Beijing 林子威 Parton Cascade to study strong interactions of QCD matter. Final-state parton interactions can be described by parton Wigner operators: the equation of motion may be written as: For 2-2 interacitons: ZPC (Zhang's Parton Cascade) solves these Boltzmann equations by the cascade method: 2 particles scatter if: their distance < Zhang, Comp.Phys.Comm.109; Zhang,Gyulassy&Pang, PRC58
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CCAST Summer School August 24-27 2002 Beijing 林子威 Parton cross sections From leading-order QCD: Use a medium-generated screening mass to regulate the divergence: In ZPC, make total cross section s-independent:
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CCAST Summer School August 24-27 2002 Beijing 林子威 Screening mass mu Near equilibrium: Gluon spectrum: dN/dy/d2K T For exponential KT spectra with boost-invariance: Estimate: Screening mass will be taken as ~ several/fm
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CCAST Summer School August 24-27 2002 Beijing 林子威 Parton processes and subdivision ZPC 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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CCAST Summer School August 24-27 2002 Beijing 林子威 Outline Why do we need a transport model? What need to be included in such a model? Current Structure of AMPT Initial condition Parton cascade Hadronization / phase transition Hadron cascade Tests at SPS energy Results at RHIC energies dN/dy, mt spectra, centrality dependence J/psi, elliptic flow, high Pt HBT Outstanding Problems Summary 1 I II III IV V Section Section II
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CCAST Summer School August 24-27 2002 Beijing 林子威 Hadronization A pp collision in the string picture: P1 P2after momentum transferP2' P1' Invariant massMp Mp>Mp particle production P1': quark+diquark with large invariant mass, a color singlet system confined by a linear potential string tension: ~1GeV/fm
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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
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CCAST Summer School August 24-27 2002 Beijing 林子威 Lund 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 produced parton
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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
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CCAST Summer School August 24-27 2002 Beijing 林子威 Default hadronization of AMPT string1'+minijet1 string2'+minijet2 HIJING producesstring3 independent minijets..... proj & targ spectators ZPC string1'+minijet1'=string1 string2'+minijet2'=string2 string3 independent minijets'..... proj & targ spectators apply Lund string fragmentation these have no actions in parton stage minijet1 -minijet1' recombine with the original string1' Zhang et al, PRC61; Lin et al, PRC64, NPA698
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CCAST Summer School August 24-27 2002 Beijing 林子威 Modified AMPT model: string melting Lin&Ko, PRC65; Lin,Ko&Pal, nucl-th/0204054 (PRL in press) Initial energy in default AMPT: soft (strings) & hard (minijets) In high density overlap area but not in parton cascade
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CCAST Summer School August 24-27 2002 Beijing 林子威 Initial energy density from minijet partons >> 1 GeV/fm^3 critical 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
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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
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CCAST Summer School August 24-27 2002 Beijing 林子威 Parton colescence after string melting Nearest partons form a hadron: find closest qbar form a meson m find closest q2 & q3 form a baryon B Determine Flavor, examples: ubar d:form pi- if invariant mass is closer to Mpi form rho- to Mrho ubar 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:
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CCAST Summer School August 24-27 2002 Beijing 林子威 HIJING energy 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 partons coalesce into hadrons Strong-decay all resonances for final particle spectra
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CCAST Summer School August 24-27 2002 Beijing 林子威 Coalescence in ALCOR Biro 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
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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
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CCAST Summer School August 24-27 2002 Beijing 林子威 Hadron Cascade Based 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,PRC65 Lin,Ko&Pal, nucl-th/0204054 (PRL in press) multistrange channels Pal,Ko&Lin, nucl/0106073 phi interactions Pal,Ko&Lin, NPA707 Include
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CCAST Summer School August 24-27 2002 Beijing 林子威 Meson-Meson channels SU(2): with strangeness:
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CCAST Summer School August 24-27 2002 Beijing 林子威 Example: phi meson cross sections Pal,Ko&Lin, NPA707
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CCAST Summer School August 24-27 2002 Beijing 林子威 Meson-Baryon channels Note: detail balance, charge conjugation, crossing symmetry
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CCAST Summer School August 24-27 2002 Beijing 林子威 Example: K-baryon cross sections Pal,Ko&Lin, nucl/0106073
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CCAST Summer School August 24-27 2002 Beijing 林子威 Baryon-Baryon channels Examples: pp inelastic cross sections Li&Ko, PRC52
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CCAST Summer School August 24-27 2002 Beijing 林子威 Pion multiplicity distribution from ppbar annihilation: Ko&Yuan, PLB192 Assumed: Baryon-AntiBaryon channels
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CCAST Summer School August 24-27 2002 Beijing 林子威 Example:
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CCAST Summer School August 24-27 2002 Beijing 林子威 Outline Why do we need a transport model? What need to be included in such a model? Current Structure of AMPT Initial condition Parton cascade Hadronization / phase transition Hadron cascade Tests at SPS energy Results at RHIC energies dN/dy, mt spectra, centrality dependence J/psi, elliptic flow, high Pt HBT Outstanding Problems Summary 1 I II III IV V Section, Section III
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CCAST Summer School August 24-27 2002 Beijing 林子威 Time evolution of a RHIC event at 130G 10 2025 30 fm/c 2 4 6 8 Tt= 0.4 0.60.8 1.0 Animation at http://nt3.phys.columbia.edu/people/zlin/ZLIN/publication.html
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CCAST Summer School August 24-27 2002 Beijing 林子威 130AGeV Central AuAu Event from AMPT
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CCAST Summer School August 24-27 2002 Beijing 林子威 Rapidity shift due to modification 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 Energies NetBaryon Stopping
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CCAST Summer School August 24-27 2002 Beijing 林子威 Defaults HIJING: Popcorn scheme: for a q-qbar string: BBbar BMBbar
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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
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CCAST Summer School August 24-27 2002 Beijing 林子威 Rapidity shift due to popcorn scheme. pbar yield decreases from HIJING due to more annihilation than production (annihilation alone gives too low) P and Pbar rapidity spectra at SPS Lin et al, PRC64
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CCAST Summer School August 24-27 2002 Beijing 林子威 After hadron scattering Net baryon: same Net p: large increase isospin equilibration
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CCAST Summer School August 24-27 2002 Beijing 林子威 In default HIJING, a=0.5, b=0.9/GeV2 changed to a=2.2, b=0.5/GeV2 a&b in the Lund splitting function: ~same Lin et al, PRC64
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CCAST Summer School August 24-27 2002 Beijing 林子威 m spectra at SPS Final-state rescatterings increase m slope of heavy particles Lin et al, NPA698
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CCAST Summer School August 24-27 2002 Beijing 林子威 Results at RHIC Energies Lin et al, PRC64
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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
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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
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CCAST Summer School August 24-27 2002 Beijing 林子威 Hadronic scattering effects on dN/dy at 130A GeV (def.)
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CCAST Summer School August 24-27 2002 Beijing 林子威 BRAHMS, PLB523 Pseudo-rapidity distribution at 130AGeV
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CCAST Summer School August 24-27 2002 Beijing 林子威 Ratios of 200G/130G: BRAHMS, PRL88 AMPT Saturation (Kharzeev&Levin)
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CCAST Summer School August 24-27 2002 Beijing 林子威 Rapidity spectra at RHIC P/Pbar Ratio
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CCAST Summer School August 24-27 2002 Beijing 林子威 p ~ at P T ~2 GeV mainly due to hadronic scatterings
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CCAST Summer School August 24-27 2002 Beijing 林子威 p ~ at P T ~2 GeV 130G b=0-3 fm
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CCAST Summer School August 24-27 2002 Beijing 林子威 Centrality dependence of Nch, Et and near =0 Npart
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CCAST Summer School August 24-27 2002 Beijing 林子威 centrality dependence from other models PHOBOS, PRC65 Kharzeev&Nardi, PLB507 Kharzeev&Levin, PLB523
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CCAST Summer School August 24-27 2002 Beijing 林子威 centrality dependence from other models
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CCAST Summer School August 24-27 2002 Beijing 林子威 Outline Why do we need a transport model? What need to be included in such a model? Current Structure of AMPT Initial condition Parton cascade Hadronization / phase transition Hadron cascade Tests at SPS energy Results at RHIC energies dN/dy, mt spectra, centrality dependence J/psi, elliptic flow, high Pt HBT Outstanding Problems Summary 1 I II III IV V Section, Section IV
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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 inside due to color screening) color Debye-screening Zhang et al, PRC62 Color deconfinement: Satz at QM02
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CCAST Summer School August 24-27 2002 Beijing 林子威 parton phase: production and annihilation Zhang et al, PRC65
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CCAST Summer School August 24-27 2002 Beijing 林子威 hadron phase: production and annihilation
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CCAST Summer School August 24-27 2002 Beijing 林子威 J/psi yield dependence on charm mass
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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 equilibrium between open charm and J/psi: Overiew of statistical model: Bialas, Rafelski & Koch at QM02 Thermal model: Cleymans, Becattini, Tounsi at QM02
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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
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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
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CCAST Summer School August 24-27 2002 Beijing 林子威 Definitions: X Y Azimuthal asymmetry in momentum: in space: According to positions at previous scatterings Elliptic Flow Flow summary: Voloshin at QM02
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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 QM02 viscosity correction of hydro: Teaney at QM02 2d hydro on v2: Heinz at QM02
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CCAST Summer School August 24-27 2002 Beijing 林子威 Inside the parton cascade ZPC: At present: partonic 2-2 elastic processes: ab ab Cross section: controled by 3.2/fm 3 mb Zhang, CompPhysComm82
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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
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CCAST Summer School August 24-27 2002 Beijing 林子威 Centrality dependence of v2 at 130A GeV:
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CCAST Summer School August 24-27 2002 Beijing 林子威 P T dependence of v2 at 130A GeV: eta (-1.3, 1.3), minimum bias (b=0-13fm)
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CCAST Summer School August 24-27 2002 Beijing 林子威 v2 at large PT: eta (-1.3, 0.3), minimum bias However, needs x50 statistics to reach 4 GeV
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CCAST Summer School August 24-27 2002 Beijing 林子威 v2 for different particles: compare with data
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CCAST Summer School August 24-27 2002 Beijing 林子威 200A GeV: centrality dependence of v2 Small increase (<1%) with energy
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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
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CCAST Summer School August 24-27 2002 Beijing 林子威 Pion PT spectra
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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
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CCAST Summer School August 24-27 2002 Beijing 林子威 Outline Why do we need a transport model? What need to be included in such a model? Current Structure of AMPT Initial condition Parton cascade Hadronization / phase transition Hadron cascade Tests at SPS energy Results at RHIC energies dN/dy, mt spectra, centrality dependence J/psi, elliptic flow, high Pt HBT Outstanding Problems Summary 1 I II III IV V Section, Section V
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CCAST Summer School August 24-27 2002 Beijing 林子威 HBT method " Hanbury-Brown Twiss effect measured star size from photon interferometry since identical particles interfere " Observed experimentally in particle physics first by Goldhaber et al, PR120 " For nuclear collisions, theorists predicts its sensitivity to Expansion velocity Source size phase transition to QGP Softest point in EOS " Measured extensively in heavy ion collisions reasonably described by models (hydro,transport) " RHIC Hanbury Brown&Twiss,Nature(London)178 Pratt,PRL53 Bertsch et al,PRC37 Pratt et al,PRC42 Rischke&Gyulassy,NPA608......
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CCAST Summer School August 24-27 2002 Beijing 林子威 From http://www.pa.msu.edu/~bauerhttp://www.pa.msu 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
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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
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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 QM02 Failure of hydro: Soff Dynamic freezeout: Tomasik non-central HBT: Kolb 3d hydro: Hirano
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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
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CCAST Summer School August 24-27 2002 Beijing 林子威 Radii from Emission function S and correlation function C If source is Gaussian in space-time, then: And R 0 ij = R ij 1) Curvature at q=0: 2) Often use 4-parameter fit for C(q) w/o Coulomb effects: Pratt,PRL84 Wiedemann,PRC57 Dx,y= -. ___ 2
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CCAST Summer School August 24-27 2002 Beijing 林子威 1) From emission function (10mb) for midrapidity charged pions, central 130AGeV:
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CCAST Summer School August 24-27 2002 Beijing 林子威 - correlation function (w/o Coulomb effects): data corrected for Coulomb effects
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CCAST Summer School August 24-27 2002 Beijing 林子威 2) From Gaussian fits to 3-d correlation function C(Q) in LCMS frame (pz1+pz2=0) obtained from CRAB Pratt, NPA566
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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)
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CCAST Summer School August 24-27 2002 Beijing 林子威 Ratio from source > ratio from fit (~=1)
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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 Positive and large, reduces Rout Values: (17fm)**2 = 185 -2*168 + 431 Source Spatial-size x-t correlationDuration time Lin,Ko&Pal, nucl-th/0204054 (PRL in press)
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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
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CCAST Summer School August 24-27 2002 Beijing 林子威 mT dependence of fitted radii (10mb):
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CCAST Summer School August 24-27 2002 Beijing 林子威 MT-scaling for fitted R Kaon source radii ~fitted radii 10 mb results
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CCAST Summer School August 24-27 2002 Beijing 林子威 Outstanding Problems The Bottom Line we do not (yet) have one consistent model for all observables on phenomenology: GoodBad or even Ugly Default AMPT:dN/dy, mt, Baryon stopping v2, HBT AMPT w. string melting: dN/dy(meson), v2, HBTdN/dy(Baryon) mt of pionsmt of heavier hadrons on theoretical foundation: coherent/multi-particle interaction at high densities AA->QGP: creation of partonic matter (now modeled by string melting) parton->hadron phase transition (now modeled by coalescence)...
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CCAST Summer School August 24-27 2002 Beijing 林子威 Example: dN/dy with String Melting, problem for baryons (3-quark coalescence)
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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
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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
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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 (gg qqbar, gq gq,...) 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
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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
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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
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