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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.

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Presentation on theme: "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."— Presentation transcript:

1 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)

2 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.

3 CCAST Summer School August 24-27 2002 Beijing 林子威 Media coverage on RHIC (QM’01)

4 CCAST Summer School August 24-27 2002 Beijing 林子威 Theorists were thinking (QM01)…

5 CCAST Summer School August 24-27 2002 Beijing 林子威 Lots of new data (QM02)

6 CCAST Summer School August 24-27 2002 Beijing 林子威 Theorists are still thinking (QM02)…

7 CCAST Summer School August 24-27 2002 Beijing 林子威 Theorists are also talking to experimentalists…

8 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

9 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

10 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

11 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

12 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,...

13 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

14 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

15 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

16 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

17 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

18 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

19 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.

20 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

21 CCAST Summer School August 24-27 2002 Beijing 林子威 Final-state saturation model Eskola et al, NPB570 Put in PDF and shadowing:

22 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

23 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

24 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:

25 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

26 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

27 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

28 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

29 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

30 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

31 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

32 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

33 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

34 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

35 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

36 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:

37 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

38 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

39 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

40 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

41 CCAST Summer School August 24-27 2002 Beijing 林子威 Meson-Meson channels SU(2): with strangeness:

42 CCAST Summer School August 24-27 2002 Beijing 林子威 Example: phi meson cross sections Pal,Ko&Lin, NPA707

43 CCAST Summer School August 24-27 2002 Beijing 林子威 Meson-Baryon channels Note: detail balance, charge conjugation, crossing symmetry

44 CCAST Summer School August 24-27 2002 Beijing 林子威 Example: K-baryon cross sections Pal,Ko&Lin, nucl/0106073

45 CCAST Summer School August 24-27 2002 Beijing 林子威 Baryon-Baryon channels Examples: pp inelastic cross sections Li&Ko, PRC52

46 CCAST Summer School August 24-27 2002 Beijing 林子威 Pion multiplicity distribution from ppbar annihilation: Ko&Yuan, PLB192 Assumed: Baryon-AntiBaryon channels

47 CCAST Summer School August 24-27 2002 Beijing 林子威 Example:

48 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

49 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

50 CCAST Summer School August 24-27 2002 Beijing 林子威 130AGeV Central AuAu Event from AMPT

51 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

52 CCAST Summer School August 24-27 2002 Beijing 林子威 Defaults HIJING: Popcorn scheme: for a q-qbar string: BBbar BMBbar

53 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

54 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

55 CCAST Summer School August 24-27 2002 Beijing 林子威 After hadron scattering Net baryon: same Net p: large increase isospin equilibration

56 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

57 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

58 CCAST Summer School August 24-27 2002 Beijing 林子威 Results at RHIC Energies Lin et al, PRC64

59 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

60 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

61 CCAST Summer School August 24-27 2002 Beijing 林子威 Hadronic scattering effects on dN/dy at 130A GeV (def.)

62 CCAST Summer School August 24-27 2002 Beijing 林子威 BRAHMS, PLB523 Pseudo-rapidity distribution at 130AGeV

63 CCAST Summer School August 24-27 2002 Beijing 林子威 Ratios of 200G/130G: BRAHMS, PRL88 AMPT Saturation (Kharzeev&Levin)

64 CCAST Summer School August 24-27 2002 Beijing 林子威 Rapidity spectra at RHIC P/Pbar Ratio

65 CCAST Summer School August 24-27 2002 Beijing 林子威 p ~  at P T ~2 GeV mainly due to hadronic scatterings

66 CCAST Summer School August 24-27 2002 Beijing 林子威 p ~  at P T ~2 GeV 130G b=0-3 fm

67 CCAST Summer School August 24-27 2002 Beijing 林子威 Centrality dependence of Nch, Et and near  =0 Npart

68 CCAST Summer School August 24-27 2002 Beijing 林子威 centrality dependence from other models PHOBOS, PRC65 Kharzeev&Nardi, PLB507 Kharzeev&Levin, PLB523

69 CCAST Summer School August 24-27 2002 Beijing 林子威 centrality dependence from other models

70 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

71 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

72 CCAST Summer School August 24-27 2002 Beijing 林子威 parton phase: production and annihilation Zhang et al, PRC65

73 CCAST Summer School August 24-27 2002 Beijing 林子威 hadron phase: production and annihilation

74 CCAST Summer School August 24-27 2002 Beijing 林子威 J/psi yield dependence on charm mass

75 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

76 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

77 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

78 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

79 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

80 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

81 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

82 CCAST Summer School August 24-27 2002 Beijing 林子威 Centrality dependence of v2 at 130A GeV:

83 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)

84 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

85 CCAST Summer School August 24-27 2002 Beijing 林子威 v2 for different particles: compare with data

86 CCAST Summer School August 24-27 2002 Beijing 林子威 200A GeV: centrality dependence of v2 Small increase (<1%) with energy

87 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

88 CCAST Summer School August 24-27 2002 Beijing 林子威 Pion PT spectra

89 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

90 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

91 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......

92 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

93 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

94 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

95 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

96 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

97 CCAST Summer School August 24-27 2002 Beijing 林子威 1) From emission function (10mb) for midrapidity charged pions, central 130AGeV:

98 CCAST Summer School August 24-27 2002 Beijing 林子威  - correlation function (w/o Coulomb effects): data corrected for Coulomb effects

99 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

100 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)

101 CCAST Summer School August 24-27 2002 Beijing 林子威 Ratio from source > ratio from fit (~=1)

102 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)

103 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

104 CCAST Summer School August 24-27 2002 Beijing 林子威 mT dependence of fitted radii (10mb):

105 CCAST Summer School August 24-27 2002 Beijing 林子威 MT-scaling for fitted R Kaon source radii ~fitted radii 10 mb results

106 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)...

107 CCAST Summer School August 24-27 2002 Beijing 林子威 Example: dN/dy with String Melting, problem for baryons (3-quark coalescence)

108 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

109 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

110 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

111 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

112 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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