Partonic Cascade and Hadronic Evolution Dynamics in AMPT

1. 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. Our Goal • Relativistic Heavy Ion Collisions: machines sqrt(s) (AGeV) main HI beam • CERN-SPS (past) 8-17 PbPb • BNL-RHIC (now) ~20-200 AuAu • 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. Media coverage on RHIC (QM’01)

4. Theorists were thinking (QM01)…

5. Lots of new data (QM02)

6. Theorists are still thinking (QM02)…

7. Theorists are also talking to experimentalists…

8. Outline Section • 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 I 1 II III IV V Section I

9. Why transport model? Formation of partonic matter: ~ 2.56 20 GeV/fm3 SPSRHIC200 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. 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. Structure of Default AMPT Zhang et al, PRC61; Lin et al, PRC64, NPA698. A+A Wang&Gyulassy, PRD43,44,45 HIJING energy in strings(soft)+ minijet partons(hard) Generate parton space-time ZPC (Zhang's Parton Cascade) Jet queching replaced by parton cascade Zhang, CompPhysComm82 Parton freezeout Lund fragmentation to hadrons ART (A Relativistic Transport model for hadrons) Li&Ko, PRC52 Strong-decay all resonancesfor final particle spectra

12. 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, ...

13. 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

14. Initial condition from HIJING • HIJING: a 2-component (soft+hard) model + nuclear geometry LUND stringpQCD minijetsWoods-Saxon • Eikonal formulism for cross sections: Probability for minijet production: Overlap function Take dipole form factor and assume

15. HIJING fit to pp/ppbar data Determine 2 parameters: (lower Pt cutoff for minijets) Wang, PRD43 P0: independent of colliding energy

16. Gluon PDF in HIJING For minijets at RHIC: XBj ~2/100 ~0.02 sizeable effects Used in HIJING: too few small-x partons

17. Nuclear shadowing in HIJING Wang&Gyulassy, PRD44 Assumed the same for g & q; no Q2 dependence

18. Other shadowing parametrizations Eskola et al, hep-ph/0110348 Different for g & q; strong Q2 dependence PDF & shadowing: Qiu at QM02

19. Recent update of PDF and shadowing in HIJING: Li&Wang, PLB527 GRV used for structure function; new shadowing parametrization different for g & q: now dependson colliding energy: ~1.7 GeV at SPS ~3.5 GeV at LHC.

20. Initial condition from final-state saturation model Eskola et al, NPB570 Tuominen at QM02 Geometrical saturation: when produced midrapidity partons occupies the whole transverse plane RA Saturation momentum scale Simple estimate:

21. Final-state saturation model Eskola et al, NPB570 Put in PDF and shadowing:

22. 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. 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. 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. Screening mass mu Near equilibrium: Gluon spectrum: dN/dy/d2KT For exponential KT spectra with boost-invariance: Estimate: Screening mass will be taken as ~ several/fm

26. 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 Zhang,Gyulassy&Pang, PRC58 Subdivide: is not changed

27. Outline Section • 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 I 1 II III IV V Section II

28. Hadronization A pp collision in the string picture: P1 P2after momentum transferP2' 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

29. Schwinger Mechanism: • particle production from an external field via tunneling Potential energy= • Production probability • Strangeness suppression: 0.3 as default value

30. 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. Schwinger vs Lund Model Mean Momentum square: In default HIJING, a=0.5, b=0.9/GeV2

32. Default hadronization of AMPT Zhang et al, PRC61; Lin et al, PRC64, NPA698 string1'+minijet1 string2'+minijet2 HIJING produces string3 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'

33. 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. Zhang et al, PRC62 QCD phase diagram: Kanaya, Fodor at QM02 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

35. 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. 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. Structure of AMPT model with String Melting HIJING energy in strings and minijet partons A+A Fragment excited strings into partons ZPC (Zhang's Parton Cascade) Till Parton freezeout Nearest partons coalesce into hadrons ART (A Relativistic Transport model for hadrons) Strong-decay all resonances for final particle spectra

38. Coalescence inALCOR 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: coalescence factor 2Nf normalization factors, determined from 2Nf equations for quark # conservation:

39. coalescence factors: • For mesons bound in a Coulomb-like potential: spin-degeneracy momentum of q in CMS Bohr radius for Debye screening length • Assume baryons created in 2-steps: baryon supression factor

40. 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. Meson-Meson channels SU(2): with strangeness:

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

43. Meson-Baryon channels Note: detail balance, charge conjugation, crossing symmetry

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

45. Baryon-Baryon channels Examples: pp inelastic cross sections Li&Ko, PRC52

46. Baryon-AntiBaryon channels Pion multiplicity distribution from ppbar annihilation: Ko&Yuan, PLB192 Assumed:

47. Example:

48. Outline Section • 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 I 1 II III IV V Section III ,

49. Time evolution of a RHIC event at 130G Tt= 0.4 0.6 0.8 1.0 2 4 6 8 10 20 25 30 fm/c Animation athttp://nt3.phys.columbia.edu/people/zlin/ZLIN/publication.html

50. 130AGeV Central AuAu Event from AMPT