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Space-time Evolution of Bulk QCD Matter at RHIC

Space-time Evolution of Bulk QCD Matter at RHIC. Chiho NONAKA Nagoya University. Contents Introduction Hydrodynamic models at RHIC Freezeout process, finite state interactions 3D hydro+UrQMD Results Single particle spectra, elliptic flow Summary.

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Space-time Evolution of Bulk QCD Matter at RHIC

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  1. Space-time Evolution of Bulk QCD Matter at RHIC Chiho NONAKA Nagoya University • Contents • Introduction • Hydrodynamic models at RHIC • Freezeout process, finite state interactions • 3D hydro+UrQMD • Results • Single particle spectra, elliptic flow • Summary In collaboration with Steffen A. Bass (Duke University & RIKEN BNL) HQ2006

  2. Success of Perfect Hydrodynamic Models at RHIC Single particle spectra Huovinen, Kolb, Heinz, Hirano, Teaney, Shuryak, Hama, Morita, ……. Strong elliptic flow Strong coupled (correlated) QGP • However…. • Elliptic flow vs.  Hirano and Tsuda, PRC66 Discrepancy at large : • Insufficient thermalization? • Viscosity effect? • Simple freezeout process? • freezeout • viscosity Hydrodynamic Models at RHIC Huovinen et.al, PLB503 at mid rapidity

  3. Freezeout process in Hydro • Single freezeout temperature? • Difference between chemical andthermal freezeout Heinz,NPA • chemical freezeout • statistical model • Tch ~170 MeV • hadron ratio • thermal freezeout • hydro • Tf ~ 110~140 MeV • Possible solutions: • Partial chemical equilibrium (PCE) • Hirano, Kolb, Rapp • Hydro + Micro Model • Bass, Dumitru, Teaney, Shuryak

  4. Final State Interactions Thermal model T = 177 MeV  = 29 MeV UrQMD 3D-Hydro +UrQMD 2. In UrQMD final state interactions are included correctly. Markert @QM2004

  5. UrQMD • Full 3-d Hydrodynamics • EoS :1st order phase transition • QGP + excluded volume model Hadronization Cooper-Frye formula final state interactions Monte Carlo TC TSW t fm/c 3D-Hydro + UrQMD Model Bass and Dumitru, PRC61,064909(2000) Teaney et al, nucl-th/0110037 • Hadron phase: viscosity effect • Freezeout process: • Chemical freezeout & thermal freezeout • Final state interactions 3D-Hydro +UrQMD Key: • Treatment of freezeout is determined by mean free path. • Brake up thermalization: viscosity effect TC:critical temperature TSW:Hydro  UrQMD

  6. nucleus nucleus 3-D Hydrodynamic Model • Relativistic hydrodynamic equation • Baryon number conservation • Coordinates • Lagrangian hydrodynamics • Tracing the adiabatic path of each volume element • Effects of phase transition on observables • Computational time • Easy application to LHC • Algorithm • Focusing on the conservation law energy momentum tensor Lagrangian hydrodynamics Flux of fluid

  7. 0=0.6 fm/c max=40 GeV/fm3, nBmax=0.15 fm-3 0=0.5 =1.5 Parameters • Initial Conditions • Energy density • Baryon number density • Parameters • Flow • Switching temperature • longitudinal direction • transverse plane Different from Pure Hydro ! vL=Bjorken’s solution); vT=0 TSW=150 [MeV]

  8. PT spectra • PT spectra at central collisions

  9. PT Spectra (Pure Hydro) Tf=110 MeV normalization of K and p: ratio at Tchem Heinz and Kolb, hep-ph/0204061

  10. Rapidity Distribution • Impact parameter dependence of rapidity distributions

  11. Centrality Dependence • Impact parameter dependence of PT

  12. PT Spectra for Strange Particles

  13. decay Reaction Dynamics • At mid rapidity • Slope becomes steeper

  14. Final State Interactions p, : flatter, pion wind : small cross section

  15. Hydrodynamic expansion final state interaction <PT> vs mass • At mid rapidity

  16. v2 in hadron phase ? • Quark number scaling of v2 v2: early stage of expansion

  17. Reaction Dynamics in v2 I

  18. Reaction Dynamics in v2 II • Hydro+decay • ~ Hydro@TSW • v2 grows in hadron • phase a bit. • v2 builds up in QGP • phase.

  19. Summary • We present the 3-D hydrodynamic +cascade model • 3-D Hydrodynamic Model • Single particle distribution • Centrality dependence • Elliptic flow • Low Tf : single spectra, elliptic flow, hadron ratios Necessity of improvement of freezeout process in Hydro • 3-D Hydro + UrQMD • Single particle distribution • Centrality dependence • Elliptic flow • Different initial conditions from pure Hydro • Hadron ratios Switching temperature from Hydro to UrQMD • Reaction dynamics in UrQMD • ,small cross section, v2:improvement at forward/backward  • Work in progress • EoS dependence: ex. lattice QCD • Switching temperature dependence

  20. Backup

  21. 0=0.6 fm/c max=55 GeV/fm3, nBmax=0.15 fm-3 0=0.5 =1.5 EOS(entropy density) =0 Parameters • Initial Conditions • Energy density • Baryon number density • Parameters (pure hydro) • Flow • Equation of State • 1st order phase transition Bag Model + Exclude volume model • Freezeout Temperature • longitudinal direction • transverse plane Different from hydo + UrQMD ! vL=Bjorken’s solution); vT=0 Tf=110 [MeV]

  22. PT Spectra Tf=110 MeV normalization of K and p: ratio at Tchem Heinz and Kolb, hep-ph/0204061

  23. Rapidity distribution

  24. b dependence of PT spectra

  25. V2 vs PT • Elliptic Flow b=6.3 fm b=4.5 fm • b=4.5 fm: consistent with experimental data • b=6.3 fm: proton  overestimate

  26. v2 vs  3-15 % 15-25 % • Forward/backward rapidity: overestimate • Pure hydro is valid around mid rapidity.

  27. Step2. 3-D Hydro + UrQMD

  28. v2 vs PT

  29. v2 vs 

  30. Hydrodynamic Model at RHIC • Relativistic Heavy Ion Collision & Hydrodynamic models • Schematic sketch t collision thermalization hydrodynamical expansion hadronization freeze-out QGP production hadron phase phase transition Hydro Model • initial conditions • parametrization • color glass • condensate… • equation of states • bag model • lattice QCD… • freezeout process • chemical equilibrium • partial chemical • equilibrium • cascade model…

  31. Introduction 1 • Success of Ideal Hydrodynamic Models at RHIC • Single particle spectra • PT spectra up to ~ 2GeV • Huovinen, Kolb, Heinz, Hirano, Teaney, • Shuryak, Hama, Morita, ……. • Strong elliptic flow • strong coupled QGP at mid rapidity Huovinen et.al, PLB503 Nonaka and Bass

  32. Introduction 2 • Success of Ideal Hydrodynamic Models at RHIC However… • Elliptic flow as a function of  Hirano and Tsuda, PRC66 Discrepancy at large : • Insufficient thermalization? • Mean free path • Viscosity effect? • freezeout • viscosity

  33. RHIC sQGP V2 vs multiplicity SPS NA49:PRC68,034903(2003)

  34. Hydrodynamic Models Au + Au GeV PHENIX:Nucl.Phys. A757 (2005) 184 PT spectra p • hadron ratio • CE • PCE  • RQMD

  35. Hydrodynamic Models Au + Au GeV PHENIX:Nucl.Phys. A757 (2005) 184 Elliptic Flow p CE PCE  RQMD

  36. EoS Initial Conditions Freeze-out Hydrodynamic Models Au + Au GeV PHENIX:Nucl.Phys. A757 (2005) 184 p p PT spectra Elliptic Flow [1]Huovinen et.al., PLB(130) [2]Kolb et.al. PRC, [3]Hirano et.al.PRC(130), [4]Teaney et al.

  37. x y Trajectories on the Phase Diagram • Lagrangian hydrodynamics transverse plane (ix,iy,iz) effect of phase transition C.N et al., Eur. Phys.J C17,663(2000)

  38. Numerical Calculation Step 1. Step 2. Step 3. Coordinates move in parallel with baryon number current and entropy density current. local velocity: from hydro eq. temperature and chemical potential CPU time is almost proportional of # of lattice points.

  39. Improvement of freezeout process Summary 1 • Pure hydro with single freezeout temperature Hadron ratio Elliptic flow at forward/backward rapidity

  40. Distribution of # of Collisions

  41. f distribution =0 =2.2 =3.2

  42. f distribution b=2.4 fm b=4.5 fm b=6.3 fm at mid rapidity

  43. Distribution of # of Collisions • finite b: • dN/ncoll becomes small • steep drop

  44. f distribution

  45. Reaction Dynamics in f (M)

  46. Reaction Dynamics in f (B)

  47. xf Distribution

  48. Reaction Dynamics I

  49. Reaction Dynamics II

  50. Reaction Dynamics IV

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