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Spectra and Flow from a Full 3D Hydro+Cascade Model

Workshop “How perfect is this matter?” in 2006 RHIC & AGS annual users’ meeting. Spectra and Flow from a Full 3D Hydro+Cascade Model. Tetsufumi Hirano Institute of Physics, University of Tokyo. References: T.Hirano and M.Gyulassy, Nucl.Phys.A 769 (2006)71.

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Spectra and Flow from a Full 3D Hydro+Cascade Model

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  1. Workshop “How perfect is this matter?” in 2006 RHIC & AGS annual users’ meeting Spectra and Flowfrom a Full 3DHydro+Cascade Model Tetsufumi Hirano Institute of Physics, University of Tokyo References: T.Hirano and M.Gyulassy, Nucl.Phys.A 769(2006)71. T.Hirano, U.Heinz, D.Kharzeev, R.Lacey, Y.Nara, Phys.Lett.B 636 (2006)299.

  2. OUTLINE • Dynamical modeling in heavy ion collisions (hydro+cascade) • Results from OUR hydro + cascade model • Discussion on hadronic dissipation • Summary

  3. A Bigger Picture Before collisions Geometric Scaling CGC “DGLAP region” Parton production Pre- equilibrium Transverse momentum Shattering CGC (N)LOpQCD Instability? Equilibration? • Parton energy loss • Inelastic • Elastic Interaction “Perfect” fluid QGP or GP • Hydrodynamics • viscosity? • non chem. eq.? Recombination Coalescence Dissipative hadron gas Hadronic cascade Fragmentation Proper time Low pT Intermediate pT High pT

  4. Ideal QGP Fluid + Dissipative Hadron Gas Models hydro cascade

  5. What needed (practically) for Dynamical Modeling in Heavy Ion Collisions • Man Power • Modeling • Coding • Computing Power • Consistency of Results • Comparison among groups • Need benchmark calculations? • Not exclusive, but supplementary • Maintenance of Codes • UrQMD: UrQMD collaboration (Frankfurt) • 3D hydro (Lagrange): C.Nonaka (Nagoya) • JAM: Y.Nara (Frankfurt) • 3D hydro (Euler): T.Hirano (Tokyo) Previous talk Current talk

  6. TH et al.(’05-) (CGC +)QGP Hydro+Hadronic Cascade Hadronic Corona (Cascade, JAM) t sQGP core (Full 3D Ideal Hydro) 0.6fm/c z 0 (Option) Color Glass Condensate

  7. TH&Gyulassy(’06),TH,Heinz,Kharzeev,Lacey,Nara(’06) Hydro Meets Data for the First Time at RHIC: “Current” Three Pillars • Perfect Fluid (s)QGP Core • Ideal hydro description of the QGP phase • Necessary to gain integrated v2 • Dissipative Hadronic Corona • Boltzmann description of the hadron phase • Necessary to gain enough radial flow • Necessary to fix particle ratio dynamically • Glauber Type Initial Condition • Diffuseness of initial geometry A Lack of each pillar leads to discrepancy!

  8. (1) Glauber and (2) CGC Hydro Initial Conditions Which Clear the First Hurdle Centrality dependence Rapidity dependence • Glauber model • Npart:Ncoll = 85%:15% • CGC model • Matching I.C. via e(x,y,h)

  9. pT Spectra for identified hadronsfrom QGP Hydro+Hadronic Cascade dN/dy and dN/dpT are o.k. by hydro+cascade. Caveat: Other components such as recombination and fragmentation should appear in the intermediate-high pT regions.

  10. TH et al.(’06) v2(Npart) from QGP Hydro + Hadronic Cascade • Glauber: • Early thermalization • Mechanism? • CGC: • No perfect fluid? • Additional viscosity • is required in QGP Result of JAM: Courtesy of M.Isse Importance of better understanding of initial condition

  11. Large Eccentricity from CGC Initial Condition Hirano and Nara(’04), Hirano et al.(’06) Kuhlman et al.(’06), Drescher et al.(’06) y x Pocket formula (ideal hydro): v2 ~ 0.2e @ RHIC energies Ollitrault(’92)

  12. v2(pT) for identified hadronsfrom QGP Hydro + Hadronic Cascade Glauber type initial condition CGC initial condition 20-30% 20-30% Mass dependence is o.k. v2(model) > v2(data)

  13. v2(h) fromQGP Hydro + Hadronic Cascade Glauber-BGK CGC

  14. Discussions: Hadronic Dissipation • Hybrid Model: QGP Fluid + Hadronic Gas + Glauber I.C. • Hydro Model: QGP Fluid + Hadronic Fluid + Glauber I.C. ComparisonTry to draw information on hadron gas • Key technique in hydro: • Partial chemical equilibrium in hadron phase • Particle ratio fixed at Tch • Chemical equilibrium changes dynamics. TH and K.Tsuda(’02),TH and M.Gyulassy(’06)

  15. Hydro ~ Hydro+Cascade for Protons • Tth ~ 100 MeV • Shape of spectrum • changes due to • radial flow rather • than hadronic • dissipation for • protons. radial flow

  16. Opposite Behavior for Pions Green line: Teaney(’03) Caveat: Transverse expansion Non-scaling solution Hadronic Gas (Viscous pressure) Hadronic Fluid (pdV work)

  17. Hadronic Dissipation Suppresses Differential Elliptic Flow Difference comes from dissipation only in the hadron phase • Relevant parameter: Gs/t • Teaney(’03) • Dissipative effect is not so • large due to small expansion • rate (1/tau ~ 0.05-0.1 fm-1) Caveat: Chemically frozen hadronic fluid is essential in differential elliptic flow. (TH and M.Gyulassy (’06))

  18. Mass Splitting Comes from the Late Hadronic Stage Pion: Generation of v2 in the hadronic stage Proton: Radial flow effects Huovinen et al.(’01) Pion Mass splitting itself is not a direct signature of perfect fluid QGP. Proton

  19. v2(h) fromQGP Hydro + Hadronic Cascade Suppression due to hadronic dissipation Glauber-BGK

  20. Excitation Function of v2 • Hadronic Dissipation • is huge at SPS. • still affects v2 at RHIC. • is almost negligible at LHC.

  21. Summary • An answer to the question, “Whether Perfect Fluid QGP is discovered”, depends on relatively unknown details of the initial state. • Perfect fluid QGP or CGC? • Hadronic dissipative (rescattering) effects after hadronization of QGP fluids are considered through a hadron cascade model. • Many discrepancy between ideal hydro and data can be interpreted by hadronic dissipation.

  22. Source Function from 3D Hydro + Cascade How much the source function differs from ideal hydro in Configuration space? Blink: Ideal Hydro, Kolb and Heinz (2003) Caveat: No resonance decays in ideal hydro

  23. Non-Gaussian Source? y px= 0.5GeV/c x

  24. v2(pT) from Hydro: Past, Present and Future 2000 (Heinz, Huovinen, Kolb…) Ideal hydro w/ chem.eq.hadrons 2002 (TH,Teaney,Kolb…) +Chemical freezeout 2002 (Teaney…) +Dissipation in hadron phase 2005 (BNL) “RHIC serves the perfect liquid.” 2004-2005 (TH,Gyulassy) Mechanism of v2(pT) slope 2005-2006(TH,Heinz,Nara,…) +Color glass condensate Future “To be or not to be (consistent with hydro), that is THE question” -- anonymous XXXXXXXXXXXXXX XXXXXXXXXXXXXX ????????????????? 20-30% History of differential elliptic flow ~History of development of hydro ~History of removing ambiguity in hydro

  25. Viscosity from a Kinetic Theory See, e.g. Danielewicz&Gyulassy(’85) For ultra-relativistic particles, the shear viscosity is Ideal hydro: l 0 shear viscosity  0 Transport cross section

  26. Viscosity and Entropy • Reynolds number Iso, Mori, Namiki (’59) R>>1 Perfect fluid where • 1+1D Bjorken flow Bjorken(’83) • Baym(’84)Hosoya,Kajantie(’85)Danielewicz,Gyulassy(’85)Gavin(’85)Akase et al.(’89)Kouno et al.(’90)… (Ideal) (Viscous) h: shear viscosity (MeV/fm2), s : entropy density (1/fm3) h/s is a good dimensionless measure (in the natural unit) to see viscous effects.

  27. Why QGP Fluid + Hadron Gas Works? h: shear viscosity, s : entropy density TH and Gyulassy (’06) Kovtun,Son,Starinets(’05) • Absolute value of viscosity • Its ratio to entropy density ! Rapid increase of entropy density can make hydro work at RHIC. Deconfinement Signal?!

  28. Temperature Dependence ofh/s • Shear Viscosity in Hadron Gas Danielewicz&Gyulassy(’85) • Assumption:h/s at Tc in the sQGP is 1/4p Kovtun, Son, Starinets(‘05) No big jump in viscosity at Tc! • We propose a possible scenario:

  29. Digression [Pa] = [N/m2] (Dynamical) Viscosity h: ~1.0x10-3 [Pa s] (Water20℃) ~1.8x10-5 [Pa s] (Air 20℃) Kinetic Viscosity n=h/r: ~1.0x10-6 [m2/s] (Water20℃) ~1.5x10-5 [m2/s] (Air20℃) hwater > hair BUT nwater < nair Non-relativistic Navier-Stokes eq. (a simple form) Neglecting external force and assuming incompressibility.

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