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Perfect Fluidity of QGP at RHIC?

Perfect Fluidity of QGP at RHIC?. 平野哲文. Tetsufumi Hirano Institute of Physics University of Tokyo Komaba, Tokyo 153-8902, Japan. 东京大学. 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. OUTLINE.

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Perfect Fluidity of QGP at RHIC?

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  1. Perfect Fluidity of QGPat RHIC? 平野哲文 Tetsufumi Hirano Institute of Physics University of Tokyo Komaba, Tokyo 153-8902, Japan 东京大学 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 • “RHIC serves the perfect liquid” • Elliptic flow • Results from hydro + cascade model • Ratio of viscosity to entropy • Summary

  3. What is “Perfect Liquid”? A possibility of “Perfect Liquid QGP” is intriguing. In this context, a lot of people say, “QGP viscosity is small”. Viscosity is “small” in comparison with …, what??? I will discuss this issue later.

  4. What is Elliptic Flow? Ollitrault (’92) How does the system respond to spatial anisotropy? No secondary interaction Hydro behavior y f x INPUT Spatial Anisotropy 2v2 Interaction among produced particles dN/df dN/df OUTPUT Momentum Anisotropy 0 f 2p 0 f 2p

  5. Elliptic Flow from a Kinetic Theory ideal hydro limit Zhang et al.(’99) View from collision axis Time evolution of v2 b = 7.5fm v2 • Gluons uniformly distributed • in the overlap region • dN/dy ~ 300 for b = 0 fm • Thermal distribution with • T = 500 MeV t(fm/c) generated through secondary collisions saturated in the early stage sensitive to cross section (~m.f.p.~viscosity) v2 is

  6. 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!

  7. 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 c.f. Similar approach by Nonaka and Bass (DNP04,QM05)

  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 y x Pocket formula (ideal hydro): v2 ~ 0.2e @ RHIC energies Ollitrault(’92)

  12. v2(pT) for identified hadrons Glauber type initial condition CGC initial condition Mass dependence is o.k. v2(model) > v2(data)

  13. 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.

  14. 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?!

  15. 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.

  16. Summary • Perfect Fluid QGP + Dissipative Hadron + Glauber initial conditions does a good job. • Manifestation of deconfinement? • CGC initial conditions spoil this agreement. • Viscous QGP may compensate “CGC effect”. • Importance of better understanding initial conditions. To be or not to be (consistent with hydro), that is THE question. --Anonymous

  17. Thank you! TH&Gyulassy(’06) QGP mixed hadron Energy in (four-)velocity plane at midrapidity Energy density in the transverse plane at midrapidity

  18. 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

  19. A Long Long Time Ago… …we obtain the value R (Reynolds number)=1~10… Thus we may infer that the assumption of the perfect fluid is not so good as supposed by Landau.

  20. A Final Piece of RHIC Jigsaw Puzzle? or Glauber CGC Or any other possible scenarios based on non-equilibrium models, instabilities, etc. for thermalization / isotropization mechanism. A much better understanding of initial condition is desperately needed. Distinguish via 3D jet tomography Adil, Gyulassy and TH (’06)

  21. Results from Hydro + Cascade (III) Glauber-BGK CGC

  22. 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

  23. 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:

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

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