Perfect Fluidity of QGP at RHIC Tetsufumi Hirano

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

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.

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

Elliptic Flow from a Kinetic Theory ideal hydro limit Zhang et al. (’ 99) v 2 Time evolution of v 2 View from collision axis b = 7. 5 fm t(fm/c) • Gluons uniformly distributed in the overlap region • d. N/dy ~ 300 for b = 0 fm • Thermal distribution with T = 500 Me. V generated through secondary collisions v 2 is saturated in the early stage sensitive to cross section (~m. f. p. ~viscosity)

TH&Gyulassy(’ 06), TH, Heinz, Kharzeev, Lacey, Nara(’ 06) Hydro Meets Data for the First Time at RHIC: “Current” Three Pillars 1. Perfect Fluid (s)QGP Core • Ideal hydro description of the QGP phase • Necessary to gain integrated v 2 2. Dissipative Hadronic Corona • • • Boltzmann description of the hadron phase Necessary to gain enough radial flow Necessary to fix particle ratio dynamically 3. Glauber Type Initial Condition • Diffuseness of initial geometry A Lack of each pillar leads to discrepancy!

TH et al. (’ 05 -) (CGC +)QGP Hydro+Hadronic Cascade Hadronic Corona (Cascade, JAM) t 0. 6 fm/c z 0 c. f. Similar approach by Nonaka and Bass (DNP 04, QM 05) s. QGP core (Full 3 D Ideal Hydro) (Option) Color Glass Condensate

(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)

p. T Spectra for identified hadrons from QGP Hydro+Hadronic Cascade d. N/dy and d. N/dp. T are o. k. by hydro+cascade. Caveat: Other components such as recombination and fragmentation should appear in the intermediate-high p. T regions.

TH et al. (’ 06) v 2(Npart) from QGP Hydro + Hadronic Cascade Glauber: ü Early thermalization ü Mechanism? CGC: ü No perfect fluid? ü Additional viscosity is required in QGP Result of JAM: Courtesy of M. Isse Importance of better understanding of initial condition

Large Eccentricity from CGC Initial Condition y x Pocket formula (ideal hydro): v 2 ~ 0. 2 e @ RHIC energies Ollitrault(’ 92)

v 2(p. T) for identified hadrons Glauber type initial condition Mass dependence is o. k. CGC initial condition v 2(model) > v 2(data)

Viscosity and Entropy • Reynolds number where Iso, Mori, Namiki (’ 59) R>>1 Perfect fluid • 1+1 D 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 (Me. V/fm 2), s : entropy density (1/fm 3) h/s is a good dimensionless measure (in the natural unit) to see viscous effects.

Why QGP Fluid + Hadron Gas Works? TH and Gyulassy (’ 06) h : shear viscosity, s : entropy density 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? !

Digression [Pa] = [N/m 2] (Dynamical) Viscosity h: ~1. 0 x 10 -3 [Pa s] (Water 20℃) ~1. 8 x 10 -5 [Pa s] (Air 20℃) Kinetic Viscosity n=h/r: ~1. 0 x 10 -6 [m 2/s] (Water 20℃) ~1. 5 x 10 -5 [m 2/s] (Air 20℃) hwater > hair BUT nwater < nair Non-relativistic Navier-Stokes eq. (a simple form) Neglecting external force and assuming incompressibility.

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

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

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

A 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.

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

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

v 2(p. T) 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 v 2(p. T) 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 ? ? ? ? ? 20 -30% History of differential elliptic flow ~History of development of hydro ~History of removing ambiguity in hydro

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

Ideal QGP Fluid + Dissipative Hadron Gas Models hydro (1+1)D with cascade Ur. QMD Bjorken flow A. Dumitru et al. , PLB 460, 411(1999); PRC 60, 021902(1999); S. Bass and A. Dumitru, PRC 61, 064909(2000). RQMD N/A JAM N/A (2+1)D with Bjorken flow N/A D. Teaney et al. , PRL 86, 4783(2001), nucl-th/0110037; D. Teaney, nucl-th/0204023. N/A Full (3+1)D C. Nonaka and S. Bass, nucl-th/0510038. N/A TH, U. Heinz, D. Kharzeev, R. Lacey, and Y. Nara, PLB 636299(2006).