Dynamics of Relativistic Heavy Ion Collisions and THE Quark Gluon PlasMA

1. Nonequilibrium Dynamics in Astrophysics and Material Science YITP, Kyoto, Japan, Oct. 31-Nov. 3, 2011 Dynamics of Relativistic Heavy Ion Collisions and THE Quark Gluon PlasMA Tetsufumi Hirano Sophia Univ./the Univ. of Tokyo

2. Outline • Introduction • Physics of the quark gluon plasma • Relativistic heavy ion collisions • Elliptic flow • “perfect fluidity” • Higher harmonics • Some topics in relativistic hydrodynamics

3. Introduction • “Condensed” matter physics for elementary particles • Heavy ion collisions as a playground of non-equilibrium physics in relativistic system • Recent findings of the quark gluon plasma and related topics

4. Physics of the quark gluon plasma

5. Two Aspects of Quantum ChromoDynamics QCD: Theory of strong interaction coupling vs. energy scale Asymptotic free of QCD Confinement of color charges

6. What is the Quark Gluon Plasma? Hadron Gas Quark Gluon Plasma (QGP) Low Temperature  High Degree of freedom: Quarks (matter) and gluons (gauge) Mechanics: Quantum ChromoDynamics (QCD) Novel matter under extreme conditions

7. How High? Suppose “transition” happens when a pion (the lightest hadron) gas is close-packed, Note 1: T inside the Sun ~ 107 K Note 2: Tc from the 1st principle calculation ~2x1012 K

8. Where/When was the QGP? History of the Universe ~ History of form of matter Micro seconds after Big Bang Our Universe is filled with the QGP!

9. relativistic heavy ion collisions

10. The QGP on the Earth Front View Side View Relativistic heavy ion collisions Turn kinetic energy (v > 0.99c) into thermal energy

11. Big Bang vs. Little Bang Figure adapted from http://www-utap.phys.s.u-tokyo.ac.jp/~sato/index-j.htm

12. Big Bang vs. Little Bang (contd.) Non-trivial issue on thermal equilibration m.f.p. = Mean Free Path

13. Non-Equilibrium Aspects of Relativistic Heavy Ion Collisions 4. hadron gas time 4. Kinetic approach for relativistic gases 3. Dissipative relativistic fluids 3. QGP fluid 2. 2. Local equilibration collision axis 1. 0 1. Entropy production Au Au

14. Hydrodynamic Simulation of a Au+AuCollision http://youtu.be/p8_2TczsxjM Time scale ~ 10-22 sec quark gluon plasma

15. Elliptic Flow • Elliptic flow (Ollitrault, ’92) • Momentum anisotropy as a response to spatial anisotropy • Known to be sensitive to properties of the system • (Shear) viscosity • Equation of state ~1035Pa 2v2 dN/df 2nd harmonics (elliptic flow)  Indicator of hydrodynamic behavior f 0 2p

16. Relativistic Boltzmann Simulations l: mean free path h: shear viscosity generated through secondary collisions saturated in the early stage sensitive to cross section (~1/m.f.p.~1/viscosity) v2 is Zhang-Gyulassy-Ko(’99)

17. “Hydrodynamic Limit” y Eccentricity x Response of the system reaches “hydrodynamic limit” vs. transverse particle density

18. Ideal Hydrodynamics at Work vs. centrality Au+Au Cu+Cu T.Hirano et al. (in preparation)

19. H.Song et al., PRL106, 192301 (2011) Viscous Fluid Simulations vs. transverse particle density Ratio of shear viscosity to entropy density

20. Strong Coupling Nature of the QGP Large expansion rate of the QGP in relativistic heavy ion collisions •  Tiny viscosity when hydrodynamic description of the QGP works in any ways • Manifestation of the strong coupling nature of the QGP • Note: Underlying theory  Quantum ChromoDynamics(theory of strong interaction)

21. Event-by-event Fluctuation • Actual collision? • Higher order deformation Ideal, but unrealistic? OK on average(?) Figure adapted from talk by J.Jia (ATLAS) at QM2011

22. Deformation at Higher Order

23. Dynamical Modeling of Relativistic Heavy Ion Collisions* hadron gas time Relativistic Boltzmann Relativistic Ideal Hydro Monte Carlo I.C. QGP fluid collision axis 0 Au Au *K.Muraseet al. (in preparation)

24. Deformation in Model Calculations Sample of entropy density profile in a plane perpendicular to collision axis

25. Higher Harmonics from Ideal QGP Fluids vs. centrality (input) vs. centrality (output) Response of the QGP to initial deformation roughly scales with

26. Comparison of vn with Data Theory Experiment Tendency similar to experimental data Absolute value  Viscosity

27. Impact of Finite Higher Harmonics coarse graining size • Most of people did not believe hydro description of the QGP (~ 1995) • Hydro at work to describe elliptic flow (~ 2001) • Hydro at work (?) to describe higher harmonics (~ 2010) initial profile

28. Thermal Radiation from the QGP Photon spectra in relativistic heavy ion collisions Blue shifted spectra with T~200-300 MeV~(2-3)x1012K

29. Relativistic Hydrodynamics

30. Several Non-Trivial Aspects of Relativistic Hydrodynamics Non conservation of particle number nor mass Choice of local rest frame Relaxation beyond Fourier, Fick and Newton laws

31. Hydrodynamic Equations (Ideal Hydro Case) Energy conservation , Momentum conservation , Charge conservation (net baryon number in QCD) ,

32. Several Non-Trivial Aspects of Relativistic Hydrodynamics Non conservation of particle number nor mass Choice of local rest frame Relaxation beyond Fourier, Fick and Newton laws

33. See also talk by Kunihiro Choice of Local Rest Frame in Dissipative Fluids Charge diffusion vanishes on average 1. Charge flow heat flow 2. Energy flow (Eigenvector of energy-momentum tensor) *Energy flow is relevant in heavy ion collisions charge diffusion No heat flow!

34. Several Non-Trivial Aspects of Relativistic Hydrodynamics Non conservation of particle number nor mass Choice of local rest frame Relaxation beyond Fourier, Fick and Newton laws

35. See also talk by Kunihiro Relaxation and Causality Constitutive equations at Navier-Stokes level • Instantaneous response violates causality • Critical issue in relativistic theory • Relaxation plays an essential role thermodynamics force Realistic response

36. Causal Hydrodynamics Within linear response Suppose one obtains differential form Maxwell-Cattaneo Eq.

37. Relativistic Fluctuating Hydrodynamics (RFH) Thermal fluctuation in event-by-event simulations thermodynamic force dissipative current ) thermal noise Fluctuation  Dissipation * In non-relativistic cases, see Landau-Lifshtiz, Fluid Mechanics ** Similar to glassy system, polymers, etc?

38. Coarse-Graining in Time Non-Markovian Markovian coarse graining ??? Navier Stokes  causality Maxwell-Cattaneo Existence of upper bound in coarse-graining time (or lower bound of frequency) in relativistic theory???

39. Finite Size Effect Fluctuation  Local volume. • Information about coarse-grained size? • Fluctuation term ~ average value? • Non-equilibrium small system? • Fluctuation would play a crucial role. • Need to consider (?) finite size effects in equation of state and transport coefficients

40. Conclusion • Physics of the quark gluon plasma • Strong coupling nature • Small viscosity • Physics of relativistic heavy ion collisions • Playground of relativistic non-equilibrium system • Relativistic dissipative hydrodynamics • Relativistic kinetic theory • Non-equilibrium field theory