1. 1 Professor Jamie Nagle University of Colorado, Boulder Quantifying Thermodynamic Properties of the Perfect Liquid Gordon Research Conference July 14, 2009, Smithfield RI

2. 2 What happens when we heat up the hadron gas?

3. 3 Hagedorn (1968) calculated a limiting temperature due to exponential increase in hadron levels. Adding more energy only excites more states, no more increase in temperature. Cannot exceed T H ~ 170 MeV, except through change in Degrees of Freedom (e.g. QGP).

4. 4 Ultimate Temperature in the Early Universe K. Huang & S. Weinberg, Phys Rev Lett 25, 1970. “…a veil, obscuring our view of the very beginning.” Steven Weinberg, The First Three Minutes (1977) Karsch, Redlich, Tawfik, Eur.Phys.J.C29:549-556 (2003). /T4/T4 Thermal QCD ”QGP” (Lattice) Temperature/T c Lattice QCD IHRG P /  ~  -2/7 A. Bazavov et al. (HotQCD), arXiv:0903.4379 [hep-lat] Energy Density  (GeV/fm 3 ) Pressure /  Slide from Paul Stankus Hadron gas

5. 5 0 fm/c 2 fm/c 7 fm/c >7 fm/c Diagram from Peter Steinberg Relativistic Heavy Ion Collisions

6. 6 Out of a maximum energy of 39.4 TeV in central Gold Gold reactions, 26 TeV is available in the fireball. Energy density is far above the expected transition point. 26 TeV Fireball Lattice  c  Bj ~ 4.6 GeV/fm 3  Bj ~ 23.0 GeV/fm 3 Lattice Critical Density

7. 7  ,  0, K , K *0 (892), K s 0, , p, d,  0, , ,  ,  0, K , K *0 (892), K s 0, , p, d,  0, , , ,  *(1385), ,  ,  *(1385),  *(1520),  ±,  (+ antiparticles) (+ antiparticles) in equilibrium at T > 170 MeV Final state hadrons yield late time information

8. 8 RHIC Becattini et al., hep-ph/9701275 At RHIC energies the late time temperature is consistent with being at the transition temperature. However, the results of this statistical analysis are not unique to thermal equilibration. Except Strangeness

9. 9 How to Access Information at Earlier Times? Electromagnetic Radiation Real and Virtual Direct Photons Any such signal integrates over the entire time evolution. However, recall the T 4 in the radiated power.

10. 10 Number of virtual photons per real photon (in a given    p T interval): Point-like process: Hadron decay: m ee (MeV) About 0.001 virtual photons with m ee > M pion for every real photon Direct photon 00 1/N  dN ee /dm ee (MeV -1 ) Avoid the  0 background at the expense of a factor 1000 in statistics form factor Real versus Virtual Photons Direct real photons  direct /  decay ~ 0.1 at low p T, and thus systematics dominate.

11. 11

12. 12 Thermalized hot matter emits EM radiation NLO pQCD (W. Vogelsang) Fit to pp Emission rate and distribution consistent with equilibrated matter:  < 1 fm/c and T ~ 2 x T c ! QGP Shine !?! PHENIX: arXiv:0804.4168 T AA scaled pp + Exponential Proton-Proton Direct Photons Gold-Gold Direct Photons T i ~ 300 MeV Measurement in d-Au is important check.

13. 13 Calculation with space-time evolution from ideal hydrodynamics ( arXiv:0904.2184v1 ) –Hydro starts early (  0 = 0.2 fm/c) to take pre-equilibrium photons into account –Thermal equilibrium expected at  0 = 0.6 fm/c (T initial = 340 MeV) –Photons from jet-plasma interaction needed Is measuring a temperature above T Hagedorn definitive proof of the QGP?

14. 14 Low High x y Low High Density, Pressure Pressure Gradient Initial (10 -24 sec) Thermalized Medium

15. 15 Hydrodynamics with no viscosity matches data. *viscosity = resistance of liquid to shear forces (and hence to flow) Large Reynolds's Number limit  inviscid fluid approximation Thermalization time  < 1 fm/c and  =20 GeV/fm 3 v2v2 p T (GeV) Perfect Fluid (AIP Story of the Year 2005)

16. 16 Weak coupling (  ~0) Strong coupling (  ↑) top region bottom region Honey – viscosity decreases at higher temperatures viscosity increases with stronger coupling Viscosity Review Inhibited diffusion ↓ Small viscosity ↓ Perfect fluid ↓ Strong Coupled QGP (i.e. sQGP)

17. 17 Calculating viscosity is very difficult in a strongly-coupled gauge theory (e.g. QCD). How about in String Theory (AdS/CFT)? The Shear Viscosity of Strongly Coupled N=4 Supersymmetric Yang-Mills Plasma G. Policasto, D.T. Son, A.O. Starinets, PRL 87: 081601 (2001). Gas-Liquid Phase Transition Superfluidity Transition Hot QCD? String Theory Lowest Bound!

18. 18 Connections / Impact Strongly interacting Li atoms Damping of breathing modes implies very low  /s  /s ~ 7 x 1/4  http://www.phy.duke.edu/research/photon/qoptics

19. 19 Non-relativistic: Damping given by Relativistic: Causal, second-order expansion: –Relativistic Fluid Dynamics: Physics for Many Different ScalesRelativistic Fluid Dynamics: Physics for Many Different Scales Neglect various terms at your own risk: –Baier et al., Relativistic viscous hydrodynamics, conformal invariance, and holographyRelativistic viscous hydrodynamics, conformal invariance, and holography –Natsuume and Okamura, Comment on “Viscous hydrodynamics relaxation time from AdS/CFT correspondence” Comment on “Viscous hydrodynamics relaxation time from AdS/CFT correspondence” Slide from W.A. Zajc Our Problem is Much Harder

20. 20 How to Quantify  /s?  /s ~ 0  /s = 1/4   /s = 2 x 1/4   /s = 3 x 1/4  Need 3-d relativistic viscous hydrodynamics to compare to bulk medium flow. Theory milestone. * with caveats * Experimental Uncertainty may be solved!

21. 21  = eccentricity S T = transverse overlap area dN/dy = number of partons Knudsen Number Alternative Approach (Boltzmann Style) Statement that this form obeys the reasonable limits for K  0 and K  ∞

22. 22 Drescher et al. with Glauber initial conditions  /s = 2.4 x 1/4  And Color Glass Condensate initial conditions  /s = 1.4 x 1/4  However, there is a mistake in the CGC case, it should be  /s = 1.9 x 1/4  Nagle, Steinberg, Zajc (manuscript in preparation) First, attempt to reproduce results of Drescher, Dumitru, Gombeaud, Ollitrault (arXiv:arXiv:0704.3553v2)arXiv:0704.3553v2 Zero viscosity limit determined from fit Deviation (less flow) due to finite viscosity

23. 23 Statement that this form obeys the correct limits for K  0 and K  ∞ So does this form based on Pade Approximants with b=e and c=a+1 * original value  /s = 2.59 ± 0.53 MINUIT FIT PROBLEM! One standard deviation range  /s x 1/4  = 0.34 - 2.55 Including below the bound.

24. 24 If one is near the Quantum Limit there must be a major change to the Boltzmann picture. Motivated by original derivation of the perfect fluid limit… However, this is a crude inclusion of the bound into the Boltzmann picture. Real physics near the bound may be quite different (think of the derivation for BEC). * original value  /s = 2.59 ± 0.53

25. 25 x=0.0 x=0.13 x=1.00 Glauber initial conditions depends on x value chosen. Drescher et al. x=0.20 Luzam & Romatschke x=1.00 Only x=0.13 matches PHOBOS data. Binary Collisions Participants b (fm)

26. 26 Slightly lower fluctuations in eccentricity for x=1.00 (but very slight). Note there are two CGC parameterizations that need reconciling too.

27. 27 t = 1 fm/c t = 3 fm/c t = 7 fm/c Hydrodynamic Calculations assume equilibration at very early times. No information on mechanism for equilibration. If no viscosity, evolution is isentropic. Thus almost all entropy generated in ~ 0.5 fm/c. Rapid Entropy Production

28. 28 BAMPS: B oltzmann A pproach of M ulti P arton S catterings Z. Xu, C. Greiner, H. Stöcker, arXiv: 0711.0961 [nucl-th] A transport algorithm solving the Boltzmann-Equations for on-shell partons with pQCD interactions (including 2  3 processes) Note that there is disagreement about this result. Also for a 1 GeV gluon at  = 1 fm/c the average ratio (DeBroglie) / (Mean Free Path) ~ 0.7

29. 29 Perfect Fluid versus Quasiparticle Transport Identify mean free path = v  and  = 2 /  Weakly coupled limit from kinetic theory: > 1 / 4  ~ Order(1) Very hard to have well defined quasiparticles at early fluid stages. L.A. Linden LevyL.A. Linden Levy, JN, C. Rosen, P. Steinberg. e-Print: arXiv:0709.3105 [nucl-th]C. RosenP. Steinberg

30. 30 Talk on thermodynamic properties, but no mention of phase transition and order. Lattice QCD results indicate a smooth cross-over at  B =0. However, experimentally no evidence for 1 st or 2 nd order transition, but no convincing case that they are experimentally excluded. Very hard in a finite system. Real challenge for energy scan for search for critical point. Phase Transition

31. 31 Hadron gas Thermal QCD ”QGP” (Lattice) Temperature/T c Lattice QCD IHRG P /  ~  -2/7 /T4/T4 Quark Gluon Plasma? …for your discussion T initial ~ 300 MeV

32. 32 The End

33. 33 “Liquid is one of the principal states of matter. A liquid is a fluid that has the particles loose and can freely form a distinct surface at the boundaries of its bulk material.” (Wikipedia)states of matter fluid Is the low shear viscosity / entropy density ratio (  /s) the only common connection to the traditional term “liquid”? Perhaps then “fluid” is a better choice since there is an obvious confusion with the term: “Quark Gluon Plasma Liquid”