Professor Jamie Nagle University of Colorado, Boulder

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

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

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 TH ~ 170 MeV, except through change in Degrees of Freedom (e.g. QGP).

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) e/T4 Lattice QCD Thermal QCD ”QGP”(Lattice) Pressure / e IHRG P/e ~ e-2/7 Hadron gas Energy Density e (GeV/fm3) Temperature/Tc A. Bazavov et al. (HotQCD), arXiv:0903.4379 [hep-lat] Karsch, Redlich, Tawfik, Eur.Phys.J.C29:549-556 (2003). Slide from Paul Stankus

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

6. 26 TeV Fireball Lattice ec eBj ~ 23.0 GeV/fm3 eBj ~ 4.6 GeV/fm3 Lattice Critical Density 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.

7. Final state hadrons yield late time information p, p0, K, K*0(892), Ks0, h, p, d, r0, f, D, L, S*(1385), L*(1520), X± , W (+ antiparticles) in equilibrium at T > 170 MeV

8. 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. RHIC Except Strangeness Becattini et al., hep-ph/9701275

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 T4 in the radiated power.

10. Real versus Virtual Photons Direct real photons gdirect/gdecay ~ 0.1 at low pT, and thus systematics dominate. Number of virtual photons per real photon (in agiven pT interval): Hadron decay: Point-likeprocess: form factor About 0.001 virtual photonswith mee > Mpion for every real photon 1/N dNee/dmee (MeV-1) Direct photon Avoid the 0 backgroundat the expense of a factor 1000 in statistics 0 mee (MeV)

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

13. Is measuring a temperature above THagedorn definitive proof of the QGP? 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 (Tinitial = 340 MeV) • Photons from jet-plasma interaction needed

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

15. Perfect Fluid (AIP Story of the Year 2005) Hydrodynamics with no viscosity matches data. v2 pT (GeV) Thermalization time t < 1 fm/c and e=20 GeV/fm3 *viscosity = resistance of liquid to shear forces (and hence to flow) Large Reynolds's Number limit  inviscid fluid approximation

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

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). Superfluidity Transition Gas-Liquid Phase Transition String Theory Lowest Bound! Hot QCD?

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

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

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

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

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

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 MINUIT FIT PROBLEM! One standard deviation range h/s x 1/4p = 0.34 - 2.55 Including below the bound. * original value h/s = 2.59 ± 0.53

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 h/s = 2.59 ± 0.53

25. Binary Collisions Participants b (fm) 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. x=0.0 x=0.13 x=1.00

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

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

28. BAMPS: Boltzmann Approachof MultiParton Scatterings 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 t = 1 fm/c the average ratio l(DeBroglie) / l (Mean Free Path) ~ 0.7

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

30. Phase Transition Talk on thermodynamic properties, but no mention of phase transition and order. Lattice QCD results indicate a smooth cross-over at mB=0. However, experimentally no evidence for 1st or 2nd 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.

31. Quark Gluon Plasma? …for your discussion e/T4 Lattice QCD Thermal QCD ”QGP”(Lattice) IHRG P/e ~ e-2/7 Hadron gas Temperature/Tc Tinitial ~ 300 MeV

32. The End

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) Is the low shear viscosity / entropy density ratio (h/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” 