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

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

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

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  ,  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 RHIC Becattini et al., hep-ph/ 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 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 Number of virtual photons per real photon (in a given    p T interval): Point-like process: Hadron decay: m ee (MeV) About 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.

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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: 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 Calculation with space-time evolution from ideal hydrodynamics ( arXiv: v1 ) –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 Low High x y Low High Density, Pressure Pressure Gradient Initial ( sec) Thermalized Medium

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 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 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: (2001). Gas-Liquid Phase Transition Superfluidity Transition Hot QCD? String Theory Lowest Bound!

18 Connections / Impact Strongly interacting Li atoms Damping of breathing modes implies very low  /s  /s ~ 7 x 1/4 

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 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  = 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 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: v2)arXiv: v2 Zero viscosity limit determined from fit Deviation (less flow) due to finite viscosity

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  = Including below the bound.

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

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 BAMPS: B oltzmann A pproach of M ulti P arton S catterings Z. Xu, C. Greiner, H. Stöcker, arXiv: [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 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: [nucl-th]C. RosenP. Steinberg

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 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 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)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”