1Professor Jamie NagleUniversity of Colorado, Boulder

Quantifying Thermodynamic Properties ofthe Perfect Liquid

Gordon Research ConferenceJuly 14, 2009, Smithfield RI

2

What happens when we heat up the

hadron gas?

3

Hadron 'level' diagram

0

500

1000

1500

0 10 20 30 40

Degeneracy

Mass (MeV)

Kfo

Density of States vs Energy

0

50

100

150

200

250

0 500 1000 1500 2000

Mass (MeV)

Number of available

states

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).

Hm/Te m ~dmdn)( m

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

Thermal QCD ”QGP” (Lattice)

Temperature/Tc

Lattice QCD

IHRG P/~ -2/7

A. Bazavov et al. (HotQCD), arXiv:0903.4379 [hep-lat]

Energy Density (GeV/fm3)

Pre

ssur

e /

Slide from Paul Stankus

Hadron gas

5

0 fm/c

2 fm/c

7 fm/c

>7 fm/cDiagram 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

Latticec

Bj ~ 4.6 GeV/fm3

Bj ~ 23.0 GeV/fm3

Lattice Critical Density

7

, , 00, K, K, K, K*0*0(892), K(892), Kss00, , , p, d, , p, d, 00, , , , ,,

, , *(1385), *(1385), *(1520), ± , ,

(+ antiparticles)(+ antiparticles) in equilibrium at T > 170 MeV

2 2

3

3 ( ) /

12 1B

i i p m T

d pN g Ve

Final state hadrons yield late time information

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.

ExceptStrangeness

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

Number of virtual photons per real photon (in agiven pT interval):

Point-likeprocess:

Hadron decay:

mee (MeV)

About 0.001 virtual photonswith mee > Mpion for every real photonDirect photon

0

1/N dNee/dmee (MeV-1)

Avoid the 0 backgroundat the expense of a factor 1000 in statistics

form factor

Real versus Virtual PhotonsDirect real photons direct/decay ~ 0.1 at low pT, and thus systematics dominate.

11

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 Tc !

QGP Shine !?!

PHENIX: arXiv:0804.4168

TAA scaled pp + Exponential

Proton-ProtonDirect Photons

Gold-GoldDirect Photons

Ti ~ 300 MeV

Measurement in d-Au is important check.

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 (Tinitial = 340 MeV)– Photons from jet-plasma interaction needed

Is measuring a temperature above THagedorn

definitive proof of the QGP?

14

Low High

xx

yy

Low High

Density, PressurePressure Gradient

Initial (10-24 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/fm3

v2

pT (GeV)

Perfect Fluid (AIP Story of the Year 2005)

16

Weak coupling (~0)

Strong coupling ( ↑)

<px> top region<px> bottom region

yv

AF xx

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 PlasmaG. Policasto, D.T. Son, A.O. Starinets, PRL 87: 081601 (2001).

Bks1

4

Gas-Liquid Phase TransitionSuperfluidity Transition

Hot QCD?

String TheoryLowest Bound!

18

Connections / ImpactStrongly 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

• 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

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

t)(experimen 0.1 (theory) 3.1 3.141

s

Need 3-d relativistic viscous hydrodynamics to compare to bulk medium flow. Theory milestone.

* with caveats

* Experimental Uncertainty may be solved!

21

= eccentricity

ST = transverse overlap area

dN/dy = number of partons

RK

dydN

SRcR

K

T

s 11

Knudsen Number

0

22

/11

KKvv

ideal

Alternative Approach (Boltzmann Style)

Statement that this form obeys the reasonable limits for K0 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:0704.3553v2)

Zero viscosity limit determined from fit

Deviation (less flow) due to finite viscosity

23

0

22

/11

KKvv

ideal

Statement that this form obeys the correct limits for K0 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 - 2.55Including 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: Boltzmann Approach of MultiParton ScatteringsZ. 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 23 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 Levy, JN, C. Rosen, P. Steinberg.e-Print: arXiv:0709.3105 [nucl-th]

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 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.

Phase Transition

31

Hadron gas

Thermal QCD ”QGP” (Lattice)

Temperature/Tc

Lattice QCD

IHRG P/~ -2/7

/T4Quark Gluon Plasma?…for your discussion

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 (/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”