Is RHIC-Produced MatterMore Like Milk or Honey?

Joe KapustaUniversity of Minnesota

ESQGP, Stony Brook, 2008

What has RHIC told us aboutthe equation of state?

How does RHIC connect toother fields like cosmology and

condensed matter physics?

Big Experimental Motivation!PHENIX data + Huovinen et al. PHENIX: First Three Years of

Operation of RHIC

.correlated are and But fT T!

2-body scattering insufficient to generate v2 unless parton-parton cross section is 45 mb! (Molnar, Gyulassy)

Big Theoretical Motivation!Viscosity in Strongly InteractingQuantum Field Theories fromBlack Hole Physics

Kovtun, Son, Starinets PRL 94, 111601 (2005)

Using the Kubo formula [ ])0(),(1

lim20

1tracelesstraceless

4

0

ijijti TxTexd !

! !" #$=

the low energy absorption cross section for gravitons on blackholes, and the black hole entropy formula they found that

!" 4/1/ =s and conjectured that this is a universal lower bound.

Is the RHIC data, in the form of elliptic and radial flow,telling us that the matter has very small viscosity, a perfect fluid ?

Atomic and Molecular Systems

vTls

free~

!

!nl

1~

freeIn classical transport theory and

so that as the density and/or cross section is reduced(dilute gas limit) the ratio gets larger.

In a liquid the particles are strongly correlated. Momentumtransport can be thought of as being carried by voids insteadof by particles (Enskog) and the ratio gets larger.

Helium

NIST data

Nitrogen

NIST data

OH2

NIST data

2D Yukawa Systemsin the Liquid State

radius Seitz-Wigner1

17parameter coupling Coulomb

at located Minimum

2

2

==

!=="

na

aT

Q

#

Applications to dusty-plasmas andmany other 2D condensed mattersystems.

Liu & Goree (2005)

QCD• Chiral perturbation theory at low T (Prakash et al.): grows with decreasing T.

• Quark-gluon plasma at high T (Arnold, Moore,Yaffe): grows with increasing T.

4

4

16

15

T

f

s

!

!

"=

)/42.2ln(

12.54

ggs=

!

!!"

#$$%

&!!"

#$$%

&

'+!!"

#$$%

&

'=

TT

TT

Tgln2ln

9

4ln

8

9

)(

1222 ((

MeV 30=!T

QCDLow T (Prakash et al.)using experimentaldata for 2-bodyinteractions.

High T (Yaffe et al.)using perturbativeQCD.

Classical quasiparticle model (Gelman, Shuryak, Zahed) → 0.34 for 1<T/Tc<1.5 Lattice w/o quarks (Meyer) → 0.134 at T/Tc=1.65 and 0.102 at T/Tc=1.24

Shear vs. Bulk Viscosity

Shear viscosity is relevant for change in shape at constant volume.

Bulk viscosity is relevant for change in volume at constant shape.

Bulk viscosity is zero for point particles and for a radiationequation of state. It is generally small unless internal degreesof freedom (rotation, vibration) can easily be excited incollisions. But this is exactly the case for a resonance gas –expect bulk viscosity to be large near the critical temperature!

Lennard-Jones potential

Meier, Laesecke, KabelacJ. Chem. Phys. (2005)

Pressure fluctuations give peak in bulk viscosity.

QCD• Chiral perturbation theory at low T (Chen, Wang): grows with increasing T.

• Quark-gluon plasma at high T (Arnold, Dogan,Moore, ): decreases with increasing T.

4

4

28

3ln

4

1ln

8

9

!!

"

f

T

TTs

pp

##$

%&&'

()

*##$

%&&'

()

*=

)/34.6ln(5000

4

g

g

s=

!

!!"

#$$%

&!!"

#$$%

&

'+!!"

#$$%

&

'=

TT

TT

Tgln2ln

9

4ln

8

9

)(

1222 ((

MeV 30=!T

QCDLow T (Chen & Wang)using chiralperturbation theory.

High T (Arnold et al.)using perturbativeQCD.

ς/s rises dramatically as Tc is approached from above (Karsch, Kharzeev, Tuchin) Lattice w/o quarks (Meyer) → 0.008 at T/Tc=1.65 and 0.065 at T/Tc=1.24

QCDLow T (Prakash et al.)using experimentaldata for 2-bodyinteractions.

High T (Arnold et al.)using perturbativeQCD.

ς/s rises dramatically as Tc is approached from above (Karsch, Kharzeev, Tuchin) Lattice w/o quarks (Meyer) → 0.008 at T/Tc=1.65 and 0.065 at T/Tc=1.24

µµµ

µ!!µµ!µ!

BBB JunJ

TuuwPgT

"+=

"++#=

( ) ( ) !

!

µ"µ""µµ" #$$ uHuuT %&+'+'='3

2

!"

"

!!#

#

µµµ

µ$$µµ$uTuTQuuguuH %&%'%&%'(&' ,,

µµµµµ µµ!

B

BBB

BJ

Tsus

Tw

TnJ "#=$

%

&'(

)"$

%

&'(

)=" ,

2

( ) ( ) ( )22

22

3

2

2kk

k

k

k

k

iji

j

j

i uTTT

uT

uuuT

s &+!+!+!"!+!=!#$

%&µ

µ

Relativistic Dissipative Fluid Dynamics

In the Landau-Lifshitz approach u is the velocity of energy transport.

Suppose the bulk viscosity increaseswith decreasing temperature.

negligible )(,)(,)( 4T

T

TTBATTP

n

i

i!"" #

$

%&'

(=)=

!"

#$%

&

+

++'(

)*+

,

+

+-!

"

#$%

&=!!

"

#$$%

&

=-+

+

++

.

.

.

/

.

/

.

.

.

/

.

0

.

0

i

iii

i

iii

i

n

i

n

iTsn

n

Tsn

n

T

T

P

1

1

41

1

41

0d

d

onillustratifor expansion Bjorken

3/)4(4

2

Should be small compared to 1

Wins atlarge time

Suppose the bulk viscosity diverges ata critical temperature.

negligible )(,)(,)( 4T

TT

TTTBATTP

n

c

ci

i!"" ##

$

%&&'

(

)

)=)=

( ) !"##$

%&&'

(##$

%&&'

()+"

=)+

+

**

+

*

+

*

,

*

,

as 1

0d

d

onillustratifor expansion Bjorken

/1/1

2

n

c

n

i

i

cic

TsTTTT

P

Takes infinite time to reach critical temperature: Critical Slowing Down

Conclusion

• Hadron/quark-gluon matter should have aminimum in shear viscosity and a maximum inbulk viscosity at or near the critical or crossoverpoint in the phase diagram analogous to atomicand molecular systems.

• Sufficiently detailed calculations andexperiments ought to allow us to infer theviscosity/entropy ratios. This are interestingdimensionless measures of dissipation relativeto disorder.

Conclusion

• RHIC is a thermometer (hadron ratios,photon and lepton pair production)

• RHIC is a barometer (elliptic flow,transverse flow)

• RHIC may be a viscometer (deviationsfrom ideal fluid flow)

• There is plenty of work for theorists (andexperimentalists)!