Download The strongly-interacting low-viscosity matter (25) Joe Kapusta

Strongly Interacting Low
Viscosity Matter Created
in Heavy Ion Collisions
Joe Kapusta*
University of Minnesota
Quark Matter 2006, Shanghai, China
* Original work done in collaboration with Laszlo Csernai and Larry McLerran.
For realistic quark masses
there may be a line of 1st
order transition terminating
at a critical point.
de Forcrand, Philipsen
The phase transition is 2nd
order for 2 massless flavors
and 1st order for 3, otherwise
a rapid crossover.
Karsch, Laermann, Peikert
What has RHIC told us about
the equation of state?
Big Experimental Motivation!
PHENIX data + Huovinen et al.
PHENIX: First Three Years of
Operation of RHIC
But T and T f are correlated .
Numerical Hydrodynamics
(Huovinen, Kolb, Heinz, Hirano, Teaney, Shuryak, Hama, Morita, Nonaka, Bass)
Assume thermalization between 0.15 and 1 fm/c.
Agreement provides strong indication for early
thermalization and collective flow.
Big Theoretical Motivation!
Viscosity in Strongly Interacting
Quantum Field Theories from
Black Hole Physics
Kovtun, Son, Starinets PRL 94, 111601 (2005)


1
1
4
i t
ij
ij


lim
d
x
e
T
(
x
),
T
(0)
Using the Kubo formula

traceless
traceless


0
20

the low energy absorption cross section for gravitons on black
holes, and the black hole entropy formula they found that
 / s  1 / 4 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

1
In classical transport theory
and
s
n
so that as the density and/or cross section is reduced
(dilute gas limit) the ratio gets larger.
~ Tlfree v
lfree ~
In a liquid the particles are strongly correlated. Momentum
transport can be thought of as being carried by voids instead
of by particles (Enskog) and the ratio gets larger.
Helium
NIST data
Nitrogen
NIST data
H 2O
NIST data
2D Yukawa Systems
in the Liquid State
Minimum located at
Q2

 Coulomb coupling parameter  17
aT
1
a2 
 Wigner - Seitz radius
n
Applications to dusty-plasmas and
many other 2D condensed matter
systems.
Liu & Goree
QCD
• Chiral perturbation theory at low T
(Prakash et al.): grows with decreasing T.

15 f4

s 16 T 4
• Quark-gluon plasma at high T (Arnold, Moore,
Yaffe): grows with increasing T.

s

5.12
g 4 ln( 2.42 / g )

 T 
 T
1
9
4
  2 ln  2 ln 
 2 ln 
2

g (T ) 8

9

 T
 T


 


T  30 MeV
QCD
Low T (Prakash et al.)
using experimental
data for 2-body
interactions.
High T (Yaffe et al.)
using perturbative
QCD.
η/s≈1/2 just above Tc
from lattice (Nakamura, Sakai)
and classical quasiparticle model (Gelman, Shuryak, Zahed)
Large Nc Limit at Low T
• Baryon masses are proportional to Nc and can be neglected,
meson masses are essentially independent of Nc. Hagedorn
temperature and critical temperature should not change by
much. Meson-meson cross sections scale as 1/ Nc2, therefore
η/s should scale as Nc2 in the hadronic phase.
• From Yaffe et al. η/s = A/[(g2 Nc)2 ln(Bg2 Nc)] with A and B known
constants, therefore η/s has a finite limit as Nc becomes large in
the plasma phase.
• Implication: There is a jump in η/s of order Nc2 in going from the
low to the high temperature phases.
Huot,Jeon,Moore
Policastro,Son,Starinets & Buchel,Liu,Starinets
SYM
•SYM has no running coupling and
no phase transition
•SYM has many more d.o.f. as
scattering targets than QCD
Relativistic Dissipative Fluid Dynamics
T    Pg   wu  u  T 
J B  nB u    J B
In the Eckart approach u is the velocity of baryon number flow.




T     u   u    23    H    u    H u  H  u  Q
H   u  u  g  ,       u u    , Q   T  Tu    u
1
s  su  u T 
T


 s 


u
2T
i
j

  ju    k u
i
2
3
ij

k 2



 u 
T
k 2
k


T
2




T

T
u
k
k
2
Relativistic Dissipative Fluid Dynamics
T    Pg   wu  u  T 
J B  nB u    J B
In the Landau-Lifshitz approach u is the velocity of energy transport.


T     u   u    23    H    u 
H   u  u  g  ,       u u    , Q   T  Tu    u
B
 n BT     B 



JB  
 J B
  
 , s  su 
T
 w 
T 
2

 s 


u
2T
i
j
  ju    k u
i
2
3
ij

k 2



 u 
T
k 2
k


T
2




T

T
u
k
k
2
How is this relevant for RHIC?
For baryon-free matter:
  iDt k 2  0
transverse waves
 2  vs2  iDl  k 2  0 sound waves
Momentum diffusion constants:
Dt 

Ts
4 / 3  
Dl 
Ts
Bulk viscosity is generally small unless internal degrees
of freedom (rotation, vibration) can easily be excited in
collisions.
How is this relevant for RHIC?
• Solve relativistic viscous fluid equations, with
appropriate initial conditions and with a hadron
cascade afterburner, over a range of beam
energies and nuclei and extract η(T)/s(T) from
comparison with data.
• An analogous program was successful in
obtaining information on the compressibility of
nuclear matter and on the momentumdependence of the nuclear mean-field at low
beam energies.
Viscosity smoothes
out gradients in
temperature,
velocity, pressure,
etc.

2
3
mT

 0  
1

T
m
Viscous Heating of Expanding Fireballs
JK, PRC 24, 2545 (1981)
Extracting η/s from RHIC data
•
•
•
•
•
•
•
Elliptic flow (Teaney,…)
HBT (Teaney,…)
Momentum spectra (Teaney, Baier & Romatschke,…)
Momentum fluctuations (Gavin & Abdel-Aziz,…)
Fluctuations in v2 (Csernai,…)
Photon & dilepton spectra
Jet quenching
Preliminar y studies suggest th at  / s  0.1  0.5 at RHIC.
Work in progress…and complications
• Numerical relativistic viscous fluid dynamics
(Baier & Romatschke; Heinz & Song, Chaudhuri; Muronga &
Rischke) Large gradients (Baier & Romatschke) may require
second-order Israel-Stewart equations (Muronga).
• Initial conditions
(Lappi & Venugopalan CGC,…)
• Hadron afterburner
(Hirano, Heinz, Kharzeev, Lacey, Nora; Bass & Nonaka)
• Turbulent plasmas
(Asakawa, Bass, Muller) Charged particles scatter coherently from
dynamically generated color fields leading to “anomalous” viscosity.
Conclusion
• Hadron/quark-gluon matter should have a
minimum at or near the critical or crossover point
in the phase diagram analogous to atomic and
molecular systems.
• Sufficiently detailed calculations and
experiments ought to allow us to infer the
viscosity/entropy ratio. This is an interesting
dimensionless measure of dissipation relative to
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 (deviations
from ideal fluid flow)
• There is plenty of work for theorists (and
experimentalists)!