# Presentation: 870744

## On the Strongly-InteractingLow-Viscosity Matter Createdin Relativistic Heavy Ion Collisions

- Joe Kapusta, Laszlo Csernai, Larry McLerran

- Why is viscosity interesting?
- How can it be inferred from experiments?

## Big Experimental Motivation!

- PHENIX data + Huovinen *et al.*

- PHENIX: First Three Years of
- Operation of RHIC

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

## Big Theoretical Motivation!

**Viscosity in Strongly Interacting Quantum Field Theories from Black Hole Physics**

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

- Using the Kubo formula

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

- and conjectured that this is a universal lower bound.

## Atomic and Molecular Systems

- In 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.  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

## NIST data

## 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.

##              QCD

-              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.

## How is this relevant for RHIC?

- For baryon-free matter:
-                                       transverse waves
-                                       sound waves

- Momentum diffusion constants:

- 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 (Nonaka), 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 momentum-dependence of the nuclear mean-field at low beam energies.

## BUU with K=215 MeV

- Gale *et al*. PRC 41, 1545 (1990)

- and momentum-dependent
- mean field

- Data (solid circles) from
- Danielewicz *et al*. PRC 38, 120 (1988)

- Directed flow at
- 800 MeV/nucleon

## Balance Energy

- Krofcheck *et al.* PRC 43, 350 (1991)

- Balance Energy

- attractive mean field
-              vs
- Coulomb repulsion
-              &
-     NN scattering

- low E

- high E

## Ar+Sc

- Au+Au

- Magestro, Bauer, Westfall PRC 62, 041603R (2000)

## 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.

## Use RHIC as 

- a viscometer!

## Finite-Temperature Field TheoryPrinciples and ApplicationsJoseph Kapusta and Charles Gale

- 1.  Review of quantum statistical mechanics
- 2.  Functional integral representation of the partition function
- 3.  Interactions and diagrammatic techniques
- 4.  Renormalization
- 5.  Quantum electrodynamics
- 6.  Linear response theory
- 7.  Spontaneous symmetry breaking and restoration
- 8.  Quantum chromodynamics

- Resummation and hard thermal        loops
- Lattice gauge theory
- Dense nuclear matter
- Hot hadronic matter
- Nucleation theory
- Heavy ion collisions
- Weak interactions
- Astrophysics and cosmology
-          Conclusion
-          Appendix