# Presentation: 002420

## Conformal symmetry breaking in QCD and implications for hot quark-gluon matter

- D. Kharzeev

-  “Heavy quarks”, LBNL, November 1-3, 2007

## Bulk viscosity of QCD matter:the tale of “the least studied transport coefficient”

- Bulk viscosity of QCD matter:the tale of “the least studied transport coefficient”

- Based on:
- DK, K. Tuchin, arXiv:0705.4280 [hep-ph]
- F. Karsch, DK, K. Tuchin, to appear

## Shear and bulk viscosities: the definitions

- The energy-momentum tensor:

- shear viscosity

- bulk viscosity

## Shear viscosity has attracted a lot of attention: 

- A.Nakamura and S.Sakai,
- hep-lat/0406009;
- Recent work:
- H.Meyer, 0704.1801

- Perfect liquid

- Shear viscosity has attracted a lot of attention:

- Kovtun - Son - Starinets bound:
- strongly coupled SUSY QCD = classical supergravity

## Kubo’s formula:

- Bulk viscosity is defined as the static limit of
- the correlation function:

## Kubo’s formula for bulk viscosity can be written

- down in the form involving Lorentz-invariant operators:

- Since 00’s commute, we get

- Bulk viscosity is determined by the correlation function
- of the trace of the energy-momentum tensor

## Physical picture:

- transformation of shape at constant volume

- Bulk viscosity: how much entropy is produced by
- transformation of volume at constant shape

- Generated by
- translations

- Generated by
- dilatations

## Scale invariance in field theory

## Scale invariance and confinement

- R

- T

- R

## Scale invariance and confinement

- R

- T

## Scale anomaly in QCD

- trace of the energy-
- momentum tensor

- Classical scale invariance is broken by quantum effects:
- scale anomaly

- Hadrons get masses              coupling runs with the distance

- “beta-function”; describes the dependence
- of coupling on momentum

## Asymptotic Freedom

- At short distances,
- the strong force becomes weak
- (anti-screening) -
- one can access the “asymptotically
- free” regime in hard processes
- and in super-dense matter
- (inter-particle distances ~ 1/T)

- number
- of colors

- number
- of flavors

## Renormalization group:running with the field strength

- RG constraints the form of the effective action:

- the coupling is defined through

- At large t (strong color field),

- and

## Classical QCD in action

- Running coupling
- essential for understanding
- hadron multiplicities

- KLN

## Running coupling in QGP

- F.Karsch et al

- T-dependence of
- the running coupling
- develops in
- the non-perturbative region
- at T < 3 Tc ;  E/T > 1
- - “cold” plasma

- Strong force is
- screened by
- the presence of
- thermal gluons
- and quarks

## Running coupling (and perhaps “remnants

- of confinement”) seen in the lattice data
- indicate:
- Scale invariance in the quark-gluon plasma is at best approximate
- What does it mean for bulk viscosity?

## Perturbation theory:bulk viscosity is negligibly small

- P.Arnold, C.Dogan,
- G.Moore, hep-ph/0608012

- < 10-3

##           can get large?

- and bulk viscosity is “small”:

- At strong coupling, is apparently small;
-           can get large?

## Can we say anything about non-perturbative effects?

- At zero temperature, broken scale invariance leads to
- a chain of low-energy theorems for the correlation
- functions of

- Novikov, Shifman,
- Vainshtein, Zakharov ‘81

- Elegant geometrical interpretation - classical theory
- in a curved gravitational background -     Migdal, Shifman ‘82;
- Einstein-Hilbert action, etc                               DK, Levin, Tuchin ‘04

- These theorems have been generalized to finite T:

- Ellis, Kapusta,
- Tang ‘98

## Sketch of the derivation

- Consider an operator with a canonical dimension d:

- The dependence of QCD Lagrangian on the coupling:

- Write down an expectation value for O as
- a functional integral and differentiate w.r.t. 1/4g2:

- Repeat n times - get n-point correlation functions

## An exact sum rule for  bulk viscosity

- Basing on LET’s and Kubo’s formula, we derive
-  an _exact_ sum rule for the spectral density:

- Using _ansatz_                    we get

- DK, K.Tuchin, arXiv:0705.4280 [hep-ph]

- 0

## Use the lattice data from G.Boyd, J.Engels, F.Karsch, E.Laermann,

- Use the lattice data from G.Boyd, J.Engels, F.Karsch, E.Laermann,
-                                  C.Legeland, M.Lutgeimer, B.Petersson, hep-lat/9602007

- SU(3),
- pure gauge

## The result

- DK, K.Tuchin, arXiv:0705.4280 [hep-ph]

- Bulk viscosity is small at high T,
- but becomes _very_ large close to Tc

## Condensed matter analogies?

- Example:  3He near the critical point
- at (T-Tc)/Tc = 10-4 on the critical isochore,
- shear viscosity is -6Poise
- whereas bulk viscosity is Poise
- The ratio is in excess of a million

## S.Sakai, A.Nakamura, arXiv:0710.3625[hep-lat], Oct 19, 2007

## H.Meyer, arXiv:0710.3717[hep-lat], Oct 19, 2007

## H.Meyer, arXiv:0710.3717[hep-lat], Oct 19, 2007

## Meyer

- Kharzeev-Tuchin

## Bulk viscosity in full QCD

- F.Karsch, DK, K.Tuchin,
- to appear

- Qualitatively similar results:

- SU(3), pure gauge

- QCD, 2+1 quark flavors (pion mass 220 MeV)

- BNL-Columbia-RBRC-Bielefeld
- arXiv:0710.0354

## Universal properties of bulk viscosity near the phase transition

- F.Karsch, DK, K.Tuchin,
- to appear

- Consider 2 massless (light) quarks and a strange quark:
- 2nd order phase transition
- Sum rule shows that the behavior of bulk viscosity is
- driven by the latent heat

## Universal properties of bulk viscosity near the phase transition

- F.Karsch, DK, K.Tuchin,
- to appear

- The behavior of latent heat near the phase transition
- is driven by the critical exponent:

- 2+1 flavors, zero baryon density: O(4) universality class:
- = -0.19(6):  cV= const - t0.19 - a spike in bulk viscosity
- What happens near the critical point at finite ?

## Bulk viscosity near the critical point

- Near the tri-critical point: Z(2) universality class

- = 0.11 : cV ~  t-0.11 bulk viscosity diverges !
- Growth of entropy production, large multiplicity,
- small transverse momenta

## Bulk viscosity and the mechanism of hadronization

- Scale transformation

- Scale anomaly

- What is the meaning of the bulk viscosity growth?

## Bulk viscosity and the mechanism of hadronization

- Scale transformation

- Bulk viscosity:
- growth of entropy,
- particle production

- Bulk viscosity growth = soft statistical hadronization (?)

## Bulk viscosity and the mechanism of hadronization

- Scale transformation

- _Not_ a recombination of pre-existing quarks -
- Bulk viscosity saves the 2nd law of thermodynamics
- in the process of hadronization

## Confinement as seen by the

- Meyer

- Kharzeev-Tuchin

- off-equilibrium thermodynamics

## Summary

- Bulk viscosity is small away from Tc - approximately
- scale-invariant dynamics, “perfect liquid”
- 2. Bulk viscosity grows dramatically (3 orders!) close
- to the critical temperature (most likely, a peak at Tc):
- by far, the dominant viscous effect at this temperature
- 3. This suggests a new scenario for
- _soft statistical hadronization_
- 4. Understanding the associated “microscopic”
- dynamics is crucial for understanding hadronization
- and confinement
-       _Need to devise the methods of experimental study_