kharzeev

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

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

Slide3: 

Shear and bulk viscosities: the definitions The energy-momentum tensor: shear viscosity bulk viscosity

Slide4: 

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

Slide5: 

Kubo’s formula: Bulk viscosity is defined as the static limit of the correlation function:

Slide6: 

Kubo’s formula for bulk viscosity can be written down in the form involving Lorentz-invariant operators: Since q00’s commute, we get Bulk viscosity is determined by the correlation function of the trace of the energy-momentum tensor

Slide7: 

Shear viscosity: how much entropy is produced by transformation of shape at constant volume Bulk viscosity: how much entropy is produced by transformation of volume at constant shape Physical picture: Generated by translations Generated by dilatations

Scale invariance in field theory: 

Scale invariance in field theory

Scale invariance and confinement: 

Scale invariance and confinement R T R

Scale invariance and confinement: 

Scale invariance and confinement R T

Scale anomaly in QCD: 

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: 

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: 

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: 

Classical QCD in action Running coupling essential for understanding hadron multiplicities KLN

Running coupling in QGP: 

Running coupling in QGP F.Karsch et al T-dependence of the running coupling develops in the non-perturbative region at T < 3 Tc ; DE/T > 1 - “cold” plasma Strong force is screened by the presence of thermal gluons and quarks

Slide16: 

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: 

Perturbation theory: bulk viscosity is negligibly small P.Arnold, C.Dogan, G.Moore, hep-ph/0608012 z/h < 10-3

Slide18: 

In perturbation theory, shear viscosity is “large”: and bulk viscosity is “small”: At strong coupling, h is apparently small; can z get large?

Can we say anything about non-perturbative effects?: 

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: 

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: 

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

Slide22: 

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: 

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?: 

Condensed matter analogies? Example: 3He near the critical point at (T-Tc)/Tc = 10-4 on the critical isochore, shear viscosity is h=17 10-6 Poise whereas bulk viscosity is z=50 Poise The ratio z/h is in excess of a million

Slide25: 

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

Slide26: 

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

Slide27: 

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

Slide28: 

Meyer Kharzeev-Tuchin

Bulk viscosity in full QCD: 

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: 

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: 

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 m?

Bulk viscosity near the critical point: 

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

Slide33: 

Bulk viscosity and the mechanism of hadronization Scale transformation Scale anomaly What is the meaning of the bulk viscosity growth?

Slide34: 

Bulk viscosity and the mechanism of hadronization Scale transformation Bulk viscosity: growth of entropy, particle production Bulk viscosity growth = soft statistical hadronization (?)

Slide35: 

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

Slide36: 

Meyer Kharzeev-Tuchin Confinement as seen by the off-equilibrium thermodynamics

Slide37: 

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