Shear viscosity to electric conductivity el ratio for the - - PowerPoint PPT Presentation

Shear viscosity η to electric conductivity σel ratio for the quark-gluon plasma

Armando Puglisi Salvatore Plumari and Vincenzo Greco

Universit` a degli Studi di Catania, INFN-LNS

arxiv:1407.2559 53rd International Winter Meeting on Nuclear Physics, Bormio 25-30 Jan 2015

Shear viscosity to Electric Conductivity ratio @ 53rd International Winter Meeting on Nuclear Physics Armando Puglisi 1

Transport Coefficients Transport coefficients like η, ζ, σel, χ, D, characterize the non-equilibrium behavior of a system due to an external perturbation. Motivations in QGP Shear viscosity F Ayz = −η ∂ux ∂y Collective behavior v2 Perfect fluid η/s = 1/4π Lattice QCD Electric conductivity

• J = σel

E

• 10
• 5

5 10

• 10
• 5

5 10

y (fm) x (fm)

Electric field Au nucleus Cu nucleus

Strong electric fields Collective behavior v1 Photon rate ∝ σel Lattice QCD

Shear viscosity to Electric Conductivity ratio @ 53rd International Winter Meeting on Nuclear Physics Armando Puglisi 2

η/s = 1 15Ts p4 E 2

• Thermodynamics

Dynamics

• τqρtot

q

+ τg ρg

• σel/T =

e2

⋆

3T 2 p2 E 2

• Thermodynamics

Dynamics

• τq

ρq Relaxation Times τ −1

q

∼ ρqσqq + ρ¯

qσq¯ q + ρgσqg ⇒ info about quark-(anti-)quark and quark-gluon

scatterings τ −1

g

∼ ρqσqg + ρgσgg ⇒ info about quark-gluon and gluon-gluon scatterings Taking the ratio η/s σel/T ∼

fixed by lQCD

• Thermodynamics ×
• 1 + τg

τq ρg ρtot

q

• ∝ quark to gluon scattering rates

How to fix the Thermodynamics? What is the behavior of the ratio as a function of the temperature? Can we really extract information about the relative role of quarks and gluons? Does the ratio depend on the running coupling?

Shear viscosity to Electric Conductivity ratio @ 53rd International Winter Meeting on Nuclear Physics Armando Puglisi 3