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

Shear viscosity η to electric conductivity σ el 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 , σ el , χ , D , characterize the non-equilibrium behavior of a system due to an external perturbation. Motivations in QGP Shear viscosity Electric conductivity 10 Electric field Au nucleus Cu nucleus 5 y (fm) 0 J = σ el � � F = − η ∂ u x E -5 A yz ∂ y -10 -10 -5 0 5 10 x (fm) Strong electric fields Collective behavior v 1 Collective behavior v 2 Photon rate ∝ σ el Perfect fluid η/ s = 1 / 4 π Lattice QCD Lattice QCD Shear viscosity to Electric Conductivity ratio @ 53rd International Winter Meeting on Nuclear Physics Armando Puglisi 2

Dynamics � p 4 � p 2 Dynamics � � e 2 � �� � 1 � � ���� τ q ρ tot η/ s = + τ g ρ g σ el / T = ⋆ τ q ρ q q E 2 3 T 2 E 2 15 Ts � �� � � �� � Thermodynamics Thermodynamics Relaxation Times τ − 1 ∼ ρ q σ qq + ρ ¯ q + ρ g σ qg ⇒ info about quark-(anti-)quark and quark-gluon q σ q ¯ q scatterings τ − 1 ∼ ρ q σ qg + ρ g σ gg ⇒ info about quark-gluon and gluon-gluon scatterings g Taking the ratio fixed by lQCD � � η/ s � �� � 1 + τ g ρ g Thermodynamics × σ el / T ∼ ρ tot τ q 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