Shear Viscosity of a Hot Pion Gas

Abstract

The shear viscosity of an interacting pion gas is studied using the Kubo formalism as a microscopic description of thermal systems close to global equilibrium. We implement the skeleton expansion in order to approximate the retarded correlator of the viscous part of the energy-momentum tensor. After exploring this in $g{\varphi }^4$ theory we show how the skeleton expansion can be consistently applied to pions in chiral perturbation theory. The shear viscosity $\eta$ is determined by the spectral width, or equivalently, the mean free path of pions in the heat bath. We derive a new analytical result for the mean free path which is well-conditioned for numerical evaluation and discuss the temperature and pion-mass dependence of the mean free path and the shear viscosity. The ratio $\eta /s$ of the interacting pion gas exceeds the lower bound $1/4\pi$ from AdS/CFT correspondence.

12 pages, 7 figures. Revision includes additional Appendix B. Matches published version

References in corpus (12)

• Viscosity in Strongly Interacting Quantum Field Theories from Black Hole Physics
• Viscosity Information from Relativistic Nuclear Collisions: How Perfect is the Fluid Observed at RHIC?
• The QCD transition temperature: results with physical masses in the continuum limit
• Equation of state and QCD transition at finite temperature
• Heavy-Quark Kinetics in the QGP at LHC
• Thermal Dileptons at LHC
• Has the QCD Critical Point been Signaled by Observations at RHIC ?
• Is there a "most perfect fluid" consistent with quantum field theory?
• Hydrodynamic radial and elliptic flow in heavy-ion collisions from AGS to LHC energies
• Three-body collisions in Boltzmann-Uehling-Uhlenbeck theory
• Transport coefficients in Chiral Perturbation Theory
• Shear viscosity of the quark matter

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