Equation of State of an Interacting Pion Gas with Realistic $π$--$π$ Interactions

Abstract

Within the finite-temperature Greens-function formalism we study the equation of state of a hot interacting pion gas at zero chemical potential. Employing realistic $ππ$ meson-exchange interactions we selfconsistently calculate the in-medium single-pion selfenergy and the $ππ$ scattering amplitude in the quasiparticle approximation. These quantities are then used to evaluate the thermodynamic potential, $Ω_π$(T), from which the state variables: pressure-, entropy- and energy-density can be derived. In contrast to earlier calculations based on the low-energy Weinberg Lagrangian we find an overall increase as compared to the free-gas results. We also consider the possibility of a dropping $ρ$-meson mass as suggested by the 'Brown-Rho Scaling' law.

30 pages LaTeX, 3 postscript figures appended as uuencoded file