ρ-meson self-energy and dielectron emissivity in an isospin-asymmetric pion medium

The ρ-meson self-energy in an isospin-asymmetric pion gas at finite temperature and charged-pion chemical potential is evaluated. We utilize a conventional effective π-ρ Lagrangian and the functional integral representation of the partition function in the second order in the ρππ coupling constant. We analyze the ρ-meson polarization operator and its dependence on the invariant mass M and spatial momentum ‖p‖ of the ρ meson. The pole positions and the values of the imaginary parts of the self-energy for different polarization states have different functional dependences on M and ‖p‖. The corresponding dielectron rate (calculated from the imaginary part of the in-medium ρ-meson propagator) shows a distinctive asymmetry when the momentum t=${\mathit{p}}_{+}$-${\mathit{p}}_{\mathrm{-}}$ is perpendicular or parallel to p, where ${\mathit{p}}_{\pm }$ are the ${\mathit{e}}^{\pm }$ momenta of the electron pair. © 1996 The American Physical Society.