Self-consistent calculations of spectral densities in the [formula omitted] model: improving the Hartree–Fock approximation by including nonzero decay widths

Abstract

We study the linear sigma model with O ( N ) symmetry at nonzero temperature in the framework of the Cornwall–Jackiw–Tomboulis formalism. Extending the set of two-particle irreducible diagrams by adding sunset diagrams to the usual Hartree–Fock contributions, we derive a new approximation scheme which extends the standard Hartree–Fock approximation by the inclusion of nonzero decay widths. In this approximation, in-medium modifications of the meson masses as well as decay and collisional broadening effects are self-consistently taken into account. As compared to the standard Hartree–Fock approximation, the temperature for the chiral symmetry restoring phase transition is lowered by ∼ 20 – 25 % . For large temperatures, the spectral densities of the σ-meson and the pion become degenerate, as required for the chirally symmetric phase.