Self-consistent calculations of spectral densities in the O(N) model: improving the Hartree–Fock approximation by including nonzero decay widths

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 . For large temperatures, the spectral densities of the σ-meson and the pion become degenerate, as required for the chirally symmetric phase.