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

摘要

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 similar to 20-25%. For large temperatures, the spectral densities of the sigma-meson and the pion become degenerate, as required for the chirally symmetric phase. (c) 2006 Elsevier B.V. All rights reserved.