Chiral meson masses at finite temperature and density - art. no. 074002

The ratio of the sigma mass to the pion mass at finite temperatures and den sities provides for a quantitative signal of chiral symmetry breaking. We c alculate this ratio by using an extension to finite chemical potential of t he field theoretic composite operator formalism as applied to QCD. The calc ulation is limited to regions of the phase diagram where only quark-antiqua rk condensates dominate (no quark-quark condensates) and it confirms the ex pected behaviors. In particular the sigma becomes an essentially stable par ticle in a narrow region bordering the transition line from broken to resto red chirality. This pattern is qualitatively the same both for the region w here the transition is of second order as for the region where it is of fir st order (apart from the discontinuities expected in the latter case).