Chiral meson masses at finite temperature and density

The ratio of the sigma mass to the pion mass at finite temperatures and densities provides for a quantitative signal of chiral symmetry breaking. We calculate this ratio by using an extension to finite chemical potential of the field theoretic composite operator formalism as applied to QCD. The calculation is limited to regions of the phase diagram where only quark-antiquark condensates dominate (no quark-quark condensates) and it confirms the expected behaviors. In particular the sigma becomes an essentially stable particle in a narrow region bordering the transition line from broken to restored chirality. This pattern is qualitatively the same both for the region where the transition is of second order as for the region where it is of first order (apart from the discontinuities expected in the latter case).