  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
behaviours. 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).
