Chiral condensate thermal evolution at finite baryon chemical potential within chiral perturbation theory

We present a model independent study of the chiral condensate evolution in a hadronic gas, in terms of temperature and baryon chemical potential. The meson- eson interactions are described within chiral perturbation theory and the pion-nucleon interaction by means of heavy baryon chiral perturbation theory, both at one loop, and nucleon-nucleon interactions can be safely neglected within our hadronic gas domain of validity. Together with the virial expansion, this provides a systematic expansion at low temperatures and chemical potentials, which includes the physical quark masses. This can serve as a guideline for further studies on the lattice. We also obtain estimates of the critical line of temperature and chemical potential where the chiral condensate melts, which systematically lie somewhat higher than recent lattice calculations but are consistent with several hadronic models. We have also estimated uncertainties due to chiral parameters, heavier hadrons, and higher orders through unitarized chiral perturbation theory