Effective models of two-flavor QCD: from small towards large $m_q$

We study effective models of chiral fields and Polyakov loop expected to describe the dynamics responsible for the phase structure of two-flavor QCD. We consider chiral sector described either using linear sigma model or Nambu-Jona-Lasinio model and study how these models, on the mean-field level when coupled with the Polyakov loop, behave as a function of increasing bare quark (or pion) mass. We find qualitatively similar behaviors for the cases of linear sigma model and Nambu-Jona-Lasinio model and, relating to existing lattice data, show that one cannot conclusively decide which or the two approximate symmetries drives the phase transitions near the physical point.