Effective models of two-flavor QCD: Finite μ and mq dependence

We study the effective models of chiral fields and the Polyakov loop expected to describe the dynamics responsible for the phase structure of two-flavor QCD at finite temperature and density. We consider the chiral sector described either using the linear sigma model, including the fermion vacuum fluctuations, or the Nambu-Jona-Lasinio model and study the phase diagram and determine the location of the critical point as a function of the explicit chiral symmetry breaking (i.e. the bare quark mass m(q)). We also discuss the possible emergence of the quarkyonic phase in this model.