Some properties of two Nambu--Jona-Lasinio -type models with inputs from lattice QCD

We investigate the phase diagram of the so-called Polyakov--Nambu--Jona-Lasinio (PNJL) model at finite temperature and nonzero chemical potential. The calculations are performed in the light and strange quark sectors ($u$, $d$, $s$), which includes the 't Hooft instanton induced interaction term that breaks the axial symmetry, and the quarks are coupled to the (spatially constant) temporal background gauge field. On one hand, a special attention is payed to the critical end point (CEP). The strength of the flavor-mixing interaction alters the CEP location, since when it becomes weaker the CEP moves to low temperatures and can even disappear. On the other hand, we also explore the connection between QCD, a nonlocal Nambu--Jona-Lasinio type model and the Landau gauge gluon propagator. Possible links between the quenched gluon propagator and low energy hadronic phenomenology are investigated.