The 3-flavor A-scaled Nambu-Jona-Lasinio model

We review the so called A-scaled Nambu-Jona-Lasinio model both in the vacuum and at finite temperature and density in the case of three flavors. Starting from QCD and integrating out the gluons, we show how to reintroduce some of their effects in order to take into account the trace (or scale) anomaly of QCD. The axial U_A(1) anomaly is also present in the model in order to discuss the eta' particle. In the present work we treat the pseudoscalar and scalar sectors, pointing out the defects related to the omission of the vector particles. We use our model to study the restoration of chiral symmetry as a function of temperature, the thermodynamical functions and the equation of state, and we survey the mixing between the scalar isoscalar particles and the glueball.