SU (3) scaled effective lagrangians for a hot and strange system

We construct two effective lagrangians which reproduce the explicit flavor SU(3) symmetry breaking and the trace and axial anomalies of QCD. All analytical expressions are derived for a hot strange matter but the results are only shown for zero baryonic density. We study the coupling of the quark condensates (u and s) to the gluon condensate. We also consider the temperature behavior of the pion and of the kaon masses. We show that the results crucially depend on the choice of the two free parameters of the model: the chiral transition can be of first or of second order; the coupling between the gluon and the quark condensates can be large or not; the meson masses can increase or decrease with temperature. The introduction of the QCD trace anomaly in the SU(3) NJL model kills the predictive character of the NJL.