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Several relevant thermodynamic observables obtained within the (2+1) flavorand spin zero NJL and PNJL models with inclusion of the 't Hooft determinantand $8q$ interactions are compared with lattice-QCD (lQCD) results. In the casethat a small ratio $R=\frac{\mu_B}{T_c}\sim 3$ at the critical end point (CEP)associated with the hadron gas to quark-gluon plasma transition is considered,combined with fits to the lQCD data of the trace anomaly[1], subtracted lightquark condensate[1] and continuum extrapolated data of the light quark chiralcondensate[2], a reasonable description for the PNJL model is obtained with astrength $g_1\sim 5...6 \times 10^3$ GeV$^{-8}$ of the $8q$ interactions. Thedependence on the further model parameters is discussed.

Observables in the 3 Flavor PNJL Model and their Relation to Eight Quark Interactions