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

Several relevant thermodynamic observables obtained within the (2+1) flavor and spin zero NJL and PNJL models with inclusion of the 't Hooft determinant and $8q$ interactions are compared with lattice-QCD (lQCD) results. In the case that 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 light quark condensate[1] and continuum extrapolated data of the light quark chiral condensate[2], a reasonable description for the PNJL model is obtained with a strength $g_1\sim 5...6 \times 10^3$ GeV$^{-8}$ of the $8q$ interactions. The dependence on the further model parameters is discussed.