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The \textit{optimized perturbation theory} (OPT) is implemented in the$SU_f(3)$ flavor symmetric Nambu--Jona-Lasinio (NJL) model to generatenon-pertubative corrections to the quark pressure beyond the large-$N$approximation. The correctness of this implementation is verified by therecovery of the already known non-perturbative results in the Hartree-Fockapproximation, and by having the large-$N$ approximation as a limiting case.This formalism is then used to revisit a discussion on the discordance betweenthe lattice data and the two flavor model prediction of the dynamical vectorrepulsive interactions, beyond the pseudocritical temperature. It is shown thatthese contradictory predictions can be corrected by considering a three quarkflavor system.

Optimized Perturbation Theory Applied to a Model with Flavour Symmetry $SU_f(3)$