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

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