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The Nambu--Jona-Lasinio model with two flavors, three colors and diquarkinteractions is analyzed in the context of optimized perturbation theory (OPT).Corrections to the thermodynamical potential that go beyond the large-$N_c$(LN) approximation are taken into account, and the region of the phase diagramcorresponding to intermediate chemical potentials and very low temperatures isexplored. The simultaneous presence of both the quark-antiquark and diquarkcondensates can cause the system to behave as a fluid composed of aBose-Einstein condensate (BEC) or a color superconductor one, in the form of aBardeen-Cooper-Schrieffer (BCS) superfluid. The BEC-BCS crossover is thenstudied in the nonperturbative OPT scheme. The results obtained in the contextof the OPT method are then contrasted with those obtained in the LNapproximation. We show that there are values for the coupling constants relatedto quark-quark and quark-antiquark interactions where the corrections beyond LNbrought by the OPT method can influence the behavior of the diquark condensateand the effective quark mass as a function of the baryon chemical potential.These changes in the behavior of the phase structure of the model modify thelocation of the critical point related to the phase structure as a whole of themodel. Also, when we impose the color neutrality condition, our results showthat the nature of the phase transition can change as well, shifting the ratioof the quark-antiquark and quark-quark interactions to higher values in the OPTcase as compared to the LN approximation.

Optimized perturbation theory applied to the study of the thermodynamics and BEC-BCS crossover in the three-color Nambu--Jona-Lasinio model