  Two-loop corrections for the standard Abelian Nambu-Jona-Lasinio model are
obtained with the Optimized Perturbation Theory (OPT) method. These
contributions improve the usual mean-field and Hartree-Fock results by
generating a $1/N_c$ suppressed term, which only contributes at finite chemical
potential. We take the zero temperature limit observing that, within the OPT,
chiral symmetry is restored at a higher chemical potential $\mu$, while the
resulting equation of state is stiffer than the one obtained when mean-field is
applied to the standard version of the model. In order to understand the
physical nature of these finite $N_c$ contributions, we perform a numerical
analysis to show that the OPT quantum corrections mimic effective repulsive
vector-vector interaction contributions. We also derive a simple analytical
approximation for the mass gap, accurate at the percent level, matching the
mean-field approximation extended by an extra vector channel to OPT. For $\mu
\gtrsim \mu_c$ the effective vector coupling matching OPT is numerically close
(for the Abelian model) to the Fierz-induced Hartree-Fock value $G/(2N_c)$,
where $G$ is the scalar coupling, and then increases with $\mu$ in a
well-determined manner.
