  By considering the background field method we calculate one-loop polarization
corrections to the coupling constant of the flavor-U(5) Nambu-Jona-Lasinio
(NJL) model with degenerate up and down quarks. They break flavor and chiral
symmetries, and they can be written as $G_{ij}^\Gamma (\bar{\psi} \lambda_i
\Gamma \psi) ( \bar{\psi} \lambda_j \Gamma \psi)$, for the scalar and
pseudoscalar channels ($\Gamma=I , i \gamma_5$) and $i,j = 0,1,...,N_f^2-1$.
Therefore, these coupling constants do not introduce further free parameters in
the model which amount to five, six or seven in total. Their contributions to
different observables are computed. The non-covariant three-dimensional
regularization scheme is employed. Besides that, flavor dependence of cutoffs
is implemented in an unambiguous way. It turns out that only two UV cutoffs
($\Lambda_f$) are best suitable. Nevertheless, the best results are obtained
for nearly flavor-independent cutoffs. A quantum mixing due to the
representations of the flavor group leads to different interactions for the
quarks and for the meson states, respectively denoted by $G_{ff}$ and $G_{ij}$.
This quantum mixing effect is responsible for a lowering of quark effective
masses and a slight improvement of predictions of observables. A quite
surprisingly good description of almost all the pseudoscalar meson masses
(within nearly $5\%$) and most of the scalar meson masses -is obtained within
nearly 10$\%$. Some problems to describe light scalar mesons masses still
remain. The NJL-gap equations seems to overestimate the heavy quark condensates
at the usual mean field level usually adopted for model. In spite of the good
description of the meson masses, the pseudoscalar meson weak decay constant
cannot be described by the NJL model with relativistic heavy quark propagators
without further interactions or effects.
