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By considering the background field method we calculate one-loop polarizationcorrections to the coupling constant of the flavor-U(5) Nambu-Jona-Lasinio(NJL) model with degenerate up and down quarks. They break flavor and chiralsymmetries, and they can be written as $G_{ij}^\Gamma (\bar{\psi} \lambda_i\Gamma \psi) ( \bar{\psi} \lambda_j \Gamma \psi)$, for the scalar andpseudoscalar 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 inthe model which amount to five, six or seven in total. Their contributions todifferent observables are computed. The non-covariant three-dimensionalregularization scheme is employed. Besides that, flavor dependence of cutoffsis implemented in an unambiguous way. It turns out that only two UV cutoffs($\Lambda_f$) are best suitable. Nevertheless, the best results are obtainedfor nearly flavor-independent cutoffs. A quantum mixing due to therepresentations of the flavor group leads to different interactions for thequarks and for the meson states, respectively denoted by $G_{ff}$ and $G_{ij}$.This quantum mixing effect is responsible for a lowering of quark effectivemasses and a slight improvement of predictions of observables. A quitesurprisingly good description of almost all the pseudoscalar meson masses(within nearly $5\%$) and most of the scalar meson masses -is obtained withinnearly 10$\%$. Some problems to describe light scalar mesons masses stillremain. The NJL-gap equations seems to overestimate the heavy quark condensatesat the usual mean field level usually adopted for model. In spite of the gooddescription of the meson masses, the pseudoscalar meson weak decay constantcannot be described by the NJL model with relativistic heavy quark propagatorswithout further interactions or effects.

U(5) Nambu-Jona-Lasinio model with flavor dependent coupling constants: pseudoscalar and scalar mesons masses