  A local and gauge invariant alternative version of QCD for massive fermions
introduced in previous works, is considered here to just propose a theory which
includes Nambu-Jona-Lasinio (NJL) terms in its defining action in a
renormalizable form. The Lagrangian includes a special kind of new vertices
which at first sight, look as breaking power counting renormalizability.
However, these terms also modify the quark propagators, to become more
decreasing that the Dirac propagator at large momenta, indicating that the
theory is renormalizable. Therefore, it follows the surprising conclusion that
the added NJL four fermions terms does not break renormalizability. The
approach, can also be interpreted as a slightly generalized renormalization
procedure for massless QCD, which seems able to incorporate the mass generating
properties for the quarks of the NJL model, in a renormalizable way. The
structure of the free propagator, given by the substraction between a massive
and a massless Dirac one in the Lee-Wick form, also suggests that the theory
retains unitarity, if the radiative corrections make the massless quarks become
non propagating. The appearance of finite masses in the theory is justified by
the fact that the new action terms break chiral invariance. The scheme looks as
being able to implement the Fritzsch Democratic Symmetry breaking approach to
quark mass hierarchy. It seems also possible to further link the theory with
the SM after employing the Zimmermann's coupling constant reduction scheme in a
similar way as the Top quark condensation model had been approximately
reformulated as a Higgs field one.
