  A local and gauge invariant version of QCD Lagrangian is introduced. The
model includes Nambu-Jona-Lasinio (NJL) terms within its action in a
surprisingly renormalizable form. This occurs thanks to the presence of action
terms which at first sight, look as breaking power counting renormalizability.
However, those terms also modify the quark propagators, to become more
decreasing that the Dirac one at large momenta, indicating power counting
renormalizability. The approach, can also be interpreted as generalized
renormalization procedure for massless QCD. The free propagator, given by the
substraction between a massive and a massless Dirac ones, in the Lee-Wick form,
suggests that the theory also retains unitarity. The appearance of finite quark
masses already in the tree approximation in the scheme is determined by the
fact that the new action terms explicitly break chiral invariance. The approach
looks as being able to implement the Fritzsch Democratic Symmetry breaking
ideas about the quark mass hierarchy. Also, a link of the theory with the SM
seems that can follow after employing the Zimmermann's couplings reduction
scheme. The renormalized Feynman diagram expansion of the model is written here
and the formula for the degree of divergence of the diagrams is derived. The
primitive divergent graphs are identified. We start their evaluation through
the calculation of the divergence of the gluon polarization operator. The
divergent part of the gluon selfenergy results to be transverse as required by
gauge invariance and also independent of the new couplings appearing. The
calculations of the rest of primitive divergences will be presented elsewhere.

High Energy Physics - Theory