A non-abelian model $SU(N) \times SU(N)$

A composite non-abelian model $SU(N) \times SU(N)$ is proposed as possible extension of the Yang-Mills symmetry. We obtain the corresponding gauge symmetry of the model and the most general lagrangian invariant by $SU(N) \times SU(N)$. The corresponding Feynman rules of the model are studied. Propagators and vertices are derived in the momentum space. As physical application, instead of considering the color symmetry $SU_{c}(3)$ for $QCD$ , we substitute it by the combination $SU_{c}(3) \times SU_{c}(3)$. It yields a possibility to go beyond $QCD$ symmetry in the sense that quarks are preserved with three colors. This extension provides composite quarks in triplets and sextets multiplets accomplished with the usual massless gluons plus massive gluons. We present a power counting analysis that satisfies the renormalization conditions as well as one studies the structure of radiative corrections to one loop approximation. Unitary condition is verified at tree level. Tachyons are avoided. For end, one extracts a BRST symmetry from lagrangian and Slavnov-Taylor identities.