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

TL;DR

This paper introduces a novel non-abelian $SU(N) imes SU(N)$ gauge model as an extension of Yang-Mills theory, exploring its symmetry, Feynman rules, and potential implications for QCD-like theories with composite quarks.

Contribution

It proposes a new non-abelian gauge model extending Yang-Mills symmetry, deriving its Feynman rules, and analyzing its physical and renormalization properties, including potential applications to QCD.

Findings

Derives gauge symmetry and invariant Lagrangian for the model.

Provides Feynman rules, propagators, and vertices in momentum space.

Shows the model's renormalization consistency and absence of tachyons.

Abstract

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.