On the Generating Functional for Proper Vertices of Local Composite Operators in the Gauged Nambu-Jona-Lasinio Model

The generating functional (effective action) for proper vertices of local composite operators Formula: see text and Formula: see text in the gauged Nambu-Jona-Lasinio model is considered. We show that, unlike QCD-like dynamics, it is a well-defined object in the continuum limit (at the critical line of the model). The effective action is applied for studying spinless bound states in the model. In particular, we show that the bound states disappear with cutoff Λ→∞ in the symmetric phase, near the part of the critical line with α=α c =π/3. A mass relation for scalar bound states is derived in the nonsymmetric phase, near this part of the critical line.