Is the effective Lagrangian for quantum chromodynamics aσmodel?

Abstract

A fully interacting effective chiral Lagrangian obeying the anomalous axial-baryon-current conservation law is constructed. This Lagrangian is a generalization of one implied by the $\frac{1}{N}$ approximation. In a certain sense, the old $\sigma$ model is recovered. Our Lagrangian displays the dependence of amplitudes on the quantum-chromodynamic vacuum angle $\theta$, gives soft ${\eta }^{\prime }$ theorems, and hints at a possible complementarity between the instanton and $\frac{1}{N}$ approaches. We can rewrite our model in terms of a gauge-invariant gluon field.