The Nambu--Jona--Lasinio model and the chiral anomaly

An approximate bosonization of the Nambu--Jona--Lasinio model is shown to lead to either form of two low energy effective Lagrangians: i.e., the massive Yang--Mills form or the hidden local symmetry form of Bando et al. The specific underlying quark Lagrangian restricts the freedom in obtaining the anomalous effective action on one and the other scheme. This enables us to show the equivalence of the two schemes not only for the physics of the nonanomalous sector but also for the physics of the anomalous sector. Our model in either representation however breaks low energy theorems for some of the anomalous processes. In pursuit of its origin, we investigate the general structure of the hadronic currents in the present model, putting special emphasis upon the underlying Lagrangian at the quark level. As an interesting byproduct of the present analysis, we gain a new insight into the dynamical meaning of the parameter a, which appears as a free parameter in the hidden symmetry model of Bando et al. copyright 1989 Academic Press, Inc