Instantons As Unitary Spin Maker

Abstract

We investigate the relevance of the instanton-induced determinantal 't Hooft interaction to the eta-nucleon coupling within the framework of a three-flavor linear sigma model in the OZI-rule-respecting basis. Instantons, in combination with the spontaneous breaking of chiral symmetry, are shown to provide the major mechanism for the ideal mixing between pseudoscalar strange and non-strange quarkonia. As long as 't Hooft's interaction captures most of the basic features of the axial QCD gluon anomaly, we identify the anomaly as the main culprit for the appearance of octet flavor symmetry in the anomalous sectors of the pseudoscalar (and axial vector) mesons. Within this context, unitary spin is shown to be an accidental symmetry due to anomalous gluon dynamics rather than a fundamental symmetry in its own right. Though we find the eta-nucleon coupling constant to obey a Goldberger-Treiman like relation, the latter does not take its origin from a pole dominance of the induced pseudoscalar form factor of the octet axial current, but from a subtle flavor-mixing mechanism that is traced back to instanton dynamics. The model presented allows for possible generalizations to non-ideal mixing angles and different values of the meson decay constants in the strange and non-strange sectors, respectively. Finally, we discuss the issue as to what extent the eta meson may be considered as a Goldstone boson under the constraints of the anomaly-produced unitary spin.