Solving the anomalous Ward identities for the U(1) problem

Abstract

Anomalous Ward identities are obtained for spontaneously realized SU(3)\ifmmode\times\else\texttimes\fi{}SU(3)\ifmmode\times\else\texttimes\fi{}${\mathrm{U}}_{3}$(1) in the presence of realistic symmetry-breaking quark mass terms in the Lagrangian. It is shown that the Ward identities contain more information than has hitherto been utilized. Together with low-energy theorems for ${\ensuremath{\pi}}^{0}$, $\ensuremath{\eta}$, and ${\ensuremath{\eta}}^{\ensuremath{'}}\ensuremath{\rightarrow}2\ensuremath{\gamma}$ decays these provide a set of equations which are solved for the axial-vector couplings and topological-charge (or glueball) components of $\ensuremath{\eta}$ and ${\ensuremath{\eta}}^{\ensuremath{'}}$.