Finite-Dispersion-Relation Restrictions on Interfering Meson Models

Using the finite-dispersion-relation method for treating three-body decays, we find that bounds can be placed upon the coupling strengths of two interfering resonances. A special result is that two narrow interfering coherent (or incoherent) resonances for the $A_2$ meson fail to satisfy a finite-dispersion-relation, finite-energy sum rule for coupling strengths (widths) which follows from the $\eta \to {\pi }^{+}{\pi }^{-}\gamma$ decay rate. This appears to be the first evidence independent of mass distributions indicating that one of the tabulated descriptions of the $A_2$ is wrong.