Predictions of three-body decays of mesons from pole-dominated dispersion relations

The meson decays $\eta \to \pi \pi \gamma$, ${\eta }^{\prime }\to \pi \pi \gamma$, ${\eta }^{\prime }\to \eta \pi \pi$, $\omega \to 3\pi$, $\phi \to 3\pi$, and $K^{*}\to K\pi \pi$ are studied, using dispersion relations for the related two-body "scattering" amplitudes. Pole dominance of the low-energy part of the dispersion integral with Regge-pole dominance of the highenergy part leads to relations between these three-body decays and various meson two-body decays. When these are known, the approach leads to predictions for the three-body decays in agreement with experiment. In other cases, consistency is shown with the results of vector-meson-dominance couplings, SU(3)-symmetric couplings with $\eta -{\eta }^{\prime }$ mixing, and upper limits for unobserved decays.