Mass Dispersion Relations in the Light of the Light Cone

Operator-product expansions near the light cone are used to study the convergence and saturation properties of some mass dispersion relations. We develop a general formalism and apply it to justify partial conservation of axial-vector current and to correct vector-meson dominance. We specifically treat the $K_{l3\mathrm{}}$ form factors and the decays ${\pi }^0\to \gamma \gamma$, $\omega \to \pi \gamma$, and $\omega \to 3\pi$.