Anomalous Ward Identities, Hard-Meson Calculations, and theπ0γγForm Factor

Abstract

Assuming the anomalous axial-vector Ward identity for the $〈\mathrm{VVA}〉$ three-point functions, we calculate the $\ensuremath{\rho}\ensuremath{-}\ensuremath{\omega}\ensuremath{-}\ensuremath{\pi}$ and $\ensuremath{\rho}\ensuremath{-}\ensuremath{\phi}\ensuremath{-}\ensuremath{\pi}$ vertex functions and the off-mass-shell ${\ensuremath{\pi}}^{0}\ensuremath{\gamma}\ensuremath{\gamma}$ form factor in the framework of Schnitzer and Weinberg's hard-meson calculations. The mass-shell value of the form factor reduces to a result of Adler; and its off-mass-shell values are used to predict certain electron-positron annihilation cross sections. We compare the results of the present model with those of the conventional vector-meson-dominance model.