A double-dispersion-relation model for the neutral-pseudoscalar-meson–two-photon vertex function is proposed. Several spectral-function sum rules are derived. Quark-hadron duality is established in the model, so that the low-energy behavior of the vertex function is dominated by vector-meson resonances, and the high-energy behavior of the vertex function is determined by QCD dynamics and light-cone algebra. The vertex function is then applied to study the decay processes ${\pi }^0$(${\eta }^0$)→γγ, ${\pi }^0$(${\eta }^0$)→$e^{+}$$e^{\mathrm{-}}$(${\mu }^{+}$μ ${}_{}{}^{\mathrm{-}}{}_{}{}^{}$), ${\pi }^0$(${\eta }^0$)→$e^{+}$$e^{\mathrm{-}}$(${\mu }^{+}$μ ${}_{}{}^{\mathrm{-}}{}_{}{}^{}$)γ, and the scattering process $e^{+}$$e^{\mathrm{-}}$→${\pi }^0$(${\eta }^0$)γ.

• Received 25 March 1985

DOI:https://doi.org/10.1103/PhysRevD.32.1744