Sum Rule Connecting Mesonic and Photonic Matrix Elements and the Rate forω0→π0+γ

The Gell-Mann current-commutation relations are used to obtain a relation between matrix elements involving vector currents and matrix elements involving axial currents, in the infinite energy limit. This relation leads to a set of sum rules. One of these is used to calculate the rate for ${\omega }^0\to {\pi }^0+\gamma$ in terms of the $\rho$-meson width and the axial-current renormalization constant, under the assumption that only states with spin and parity $0^{\pm }$ and $1^{-}$ need be taken into account. The result, $\Gamma ({\omega }^0\to {\pi }^0+\gamma )=1.2\mathrm{}$ MeV, is in reasonable agreement with experiment.