Nucleon polarizabilities andπ0→2γ,η0→2γdecay rates from Compton-scattering amplitudes

The difference of the dynamic electric and magnetic polarizabilities of the nucleon $\alpha -\beta$ is estimated on the basis of sum rules obtained from unsubtracted backward dispersion relations for the relevant nucleon Compton-scattering amplitudes in the framework of the two-particle unitarity approximation. The $s$- and $u$-channel contributions are then evaluated in terms of pion photoproduction data while the contribution of the two-pion state in the $t$ channel is shown to contain a large positive piece, explicitly computed, which could bring the theoretical prediction into qualitative agreement with the existing experimental results. It is consequently pointed out that if the ordering $\alpha >\beta$ is further confirmed experimentally, the annihilation-channel exchanges should be strongly responsible for this fact. The importance of the two-pion continuum for the dispersion determination of the ${\eta }^0\to 2\gamma$ decay rate from the superconvergence of certain nucleon Compton-scattering amplitudes for fixed $s$ and large $t$ is also particularly emphasized.