Comment on proton electromagnetic polarizabilities

A previous analysis concerning the evaluation of the annihilation-channel contributions to the difference ($\alpha -\beta$) of the generalized electric and magnetic polarizabilities of the proton is corrected and completed. The ($I=J=0\mathrm{}$) $\pi \pi$ contribution to $\alpha -\beta$ is expressed in terms of the $N\overline{N}\to \pi \pi$ $\pi \pi \to \gamma \gamma$ amplitudes and an estimation within a simple model is presented.