Pion polarizabilities from backward and fixed-usum rules

Various contributions to the pion polarizabilities are estimated using sum rules obtained from backward and fixed-$u={\mu }^2$ ($\mu =\mathrm{pion}\mathrm{mass}$) dispersion relations for the relevant pion Compton-scattering amplitude. While the $s$-channel part can be quite reliably computed in terms of the strong and radiative widths of known meson resonances, the evaluation of the $t$-channel piece remains highly model dependent despite important clarifications provided recently by measurements of the $\gamma \gamma \to \pi \pi$ reaction.