  Recent attempts to determine the pion polarizability by dispersion relations
yield values that disagree with the predictions of chiral perturbation theory.
These dispersion relations are based on specific forms for the absorptive part
of the Compton amplitudes. The analytic properties of these forms are examined,
and the strong enhancement of intermediate-meson contributions is shown to be
connected with spurious singularities. If the basic requirements of dispersion
relations are taken into account, the results of dispersion theory and
effective field theory are not inconsistent.
