The polarizability of the pion: no conflict between dispersion theory and chiral perturbation theory

TL;DR

This paper reconciles dispersion theory and chiral perturbation theory in calculating the pion's polarizability by analyzing the analytic properties and addressing spurious singularities, showing they are not fundamentally conflicting.

Contribution

It demonstrates that when proper dispersion relation conditions are applied, dispersion theory and chiral perturbation theory yield consistent results for pion polarizability.

Findings

Spurious singularities are linked to strong intermediate-meson contributions.

Proper analytic conditions reconcile dispersion relations with chiral perturbation theory.

No fundamental conflict exists between the two theoretical approaches.

Abstract

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.