Comment on "Polarizability of the pion: No conflict between dispersion theory and chiral perturbation theory"

TL;DR

This paper clarifies that the dispersion relation approach does not have spurious singularities and confirms the disagreement with chiral perturbation theory regarding pion polarizability.

Contribution

It demonstrates that the dispersion relation method is free of spurious singularities and discusses the persistent disagreement with chiral perturbation theory.

Findings

No spurious singularities in the dispersion approach.

Disagreement between dispersion relations and chiral perturbation theory remains.

Dispersion approach accurately models meson resonance contributions.

Abstract

The statement of the authors of the article Phys. Rev. C 77, 065211 (2008) that spurious singularities occur in the dispersion relation approach, where imaginary parts of the amplitudes of the process \gamma\gamma->\pi\pi are saturated by the contributions of meson resonances by using Breit-Wigner expressions, is analyzed. It is shown that there are no any additional singularities in this approach and the disagreement between the predictions of the dispersion relations and the chiral perturbation theory for (\alpha_1-\beta_1)_\pi^{\pm} remains.