Dispersive Approach to Chiral Perturbation Theory

TL;DR

This paper extends the dispersive reconstruction theorem to all pseudoscalar octet meson scattering processes, providing a general framework for calculating amplitudes at one-loop order in chiral perturbation theory.

Contribution

It generalizes the dispersive approach to include all pseudoscalar meson scattering, independent of specific power-counting schemes, and discusses the theorem's assumptions.

Findings

Derived amplitudes for meson scattering processes in the isospin limit

Formulated a general dispersive reconstruction theorem

Extended the theorem to one-loop order, with potential for two-loop extension

Abstract

We generalise the reconstruction theorem of Stern, Sazdjian, and Fuchs based on the dispersion relations to the case of the (2 -> 2) scattering of all the pseudoscalar octet mesons (pi, K, eta). We formulate it in a general way and include also a discussion of the assumptions of the theorem. It is used to obtain the amplitudes of all such processes in the isospin limit to the one-loop order (and can be straightforwardly extended to two loops) independently on the particular power-counting scheme of the chiral perturbation theory in question. The results in this general form are presented.