Pion-Kaon Scattering near the Threshold in Chiral SU(2) Perturbation Theory

TL;DR

This paper analyzes pion-kaon scattering near the threshold within chiral SU(2) perturbation theory up to fourth order, deriving relations between threshold parameters and estimating low-energy constants, though experimental data is insufficient for testing.

Contribution

It provides a detailed calculation of pion-kaon scattering amplitude in both relativistic and heavy baryon frameworks, establishing threshold relations and estimating low-energy constants.

Findings

Equivalent results from both calculation methods

Derived threshold parameter relations valid to fourth order

Estimated low-energy constants using chiral SU(3) symmetry

Abstract

In the context of chiral SU(2) perturbation theory, pion-kaon scattering is analysed near the threshold to fourth chiral order. The scattering amplitude is calculated both in the relativistic framework and by using an approach similar to heavy baryon chiral perturbation theory. Both methods lead to equivalent results. We obtain relations between threshold parameters, valid to fourth chiral order, where all those combinations of low-energy constants which are not associated with chiral-symmetry breaking terms drop out. The remaining low-energy constants can be estimated using chiral SU(3) symmetry. Unfortunately, the experimental information is not precise enough to test our low-energy theorems.