Axial and electromagnetic observables of hyperons in 2-flavor chiral perturbation theory

TL;DR

This paper examines how two-flavor chiral perturbation theory can effectively describe hyperon properties, focusing on virtual kaon thresholds and their impact on axial and electromagnetic observables, with distinctions between spin-half and spin-three-half hyperons.

Contribution

It identifies the conditions under which two-flavor chiral expansions are valid for hyperons and analyzes the role of kaon thresholds in these effective theories.

Findings

Spin-half hyperons are well described by two-flavor theory with analytic terms.

Breakdown occurs near kaon production thresholds for spin-three-half hyperons.

Perturbative expansion remains useful for axial charges and magnetic moments despite thresholds.

Abstract

Two-flavor chiral expansions provide a useful perturbative framework to study hadron properties. Such expansions should exhibit marked improvement over the conventional three-flavor chiral expansion. Although in principle one can formulate two-flavor theories for the various hyperon multiplets, the nearness of kaon thresholds can seriously undermine the effectiveness of such two-flavor theories in practice. We investigate the importance of virtual kaon thresholds on hyperon properties, specifically their isovector axial charges and electromagnetic observables. In particular we uncover the underlying expansion parameter governing the description of virtual kaon thresholds. For spin-half hyperons, this expansion parameter is under theoretical control. As a result, the virtual kaon contributions are well described in the two-flavor theory by terms analytic in the pion mass-squared. For spin three-half hyperons, however, one is closer to the kaon production threshold, and the expansion parameter is not as small. Breakdown of $SU(2)$ chiral perturbation theory is shown to arise from a pole in the expansion parameter associated with the kaon threshold. We find that, despite the fact that higher-order corrections to the expansion parameter is necessary to ascertain whether the two-flavor theory of spin three-half hyperons remains perturbative, there is a useful perturbative expansion for isovector axial charges and magnetic moments of both spin-half and spin three-half hyperons.