Kaon Thresholds and Two-Flavor Chiral Expansions for Hyperons

TL;DR

This paper examines how virtual kaon thresholds affect two-flavor chiral expansions of hyperon properties, finding that the expansion remains useful for spin-half hyperons but is more limited for spin three-half hyperons due to proximity to kaon production thresholds.

Contribution

The study analyzes the impact of kaon thresholds on hyperon properties within two-flavor chiral expansions, clarifying the conditions under which the expansion is perturbative.

Findings

Two-flavor expansions are effective for spin-half hyperons.

Proximity to kaon thresholds challenges the expansion for spin three-half hyperons.

Higher-order corrections are necessary to confirm perturbativity.

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 one can theoretically formulate two-flavor theories for the various hyperon multiplets, the nearness of kaon thresholds can seriously undermine the effectiveness of the perturbative expansion in practice. We investigate the importance of virtual kaon thresholds on hyperon properties, specifically their masses and isovector axial charges. Using a three-flavor expansion that includes SU(3) breaking effects, we uncover the underlying expansion parameter governing the description of virtual kaon thresholds. For spin-half hyperons, this expansion parameter is quite small. Consequently 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. Estimating higher-order corrections to the expansion parameter is necessary to ascertain whether the two-flavor theory of spin three-half hyperons remains perturbative. We find that, despite higher-order corrections, there is a useful perturbative expansion for the masses and isovector axial charges of both spin-half and spin three-half hyperons.