  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.
