The role of the Delta isobar in chiral perturbation theory and hedgehog soliton models

Abstract

Hedgehog model predictions for the leading nonanalytic behavior (in $m^{2}_{\pi }$) of certain observables are shown to agree with the predictions of chiral perturbation theory up to an overall factor which depends on the operator. This factor can be understood in terms of contributions of the $\Delta$ isobar in chiral loops. These physically motivated contributions are analyzed in an expansion in which both $m_{\pi}$ and $M_{\Delta}-M_N$ are taken as small parameters, and are shown to yield large corrections to both hedgehog models and chiral perturbation theory.