Effective field theory and the quark model. II. Structure of loop corrections

Abstract

We analyze the structure of meson loop corrections to the $\mathrm{O}{(m}_{s})$ expressions for the baryon masses and magnetic moments in heavy-baryon chiral perturbation theory (HBChPT), and show in detail how the bulk of the corrections are absorbed into redefinitions of the unknown parameters of the $\mathrm{O}{(m}_{s})$ chiral expansion. To effect this analysis, we use the three-flavor-index representation of the effective baryon fields and HBChPT developed in a preceding paper, and a decomposition of the corrections in terms of effective one-, two-, and three-quark operators. The results show why the loop corrections have so little effect on fits to the masses and moments, and do not seriously disrupt the Gell-Mann--Okubo relations for the masses and the Okubo relation for the moments even though individual loops can be quite large. We also examine the momentum structure of the residual loop corrections, and comment on limits on their validity in HBChPT. The structural analysis can be generalized straightforwardly to other problems in HBChPT using the three-flavor-index representation of the effective baryon fields, and provides a fairly simple way to determine what parts of the loop corrections are actually significant in a given setting.