Decuplet reexamined in chiral perturbation theory

This paper deals with two issues. First, we explore the quantitative importance of higher multiplets for properties of the $\Delta$ decuplet in chiral perturbation theory. In particular, it is found that the lowest order one-loop contributions from the Roper octet and the $\Delta \mathrm{}\left(1600\right)\mathrm{}$ to the decuplet masses and magnetic moments are substantial. The relevance of these results to the chiral expansion in general is discussed. The exact values of the magnetic moments depend upon delicate cancellations involving ill-determined coupling constants. Second, we present new relations between the magnetic moments of the $\Delta$ decuplet that are independent of all couplings. They are exact at the order of the chiral expansion used in this paper.