Improved tests of relations for baryon isomultiplet splittings

The least well-known octet baryon mass is $M_{{\Xi }^0}=1314.9\mathrm{}\pm 0.6\mathrm{MeV}.$ The prospect of an improved measurement of its mass by the KTeV experimental program at Fermilab, and opportunities for improvements in charged and excited hyperon and Δ mass measurements, makes it timely to reexamine descriptions of isospin splittings in baryons containing light quarks. It is possible by examining such relations as the Coleman-Glashow relation $M_n-M_p{+M}_{{\Xi }^{-}}-M_{{\Xi }^0}{=M}_{{\Sigma }^{-}}-M_{{\Sigma }^{+}}$ to distinguish between those models making use of one- or two-body effects involving quarks and those involving genuine three-body effects. A hierarchy based on an expansion in ${1/N}_c,$ where $N_c$ is the number of quark colors, is useful in this respect. The present status of other quark-model mass relations involving $\Lambda -{\Sigma }^0$ mixing and the baryon decuplet is also noted, and the degree to which one can determine parameters such as quark mass differences and individual electromagnetic contributions to splittings is discussed.