Improved Tests of Relations for Baryon Isomultiplet Splittings

The least well-known octet baryon mass is $M_{\Xi^0} = 1314.9 \pm 0.6$ 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 $\Delta$ mass measurements, makes it timely to re-examine 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.