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 next most poorly measured mass is $M_{\Xi^-} = 1321.32 \pm 0.13$ MeV, while the masses of the remaining octet members are measured to better than $\pm 0.1$ MeV. The KTeV experimental program at Fermilab holds the prospect of a substantial improvement in measurement of $M_{\Xi^0}$, while other improvements in charged and excited hyperon and $\Delta$ mass measurements are also possible. The significance of such improvements for tests of descriptions of isospin splittings is discussed. One example is a better test of the Coleman-Glashow relation $M_n - M_p + M_{\Xi^-} - M_{\Xi^0} = M_{\Sigma^-} - M_{\Sigma^+}$. Other quark-model mass relations involving $\Lambda - \Sigma^0$ mixing and the baryon decuplet are also noted.