Determination of SU(6) Clebsch-Gordan coefficients and baryon mass and electromagnetic moment relations

We develop a new method to compute and tabulate the Clebsch-Gordan coefficients of the SU(6)⊃SU(3)×SU(2) product 56¯⊗56, which are relevant to the nonrelativistic spin-flavor symmetry of the lightest baryons. Under the assumption that the largest representation in this product, the 2695, gives rise to operators in a chiral expansion that produce numerically small effects, we obtain a set of relations among the masses of the baryons, as well as among their magnetic dipole and higher multipole moments. We compare the mass relations to experiment, and find numerical predictions for the ${\mathrm{\Sigma }}^{0\mathrm{-}}$Λ mass mixing parameter and 18 of the 27 magnetic moments in the 56.