Mass splitting in SU(4)

A simple and rather general way to break SU(4) is to assume that the mass operator consists of a term which transforms as a scalar in the subgroup SU(3)_c (which operates on u, d, and s quarks) and a term which transforms as a scalar in SU(3)_s (which operates on u, d, and c). It is shown that this leads to a number of parallelogram laws between the masses. The generalized Okubo assumption falls within this framework and leads directly to Gell-Mann-Okubo relations between multiplets in the two subgroups. The specific SU(4) assumption of Okubo and others is a still further restriction. This group theoretic approach is compared with the results of the quark model.