Mass Formulas and Mass Inequalities for Reducible Unitary Multiplets

Abstract

For irreducible unitary multiplets of elementary particles, the Gell-Mann-Okubo mass formula is equivalent to the assertion that the effective masses transform under SU(3) like a superposition of a singlet and the neutral member of an octet. We consider the implications of this assertion for reducible unitary multiplets. We find weaker mass formulas, which allow for the mixing between different irreducible components; moreover, we find that certain inequalities must be satisfied. Specific examples are described.