Some Properties of Triangular Representations of SU(3)

Abstract

The occurrence of an equal‐spacing mass rule in the unitary decuplet can be explained either by observing that the isotopic spin and hypercharge of each particle are related by T = 1 + ½Y, or by making use of a theorem due to Diu and Ginibre. This theorem states that, in all triangular representations of SU(3), the matrix elements of an arbitrary tensor operator depend upon one reduced matrix element instead of two. Here we present a new proof of the Diu‐Ginibre theorem and use it show that relations of the form T = λ ± ½Y exist for all triangular representations. We also show that the L and K spins are related to their corresponding hypercharges by L = λ ± ½Y_L and K = λ ± ½Y_K. One consequence is that the masses and magnetic moments of particles in a triangular multiplet are equally spaced. Other consequences are also discussed.