Baryon-Baryon Interactions and the Eightfold Way

ECENTLY, Gell-Mann' and Ne'eman have independently proposed a scheme, called the eightfold way, in which the eight baryons (ftT, A., Z, and ) are assumed to form a supermultiplet, degenerate in the limit of a certain symmetry, and split into the familiar isotopic multiplets by a dynamical interaction. The symmetry is called unitary symmetry and the relevant group is the group of unitary unimodular transforrnations in three dimensions, which is denoted by SU(3). The eight baryons belong to the regular (eight-dimensional) representation of SU(3). All the known pseudoscalar mesons, vector mesons, and meson-baryon resonances have been tentatively identified with various representations of SU(3).' In this note, we examine the role of the deuteron in the eightfold way and find it must belong to a tendimensional representation of SU(3). In the limit of exact unitary symmetry, the implication is that all ten of the baryon-baryon states which comprise the supermultiplet are similarly bound. Since it is clear that unitary symmetry is not exact in the physical world, some of these might not occur as actual bound states. However, unless the symmetry is broken so badly that it is meaningless, one might expect these states to be nearly bound, or resonant. ' As will be discussed below, there is some evidence to support this point of view. Since the symmetry of the eightfold way seems to be broken in a particularly simple and definite way, the mass splittings in the supermultiplets are related. Using this fact and certain existing data, the masses of the heretofore unobserved constituents of this deuteron decuplet are estimated. It is suggested that these be looked for as a test of the applicability of unitary symmetry and the eightfold way to the study of the hyperon and cascade interactions.