Meson symmetries based on nonchiral SU(3)×SU(3)

A scheme for meson symmetries based on the SU(3)×SU(3) group is presented. First, the phenomenological nonet model of Okubo is reinterpreted in terms of the representation (3,3∗) of SU(3)×SU(3). More general representations of the form (d, d∗), with d a triangular representation of SU(3), are next considered. It is noted that the assumption of the symmetry violation being generated by a hyperchargelike operator always leads to an equal-spacing rule for the meson masses, and to a degeneracy of several meson components. The origin of this degeneracy is discussed in some detail. The representation (6,6∗) is treated at length. The possibility of realizing meson 36-plet (6,6∗) is discussed with reference to existing experimental information