Dynamical Approach to the Unitary-Symmetry Mass Formula Based onω−ϕMixing

Possible dynamical mechanisms that give rise to the unitary-symmetry mass formula of Gell-Mann and Okubo are discussed with special emphasis on a model based on ω-φ mixing. In addition to accounting for the mass formula in a rather natural manner, the ω-φ mixing model has the following distinctive features: (1) It explains why the mass formula fails for the vector meson octet. (2) It requires m_ρ<mM provided m_π<mK. (3) It leads to |m_Ξ-mN||m_Σ-m_Λ|, provided the couplings of the vector mesons to the baryons are predominantly of the F type (as expected from the point of view of the conserved-vector-current theory). (4) It justifies the conjecture that it is more proper to use, in the mass formula, (mass)² for the mesons, but just the mass for the baryons. (5) The corrections to the mass formula are expected to be of the order of a few percent if the major contribution to the self-energies of the strongly interacting states comes from the region of a few BeV. A quantitative estimate of the ω-φ mixing is made, and it is shown that the observed 1020-MeV φ meson (the observed 780-MeV ω meson) is about a 60-40 mixture (a 40-60 mixture) in intensity of the $T=0$ member of a unitary octet and a unitary singlet. We also show that a pair of mass formulas of the Gell-Mann-Okubo type are "self-consistent" provided the cutoff momentum (in the perturbation-theoretic sense) is much greater than a typical difference within a unitary multiplet.