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 $\omega -\varphi$ mixing. In addition to accounting for the mass formula in a rather natural manner, the $\omega -\varphi$ mixing model has the following distinctive features: (1) It explains why the mass formula fails for the vector meson octet. (2) It requires $m_{\rho }<m_M$ provided $m_{\pi }<m_K$. (3) It leads to $|m_{\Xi }-m_N|\gg |m_{\Sigma }-m_{\Lambda }|$, 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, ${\mathrm{}\left(\mathrm{mass}\right)\mathrm{}}^2$ 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 $\omega -\varphi$ mixing is made, and it is shown that the observed 1020-MeV $\varphi$ meson (the observed 780-MeV $\omega$ meson) is about a 60-40 mixture (a 40-60 mixture) in intensity of the $T=0\mathrm{}$ 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.