1963/10/01 by J. J. Sakurai · 1 citation
Physics and Astronomy · #Quantum Chromodynamics and Particle Interactions #Particle physics theoretical and experimental studies #High-Energy Particle Collisions Research
paper · doi:10.1103/physrev.132.434
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 \ensuremathω\ensuremath-\ensuremathφ mixing. In addition to accounting for the mass formula in a rather natural manner, the \ensuremathω\ensuremath-\ensuremathφ mixing model has the following distinctive features: (1) It explains why the mass formula fails for the vector meson octet. (2) It requires m_\ensuremathρ<mM provided m_\ensuremathπ<mK. (3) It leads to |m_\ensuremathΞ\ensuremath-mN|\ensuremath≫|m_\ensuremathΣ\ensuremath-m_\ensuremathΛ|, 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 \ensuremathω\ensuremath-\ensuremathφ mixing is made, and it is shown that the observed 1020-MeV \ensuremathφ meson (the observed 780-MeV \ensuremathω 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.