Infinitesimal Spontaneous Mass Splitting. II

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Abstract
The spontaneous mass splitting is investigated from a rather more general viewpoint for the system governed with the Hamiltonian fully symmetric under SU3 transformations. After a general formulation of the spontaneous splitting, comparison is made between the condition of the spontaneous splitting and that of bound state problem by means of the N/D method. Then, the Gell-Mann-Okubo mass formula requires that there should exist an octet scalar meson family and that its T=Y=0 member is the lightest among them and especially much lighter than the T=1, T3=Y=0 member. We can tentatively assign the ABC anomaly and the Kπ resonances at ≃730 MeV to the T=Y=0 and the T=½, |Y|=1 members, respectively. The remaining members (T=1, Y=0) are predicted to be around 1350 MeV. It is also pointed out that all the members except the Kπ resonances (730 MeV) may escape observation owing to a kinematical reason. Our conclusions are shown to be unchanged even after the spontaneous mass splitting of all the mesons, the spontaneous deviation of the strong coupling constants and all the other kinds of spontaneous inductions may be included into our arguments. The existing physical pictures are summarized of the selection of the most stable solution.
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