Results of calculations based on a new field theory of matter are presented. The theory utilizes an analogy between nucleonic charge and electric charge. Predictions of these calculations are discussed. (R.E.U.)

A ninth baryon

Relativistic formulation of the SU(6) symmetry scheme

The groupSU4 is probably the most straightforward and economical generalization ofSU3 which allows for basic triplets of integral charges. In this paper we analyse in detail the predictions of a few models for strong interactions based ouSU4. In addition to the usual (nonpeculiar) eightfold-way particles new peculiar particles are predicted. However they can be allowed to be created and to decay semi-strongly by the mass-breaking interactions. Mass relations are obtained. It is pointed out that some difficulties concerning these mass formulae occur when one tries to attribute the ρ, K*, ω and ϕ vector mesons to the regular representation ofSU4.

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SU 4 and strong interactions

SU4 and strong interactions

The strong decays of the $\ensuremath{\pi}(2070)$, $\ensuremath{\eta}(2010)$, $\ensuremath{\eta}(2100)$, $\ensuremath{\eta}(2190)$, and $\ensuremath{\eta}(2225)$ as the $4^{1}S_{0}$ quark-antiquark states are investigated in the framework of the $^{3}P_{0}$ meson decay model. It is found that the $\ensuremath{\pi}(2070)$, $\ensuremath{\eta}(2100)$, and $\ensuremath{\eta}(2225)$ appear to be the convincing $4^{1}S_{0}$ $q\overline{q}$ states, while the assignment of the $\ensuremath{\eta}(2010)$ and $\ensuremath{\eta}(2190)$ as the $4^{1}S_{0}$ isoscalar states is not favored by their widths. In the presence of the $\ensuremath{\pi}(2070)$, $\ensuremath{\eta}(2100)$, and $\ensuremath{\eta}(2225)$ being the members of the $4^{1}S_{0}$ meson nonet, the mass of the $4^{1}S_{0}$ kaon is phenomenologically determined to be about 2153 MeV. The width of this unobserved kaon is expected to be about 197 MeV in the $^{3}P_{0}$ decay model.

Towards the assignment for the 4 S 0 1 meson nonet

We apply the $\mathrm{SU}(6)$ algebra of Gell-Mann to nonleptonic decays of hadrons. We assume that the weak-interaction Hamiltonian for $s$-wave decays transforms like $S_{7}^{}{}_{}{}^{5}$ (the seventh component of the space integral of the pseudoscalar quark density). Using the Fubini-Furlan-Adler-Weisberger technique and the partially conserved axial-vector current, we express the $s$-wave decay amplitudes in terms of the reduced matrix elements, which are the same as the ones that appear in the expression for mass splittings if one assumes that the symmetry-breaking part of the mass operator transforms like ${S}_{8}$ (the eighth component of the space integral of the scalar quark density). Making use of the fact that the mass-splitting parameter is universal, and assuming that the $s$-wave coupling constant ${G}_{s}$ is also universal, we predict a ratio $\frac{(K_{1}^{}{}_{}{}^{0}\ensuremath{\rightarrow}2\ensuremath{\pi})}{A(\ensuremath{\Sigma}_{\ensuremath{-}}^{}{}_{}{}^{\ensuremath{-}})}$ which is in excellent agreement with experiment. Knowing any one of the hyperon $s$-way decay amplitudes we can predict the others. Also we get $A(\ensuremath{\Sigma}_{+}^{}{}_{}{}^{+})=0$. The implications of these results are discussed.

A ninth baryon

Citations

Relativistic formulation of the SU(6) symmetry scheme

SU 4 and strong interactions

SU4 and strong interactions

Towards the assignment for the 4 S 0 1 meson nonet

SU(6) Algebra of Gell-Mann: Mass Splittings and Nonleptonic Decays of Hadrons

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