From Sakata Model to Goldberg-Ne'eman Quarks and Nambu QCD Phenomenology and “Right" and “Wrong" Experiments

Abstract

The basic theoretical milestones were the Sakata SU(3) symmetry, the Goldberg-Ne'eman composite model with SU(3) triplets having baryon number (1/3) and the Nambu color gauge Lagrangian. The transition was led in right and wrong directions by interpreted by phenomenology. A experiment on $\bar p p$ annihilation at rest showed that the Sakata model predictions disagreed with experiment. A bad experiment prevented the use of the Goldberg-Ne'eman triplet model to predict the existence and masses of the of the $\Xi^*$ and $\Omega^-$. More revealed the existence and mass of the $\Xi^*$ and the $\Omega^-$ and the absence of positive strangeness baryon resonances, thus confirming the tenfold way. Further good experiments revealed the existence of the vector meson nonet, SU(3) breaking with singlet-octet mixing and the suppression of the $\phi \to \rho \pi$ decay. These led to the quark triplet model. The paradox of peculiar statistics then arose as the $\Delta^{++}$ and $\Omega^-$ contained three identical spin-1/2 fermions coupled symmetrically to spin (3/2). This led to color and the Nambu QCD. The book Lie Groups for Pedestrians used the Sakata model with the name sakaton for the $pn\Lambda$ triplet to teach the algebra of SU(3) to particle physicists in the U.S. and Europe who knew no group theory. The Sakata model had a renaissance in hypernuclear physics in the 1970's.