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 experiments interpreted by phenomenology. A "good" 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 $Ξ^*$ and $Ω^-$. More "good" experiments revealed the existence and mass of the $Ξ^*$ and the $Ω^-$ 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 $ϕ\to ρπ$ decay. These led to the quark triplet model. The paradox of peculiar statistics then arose as the $Δ^{++}$ and $Ω^-$ 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 $pnΛ$ 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.