Physics – High Energy Physics – High Energy Physics - Phenomenology
Scientific paper
2007-01-04
Prog.Theor.Phys.Suppl.167:155-162,2007
Physics
High Energy Physics
High Energy Physics - Phenomenology
8 pages
Scientific paper
10.1143/PTPS.167.155
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 $\Xi^*$ and $\Omega^-$. More "good" experiments 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.
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