### Preons: Generation Number from Space Dimension

The preon model, ie. that quarks and leptons and some other particles would be composites of more elementary constituents, has been under consideration for some thirty years. These days only really few people seem to give any attention to preons. On the other hand, the motivation of the preons has been in grand unification schemes, and even in heterotic superstring theories.

Any preon model would need some novel features with respect to QCD: like understanding why the masses of quarks and leptons are very much smaller than their inverse sizes.

**proposes in a recent paper**

*O.W. Greenberg**A Schematic Model of Generations*a possible solution to this and other problems of preon models. He introduces for the preon interaction the group [SU(3) x SU(3)]

_{b}. The preons of his model are

- 6x6 of [SU(3)xSU(3)]
_{b}hexon: spin ½ color, lepton, flavor, helicity, - 3x3 generon: spin 0, [SU(3)xSU(3)]
_{b}degrees of freedom, and - [SU(3)xSU(3)]
_{b}bindon: gauge boson

^{-}g

^{-}, hggg

^{-}, and hgggg. For the first generation the antigeneron repulsion leads to linear quasi-one dimensional configuration, and for the second generation the (anti)generon repulsion to triangular quasi-two dimensional configuration, and for the third generation to tetrahedral quasi-three dimensional configuration. As simple as that!

The author associates the dimensionless factor L/a, where L is the large linear scale of the generations and a is small linear scale, with the mass ratios between the generations, so that the mass scales of the successive generations are proportional to La

^{2}, L

^{2}a, and L

^{3}, respectively. He finds L/a to be about 100.

Generation mixing, dark matter (gg

^{-}) and some generic predictions of preon models, like higher spin particles, are also considered. But the author postpones the discussion of the weak bosons and the Higgs mesons or their substitutes to a later paper. As well as a few other questions.

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