Three-preon models of quarks and leptons and the generation problem

Abstract

We have carried out a search for three-fermion preon models that predict at least three generations of quarks and leptons. The conditions imposed are the following: (1) The preons are (massless) Weyl spinors and belong to low-dimensional chiral representations of the gauged symmetry group $G(\mathrm{MC})\ifmmode\times\else\texttimes\fi{}G(\mathrm{CF})$, where MC stands for metacolor and CF for color-flavor. (2) $G(\mathrm{MC})$ is an asymptotically free simple group while $G(\mathrm{CF})$ is a grand-unification-theory (GUT) or partial-unification-theory (PUT) group. (3) The Pauli principle holds when generalized to the MC degree of freedom. (4) No anomalies exist in the MC and CF sectors. (5) The composite quarks and leptons are massless on the MC scale. (6) There are no low-representation exotics and no mirror fermions. The only GUT preon models satisfying these six conditions are SU(3)(MC)\ifmmode\times\else\texttimes\fi{}SO(10)(CF) with four generations and ${\mathrm{F}}_{4}$(MC)\ifmmode\times\else\texttimes\fi{}SO(10)(CF) with three generations; however, asymptotic freedom is marginal for the two GUT models. The only permissible PUT preon model is ${\mathrm{E}}_{6}(\mathrm{MC})\ifmmode\times\else\texttimes\fi{}\mathrm{SU}{(4)}_{C}\ifmmode\times\else\texttimes\fi{}\mathrm{SU}{(2)}_{L}\ifmmode\times\else\texttimes\fi{}\mathrm{SU}{(2)}_{R}$ with three generations, and satisfactory asymptotic behavior. The PUT preon model is therefore the most promising and further implications are discussed.