Search for composite models of quarks and leptons with preons having strong and electroweak quantum numbers

Abstract

The impossibility of composite models of two or more generations of quarks and leptons is shown using preons with strong $\mathrm{S}{\mathrm{U}}_{C}(3)$ quantum numbers and either the electroweak $\mathrm{S}{\mathrm{U}}_{L}(2)\ifmmode\times\else\texttimes\fi{}\mathrm{U}(1)$ or $\mathrm{S}{\mathrm{U}}_{L}(2)\ifmmode\times\else\texttimes\fi{}\mathrm{S}{\mathrm{U}}_{R}(2)\ifmmode\times\else\texttimes\fi{}{\mathrm{U}}_{B\ensuremath{-}L}(1)$ quantum numbers. The preon models considered are the simplest: $\mathrm{FFF}$ and $\mathrm{FB}$ ($F$ is fermion and $B$ is boson). The constraints imposed on the models are the absence of exotics and anomalies in the strong and electroweak sectors.