Algebraic search for candidate preon models

Abstract

A valence preon model for composite quarks and leptons is introduced in which Fermi statistics play a vital role in determining the metaflavor representations for the composite states. A computer search is carried out for solutions of the anomaly conditions of't Hooft, where the anomalies are matched on both the preon and composite levels. A number of new solutions are found, but none of them satisfy, in addition, the decoupling and $N$-independence conditions of't Hooft.