Constraints on composite models of quarks and leptons

The previously noted difficulty of obtaining Dirac magnetic moments in composite models is combined with the observation that a “light” bound fermion state with a small size must have the Dirac moment in a renormalizable theory since its anomalous moment is determined by its excitation spectrum. New constraints on composite models are given, including the decoupling of low-lying excitations and the “superconfinement” condition that creation of virtual electron-positron pairs by the superstrong gluons responsible for binding the constituents of the electron must be strictly forbidden in photon-electron scattering.