Generating a Fermion Mass Hierarchy in a Composite Supersymmetric Standard Model

A mechanism is suggested by which the dynamics of confinement could be responsible for the fermion mass matrix. In this approach the large top quark Yukawa coupling is generated naturally during confinement, while those of the other quarks and leptons stem from non-renormalizable couplings at the Planck scale and are suppressed. Below the confinement scale(s) the effective theory is minimal supersymmetric $SU(5)$ or the supersymmetric standard model. Particles in the $\bar 5$ representations of $SU(5)$ are fundamental while those in the $10$ and $5$ are composite. The standard model gauge group is weakly coupled and predictions of unification can be preserved. A hierarchy in confinement scales helps generate a hierarchical spectrum of quark and lepton masses and ensures the Kobayashi-Maskawa matrix is nearly diagonal. However, the most natural outcome is that the strange quark is heavier than the charm quark; additional structure is required to evade this conclusion. No attempt has been made to address the issues of $SU(5)$ breaking, SUSY breaking, doublet/triplet splitting or the $\mu$ parameter. While the models presented here are neither elegant nor complete, they are remarkable in that they can be analyzed without uncontrollable dynamical assumptions.