Radiative generation of quark and lepton mass hierarchies from a top-quark mass seed

Abstract

The possibility that of all the fermions in the standard model only the top quark gains mass at the tree level is investigated. Quark and lepton mass hierarchies are introduced by inducing the other fermion masses at various orders of perturbation theory. Lepton- and baryon-number-conserving scalar diquarks and leptoquarks are invoked to carry out these radiative corrections. We show that the simplest model one can construct has the following cascade: tree level\ensuremath{\rightarrow}top; one loop\ensuremath{\rightarrow}bottom; two loop\ensuremath{\rightarrow}charm, tau; three loop\ensuremath{\rightarrow}strange, mu, up, down; four loop\ensuremath{\rightarrow}electron. Neutrinos are strictly massless because we do not introduce right-handed chirality components. Phenomenological constraints on the family-lepton-number-violating scalar diquarks and lepto-quarks are considered. We elucidate the symmetry structure of the model we arrive at, thereby demonstrating the importance of a certain ${Z}_{3}$ discrete symmetry in preventing the appearance of unwanted Higgs-Yukawa couplings.