A Supersymmetric Theory of Flavor with Radiative Fermion Masses

Supersymmetric theories involving a spontaneously broken flavor symmetry can lead to fermion masses which vanish at tree level but are generated by radiative corrections. In the context of supersymmetric theories with minimal low energy field content we discuss which fermion masses and mixings may be obtained radiatively, and find that constraints from flavor changing phenomenology imply that only the first generation fermion masses and some (but not all) CKM mixings can naturally come from radiative corrections. We also consider general conditions on theories of flavor which guarantee the existence of tree level massless fermions while having non-trivial CKM matrix elements at tree level. Two complete models of flavor are presented. In the first model, all first generation fermion masses are radiatively generated. In the second model, the electron and up quark mass are due to radiative corrections whereas the down mass appears at tree level, as does a successful prediction for the Cabibbo angle $\sin \theta_c = \sqrt{m_d/m_s}$.