Lepton Flavour Violation in Unified Models with U(1)-Family Symmetries

Lepton flavour non-conserving processes are examined in the context of unified models with U(1)-family symmetries which reproduce successfully the low-energy hierarchy of the fermion mass spectrum and the Kobayashi - Maskawa mixing. These models usually imply mixing effects in the supersymmetric scalar sector. We construct the fermion and scalar mass matrices in two viable models, and calculate the mixing effects on the $\mu \to e\gamma$, $\mu \to 3 e$ and $\tau \to \mu\gamma$ rare decays. The relevant constraints on the sparticle mass spectrum as well as the role of various MSSM parameters are discussed.